**By the author of the acclaimed bestseller *Benjamin Franklin*, this is the first full biography of Albert Einstein since all of his papers have become available.**
How did his mind work? What made him a genius? Isaacson's biography shows how his scientific imagination sprang from the rebellious nature of his personality. His fascinating story is a testament to the connection between creativity and freedom.
Based on newly released personal letters of Einstein, this book explores how an imaginative, impertinent patent clerk -- a struggling father in a difficult marriage who couldn't get a teaching job or a doctorate -- became the mind reader of the creator of the cosmos, the locksmith of the mysteries of the atom and the universe. His success came from questioning conventional wisdom and marveling at mysteries that struck others as mundane. This led him to embrace a morality and politics based on respect for free minds, free spirits, and free individuals.
These traits are just as vital for this new century of globalization, in which our success will depend on our creativity, as they were for the beginning of the last century, when Einstein helped usher in the modern age.
/storebooks/W/W-Isaacson/Einstein-His-Life-And-Universe//storebooks/W/W-Isaacson/Einstein-His-Life-And-Universe//storebooks/W/W-Isaacson/Einstein-His-Life-And-Universe/ Amazon.com Review
As a scientist, Albert Einstein is undoubtedly the most epic among 20th-century thinkers. Albert Einstein as a man, however, has been a much harder portrait to paint, and what we know of him as a husband, father, and friend is fragmentary at best. With *Einstein: His Life and Universe*, Walter Isaacson (author of the bestselling biographies *Benjamin Franklin* and *Kissinger*) brings Einstein's experience of life, love, and intellectual discovery into brilliant focus. The book is the first biography to tackle Einstein's enormous volume of personal correspondence that heretofore had been sealed from the public, and it's hard to imagine another book that could do such a richly textured and complicated life as Einstein's the same thoughtful justice. Isaacson is a master of the form and this latest opus is at once arresting and wonderfully revelatory. *--Anne Bartholomew*
**Read "The Light-Beam Rider," the first chapter of Walter Isaacson's *Einstein: His Life and Universe*.**
* * *
**Five Questions for Walter Isaacson**
**Amazon.com:** What kind of scientific education did you have to give yourself to be able to understand and explain Einstein's ideas?
**Isaacson:** I've always loved science, and I had a group of great physicists--such as Brian Greene, Lawrence Krauss, and Murray Gell-Mann--who tutored me, helped me learn the physics, and checked various versions of my book. I also learned the tensor calculus underlying general relativity, but tried to avoid spending too much time on it in the book. I wanted to capture the imaginative beauty of Einstein's scientific leaps, but I hope folks who want to delve more deeply into the science will read Einstein books by such scientists as Abraham Pais, Jeremy Bernstein, Brian Greene, and others.
**Amazon.com:** That Einstein was a clerk in the Swiss Patent Office when he revolutionized our understanding of the physical world has often been treated as ironic or even absurd. But you argue that in many ways his time there fostered his discoveries. Could you explain?
**Isaacson:** I think he was lucky to be at the patent office rather than serving as an acolyte in the academy trying to please senior professors and teach the conventional wisdom. As a patent examiner, he got to visualize the physical realities underlying scientific concepts. He had a boss who told him to question every premise and assumption. And as Peter Galison shows in *Einstein's Clocks, Poincare's Maps*, many of the patent applications involved synchronizing clocks using signals that traveled at the speed of light. So with his office-mate Michele Besso as a sounding board, he was primed to make the leap to special relativity.
**Amazon.com:** That time in the patent office makes him sound far more like a practical scientist and tinkerer than the usual image of the wild-haired professor, and more like your previous biographical subject, the multitalented but eminently earthly Benjamin Franklin. Did you see connections between them?
**Isaacson:** I like writing about creativity, and that's what Franklin and Einstein shared. They also had great curiosity and imagination. But Franklin was a more practical man who was not very theoretical, and Einstein was the opposite in that regard.
**Amazon.com:** Of the many legends that have accumulated around Einstein, what did you find to be least true? Most true?
**Isaacson:** The least true legend is that he failed math as a schoolboy. He was actually great in math, because he could visualize equations. He knew they were nature's brushstrokes for painting her wonders. For example, he could look at Maxwell's equations and marvel at what it would be like to ride alongside a light wave, and he could look at Max Planck's equations about radiation and realize that Planck's constant meant that light was a particle as well as a wave. The most true legend is how rebellious and defiant of authority he was. You see it in his politics, his personal life, and his science.
**Amazon.com:** At *Time* and CNN and the Aspen Institute, you've worked with many of the leading thinkers and leaders of the day. Now that you've had the chance to get to know Einstein so well, did he remind you of anyone from our day who shares at least some of his remarkable qualities?
**Isaacson:** There are many creative scientists, most notably Stephen Hawking, who wrote the essay on Einstein as "Person of the Century" when I was editor of *Time*. In the world of technology, Steve Jobs has the same creative imagination and ability to think differently that distinguished Einstein, and Bill Gates has the same intellectual intensity. I wish I knew politicians who had the creativity and human instincts of Einstein, or for that matter the wise feel for our common values of Benjamin Franklin.
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**More to Explore**
*Benjamin Franklin: An American Life*
*Kissinger: A Biography* **
**The Wise Men: Six Friends and the World They Made* ***
* * *
/storebooks/W/W-Isaacson/Einstein-His-Life-And-Universe//storebooks/W/W-Isaacson/Einstein-His-Life-And-Universe//storebooks/W/W-Isaacson/Einstein-His-Life-And-Universe/ **From Publishers Weekly**
**Acclaimed biographer Isaacson examines the remarkable life of "science's preeminent poster boy" in this lucid account (after 2003's *Benjamin Franklin* and 1992's *Kissinger*). Contrary to popular myth, the German-Jewish schoolboy Albert Einstein not only excelled in math, he mastered calculus before he was 15. Young Albert's dislike for rote learning, however, led him to compare his teachers to "drill sergeants." That antipathy was symptomatic of Einstein's love of individual and intellectual freedom, beliefs the author revisits as he relates his subject's life and work in the context of world and political events that shaped both, from WWI and II and their aftermath through the Cold War. Isaacson presents Einstein's research—his efforts to understand space and time, resulting in four extraordinary papers in 1905 that introduced the world to special relativity, and his later work on unified field theory—without equations and for the general reader. Isaacson focuses more on Einstein the man: charismatic and passionate, often careless about personal affairs; outspoken and unapologetic about his belief that no one should have to give up personal freedoms to support a state. Fifty years after his death, Isaacson reminds us why Einstein (1879–1955) remains one of the most celebrated figures of the 20th century. *500,000 firsr printing, 20-city author tour, first serial to *Time*; confirmed appearance on *Good Morning America*. (Apr.)*
Copyright © Reed Business Information, a division of Reed Elsevier Inc. All rights reserved. **
ALSO BY WALTER ISAACSON
A Benjamin Franklin Reader
Benjamin Franklin: An American Life
Kissinger: A Biography
The Wise Men: Six Friends and the World They Made (with Evan Thomas)
Pro and Con
HIS LIFE AND UNIVERSE
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Endpapers: Alan Richards, Princeton University Library
Frontispiece: Ullstein Bilderdienst/The Granger Collection, New York
Illustration credits are on page 679.
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Library of Congress Cataloging-in-Publication Data
Einstein : his life and universe / Walter Isaacson.
Includes bibliographical references and index.
1. Einstein, Albert, 1879–1955. 2. Physicists—Biography. 3. Einstein, Albert, 1879–1955—Friends and associates. 4. Relativity (Physics). 5. Unified field theories. I. Title.
To my father, the nicest, smartest, and most moral man I know
In Santa Barbara, 1933
Life is like riding a bicycle.
To keep your balance you must keep moving.
—ALBERT EINSTEIN, IN A LETTER TO HIS SON EDUARD, FEBRUARY 5, 19301
The Light-Beam Rider
The Zurich Polytechnic, 1896–1900
The Lovers, 1900–1904
The Miracle Year: Quanta and Molecules, 1905
Special Relativity, 1905
The Happiest Thought, 1906–1909
The Wandering Professor, 1909–1914
General Relativity, 1911–1915
Einstein’s Universe, 1916–1919
The Wandering Zionist, 1920–1921
Nobel Laureate, 1921–1927
Unified Field Theories, 1923–1931
Turning Fifty, 1929–1931
The Refugee, 1932–1933
Quantum Entanglement, 1935
The Bomb, 1939–1945
Red Scare, 1951–1954
The End, 1955
Einstein’s Brain and Einstein’s Mind
Diana Kormos Buchwald, the general editor of Einstein’s papers, read this book meticulously and made copious comments and corrections through many drafts. In addition, she helped me get early and complete access to the wealth of new Einstein papers that became available in 2006, and guided me through them. She was also a gracious host and facilitator during my trips to the Einstein Papers Project at Caltech. She has a passion for her work and a delightful sense of humor, which would have pleased her subject.
Two of her associates were also very helpful in guiding me through the newly available papers as well as untapped riches in the older archival material. Tilman Sauer, who likewise checked and annotated this book, in particular vetted the sections on Einstein’s quest for the equations of general relativity and his pursuit of a unified field theory. Ze’ev Rosenkranz, the historical editor of the papers, provided insights on Einstein’s attitudes toward Germany and his Jewish heritage. He was formerly curator of the Einstein archives at Hebrew University in Jerusalem.
Barbara Wolff, who is now at those archives at Hebrew University, did a careful fact-checking of every page of the manuscript, making fastidious corrections large and small. She warned that she has a reputation as a nitpicker, but I am very grateful for each and every nit she found. I also appreciate the encouragement given by Roni Grosz, the curator there.
Brian Greene, the Columbia University physicist and author of The Fabric of the Cosmos, was an indispensable friend and editor. He talked me through numerous revisions, honed the wording of the science passages, and read the final manuscript. He is a master of both science and language. In addition to his work on string theory, he and his wife, Tracy Day, are organizing an annual science festival in New York City, which will help spread the enthusiasm for physics so evident in his work and books.
Lawrence Krauss, professor of physics at Case Western Reserve and author of Hiding in the Mirror, also read my manuscript, vetted the sections on special relativity, general relativity, and cosmology, and offered many good suggestions and corrections. He, too, has an infectious enthusiasm for physics.
Krauss helped me enlist a protégé of his at Case, Craig J. Copi, who teaches relativity there. I hired him to do a thorough checking of the science and math, and I am grateful for his diligent edits.
Douglas Stone, professor of physics at Yale, also vetted the science in the book. A condensed matter theorist, he is writing what will be an important book on Einstein’s contributions to quantum mechanics. In addition to checking my science sections, he helped me write the chapters on the 1905 light quanta paper, quantum theory, Bose-Einstein statistics, and kinetic theory.
Murray Gell-Mann, winner of the 1969 Nobel Prize in physics, was a delightful and passionate guide from the beginning to the end of this project. He helped me revise early drafts, edited and corrected the chapters on relativity and quantum mechanics, and helped draft sections that explained Einstein’s objections to quantum uncertainty. With his combination of erudition and humor, and his feel for the personalities involved, he made the process a great joy.
Arthur I. Miller, emeritus professor of history and philosophy of science at University College, London, is the author of Einstein, Picasso and of Empire of the Stars. He read and reread the versions of my scientific chapters and helped with numerous revisions, especially on special relativity (about which he wrote a pioneering book), general relativity, and quantum theory.
Sylvester James Gates Jr., a physics professor at the University of Maryland, agreed to read my manuscript when he came out to Aspen for a conference on Einstein. He did a comprehensive edit filled with smart comments and rephrasing of certain scientific passages.
John D. Norton, a professor at the University of Pittsburgh, has specialized in tracing Einstein’s thought process as he developed both special and then general relativity. He read these sections of my book, made edits, and offered useful comments. I am also grateful for guidance from two of his fellow scholars specializing in Einstein’s development of his theories: Jürgen Renn of the Max Planck Institute in Berlin and Michel Janssen of the University of Minnesota.
George Stranahan, a founder of the Aspen Center for Physics, also agreed to read and review the manuscript. He was particularly helpful in editing the sections on the light quanta paper, Brownian motion, and the history and science of special relativity.
Robert Rynasiewicz, a philosopher of science at Johns Hopkins, read many of the science chapters and made useful suggestions about the quest for general relativity.
N. David Mermin, professor of theoretical physics at Cornell and author of It’s About Time: Understanding Einstein’s Relativity, edited and made corrections to the final version of the introductory chapter and chapters 5 and 6 on Einstein’s 1905 papers.
Gerald Holton, professor of physics at Harvard, has been one of the pioneers in the study of Einstein, and he is still a guiding light. I am deeply flattered that he was willing to read my book, make comments, and offer generous encouragement. His Harvard colleague Dudley Herschbach, who has done so much for science education, also was supportive. Both Holton and Herschbach made useful comments on my draft and spent an afternoon with me in Holton’s office going over suggestions and refining my descriptions of the historical players.
Ashton Carter, professor of science and international affairs at Harvard, kindly read and checked an early draft. Columbia University’s Fritz Stern, author of Einstein’s German World, provided encouragement and advice at the outset. Robert Schulmann, one of the original editors at the Einstein Papers Project, did likewise. And Jeremy Bernstein, who has written many fine books on Einstein, warned me how difficult the science would be. He was right, and I am grateful for that as well.
In addition, I asked two teachers of high school physics to give the book a careful reading to make sure the science was correct, and also comprehensible to those whose last physics course was in high school. Nancy Stravinsky Isaacson taught physics in New Orleans until, alas, Hurricane Katrina gave her more free time. David Derbes teaches physics at the University of Chicago Lab School. Their comments were very incisive and also aimed at the lay reader.
There is a corollary of the uncertainty principle that says that no matter how often a book is observed, some mistakes will remain. Those are my fault.
It also helped to have some nonscientific readers, who made very useful suggestions from a lay perspective on parts or all of the manuscript. These included William Mayer, Orville Wright, Daniel Okrent, Steve Weisman, and Strobe Talbott.
For twenty-five years, Alice Mayhew at Simon & Schuster has been my editor and Amanda Urban at ICM my agent. I can imagine no better partners, and they were again enthusiastic and helpful in their comments on the book. I also appreciate the help of Carolyn Reidy, David Rosenthal, Roger Labrie, Victoria Meyer, Elizabeth Hayes, Serena Jones, Mara Lurie, Judith Hoover, Jackie Seow, and Dana Sloan at Simon & Schuster. For their countless acts of support over the years, I am also grateful to Elliot Ravetz and Patricia Zindulka.
Natasha Hoffmeyer and James Hoppes translated for me Einstein’s German correspondence and writing, especially the new material that had not yet been translated, and I appreciate their diligence. Jay Colton, who was photo editor for Time’s Person of the Century issue, also did a creative job tracking down pictures for this book.
I had two and a half other readers who were the most valuable of all. The first was my father, Irwin Isaacson, an engineer who instilled in me a love of science and is the smartest teacher I’ve ever had. I am grateful to him for the universe that he and my late mother created for me, and to my brilliant and wise stepmother, Julanne.
The other truly valuable reader was my wife, Cathy, who read every page with her usual wisdom, common sense, and curiosity. And the valuable half-a-reader was my daughter,Betsy, who as usual read selected portions of my book. The surety with which she made her pronouncements made up for the randomness of her reading. I love them both dearly.
(1873–1955). Einstein’s closest friend. An engaging but unfocused engineer, he met Einstein in Zurich, then followed him to work at the Bern patent office. Served as a sounding board for the 1905 special relativity paper. Married Anna Winteler, sister of Einstein’s first girlfriend.
(1885–1962). Danish pioneer of quantum theory. At Solvay conferences and subsequent intellectual trysts, he parried Einstein’s enthusiastic challenges to his Copenhagen interpretation of quantum mechanics.
(1882–1970). German physicist and mathematician. Engaged in a brilliant, intimate correspondence with Einstein for forty years. Tried to convince Einstein to be comfortable with quantum mechanics; his wife, Hedwig, challenged Einstein on personal issues.
(1896–1982). Einstein’s loyal secretary, Cerberus-like guard, and housemate from 1928 until his death, and after that protector of his legacy and papers.
(1882–1944). British astrophysicist and champion of relativity whose 1919 eclipse observations dramatically confirmed Einstein’s prediction of how much gravity bends light.
(1880–1933). Austrian-born physicist, intense and insecure, who bonded with Einstein on a visit to Prague in 1912 and became a professor in Leiden, where he frequently hosted Einstein.
(1910–1965). Second son of Mileva Mari
and Einstein. Smart and artistic, he obsessed about Freud and hoped to be a psychiatrist, but he succumbed to his own schizophrenic demons in his twenties and was institutionalized in Switzerland for much of the rest of his life.
(1876–1936). Einstein’s first cousin, second wife. Mother of Margot and Ilse Einstein from her first marriage to textile merchant Max Löwenthal. She and her daughters reverted to her maiden name, Einstein, after her 1908 divorce. Married Einstein in 1919. Smarter than she pretended to be, she knew how to handle him.
(1904–1973). First son of Mileva Mari
and Einstein, a difficult role that he handled with grace. Studied engineering at Zurich Polytechnic. Married Frieda Knecht (1895–1958) in 1927. They had two sons, Bernard (1930–) and Klaus (1932–1938), and an adopted daughter, Evelyn (1941–). Moved to the United States in 1938 and eventually became a professor of hydraulic engineering at Berkeley. After Frieda’s death, married Elizabeth Roboz (1904–1995) in 1959. Bernard has five children, the only known great-grandchildren of Albert Einstein.
(1847–1902). Einstein’s father, from a Jewish family from rural Swabia. With his brother Jakob, he ran electrical companies in Munich and then Italy, but not very successfully.
(1897–1934). Daughter of Elsa Einstein from her first marriage. Dallied with adventurous physician Georg Nicolai and in 1924 married literary journalist Rudolph Kayser, who later wrote a book on Einstein using the pseudonym Anton Reiser.
(1902–?). Premarital daughter of Einstein and Mileva Mari
. Einstein probably never saw her. Likely left in her Serbian mother’s hometown of Novi Sad for adoption and may have died of scarlet fever in late 1903.
(1899–1986). Daughter of Elsa Einstein from her first marriage. A shy sculptor. Married Russian Dimitri Marianoff in 1930; no children. He later wrote a book on Einstein. She divorced him in 1937, moved in with Einstein at Princeton, and remained at 112 Mercer Street until her death.
(1881–1951). Einstein’s only sibling, and among his closest confidantes. Married Paul Winteler, had no children, and in 1938 moved without him from Italy to Princeton to live with her brother.
(1858–1920). Einstein’s strong-willed and practical mother. Daughter of a prosperous Jewish grain dealer from Württemberg. Married Hermann Einstein in 1876.
(1866–1959). American education reformer. Founded the Institute for Advanced Study in Princeton and recruited Einstein there.
(1884–1966). Austrian physicist. Succeeded his friend Einstein at German University of Prague and later wrote a book about him.
(1878–1936). Diligent classmate at Zurich Polytechnic who took math notes for Einstein and then helped him get a job in the patent office. As professor of descriptive geometry at the Polytechnic, guided Einstein to the math he needed for general relativity.
(1868–1934). German chemist and gas warfare pioneer who helped recruit Einstein to Berlin and mediated between him and Mari
. A Jew who converted to Christianity in an attempt to be a good German, he preached to Einstein the virtues of assimilation, until the Nazis came to power.
(1876–1958). Mathematician and amateur inventor, member of the “Olympia Academy” discussion trio in Bern, and recipient of two famous 1905 letters from Einstein heralding forthcoming papers.
(1901–1976). German physicist. A pioneer of quantum mechanics, he formulated the uncertainty principle that Einstein spent years resisting.
(1862–1943). German mathematician who in 1915 raced Einstein to discover the mathematical equations for general relativity.
(1906–1986). Mathematician and physicist who collaborated with Einstein in Princeton and later wrote a book about him.
(1862–1947). Hungarian-German physicist whose experimental observations on the photoelectric effect were explained by Einstein in his 1905 light quanta paper. Became an anti-Semite, Nazi, and Einstein hater.
(1853–1928). Genial and wise Dutch physicist whose theories paved the way for special relativity. Became a father figure to Einstein.
(1875–1948). Serbian physics student at Zurich Polytechnic who became Einstein’s first wife. Mother of Hans Albert, Eduard, and Lieserl. Passionate and driven, but also brooding and increasingly gloomy, she triumphed over many, but not all, of the obstacles that then faced an aspiring female physicist. Separated from Einstein in 1914, divorced in 1919.
(1868–1953). American experimental physicist who confirmed Einstein’s law of the photoelectric effect and recruited him to be a visiting scholar at Caltech.
(1864–1909). Taught Einstein math at the Zurich Polytechnic, referred to him as a “lazy dog,” and devised a mathematical formulation of special relativity in terms of four-dimensional spacetime.
born Lewinstein (1874–1964). Physician, pacifist, charismatic adventurer, and seducer. A friend and doctor of Elsa Einstein and probable lover of her daughter Ilse, he wrote a pacifist tract with Einstein in 1915.
(1918–2000). Dutch-born theoretical physicist who became a colleague of Einstein in Princeton and wrote a scientific biography of him.
(1858–1947). Prussian theoretical physicist who was an early patron of Einstein and helped recruit him to Berlin. His conservative instincts, both in life and in physics, made him a contrast to Einstein, but they remained warm and loyal colleagues until the Nazis took power.
(1887–1961). Austrian theoretical physicist who was a pioneer of quantum mechanics but joined Einstein in expressing discomfort with the uncertainties and probabilities at its core.
(1875–1958). Romanian philosophy student in Bern who founded the “Olympia Academy” with Einstein and Habicht. Became Einstein’s French publisher and lifelong correspondent.
(1898–1964). Hungarian-born physicist, charming and eccentric, who met Einstein in Berlin and patented a refrigerator with him. Conceived the nuclear chain reaction and cowrote the 1939 letter Einstein sent to President Franklin Roosevelt urging attention to the possibility of an atomic bomb.
(1874–1952). Russian-born chemist who emigrated to England and became president of the World Zionist Organization. In 1921, he brought Einstein to America for the first time, using him as the draw for a fund-raising tour. Was first president of Israel, a post offered upon his death to Einstein.
Einstein boarded with them while he was a student in Aarau, Switzerland. Jost Winteler was his history and Greek teacher; his wife, Rosa, became a surrogate mother. Of their seven children, Marie became Einstein’s first girlfriend; Anna married Einstein’s best friend, Michele Besso; and Paul married Einstein’s sister, Maja.
(1874–1957). Professor of physiology at the University of Zurich. Befriended Einstein and Mari
and helped mediate their disputes and divorce.
THE LIGHT-BEAM RIDER
“I promise you four papers,” the young patent examiner wrote his friend. The letter would turn out to bear some of the most significant tidings in the history of science, but its momentous nature was masked by an impish tone that was typical of its author. He had, after all, just addressed his friend as “you frozen whale”and apologized for writing a letter that was “inconsequential babble.” Only when he got around to describing the papers, which he had produced during his spare time, did he give some indication that he sensed their significance.1
“The first deals with radiation and the energy properties of light and is very revolutionary,” he explained. Yes, it was indeed revolutionary. It argued that light could be regarded not just as a wave but also as a stream of tiny particles called quanta. The implications that would eventually arise from this theory—a cosmos without strict causality or certainty—would spook him for the rest of his life.
“The second paper is a determination of the true sizes of atoms.” Even though the very existence of atoms was still in dispute, this was the most straightforward of the papers, which is why he chose it as the safest bet for his latest attempt at a doctoral thesis. He was in the process of revolutionizing physics, but he had been repeatedly thwarted in his efforts to win an academic job or even get a doctoral degree, which he hoped might get him promoted from a third- to a second-class examiner at the patent office.
The third paper explained the jittery motion of microscopic particles in liquid by using a statistical analysis of random collisions. In the process, it established that atoms and molecules actually exist.
“The fourth paper is only a rough draft at this point, and is an electrodynamics of moving bodies which employs a modification of the theory of space and time.” Well, that was certainly more than inconsequential babble. Based purely on thought experiments—performed in his head rather than in a lab—he had decided to discard Newton’s concepts of absolute space and time. It would become known as the Special Theory of Relativity.
What he did not tell his friend, because it had not yet occurred to him, was that he would produce a fifth paper that year, a short addendum to the fourth, which posited a relationship between energy and mass. Out of it would arise the best-known equation in all of physics: E=mc2.
Looking back at a century that will be remembered for its willingness to break classical bonds, and looking ahead to an era that seeks to nurture the creativity needed for scientific innovation, one person stands out as a paramount icon of our age: the kindly refugee from oppression whose wild halo of hair, twinkling eyes, engaging humanity, and extraordinary brilliance made his face a symbol and his name a synonym for genius. Albert Einstein was a locksmith blessed with imagination and guided by a faith in the harmony of nature’s handiwork. His fascinating story, a testament to the connection between creativity and freedom, reflects the triumphs and tumults of the modern era.
Now that his archives have been completely opened, it is possible to explore how the private side of Einstein—his nonconformist personality, his instincts as a rebel, his curiosity, his passions and detachments—intertwined with his political side and his scientific side. Knowing about the man helps us understand the wellsprings of his science, and vice versa. Character and imagination and creative genius were all related, as if part of some unified field.
Despite his reputation for being aloof, he was in fact passionate in both his personal and scientific pursuits. At college he fell madly in love with the only woman in his physics class, a dark and intense Serbian named Mileva Mari. They had an illegitimate daughter, then married and had two sons. She served as a sounding board for his scientific ideas and helped to check the math in his papers, but eventually their relationship disintegrated. Einstein offered her a deal. He would win the Nobel Prize someday, he said; if she gave him a divorce, he would give her the prize money. She thought for a week and accepted. Because his theories were so radical, it was seventeen years after his miraculous outpouring from the patent office before he was awarded the prize and she collected.
Einstein’s life and work reflected the disruption of societal certainties and moral absolutes in the modernist atmosphere of the early twentieth century. Imaginative nonconformity was in the air: Picasso, Joyce, Freud, Stravinsky, Schoenberg, and others were breaking conventional bonds. Charging this atmosphere was a conception of the universe in which space and time and the properties of particles seemed based on the vagaries of observations.
Einstein, however, was not truly a relativist, even though that is how he was interpreted by many, including some whose disdain was tinged by anti-Semitism. Beneath all of his theories, including relativity, was a quest for invariants, certainties, and absolutes. There was a harmonious reality underlying the laws of the universe, Einstein felt, and the goal of science was to discover it.
His quest began in 1895, when as a 16-year-old he imagined what it would be like to ride alongside a light beam. A decade later came his miracle year, described in the letter above, which laid the foundations for the two great advances of twentieth-century physics: relativity and quantum theory.
A decade after that, in 1915, he wrested from nature his crowning glory, one of the most beautiful theories in all of science, the general theory of relativity. As with the special theory, his thinking had evolved through thought experiments. Imagine being in an enclosed elevator accelerating up through space, he conjectured in one of them. The effects you’d feel would be indistinguishable from the experience of gravity.
Gravity, he figured, was a warping of space and time, and he came up with the equations that describe how the dynamics of this curvature result from the interplay between matter, motion, and energy. It can be described by using another thought experiment. Picture what it would be like to roll a bowling ball onto the two-dimensional surface of a trampoline. Then roll some billiard balls. They move toward the bowling ball not because it exerts some mysterious attraction but because of the way it curves the trampoline fabric. Now imagine this happening in the four-dimensional fabric of space and time. Okay, it’s not easy, but that’s why we’re no Einstein and he was.
The exact midpoint of his career came a decade after that, in 1925, and it was a turning point. The quantum revolution he had helped to launch was being transformed into a new mechanics that was based on uncertainties and probabilities. He made his last great contributions to quantum mechanics that year but, simultaneously, began to resist it. He would spend the next three decades, ending with some equations scribbled while on his deathbed in 1955, stubbornly criticizing what he regarded as the incompleteness of quantum mechanics while attempting to subsume it into a unified field theory.
Both during his thirty years as a revolutionary and his subsequent thirty years as a resister, Einstein remained consistent in his willingness to be a serenely amused loner who was comfortable not conforming. Independent in his thinking, he was driven by an imagination that broke from the confines of conventional wisdom. He was that odd breed, a reverential rebel, and he was guided by a faith, which he wore lightly and with a twinkle in his eye, in a God who would not play dice by allowing things to happen by chance.
Einstein’s nonconformist streak was evident in his personality and politics as well. Although he subscribed to socialist ideals, he was too much of an individualist to be comfortable with excessive state control or centralized authority. His impudent instincts, which served him so well as a young scientist, made him allergic to nationalism, militarism, and anything that smacked of a herd mentality. And until Hitler caused him to revise his geopolitical equations, he was an instinctive pacifist who celebrated resistance to war.
His tale encompasses the vast sweep of modern science, from the infinitesimal to the infinite, from the emission of photons to the expansion of the cosmos. A century after his great triumphs, we are still living in Einstein’s universe, one defined on the macro scale by his theory of relativity and on the micro scale by a quantum mechanics that has proven durable even as it remains disconcerting.
His fingerprints are all over today’s technologies. Photoelectric cells and lasers, nuclear power and fiber optics, space travel, and even semiconductors all trace back to his theories. He signed the letter to Franklin Roosevelt warning that it may be possible to build an atom bomb, and the letters of his famed equation relating energy to mass hover in our minds when we picture the resulting mushroom cloud.
Einstein’s launch into fame, which occurred when measurements made during a 1919 eclipse confirmed his prediction of how much gravity bends light, coincided with, and contributed to, the birth of a new celebrity age. He became a scientific supernova and humanist icon, one of the most famous faces on the planet. The public earnestly puzzled over his theories, elevated him into a cult of genius, and canonized him as a secular saint.
If he did not have that electrified halo of hair and those piercing eyes, would he still have become science’s preeminent poster boy? Suppose, as a thought experiment, that he had looked like a Max Planck or a Niels Bohr. Would he have remained in their reputational orbit, that of a mere scientific genius? Or would he still have made the leap into the pantheon inhabited by Aristotle, Galileo, and Newton?2
The latter, I believe, is the case. His work had a very personal character, a stamp that made it recognizably his, the way a Picasso is recognizably a Picasso. He made imaginative leaps and discerned great principles through thought experiments rather than by methodical inductions based on experimental data. The theories that resulted were at times astonishing, mysterious, and counterintuitive, yet they contained notions that could capture the popular imagination: the relativity of space and time, E=mc 2, the bending of light beams, and the warping of space.
Adding to his aura was his simple humanity. His inner security was tempered by the humility that comes from being awed by nature. He could be detached and aloof from those close to him, but toward mankind in general he exuded a true kindness and gentle compassion.
Yet for all of his popular appeal and surface accessibility, Einstein also came to symbolize the perception that modern physics was something that ordinary laymen could not comprehend, “the province of priest-like experts,” in the words of Harvard professor Dudley Herschbach.3 It was not always thus. Galileo and Newton were both great geniuses, but their mechanical cause-and-effect explanation of the world was something that most thoughtful folks could grasp. In the eighteenth century of Benjamin Franklin and the nineteenth century of Thomas Edison, an educated person could feel some familiarity with science and even dabble in it as an amateur.
A popular feel for scientific endeavors should, if possible, be restored given the needs of the twenty-first century. This does not mean that every literature major should take a watered-down physics course or that a corporate lawyer should stay abreast of quantum mechanics. Rather, it means that an appreciation for the methods of science is a useful asset for a responsible citizenry. What science teaches us, very significantly, is the correlation between factual evidence and general theories, something well illustrated in Einstein’s life.
In addition, an appreciation for the glories of science is a joyful trait for a good society. It helps us remain in touch with that childlike capacity for wonder, about such ordinary things as falling apples and elevators, that characterizes Einstein and other great theoretical physicists.4
That is why studying Einstein can be worthwhile. Science is inspiring and noble, and its pursuit an enchanting mission, as the sagas of its heroes remind us. Near the end of his life, Einstein was asked by the New York State Education Department what schools should emphasize. “In teaching history,” he replied, “there should be extensive discussion of personalities who benefited mankind through independence of character and judgment.”5 Einstein fits into that category.
At a time when there is a new emphasis, in the face of global competition, on science and math education, we should also note the other part of Einstein’s answer. “Critical comments by students should be taken in a friendly spirit,” he said. “Accumulation of material should not stifle the student’s independence.” A society’s competitive advantage will come not from how well its schools teach the multiplication and periodic tables, but from how well they stimulate imagination and creativity.
Therein lies the key, I think, to Einstein’s brilliance and the lessons of his life. As a young student he never did well with rote learning. And later, as a theorist, his success came not from the brute strength of his mental processing power but from his imagination and creativity. He could construct complex equations, but more important, he knew that math is the language nature uses to describe her wonders. So he could visualize how equations were reflected in realities—how the electromagnetic field equations discovered by James Clerk Maxwell, for example, would manifest themselves to a boy riding alongside a light beam. As he once declared, “Imagination is more important than knowledge.”6
That approach required him to embrace nonconformity. “Long live impudence!” he exulted to the lover who would later become his wife. “It is my guardian angel in this world.” Many years later, when others thought that his reluctance to embrace quantum mechanics showed that he had lost his edge, he lamented, “To punish me for my contempt for authority, fate made me an authority myself.”7
His success came from questioning conventional wisdom, challenging authority, and marveling at mysteries that struck others as mundane. This led him to embrace a morality and politics based on respect for free minds, free spirits, and free individuals. Tyranny repulsed him, and he saw tolerance not simply as a sweet virtue but as a necessary condition for a creative society. “It is important to foster individuality,” he said, “for only the individual can produce the new ideas.”8
This outlook made Einstein a rebel with a reverence for the harmony of nature, one who had just the right blend of imagination and wisdom to transform our understanding of the universe. These traits are just as vital for this new century of globalization, in which our success will depend on our creativity, as they were for the beginning of the twentieth century, when Einstein helped usher in the modern age.
Maja, age 3, and Albert Einstein, 5
He was slow in learning how to talk. “My parents were so worried,” he later recalled, “that they consulted a doctor.” Even after he had begun using words, sometime after the age of 2, he developed a quirk that prompted the family maid to dub him “der Depperte,” the dopey one, and others in his family to label him as “almost backwards.” Whenever he had something to say, he would try it out on himself, whispering it softly until it sounded good enough to pronounce aloud. “Every sentence he uttered,” his worshipful younger sister recalled, “no matter how routine, he repeated to himself softly, moving his lips.” It was all very worrying, she said. “He had such difficulty with language that those around him feared he would never learn.”1
His slow development was combined with a cheeky rebelliousness toward authority, which led one schoolmaster to send him packing and another to amuse history by declaring that he would never amount to much. These traits made Albert Einstein the patron saint of distracted school kids everywhere.2 But they also helped to make him, or so he later surmised, the most creative scientific genius of modern times.
His cocky contempt for authority led him to question received wisdom in ways that well-trained acolytes in the academy never contemplated. And as for his slow verbal development, he came to believe that it allowed him to observe with wonder the everyday phenomena that others took for granted. “When I ask myself how it happened that I in particular discovered the relativity theory, it seemed to lie in the following circumstance,” Einstein once explained. “The ordinary adult never bothers his head about the problems of space and time. These are things he has thought of as a child. But I developed so slowly that I began to wonder about space and time only when I was already grown up. Consequently, I probed more deeply into the problem than an ordinary child would have.”3
Einstein’s developmental problems have probably been exaggerated, perhaps even by himself, for we have some letters from his adoring grandparents saying that he was just as clever and endearing as every grandchild is. But throughout his life, Einstein had a mild form of echolalia, causing him to repeat phrases to himself, two or three times, especially if they amused him. And he generally preferred to think in pictures, most notably in famous thought experiments, such as imagining watching lightning strikes from a moving train or experiencing gravity while inside a falling elevator. “I very rarely think in words at all,” he later told a psychologist. “A thought comes, and I may try to express it in words afterwards.”4
Einstein was descended, on both parents’ sides, from Jewish trades-men and peddlers who had, for at least two centuries, made modest livings in the rural villages of Swabia in southwestern Germany. With each generation they had become, or at least so they thought, increasingly assimilated into the German culture that they loved. Although Jewish by cultural designation and kindred instinct, they displayed scant interest in the religion or its rituals.
Einstein regularly dismissed the role that his heritage played in shaping who he became. “Exploration of my ancestors,” he told a friend late in life, “leads nowhere.”5 That’s not fully true. He was blessed by being born into an independent-minded and intelligent family line that valued education, and his life was certainly affected, in ways both beautiful and tragic, by membership in a religious heritage that had a distinctive intellectual tradition and a history of being both outsiders and wanderers. Of course, the fact that he happened to be Jewish in Germany in the early twentieth century made him more of an outsider, and more of a wanderer, than he would have preferred—but that, too, became integral to who he was and the role he would play in world history.
Einstein’s father, Hermann, was born in 1847 in the Swabian village of Buchau, whose thriving Jewish community was just beginning to enjoy the right to practice any vocation. Hermann showed “a marked inclination for mathematics,”6 and his family was able to send him seventy-five miles north to Stuttgart for high school. But they could not afford to send him to a university, most of which were closed to Jews in any event, so he returned home to Buchau to go into trade.
A few years later, as part of the general migration of rural German Jews into industrial centers during the late nineteenth century, Hermann and his parents moved thirty-five miles away to the more prosperous town of Ulm, which prophetically boasted as its motto “Ulmenses sunt mathematici,” the people of Ulm are mathematicians.7
There he became a partner in a cousin’s featherbed company. He was “exceedingly friendly, mild and wise,” his son would recall.8 With a gentleness that blurred into docility, Hermann was to prove inept as a businessman and forever impractical in financial matters. But his docility did make him well suited to be a genial family man and good husband to a strong-willed woman. At age 29, he married Pauline Koch, eleven years his junior.
Pauline’s father, Julius Koch, had built a considerable fortune as a grain dealer and purveyor to the royal Württemberg court. Pauline inherited his practicality, but she leavened his dour disposition with a teasing wit edged with sarcasm and a laugh that could be both infectious and wounding (traits she would pass on to her son). From all accounts, the match between Hermann and Pauline was a happy one, with her strong personality meshing “in complete harmony” with her husband’s passivity.9
Their first child was born at 11:30 a.m. on Friday, March 14, 1879, in Ulm, which had recently joined, along with the rest of Swabia, the new German Reich. Initially, Pauline and Hermann had planned to name the boy Abraham, after his paternal grandfather. But they came to feel, he later said, that the name sounded “too Jewish.”10 So they kept the initial A and named him Albert Einstein.
In 1880, just a year after Albert’s birth, Hermann’s featherbed business foundered and he was persuaded to move to Munich by his brother Jakob, who had opened a gas and electrical supply company there. Jakob, the youngest of five siblings, had been able to get a higher education, unlike Hermann, and he had qualified as an engineer. As they competed for contracts to provide generators and electrical lighting to municipalities in southern Germany, Jakob was in charge of the technical side while Hermann provided a modicum of salesmanship skills plus, perhaps more important, loans from his wife’s side of the family.11
Pauline and Hermann had a second and final child, a daughter, in November 1881, who was named Maria but throughout her life used instead the diminutive Maja. When Albert was shown his new sister for the first time, he was led to believe that she was like a wonderful toy that he would enjoy. His response was to look at her and exclaim, “Yes, but where are the wheels?”12 It may not have been the most perceptive of questions, but it did show that during his third year his language challenges did not prevent him from making some memorable comments. Despite a few childhood squabbles, Maja was to become her brother’s most intimate soul mate.
The Einsteins settled into a comfortable home with mature trees and an elegant garden in a Munich suburb for what was to be, at least through most of Albert’s childhood, a respectable bourgeois existence. Munich had been architecturally burnished by mad King Ludwig II (1845–1886) and boasted a profusion of churches, art galleries, and concert halls that favored the works of resident Richard Wagner. In 1882, just after the Einsteins arrived, the city had about 300,000 residents, 85 percent of them Catholics and 2 percent of them Jewish, and it was the host of the first German electricity exhibition, at which electric lights were introduced to the city streets.
Einstein’s back garden was often bustling with cousins and children. But he shied from their boisterous games and instead “occupied himself with quieter things.” One governess nicknamed him “Father Bore.” He was generally a loner, a tendency he claimed to cherish throughout his life, although his was a special sort of detachment that was interwoven with a relish for camaraderie and intellectual companionship. “From the very beginning he was inclined to separate himself from children his own age and to engage in daydreaming and meditative musing,” according to Philipp Frank, a longtime scientific colleague.13
He liked to work on puzzles, erect complex structures with his toy building set, play with a steam engine that his uncle gave him, and build houses of cards. According to Maja, Einstein was able to construct card structures as high as fourteen stories. Even discounting the recollections of a star-struck younger sister, there was probably a lot of truth to her claim that “persistence and tenacity were obviously already part of his character.”
He was also, at least as a young child, prone to temper tantrums. “At such moments his face would turn completely yellow, the tip of his nose snow-white, and he was no longer in control of himself,” Maja remembers. Once, at age 5, he grabbed a chair and threw it at a tutor, who fled and never returned. Maja’s head became the target of various hard objects. “It takes a sound skull,” she later joked, “to be the sister of an intellectual.” Unlike his persistence and tenacity, he eventually outgrew his temper.14
To use the language of psychologists, the young Einstein’s ability to systemize (identify the laws that govern a system) was far greater than his ability to empathize (sense and care about what other humans are feeling), which have led some to ask if he might have exhibited mild symptoms of some developmental disorder.15 However, it is important to note that, despite his aloof and occasionally rebellious manner, he did have the ability to make close friends and to empathize both with colleagues and humanity in general.
The great awakenings that happen in childhood are usually lost to memory. But for Einstein, an experience occurred when he was 4 or 5 that would alter his life and be etched forever in his mind—and in the history of science.
He was sick in bed one day, and his father brought him a compass. He later recalled being so excited as he examined its mysterious powers that he trembled and grew cold. The fact that the magnetic needle behaved as if influenced by some hidden force field, rather than through the more familiar mechanical method involving touch or contact, produced a sense of wonder that motivated him throughout his life. “I can still remember—or at least I believe I can remember—that this experience made a deep and lasting impression on me,” he wrote on one of the many occasions he recounted the incident. “Something deeply hidden had to be behind things.”16
“It’s an iconic story,” Dennis Overbye noted in Einstein in Love,“the young boy trembling to the invisible order behind chaotic reality.” It has been told in the movie IQ, in which Einstein, played by Walter Matthau, wears the compass around his neck, and it is the focus of a children’s book, Rescuing Albert’s Compass, by Shulamith Oppenheim, whose father-in-law heard the tale from Einstein in 1911.17
After being mesmerized by the compass needle’s fealty to an unseen field, Einstein would develop a lifelong devotion to field theories as a way to describe nature. Field theories use mathematical quantities, such as numbers or vectors or tensors, to describe how the conditions at any point in space will affect matter or another field. For example, in a gravitational or an electromagnetic field there are forces that could act on a particle at any point, and the equations of a field theory describe how these change as one moves through the region. The first paragraph of his great 1905 paper on special relativity begins with a consideration of the effects of electrical and magnetic fields; his theory of general relativity is based on equations that describe a gravitational field; and at the very end of his life he was doggedly scribbling further field equations in the hope that they would form the basis for a theory of everything. As the science historian Gerald Holton has noted, Einstein regarded “the classical concept of the field the greatest contribution to the scientific spirit.”18
His mother, an accomplished pianist, also gave him a gift at around the same time, one that likewise would last throughout his life. She arranged for him to take violin lessons. At first he chafed at the mechanical discipline of the instruction. But after being exposed to Mozart’s sonatas, music became both magical and emotional to him. “I believe that love is a better teacher than a sense of duty,” he said, “at least for me.”19
Soon he was playing Mozart duets, with his mother accompanying him on the piano. “Mozart’s music is so pure and beautiful that I see it as a reflection of the inner beauty of the universe itself,” he later told a friend. “Of course,” he added in a remark that reflected his view of math and physics as well as of Mozart, “like all great beauty, his music was pure simplicity.”20
Music was no mere diversion. On the contrary, it helped him think. “Whenever he felt that he had come to the end of the road or faced a difficult challenge in his work,” said his son Hans Albert, “he would take refuge in music and that would solve all his difficulties.” The violin thus proved useful during the years he lived alone in Berlin, wrestling with general relativity. “He would often play his violin in his kitchen late at night, improvising melodies while he pondered complicated problems,” a friend recalled. “Then, suddenly, in the middle of playing, he would announce excitedly, ‘I’ve got it!’ As if by inspiration, the answer to the problem would have come to him in the midst of music.”21
His appreciation for music, and especially for Mozart, may have reflected his feel for the harmony of the universe. As Alexander Moszkowski, who wrote a biography of Einstein in 1920 based on conversations with him, noted, “Music, Nature, and God became intermingled in him in a complex of feeling, a moral unity, the trace of which never vanished.”22
Throughout his life, Albert Einstein would retain the intuition and the awe of a child. He never lost his sense of wonder at the magic of nature’s phenomena—magnetic fields, gravity, inertia, acceleration, light beams—which grown-ups find so commonplace. He retained the ability to hold two thoughts in his mind simultaneously, to be puzzled when they conflicted, and to marvel when he could smell an underlying unity. “People like you and me never grow old,” he wrote a friend later in life. “We never cease to stand like curious children before the great mystery into which we were born.”23
In his later years, Einstein would tell an old joke about an agnostic uncle, who was the only member of his family who went to synagogue. When asked why he did so, the uncle would respond, “Ah, but you never know.” Einstein’s parents, on the other hand, were “entirely irreligious” and felt no compulsion to hedge their bets. They did not keep kosher or attend synagogue, and his father referred to Jewish rituals as “ancient superstitions.”24
Consequently, when Albert turned 6 and had to go to school, his parents did not care that there was no Jewish one near their home. Instead he went to the large Catholic school in their neighborhood, the Petersschule. As the only Jew among the seventy students in his class, Einstein took the standard course in Catholic religion and ended up enjoying it immensely. Indeed, he did so well in his Catholic studies that he helped his classmates with theirs.25
One day his teacher brought a large nail to the class.“The nails with which Jesus was nailed to the cross looked like this,” he said.26 Nevertheless, Einstein later said that he felt no discrimination from the teachers. “The teachers were liberal and made no distinction based on denominations,” he wrote. His fellow students, however, were a different matter. “Among the children at the elementary school, anti-Semitism was prevalent,” he recalled.
Being taunted on his walks to and from school based on “racial characteristics about which the children were strangely aware” helped reinforce the sense of being an outsider, which would stay with him his entire life. “Physical attacks and insults on the way home from school were frequent, but for the most part not too vicious. Nevertheless, they were sufficient to consolidate, even in a child, a lively sense of being an outsider.”27
When he turned 9, Einstein moved up to a high school near the center of Munich, the Luitpold Gymnasium, which was known as an enlightened institution that emphasized math and science as well as Latin and Greek. In addition, the school supplied a teacher to provide religious instruction for him and other Jews.
Despite his parents’ secularism, or perhaps because of it, Einstein rather suddenly developed a passionate zeal for Judaism. “He was so fervent in his feelings that, on his own, he observed Jewish religious strictures in every detail,” his sister recalled. He ate no pork, kept kosher dietary laws, and obeyed the strictures of the Sabbath, all rather difficult to do when the rest of his family had a lack of interest bordering on disdain for such displays. He even composed his own hymns for the glorification of God, which he sang to himself as he walked home from school.28
One widely held belief about Einstein is that he failed math as a student, an assertion that is made, often accompanied by the phrase “as everyone knows,” by scores of books and thousands of websites designed to reassure underachieving students. It even made it into the famous “Ripley’s Believe It or Not!” newspaper column.
Alas, Einstein’s childhood offers history many savory ironies, but this is not one of them. In 1935, a rabbi in Princeton showed him a clipping of the Ripley’s column with the headline “Greatest Living Mathematician Failed in Mathematics.” Einstein laughed. “I never failed in mathematics,” he replied, correctly. “Before I was fifteen I had mastered differential and integral calculus.”29
In fact, he was a wonderful student, at least intellectually. In primary school, he was at the top of his class. “Yesterday Albert got his grades,” his mother reported to an aunt when he was 7. “Once again he was ranked first.” At the gymnasium, he disliked the mechanical learning of languages such as Latin and Greek, a problem exacerbated by what he later said was his “bad memory for words and texts.” But even in these courses, Einstein consistently got top grades. Years later, when Einstein celebrated his fiftieth birthday and there were stories about how poorly the great genius had fared at the gymnasium, the school’s current principal made a point of publishing a letter revealing how good his grades actually were.30
As for math, far from being a failure, he was “far above the school requirements.” By age 12, his sister recalled, “he already had a predilection for solving complicated problems in applied arithmetic,” and he decided to see if he could jump ahead by learning geometry and algebra on his own. His parents bought him the textbooks in advance so that he could master them over summer vacation. Not only did he learn the proofs in the books, he tackled the new theories by trying to prove them on his own. “Play and playmates were forgotten,” she noted. “For days on end he sat alone, immersed in the search for a solution, not giving up before he had found it.”31
His uncle Jakob Einstein, the engineer, introduced him to the joys of algebra. “It’s a merry science,” he explained. “When the animal that we are hunting cannot be caught, we call it X temporarily and continue to hunt until it is bagged.” He went on to give the boy even more difficult challenges, Maja recalled, “with good-natured doubts about his ability to solve them.” When Einstein triumphed, as he invariably did, he “was overcome with great happiness and was already then aware of the direction in which his talents were leading him.”
Among the concepts that Uncle Jakob threw at him was the Pythagorean theorem (the square of the lengths of the legs of a right triangle add up to the square of the length of the hypotenuse). “After much effort I succeeded in ‘proving’ this theorem on the basis of the similarity of triangles,” Einstein recalled. Once again he was thinking in pictures. “It seemed to me ‘evident’ that the relations of the sides of the right-angled triangles would have to be completely determined by one of the acute angles.”32
Maja, with the pride of a younger sister, called Einstein’s Pythagorean proof “an entirely original new one.” Although perhaps new to him, it is hard to imagine that Einstein’s approach, which was surely similar to the standard ones based on the proportionality of the sides of similar triangles, was completely original. Nevertheless, it did show Einstein’s youthful appreciation that elegant theorems can be derived from simple axioms—and the fact that he was in little danger of failing math. “As a boy of 12, I was thrilled to see that it was possible to find out truth by reasoning alone, without the help of any outside experience,” he told a reporter from a high school newspaper in Princeton years later. “I became more and more convinced that nature could be understood as a relatively simple mathematical structure.”33
Einstein’s greatest intellectual stimulation came from a poor medical student who used to dine with his family once a week. It was an old Jewish custom to take in a needy religious scholar to share the Sabbath meal; the Einsteins modified the tradition by hosting instead a medical student on Thursdays. His name was Max Talmud (later changed to Talmey, when he immigrated to the United States), and he began his weekly visits when he was 21 and Einstein was 10. “He was a pretty, dark-haired boy,” remembered Talmud. “In all those years, I never saw him reading any light literature. Nor did I ever see him in the company of schoolmates or other boys his age.”34
Talmud brought him science books, including a popular illustrated series called People’s Books on Natural Science, “a work which I read with breathless attention,” said Einstein. The twenty-one little volumes were written by Aaron Bernstein, who stressed the interrelations between biology and physics, and he reported in great detail the scientific experiments being done at the time, especially in Germany.35
In the opening section of the first volume, Bernstein dealt with the speed of light, a topic that obviously fascinated him. Indeed, he returned to it repeatedly in his subsequent volumes, including eleven essays on the topic in volume 8. Judging from the thought experiments that Einstein later used in creating his theory of relativity, Bernstein’s books appear to have been influential.
For example, Bernstein asked readers to imagine being on a speeding train. If a bullet is shot through the window, it would seem that it was shot at an angle, because the train would have moved between the time the bullet entered one window and exited the window on the other side. Likewise, because of the speed of the earth through space, the same must be true of light going through a telescope. What was amazing, said Bernstein, was that experiments showed the same effect no matter how fast the source of the light was moving. In a sentence that, because of its relation to what Einstein would later famously conclude, seems to have made an impression, Bernstein declared, “Since each kind of light proves to be of exactly the same speed, the law of the speed of light can well be called the most general of all of nature’s laws.”
In another volume, Bernstein took his young readers on an imaginary trip through space. The mode of transport was the wave of an electric signal. His books celebrated the joyful wonders of scientific investigation and included such exuberant passages as this one written about the successful prediction of the location of the new planet Uranus: “Praised be this science! Praised be the men who do it! And praised be the human mind, which sees more sharply than does the human eye.”36
Bernstein was, as Einstein would later be, eager to tie together all of nature’s forces. For example, after discussing how all electromagnetic phenomena, such as light, could be considered waves, he speculated that the same may be true for gravity. A unity and simplicity, Bernstein wrote, lay beneath all the concepts applied by our perceptions. Truth in science consisted in discovering theories that described this underlying reality. Einstein later recalled the revelation, and the realist attitude, that this instilled in him as a young boy: “Out yonder there was this huge world, which exists independently of us human beings and which stands before us like a great, eternal riddle.”37
Years later, when they met in New York during Einstein’s first visit there, Talmud asked what he thought, in retrospect, of Bernstein’s work. “A very good book,” he said. “It has exerted a great influence on my whole development.”38
Talmud also helped Einstein continue to explore the wonders of mathematics by giving him a textbook on geometry two years before he was scheduled to learn that subject in school. Later, Einstein would refer to it as “the sacred little geometry book” and speak of it with awe: “Here were assertions, as for example the intersection of the three altitudes of a triangle in one point, which—though by no means evident—could nevertheless be proved with such certainty that any doubt appeared to be out of the question. This lucidity and certainty made an indescribable impression upon me.” Years later, in a lecture at Oxford, Einstein noted, “If Euclid failed to kindle your youthful enthusiasm, then you were not born to be a scientific thinker.”39
When Talmud arrived each Thursday, Einstein delighted in showing him the problems he had solved that week. Initially, Talmud was able to help him, but he was soon surpassed by his pupil. “After a short time, a few months, he had worked through the whole book,” Talmud recalled. “He thereupon devoted himself to higher mathematics . . . Soon the flight of his mathematical genius was so high that I could no longer follow.”40
So the awed medical student moved on to introducing Einstein to philosophy. “I recommended Kant to him,” he recalled. “At that time he was still a child, only thirteen years old, yet Kant’s works, incomprehensible to ordinary mortals, seemed to be clear to him.” Kant became, for a while, Einstein’s favorite philosopher, and his Critique of Pure Reason eventually led him to delve also into David Hume, Ernst Mach, and the issue of what can be known about reality.
Einstein’s exposure to science produced a sudden reaction against religion at age 12, just as he would have been readying for a bar mitzvah. Bernstein, in his popular science volumes, had reconciled science with religious inclination. As he put it, “The religious inclination lies in the dim consciousness that dwells in humans that all nature, including the humans in it, is in no way an accidental game, but a work of lawfulness, that there is a fundamental cause of all existence.”
Einstein would later come close to these sentiments. But at the time, his leap away from faith was a radical one. “Through the reading of popular scientific books, I soon reached the conviction that much in the stories of the Bible could not be true. The consequence was a positively fanatic orgy of freethinking coupled with the impression that youth is intentionally being deceived by the state through lies; it was a crushing impression.”41
As a result, Einstein avoided religious rituals for the rest of his life. “There arose in Einstein an aversion to the orthodox practice of the Jewish or any traditional religion, as well as to attendance at religious services, and this he has never lost,” his friend Philipp Frank later noted. He did, however, retain from his childhood religious phase a profound reverence for the harmony and beauty of what he called the mind of God as it was expressed in the creation of the universe and its laws.42
Einstein’s rebellion against religious dogma had a profound effect on his general outlook toward received wisdom. It inculcated an allergic reaction against all forms of dogma and authority, which was to affect both his politics and his science. “Suspicion against every kind of authority grew out of this experience, an attitude which has never again left me,” he later said. Indeed, it was this comfort with being a nonconformist that would define both his science and his social thinking for the rest of his life.
He would later be able to pull off this contrariness with a grace that was generally endearing, once he was accepted as a genius. But it did not play so well when he was merely a sassy student at a Munich gymnasium. “He was very uncomfortable in school,” according to his sister. He found the style of teaching—rote drills, impatience with questioning—to be repugnant. “The military tone of the school, the systematic training in the worship of authority that was supposed to accustom pupils at an early age to military discipline, was particularly unpleasant.”43
Even in Munich, where the Bavarian spirit engendered a less regimented approach to life, this Prussian glorification of the military had taken hold, and many of the children loved to play at being soldiers. When troops would come by, accompanied by fifes and drums, kids would pour into the streets to join the parade and march in lockstep. But not Einstein. Watching such a display once, he began to cry. “When I grow up, I don’t want to be one of those poor people,” he told his parents. As Einstein later explained, “When a person can take pleasure in marching in step to a piece of music it is enough to make me despise him. He has been given his big brain only by mistake.”44
The opposition he felt to all types of regimentation made his education at the Munich gymnasium increasingly irksome and contentious. The mechanical learning there, he complained, “seemed very much akin to the methods of the Prussian army, where a mechanical discipline was achieved by repeated execution of meaningless orders.” In later years, he would liken his teachers to members of the military. “The teachers at the elementary school seemed to me like drill sergeants,” he said, “and the teachers at the gymnasium like lieutenants.”
He once asked C. P. Snow, the British writer and scientist, whether he was familiar with the German word Zwang. Snow allowed that he was; it meant constraint, compulsion, obligation, coercion. Why? In his Munich school, Einstein answered, he had made his first strike against Zwang, and it had helped define him ever since.45
Skepticism and a resistance to received wisdom became a hallmark of his life. As he proclaimed in a letter to a fatherly friend in 1901, “A foolish faith in authority is the worst enemy of truth.”46
Throughout the six decades of his scientific career, whether leading the quantum revolution or later resisting it, this attitude helped shape Einstein’s work. “His early suspicion of authority, which never wholly left him, was to prove of decisive importance,” said Banesh Hoffmann, who was a collaborator of Einstein’s in his later years. “Without it he would not have been able to develop the powerful independence of mind that gave him the courage to challenge established scientific beliefs and thereby revolutionize physics.”47
This contempt for authority did not endear him to the German “lieutenants” who taught him at his school. As a result, one of his teachers proclaimed that his insolence made him unwelcome in class. When Einstein insisted that he had committed no offense, the teacher replied, “Yes, that is true, but you sit there in the back row and smile, and your mere presence here spoils the respect of the class for me.”48
Einstein’s discomfort spiraled toward depression, perhaps even close to a nervous breakdown, when his father’s business suffered a sudden reversal of fortune. The collapse was a precipitous one. During most of Einstein’s school years, the Einstein brothers’ company had been a success. In 1885, it had two hundred employees and provided the first electrical lights for Munich’s Oktoberfest. Over the next few years, it won the contract to wire the community of Schwabing, a Munich suburb of ten thousand people, using gas motors to drive twin dynamos that the Einsteins had designed. Jakob Einstein received six patents for improvements in arc lamps, automatic circuit breakers, and electric meters. The company was poised to rival Siemens and other power companies then flourishing. To raise capital, the brothers mortgaged their homes, borrowed more than 60,000 marks at 10 percent interest, and went deeply in debt.49
But in 1894, when Einstein was 15, the company went bust after it lost competitions to light the central part of Munich and other locations. His parents and sister, along with Uncle Jakob, moved to northern Italy—first Milan and then the nearby town of Pavia—where the company’s Italian partners thought there would be more fertile territory for a smaller firm. Their elegant home was torn down by a developer to build an apartment block. Einstein was left behind in Munich, at the house of a distant relative, to finish his final three years of school.
It is not quite clear whether Einstein, in that sad autumn of 1894, was actually forced to leave the Luitpold Gymnasium or was merely politely encouraged to leave. Years later, he recalled that the teacher who had declared that his “presence spoils the respect of the class for me” had gone on to “express the wish that I leave the school.” An early book by a member of his family said that it was his own decision. “Albert increasingly resolved not to remain in Munich, and he worked out a plan.”
That plan involved getting a letter from the family doctor, Max Talmud’s older brother, who certified that he was suffering from nervous exhaustion. He used this to justify leaving the school at Christmas vacation in 1894 and not returning. Instead, he took a train across the Alps to Italy and informed his “alarmed” parents that he was never going back to Germany. Instead, he promised, he would study on his own and attempt to gain admission to a technical college in Zurich the following autumn.
There was perhaps one other factor in his decision to leave Germany. Had he remained there until he was 17, just over a year away, he would have been required to join the army, a prospect that his sister said “he contemplated with dread.” So, in addition to announcing that he would not go back to Munich, he would soon ask for his father’s help in renouncing his German citizenship.50
Einstein spent the spring and summer of 1895 living with his parents in their Pavia apartment and helping at the family firm. In the process, he was able to get a good feel for the workings of magnets, coils, and generated electricity. Einstein’s work impressed his family. On one occasion, Uncle Jakob was having problems with some calculations for a new machine, so Einstein went to work on it. “After my assistant engineer and I had been racking our brain for days, that young sprig had got the whole thing in just fifteen minutes,” Jakob reported to a friend. “You will hear of him yet.”51
With his love of the sublime solitude found in the mountains, Einstein hiked for days in the Alps and Apennines, including an excursion from Pavia to Genoa to see his mother’s brother Julius Koch. Wherever he traveled in northern Italy, he was delighted by the non-Germanic grace and “delicacy” of the people. Their “naturalness” was a contrast to the “spiritually broken and mechanically obedient automatons” of Germany, his sister recalled.
Einstein had promised his family that he would study on his own to get into the local technical college, the Zurich Polytechnic.* So he bought all three volumes of Jules Violle’s advanced physics text and copiously noted his ideas in the margins. His work habits showed his ability to concentrate, his sister recalled. “Even in a large, quite noisy group, he could withdraw to the sofa, take pen and paper in hand, set the inkstand precariously on the armrest, and lose himself so completely in a problem that the conversation of many voices stimulated rather than disturbed him.”52
That summer, at age 16, he wrote his first essay on theoretical physics, which he titled “On the Investigation of the State of the Ether in a Magnetic Field.” The topic was important, for the notion of the ether would play a critical role in Einstein’s career. At the time, scientists conceived of light simply as a wave, and so they assumed that the universe must contain an all-pervasive yet unseen substance that was doing the rippling and thus propagating the waves, just as water was the medium rippling up and down and thus propagating the waves in an ocean. They dubbed this the ether, and Einstein (at least for the time being) went along with the assumption. As he put it in his essay, “An electric current sets the surrounding ether in a kind of momentary motion.”
The fourteen-paragraph handwritten paper echoed Violle’s textbook as well as some of the reports in the popular science magazines about Heinrich Hertz’s recent discoveries about electromagnetic waves. In it, Einstein made suggestions for experiments that could explain “the magnetic field formed around an electric current.” This would be interesting, he argued, “because the exploration of the elastic state of the ether in this case would permit us a look into the enigmatic nature of electric current.”
The high school dropout freely admitted that he was merely making a few suggestions without knowing where they might lead. “As I was completely lacking in materials that would have enabled me to delve into the subject more deeply than by merely meditating about it, I beg you not to interpret this circumstance as a mark of superficiality,” he wrote.53
He sent the paper to his uncle Caesar Koch, a merchant in Belgium, who was one of his favorite relatives and occasionally a financial patron. “It is rather naïve and imperfect, as might be expected from such a young fellow like myself,” Einstein confessed with a pretense of humility. He added that his goal was to enroll the following fall at the Zurich Polytechnic, but he was concerned that he was younger than the age requirement. “I should be at least two years older.”54
To help him get around the age requirement, a family friend wrote to the director of the Polytechnic, asking for an exception. The tone of the letter can be gleaned from the director’s response, which expressed skepticism about admitting this “so-called ‘child prodigy.’ ” Nevertheless, Einstein was granted permission to take the entrance exam, and he boarded the train for Zurich in October 1895 “with a sense of well-founded diffidence.”
Not surprisingly, he easily passed the section of the exam in math and science. But he failed to pass the general section, which included sections on literature, French, zoology, botany, and politics. The Polytechnic’s head physics professor, Heinrich Weber, suggested that Einstein stay in Zurich and audit his classes. Instead, Einstein decided, on the advice of the college’s director, to spend a year preparing at the cantonal school in the village of Aarau, twenty-five miles to the west.55
It was a perfect school for Einstein. The teaching was based on the philosophy of a Swiss educational reformer of the early nineteenth century, Johann Heinrich Pestalozzi, who believed in encouraging students to visualize images. He also thought it important to nurture the “inner dignity” and individuality of each child. Students should be allowed to reach their own conclusions, Pestalozzi preached, by using a series of steps that began with hands-on observations and then proceeded to intuitions, conceptual thinking, and visual imagery.56 It was even possible to learn—and truly understand—the laws of math and physics that way. Rote drills, memorization, and force-fed facts were avoided.
Einstein loved Aarau. “Pupils were treated individually,” his sister recalled, “more emphasis was placed on independent thought than on punditry, and young people saw the teacher not as a figure of authority, but, alongside the student, a man of distinct personality.” It was the opposite of the German education that Einstein had hated. “When compared to six years’ schooling at a German authoritarian gymnasium,” Einstein later said, “it made me clearly realize how much superior an education based on free action and personal responsibility is to one relying on outward authority.”57
The visual understanding of concepts, as stressed by Pestalozzi and his followers in Aarau, became a significant aspect of Einstein’s genius. “Visual understanding is the essential and only true means of teaching how to judge things correctly,” Pestalozzi wrote, and “the learning of numbers and language must be definitely subordinated.”58
Not surprisingly, it was at this school that Einstein first engaged in the visualized thought experiment that would help make him the greatest scientific genius of his time: he tried to picture what it would be like to ride alongside a light beam. “In Aarau I made my first rather childish experiments in thinking that had a direct bearing on the Special Theory,” he later told a friend. “If a person could run after a light wave with the same speed as light, you would have a wave arrangement which could be completely independent of time. Of course, such a thing is impossible.”59
This type of visualized thought experiments—Gedankenexperiment—became a hallmark of Einstein’s career. Over the years, he would picture in his mind such things as lightning strikes and moving trains, accelerating elevators and falling painters, two-dimensional blind beetles crawling on curved branches, as well as a variety of contraptions designed to pinpoint, at least in theory, the location and velocity of speeding electrons.
While a student in Aarau, Einstein boarded with a wonderful family, the Wintelers, whose members would long remain entwined in his life. There was Jost Winteler, who taught history and Greek at the school; his wife, Rosa, soon known to Einstein as Mamerl, or Mama; and their seven children. Their daughter Marie would become Einstein’s first girlfriend. Another daughter, Anna, would marry Einstein’s best friend, Michele Besso. And their son Paul would marry Einstein’s beloved sister, Maja.
“Papa” Jost Winteler was a liberal who shared Einstein’s allergy to German militarism and to nationalism in general. His edgy honesty and political idealism helped to shape Einstein’s social philosophy. Like his mentor, Einstein would become a supporter of world federalism, internationalism, pacifism, and democratic socialism, with a strong devotion to individual liberty and freedom of expression.
More important, in the warm embrace of the Winteler family, Einstein became more secure and personable. Even though he still fancied himself a loner, the Wintelers helped him flower emotionally and open himself to intimacy. “He had a great sense of humor and at times could laugh heartily,” recalled daughter Anna. In the evenings he would sometimes study, “but more often he would sit with the family around the table.”60
Einstein had developed into a head-turning teenager who possessed, in the words of one woman who knew him, “masculine good looks of the type that played havoc at the turn of the century.” He had wavy dark hair, expressive eyes, a high forehead, and jaunty demeanor. “The lower half of his face might have belonged to a sensualist who found plenty of reasons to love life.”
One of his schoolmates, Hans Byland, later wrote a striking description of “the impudent Swabian” who made such a lasting impression. “Sure of himself, his gray felt hat pushed back on his thick, black hair, he strode energetically up and down in the rapid, I might say crazy, tempo of a restless spirit which carries a whole world in itself. Nothing escaped the sharp gaze of the large bright brown eyes. Whoever approached him was captivated by his superior personality. A mocking curl of his fleshy mouth with its protruding lower lip did not encourage Philistines to fraternize with him.”
Most notably, Byland added, young Einstein had a sassy, sometimes intimidating wit. “He confronted the world spirit as a laughing philosopher, and his witty sarcasm mercilessly castigated all vanity and artificiality.”61
Einstein fell in love with Marie Winteler at the end of 1895, just a few months after he moved in with her parents. She had just completed teacher training college and was living at home while waiting to take a job in a nearby village. She was just turning 18, he was still 16. The romance thrilled both families. Albert and Marie sent New Year’s greetings to his mother; she replied warmly, “Your little letter, dear Miss Marie, brought me immense joy.”62
The following April, when he was back home in Pavia for spring break, Einstein wrote Marie his first known love letter:
Many, many thanks sweetheart for your charming little letter, which made me endlessly happy. It was so wonderful to be able to press to one’s heart such a bit of paper which two so dear little eyes have lovingly beheld and on which the dainty little hands have charmingly glided back and forth. I was now made to realize, my little angel, the meaning of homesickness and pining. But love brings much happiness—much more so than pining brings pain . . .
My mother has also taken you to her heart, even though she does not know you; I only let her read two of your charming little letters. And she always laughs at me because I am no longer attracted to the girls who were supposed to have enchanted me so much in the past. You mean more to my soul than the whole world did before.
To which his mother penned a postscript: “Without having read this letter, I send you cordial greetings!”63
Although he enjoyed the school in Aarau, Einstein turned out to be an uneven student. His admission report noted that he needed to do remedial work in chemistry and had “great gaps” in his knowledge of French. By midyear, he still was required to “continue with private lessons in French & chemistry,” and “the protest in French remains in effect.” His father was sanguine when Jost Winteler sent him the midyear report. “Not all its parts fulfill my wishes and expectations,” he wrote, “but with Albert I got used to finding mediocre grades along with very good ones, and I am therefore not disconsolate about them.”64
Music continued to be a passion. There were nine violinists in his class, and their teacher noted that they suffered from “some stiffness in bowing technique here and there.” But Einstein was singled out for praise: “One student, by the name of Einstein, even sparkled by rendering an adagio from a Beethoven sonata with deep understanding.” At a concert in the local church, Einstein was chosen to play first violin in a piece by Bach. His “enchanting tone and incomparable rhythm” awed the second violinist, who asked, “Do you count the beats?” Einstein replied, “Heavens no, it’s in my blood.”
His classmate Byland recalled Einstein playing a Mozart sonata with such passion—“What fire there was in his playing!”—that it seemed like hearing the composer for the first time. Listening to him, Byland realized that Einstein’s wisecracking, sarcastic exterior was a shell around a softer inner soul. “He was one of those split personalities who know how to protect, with a prickly exterior, the delicate realm of their intense personal life.”65
Einstein’s contempt for Germany’s authoritarian schools and militarist atmosphere made him want to renounce his citizenship in that country. This was reinforced by Jost Winteler, who disdained all forms of nationalism and instilled in Einstein the belief that people should consider themselves citizens of the world. So he asked his father to help him drop his German citizenship. The release came through in January 1896, and for the time being he was stateless.66
He also that year became a person without a religious affiliation. In the application to renounce his German citizenship, his father had written, presumably at Albert’s request, “no religious denomination.” It was a statement Albert would also make when applying for Zurich residency a few years later, and on various occasions over the ensuing two decades.
His rebellion from his childhood fling with ardent Judaism, coupled with his feelings of detachment from Munich’s Jews, had alienated him from his heritage. “The religion of the fathers, as I encountered it in Munich during religious instruction and in the synagogue, repelled rather than attracted me,” he later explained to a Jewish historian. “The Jewish bourgeois circles that I came to know in my younger years, with their affluence and lack of a sense of community, offered me nothing that seemed to be of value.”67
Later in life, beginning with his exposure to virulent anti-Semitism in the 1920s, Einstein would begin to reconnect with his Jewish identity. “There is nothing in me that can be described as a ‘Jewish faith,’ ” he said, “however I am happy to be a member of the Jewish people.” Later he would make the same point in more colorful ways. “The Jew who abandons his faith,” he once said, “is in a similar position to a snail that abandons his shell. He is still a snail.”68
His renunciation of Judaism in 1896 should, therefore, be seen not as a clean break but as part of a lifelong evolution of his feelings about his cultural identity. “At that time I would not even have understood what leaving Judaism could possibly mean,” he wrote a friend the year before he died. “But I was fully aware of my Jewish origin, even though the full significance of belonging to Jewry was not realized by me until later.”69
Einstein ended his year at the Aarau school in a manner that would have seemed impressive for anyone except one of history’s great geniuses, scoring the second highest grades in his class. (Alas, the name of the boy who bested Einstein is lost to history.) On a 1 to 6 scale, with 6 being the highest, he scored a 5 or 6 in all of his science and math courses as well as in history and Italian. His lowest grade was a 3, in French.
That qualified him to take a series of exams, written and oral, that would permit him, if he passed, to enter the Zurich Polytechnic. On his German exam, he did a perfunctory outline of a Goethe play and scored a 5. In math, he made a careless mistake, calling a number “imaginary” when he meant “irrational,” but still got a top grade. In physics, he arrived late and left early, completing the two-hour test in an hour and fifteen minutes; he got the top grade. Altogether, he ended up with a 5.5, the best grade among the nine students taking the exams.
The one section on which he did poorly was French. But his three-paragraph essay was, to those of us today, the most interesting part of all of his exams. The topic was “Mes Projets d’avenir,” my plans for the future. Although the French was not memorable, the personal insights were:
If I am lucky and pass my exams, I will enroll in the Zurich Polytechnic. I will stay there four years to study mathematics and physics. I suppose I will become a teacher in these fields of science, opting for the theoretical part of these sciences.
Here are the reasons that have led me to this plan. They are, most of all, my personal talent for abstract and mathematical thinking ... My desires have also led me to the same decision. That is quite natural; everybody desires to do that for which he has a talent. Besides, I am attracted by the independence offered by the profession of science.
In the summer of 1896, the Einstein brothers’ electrical business again failed, this time because they bungled getting the necessary water rights to build a hydroelectric system in Pavia. The partnership was dissolved in a friendly fashion, and Jakob joined a large firm as an engineer. But Hermann, whose optimism and pride tended to overwhelm any prudence, insisted on opening yet another new dynamo business, this time in Milan. Albert was so dubious of his father’s prospects that he went to his relatives and suggested that they not finance him again, but they did.71
Hermann hoped that Albert would someday join him in the business, but engineering held little appeal for him. “I was originally supposed to become an engineer,” he later wrote a friend, “but the thought of having to expend my creative energy on things that make practical everyday life even more refined, with a bleak capital gain as the goal, was unbearable to me. Thinking for its own sake, like music!”72 And thus he headed off to the Zurich Polytechnic.
THE ZURICH POLYTECHNIC
The Impudent Scholar
The Zurich Polytechnic, with 841 students, was mainly a teachers’ and technical college when 17-year-old Albert Einstein enrolled in October 1896. It was less prestigious than the neighboring University of Zurich and the universities in Geneva and Basel, all of which could grant doctoral degrees (a status that the Polytechnic, officially named the Eidgenössische Polytechnische Schule, would attain in 1911 when it became the Eidgenössische Technische Hochschule, or ETH). Nevertheless, the Polytechnic had a solid reputation in engineering and science. The head of the physics department, Heinrich Weber, had recently procured a grand new building, funded by the electronics magnate (and Einstein Brothers competitor) Werner von Siemens. It housed showcase labs famed for their precision measurements.
Einstein was one of eleven freshmen enrolled in the section that provided training “for specialized teachers in mathematics and physics.” He lived in student lodgings on a monthly stipend of 100 Swiss francs from his Koch family relatives. Each month he put aside 20 of those francs toward the fee he would eventually have to pay to become a Swiss citizen.1
Theoretical physics was just coming into its own as an academic discipline in the 1890s, with professorships in the field sprouting up across Europe. Its pioneer practitioners—such as Max Planck in Berlin, Hendrik Lorentz in Holland, and Ludwig Boltzmann in Vienna—combined physics with math to suggest paths where experimentalists had yet to tread. Because of this, math was supposed to be a major part of Einstein’s required studies at the Polytechnic.
Einstein, however, had a better intuition for physics than for math, and he did not yet appreciate how integrally the two subjects would be related in the pursuit of new theories. During his four years at the Polytechnic, he got marks of 5 or 6 (on a 6-point scale) in all of his theoretical physics courses, but got only 4s in most of his math courses, especially those in geometry. “It was not clear to me as a student,” he admitted, “that a more profound knowledge of the basic principles of physics was tied up with the most intricate mathematical methods.”2
That realization would sink in a decade later, when he was wrestling with the geometry of his theory of gravity and found himself forced to rely on the help of a math professor who had once called him a lazy dog. “I have become imbued with great respect for mathematics,” he wrote to a colleague in 1912, “the subtler part of which I had in my simple-mindedness regarded as pure luxury until now.” Near the end of his life, he expressed a similar lament in a conversation with a younger friend. “At a very early age, I made an assumption that a successful physicist only needs to know elementary mathematics,” he said. “At a later time, with great regret, I realized that the assumption of mine was completely wrong.”3
His primary physics professor was Heinrich Weber, the one who a year earlier had been so impressed with Einstein that, even after he had failed his entrance exam to the Polytechnic, he urged him to stay in Zurich and audit his lectures. During Einstein’s first two years at the Polytechnic, their mutual admiration endured. Weber’s lectures were among the few that impressed him. “Weber lectured on heat with great mastery,” he wrote during their second year. “One lecture after another of his pleases me.” He worked in Weber’s laboratory “with fervor and passion,” took fifteen courses (five lab and ten classroom) with him, and scored well in them all.4
Einstein, however, gradually became disenchanted with Weber. He felt that the professor focused too much on the historical foundations of physics, and he did not deal much with contemporary frontiers. “Anything that came after Helmholtz was simply ignored,” one contemporary of Einstein complained. “At the close of our studies, we knew all the past of physics but nothing of the present and future.”
Notably absent from Weber’s lectures was any exploration of the great breakthroughs of James Clerk Maxwell, who, beginning in 1855, developed profound theories and elegant mathematical equations that described how electromagnetic waves such as light propagated. “We waited in vain for a presentation of Maxwell’s theory,” wrote another fellow student. “Einstein above all was disappointed.”5
Given his brash attitude, Einstein didn’t hide his feelings. And given his dignified sense of himself, Weber bristled at Einstein’s ill-concealed disdain. By the end of their four years together they were antagonists.
Weber’s irritation was yet another example of how Einstein’s scientific as well as personal life was affected by the traits deeply bred into his Swabian soul: his casual willingness to question authority, his sassy attitude in the face of regimentation, and his lack of reverence for received wisdom. He tended to address Weber, for example, in a rather informal manner, calling him “Herr Weber” instead of “Herr Professor.”
When his frustration finally overwhelmed his admiration, Professor Weber’s pronouncement on Einstein echoed that of the irritated teacher at the Munich gymnasium a few years earlier. “You’re a very clever boy, Einstein,” Weber told him. “An extremely clever boy. But you have one great fault: you’ll never let yourself be told anything.”
There was some truth to that assessment. But Einstein was to show that, in the jangled world of physics at the turn of the century, this insouciant ability to tune out the conventional wisdom was not the worst fault to have.6
Einstein’s impertinence also got him into trouble with the Polytechnic’s other physics professor, Jean Pernet, who was in charge of experimental and lab exercises. In his course Physical Experiments for Beginners, Pernet gave Einstein a 1, the lowest possible grade, thus earning himself the historic distinction of having flunked Einstein in a physics course. Partly it was because Einstein seldom showed up for the course. At Pernet’s written request, in March 1899 Einstein was given an official “director’s reprimand due to lack of diligence in physics practicum.”7
Why are you specializing in physics, Pernet asked Einstein one day, instead of a field like medicine or even law? “Because,” Einstein replied, “I have even less talent for those subjects. Why shouldn’t I at least try my luck with physics?”8
On those occasions when Einstein did deign to show up in Pernet’s lab, his independent streak sometimes got him in trouble, such as the day he was given an instruction sheet for a particular experiment. “With his usual independence,” his friend and early biographer Carl Seelig reports, “Einstein naturally flung the paper in the waste paper basket.” He proceeded to pursue the experiment in his own way. “What do you make of Einstein?” Pernet asked an assistant. “He always does something different from what I have ordered.”
“He does indeed, Herr Professor,” the assistant replied, “but his solutions are right and the methods he uses are of great interest.”9
Eventually, these methods caught up with him. In July 1899, he caused an explosion in Pernet’s lab that “severely damaged” his right hand and required him to go to the clinic for stitches. The injury made it difficult for him to write for at least two weeks, and it forced him to give up playing the violin for even longer. “My fiddle had to be laid aside,” he wrote to a woman he had performed with in Aarau. “I’m sure it wonders why it is never taken out of the black case. It probably thinks it has gotten a stepfather.”10 He soon resumed playing the violin, but the accident seemed to make him even more wedded to the role of theorist rather than experimentalist.
Despite the fact that he focused more on physics than on math, the professor who would eventually have the most positive impact on him was the math professor Hermann Minkowski, a square-jawed, handsome Russian-born Jew in his early thirties. Einstein appreciated the way Minkowski tied math to physics, but he avoided the more challenging of his courses, which is why Minkowski labeled him a lazy dog: “He never bothered about mathematics at all.”11
Einstein preferred to study, based on his own interests and passions, with one or two friends.12 Even though he was still priding himself on being “a vagabond and a loner,” he began to hang around the coffee-houses and attend musical soirees with a congenial crowd of bohemian soul mates and fellow students. Despite his reputation for detachment, he forged lasting intellectual friendships in Zurich that became important bonds in his life.
Among these was Marcel Grossmann, a middle-class Jewish math wizard whose father owned a factory near Zurich. Grossmann took copious notes that he shared with Einstein, who was less diligent about attending lectures. “His notes could have been printed and published,” Einstein later marveled to Grossmann’s wife. “When it came time to prepare for my exams, he would always lend me those notebooks, and they were my savior. What I would have done without these books I would rather not speculate on.”
Together Einstein and Grossmann smoked pipes and drank iced coffee while discussing philosophy at the Café Metropole on the banks of the Limmat River. “This Einstein will one day be a great man,” Grossmann predicted to his parents. He would later help make that prediction true by getting Einstein his first job, at the Swiss Patent Office, and then aiding him with the math he needed to turn the special theory of relativity into a general theory.13
Because many of the Polytechnic lectures seemed out of date, Einstein and his friends read the most recent theorists on their own. “I played hooky a lot and studied the masters of theoretical physics with a holy zeal at home,” he recalled. Among those were Gustav Kirchhoff on radiation, Hermann von Helmholtz on thermodynamics, Heinrich Hertz on electromagnetism, and Boltzmann on statistical mechanics.
He was also influenced by reading a lesser-known theorist, August Föppl, who in 1894 had written a popular text titled Introduction to Maxwell’s Theory of Electricity. As science historian Gerald Holton has pointed out, Föppl’s book is filled with concepts that would soon echo in Einstein’s work. It has a section on “The Electrodynamics of Moving Conductors” that begins by calling into question the concept of “absolute motion.” The only way to define motion, Föppl notes, is relative to another body. From there he goes on to consider a question concerning the induction of an electric current by a magnetic field: “if it is all the same whether a magnet moves in the vicinity of a resting electric circuit or whether it is the latter that moves while the magnet is at rest.” Einstein would begin his 1905 special relativity paper by raising this same issue.14
Einstein also read, in his spare time, Henri Poincaré, the great French polymath who would come tantalizingly close to discovering the core concepts of special relativity. Near the end of Einstein’s first year at the Polytechnic, in the spring of 1897, there was a mathematics conference in Zurich where the great Poincaré was due to speak. At the last minute he was unable to appear, but a paper of his was read there that contained what would become a famous proclamation. “Absolute space, absolute time, even Euclidean geometry, are not conditions to be imposed on mechanics,” he wrote.15
The Human Side
One evening when Einstein was at home with his landlady, he heard someone playing a Mozart piano sonata. When he asked who it was, his landlady told him that it was an old woman who lived in the attic next door and taught piano. Grabbing his violin, he dashed out without putting on a collar or a tie. “You can’t go like that, Herr Einstein,” the landlady cried. But he ignored her and rushed into the neighboring house. The piano teacher looked up, shocked. “Go on playing,” Einstein pleaded. A few moments later, the air was filled with the sounds of a violin accompanying the Mozart sonata. Later, the teacher asked who the intruding accompanist was. “Merely a harmless student,” her neighbor reassured her.16
Music continued to beguile Einstein. It was not so much an escape as it was a connection: to the harmony underlying the universe, to the creative genius of the great composers, and to other people who felt comfortable bonding with more than just words. He was awed, both in music and in physics, by the beauty of harmonies.
Suzanne Markwalder was a young girl in Zurich whose mother hosted musical evenings featuring mostly Mozart. She played piano, while Einstein played violin. “He was very patient with my shortcomings,” she recalled. “At the worst he used to say, ‘There you are, stuck like the donkey on the mountain,’ and he would point with his bow to the place where I had to come in.”
What Einstein appreciated in Mozart and Bach was the clear architectural structure that made their music seem “deterministic” and, like his own favorite scientific theories, plucked from the universe rather than composed. “Beethoven created his music,” Einstein once said, but “Mozart’s music is so pure it seems to have been ever-present in the universe.” He contrasted Beethoven with Bach: “I feel uncomfortable listening to Beethoven. I think he is too personal, almost naked. Give me Bach, rather, and then more Bach.”
He also admired Schubert for his “superlative ability to express emotion.” But in a questionnaire he once filled out, he was critical about other composers in ways that reflect some of his scientific sentiments: Handel had “a certain shallowness”; Mendelssohn displayed “considerable talent but an indefinable lack of depth that often leads to banality”; Wagner had a “lack of architectural structure I see as decadence”; and Strauss was “gifted but without inner truth.”17
Einstein also took up sailing, a more solitary pursuit, in the glorious Alpine lakes around Zurich. “I still remember how when the breeze dropped and the sails drooped like withered leaves, he would take out his small notebook and he would start scribbling,” recalled Suzanne Markwalder. “But as soon as there was a breath of wind he was immediately ready to start sailing again.”18
The political sentiments he had felt as a boy—a contempt for arbitrary authority, an aversion to militarism and nationalism, a respect for individuality, a disdain for bourgeois consumption or ostentatious wealth, and a desire for social equality—had been encouraged by his landlord and surrogate father in Aarau, Jost Winteler. Now, in Zurich, he met a friend of Winteler’s who became a similar political mentor: Gustav Maier, a Jewish banker who had helped arrange Einstein’s first visit to the Polytechnic. With support from Winteler, Maier founded the Swiss branch of the Society for Ethical Culture, and Einstein was a frequent guest at their informal gatherings in Maier’s home.
Einstein also came to know and like Friedrich Adler, the son of Austria’s Social Democratic leader, who was studying in Zurich. Einstein later called him the “purest and most fervent idealist” he had ever met. Adler tried to get Einstein to join the Social Democrats. But it was not Einstein’s style to spend time at meetings of organized institutions.19
His distracted demeanor, casual grooming, frayed clothing, and forgetfulness, which were later to make him appear to be the iconic absentminded professor, were already evident in his student days. He was known to leave behind clothes, and sometimes even his suitcase, when he traveled, and his inability to remember his keys became a running joke with his landlady. He once visited the home of family friends and, he recalled, “I left forgetting my suitcase. My host said to my parents, ‘That man will never amount to anything because he can’t remember anything.’ ”20
This carefree life as a student was clouded by the continued financial failings of his father, who, against Einstein’s advice, kept trying to set up his own businesses rather than go to work for a salary at a stable company, as Uncle Jakob had finally done. “If I had my way, papa would have looked for salaried employment two years ago,” he wrote his sister during a particularly gloomy moment in 1898 when his father’s business seemed doomed to fail again.
The letter was unusually despairing, probably more than his parents’ financial situation actually warranted:
What depresses me most is the misfortune of my poor parents who have not had a happy moment for so many years. What further hurts me deeply is that as an adult man, I have to look on without being able to do anything. I am nothing but a burden to my family . . . It would be better off if I were not alive at all. Only the thought that I have always done what lay in my modest powers, and that I do not permit myself a single pleasure or distraction save for what my studies offer me, sustains me and sometimes protects me from despair.
Perhaps this was all merely an attack of teenage angst. In any event, his father seemed to get through the crisis with his usual optimism. By the following February, he had won contracts for providing street lights to two small villages near Milan. “I am happy at the thought that the worst worries are over for our parents,” Einstein wrote Maja. “If everyone lived such a way, namely like me, the writing of novels would never have been invented.”22
Einstein’s new bohemian life and old self-absorbed nature made it unlikely that he would continue his relationship with Marie Winteler, the sweet and somewhat flighty daughter of the family he had boarded with in Aarau. At first, he still sent her, via the mail, baskets of his laundry, which she would wash and then return. Sometimes there was not even a note attached, but she would cheerfully try to please him. In one letter she wrote of “crossing the woods in the pouring rain” to the post office to send back his clean clothes. “In vain did I strain my eyes for a little note, but the mere sight of your dear handwriting in the address was enough to make me happy.”
When Einstein sent word that he planned to visit her, Marie was giddy. “I really thank you, Albert, for wanting to come to Aarau, and I don’t have to tell you that I will be counting the minutes until that time,” she wrote.“I could never describe, because there are no words for it, how blissful I feel ever since the dear soul of yours has come to live and weave in my soul. I love you for all eternity, sweetheart.”
But he wanted to break off the relationship. In one of his first letters after arriving at the Zurich Polytechnic, he suggested that they refrain from writing each other. “My love, I do not quite understand a passage in your letter,” she replied. “You write that you do not want to correspond with me any longer, but why not, sweetheart? ... You must be quite annoyed with me if you can write so rudely.” Then she tried to laugh off the problem: “But wait, you’ll get some proper scolding when I get home.”23
Einstein’s next letter was even less friendly, and he complained about a teapot she had given him. “The matter of my sending you the stupid little teapot does not have to please you at all as long as you are going to brew some good tea in it,” she replied. “Stop making that angry face which looked at me from all the sides and corners of the writing paper.” There was a little boy in the school where she taught named Albert, she said, who looked like him. “I love him ever so much,” she said. “Something comes over me when he looks at me and I always believe that you are looking at your little sweetheart.”24
But then the letters from Einstein stopped, despite Marie’s pleas. She even wrote his mother for advice. “The rascal has become frightfully lazy,” Pauline Einstein replied. “I have been waiting in vain for news for these last three days; I will have to give him a thorough talking-to once he’s here.”25
Finally, Einstein declared the relationship over in a letter to Marie’s mother, saying that he would not come to Aarau during his academic break that spring. “It would be more than unworthy of me to buy a few days of bliss at the cost of new pain, of which I have already caused too much to the dear child through my fault,” he wrote.
He went on to give a remarkably introspective—and memorable—assessment of how he had begun to avoid the pain of emotional commitments and the distractions of what he called the “merely personal” by retreating into science:
It fills me with a peculiar kind of satisfaction that now I myself have to taste some of the pain that I brought upon the dear girl through my thoughtlessness and ignorance of her delicate nature. Strenuous intellectual work and looking at God’s nature are the reconciling, fortifying yet relentlessly strict angels that shall lead me through all of life’s troubles. If only I were able to give some of this to the good child. And yet, what a peculiar way this is to weather the storms of life—in many a lucid moment I appear to myself as an ostrich who buries his head in the desert sand so as not to perceive the danger.
Einstein’s coolness toward Marie Winteler can seem, from our vantage, cruel. Yet relationships, especially those of teenagers, are hard to judge from afar. They were very different from each other, particularly intellectually. Marie’s letters, especially when she was feeling insecure, often descended into babble. “I’m writing a lot of rubbish, isn’t that so, and in the end you’ll not even read it to the finish (but I don’t believe that),” she wrote in one. In another, she said, “I do not think about myself, sweetheart, that’s quite true, but the only reason for this is that I do not think at all, except when it comes to some tremendously stupid calculation that requires, for a change, that I know more than my pupils.”27
Whoever was to blame, if either, it was not surprising that they ended up on different paths. After her relationship with Einstein ended, Marie lapsed into a nervous depression, often missing days of teaching, and a few years later married the manager of a watch factory. Einstein, on the other hand, rebounded from the relationship by falling into the arms of someone who was just about as different from Marie as could be imagined.
Mileva Mari was the first and favorite child of an ambitious Serbian peasant who had joined the army, married into modest wealth, and then dedicated himself to making sure that his brilliant daughter was able to prevail in the male world of math and physics. She spent most of her childhood in Novi Sad, a Serbian city then held by Hungary,28 and attended a variety of ever more demanding schools, at each of which she was at the top of her class, culminating when her father convinced the all-male Classical Gymnasium in Zagreb to let her enroll. After graduating there with the top grades in physics and math, she made her way to Zurich, where she became, just before she turned 21, the only woman in Einstein’s section of the Polytechnic.
More than three years older than Einstein, afflicted with a congenital hip dislocation that caused her to limp, and prone to bouts of tuberculosis and despondency, Mileva Mari was known for neither her looks nor her personality. “Very smart and serious, small, delicate, brunette, ugly,” is how one of her female friends in Zurich described her.
But she had qualities that Einstein, at least during his romantic scholar years, found attractive: a passion for math and science, a brooding depth, and a beguiling soul. Her deep-set eyes had a haunting intensity, her face an enticing touch of melancholy.29 She would become, over time, Einstein’s muse, partner, lover, wife, bête noire, and antagonist, and she would create an emotional field more powerful than that of anyone else in his life. It would alternately attract and repulse him with a force so strong that a mere scientist like himself would never be able to fathom it.
They met when they both entered the Polytechnic in October 1896, but their relationship took a while to develop. There is no sign, from their letters or recollections, that they were anything more than classmates that first academic year. They did, however, decide to go hiking together in the summer of 1897. That fall, “frightened by the new feelings she was experiencing” because of Einstein, Mari decided to leave the Polytechnic temporarily and instead audit classes at Heidelberg University.30
Her first surviving letter to Einstein, written a few weeks after she moved to Heidelberg, shows glimmers of a romantic attraction but also highlights her self-confident nonchalance. She addresses Einstein with the formal Sie in German, rather than the more intimate du. Unlike Marie Winteler, she teasingly makes the point that she has not been obsessing about him, even though he had written an unusually long letter to her. “It’s now been quite a while since I received your letter,” she said, “and I would have replied immediately and thanked you for the sacrifice of writing four long pages, would have also told of the joy you provided me through our trip together, but you said I should write to you someday when I happened to be bored. And I am very obedient, and I waited and waited for boredom to set in; but so far my waiting has been in vain.”
Distinguishing Mari even more from Marie Winteler was the intellectual intensity of her letters. In this first one, she enthused over the lectures she had been attending of Philipp Lenard, then an assistant professor at Heidelberg, on kinetic theory, which explains the properties of gases as being due to the actions of millions of individual molecules. “Oh, it was really neat at the lecture of Professor Lenard yesterday,” she wrote. “He is talking now about the kinetic theory of heat and gases. So, it turns out that the molecules of oxygen move with a velocity of over 400 meters per second, then the good professor calculated and calculated . . . and it finally turned out even though molecules do move with this velocity, they travel a distance of only 1/100 of a hairbreadth.”
Kinetic theory had not yet been fully accepted by the scientific establishment (nor, for that matter, had even the existence of atoms and molecules), and Mari’s letter indicated that she did not have a deep understanding of the subject. In addition, there was a sad irony: Lenard would be one of Einstein’s early inspirations but later one of his most hateful anti-Semitic tormentors.
Mari also commented on ideas Einstein had shared in his earlier letter about the difficulty mortals have in comprehending the infinite. “I do not believe that the structure of the human brain is to be blamed for the fact that man cannot grasp infinity,” she wrote. “Man is very capable of imagining infinite happiness, and he should be able to grasp the infinity of space—I think that should be much easier.” There is a slight echo of Einstein’s escape from the “merely personal” into the safety of scientific thinking: finding it easier to imagine infinite space than infinite happiness.
Yet Mari was also, it is clear from her letter, thinking of Einstein in a more personal way. She had even talked to her adoring and protective father about him. “Papa gave me some tobacco to take with me and I was supposed to hand it to you personally,” she said. “He wanted so much to whet your appetite for our little land of outlaws. I told him all about you—you must absolutely come back with me someday. The two of you would really have a lot to talk about!” The tobacco, unlike Marie Winteler’s teapot, was a present Einstein would likely have wanted, but Mari teased that she wasn’t sending it.“You would have to pay duty on it, and then you would curse me.”31
That conflicting admixture of playfulness and seriousness, of insouciance and intensity, of intimacy and detachment—so peculiar yet also so evident in Einstein as well—must have appealed to him. He urged her to return to Zurich. By February 1898, she had made up her mind to do so, and he was thrilled. “I’m sure you won’t regret your decision,” he wrote. “You should come back as soon as possible.”
He gave her a thumbnail of how each of the professors was performing (admitting that he found the one teaching geometry to be “a little impenetrable”), and he promised to help her catch up with the aid of the lecture notes he and Marcel Grossmann had kept. The one problem was that she would probably not be able to get her “old pleasant room” at the nearby pension back. “Serves you right, you little runaway!”32
By April she was back, in a boarding house a few blocks from his, and now they were a couple. They shared books, intellectual enthusiasms, intimacies, and access to each other’s apartments. One day, when he again forgot his key and found himself locked out of his own place, he went to hers and borrowed her copy of a physics text. “Don’t be angry with me,” he said in the little note he left her. Later that year, a similar note left for her added, “If you don’t mind, I’d like to come over this evening to read with you.”33
Friends were surprised that a sensuous and handsome man such as Einstein, who could have almost any woman fall for him, would find himself with a short and plain Serbian who had a limp and exuded an air of melancholy. “I would never be brave enough to marry a woman unless she were absolutely healthy,” a fellow student said to him. Einstein replied, “But she has such a lovely voice.”34
Einstein’s mother, who had adored Marie Winteler, was similarly dubious about the dark intellectual who had replaced her. “Your photograph had quite an effect on my old lady,” Einstein wrote from Milan, where he was visiting his parents during spring break of 1899. “While she studied it carefully, I said with the deepest sympathy: ‘Yes, yes, she certainly is a clever one.’ I’ve already had to endure much teasing about this.”35
It is easy to see why Einstein felt such an affinity for Mari. They were kindred spirits who perceived themselves as aloof scholars and outsiders. Slightly rebellious toward bourgeois expectations, they were both intellectuals who sought as a lover someone who would also be a partner, colleague, and collaborator. “We understand each other’s dark souls so well, and also drinking coffee and eating sausages, etcetera,” Einstein wrote her.
He had a way of making the etcetera sound roguish. He closed another letter: “Best wishes etc., especially the latter.” After being apart for a few weeks, he listed the things he liked to do with her: “Soon I’ll be with my sweetheart again and can kiss her, hug her, make coffee with her, scold her, study with her, laugh with her, walk with her, chat with her, and ad infinitum!” They took pride in sharing a quirkiness. “I’m the same old rogue as I’ve always been,” he wrote, “full of whims and mischief, and as moody as ever!”36
Above all, Einstein loved Mari for her mind. “How proud I will be to have a little Ph.D. for a sweetheart,” he wrote to her at one point. Science and romance seemed to be interwoven. While on vacation with his family in 1899, Einstein lamented in a letter to Mari, “When I read Helmholtz for the first time I could not—and still cannot—believe that I was doing so without you sitting next to me. I enjoy working together and I find it soothing and also less boring.”
Indeed, most of their letters mixed romantic effusions with scientific enthusiasms, often with an emphasis on the latter. In one letter, for example, he foreshadowed not only the title but also some of the concepts of his great paper on special relativity. “I am more and more convinced that the electrodynamics of moving bodies as it is presented today does not correspond to reality and that it will be possible to present it in a simpler way,” he wrote. “The introduction of the term ‘ether’ into theories of electricity has led to the conception of a medium whose motion can be described without, I believe, being able to ascribe physical meaning to it.”37
Even though this mix of intellectual and emotional companionship appealed to him, every now and then he recalled the enticement of the simpler desire represented by Marie Winteler. And with the tactlessness that masqueraded for him as honesty (or perhaps because of his puckish desire to torment), he let Mari know it. After his 1899 summer vacation, he decided to take his sister to enroll in school in Aarau, where Marie lived. He wrote Mari to assure her that he would not spend much time with his former girlfriend, but the pledge was written in a way that was, perhaps intentionally, more unsettling than reassuring. “I won’t be going to Aarau as often now that the daughter I was so madly in love with four years ago is coming back home,” he said. “For the most part I feel quite secure in my high fortress of calm. But I know that if I saw her a few more times, I would certainly go mad. Of that I am certain, and I fear it like fire.”
But the letter goes on, happily for Mari, with a description of what they would do when they met back in Zurich, a passage in which Einstein showed once again why their relationship was so special. “The first thing we’ll do is climb the Ütliberg,” he said, referring to a high point just out of town. There they would be able to “take pleasure in unpacking our memories” of the things they had done together on other hiking trips. “I can already imagine the fun we will have,” he wrote. Finally, with a flourish only they could have fully appreciated, he concluded, “And then we’ll start in on Helmholtz’s electromagnetic theory of light.”38
In the ensuing months, their letters became even more intimate and passionate. He began calling her Doxerl (Dollie), as well as “my wild little rascal” and “my street urchin”; she called him Johannzel (Johnnie) and “my wicked little sweetheart.” By the start of 1900, they were using the familiar du with one another, a process that began with a little note from her that reads, in full:
My little Johnnie,
Because I like you so much, and because you’re so far away that I can’t give you a little kiss, I’m writing this letter to ask if you like me as much as I do you? Answer me immediately.
A thousand kisses from your Dollie39
Graduation, August 1900
Academically, things were also going well for Einstein. In his intermediate exams in October 1898, he had finished first in his class, with an average of 5.7 out of a possible 6. Finishing second, with a 5.6, was his friend and math note-taker Marcel Grossmann.40
To graduate, Einstein had to do a research thesis. He initially proposed to Professor Weber that he do an experiment to measure how fast the earth was moving through the ether, the supposed substance that allowed light waves to propagate through space. The accepted wisdom, which he would famously destroy with his special theory of relativity, was that if the earth were moving through this ether toward or away from the source of a light beam, we’d be able to detect a difference in the observed speed of the light.
During his visit to Aarau at the end of his summer vacation of 1899, he worked on this issue with the rector of his old school there. “I had a good idea for investigating the way in which a body’s relative motion with respect to the ether affects the velocity of the propagation of light,” he wrote Mari. His idea involved building an apparatus that would use angled mirrors “so that light from a single source would be reflected in two different directions,” sending one part of the beam in the direction of the earth’s movement and the other part of the beam perpendicular to it. In a lecture on how he discovered relativity, Einstein recalled that his idea was to split a light beam, reflect it in different directions, and see if there was “a difference in energy depending on whether or not the direction was along the earth’s motion through the ether.” This could be done, he posited, by “using two thermoelectric piles to examine the difference of the heat generated in them.”41
Weber rejected the proposal. What Einstein did not fully realize was that similar experiments had already been done by many others, including the Americans Albert Michelson and Edward Morley, and none had been able to detect any evidence of the perplexing ether—or that the speed of light varied depending on the motion of the observer or the light source. After discussing the topic with Weber, Einstein read a paper delivered the previous year by Wilhelm Wien, which briefly described thirteen experiments that had been conducted to detect the ether, including the Michelson-Morley one.
Einstein sent Professor Wien his own speculative paper on that topic and asked him to write him back. “He’ll write me via the Polytechnic,” Einstein predicted to Mari. “If you see a letter there for me, you may go ahead and open it.” There is no evidence that Wien ever wrote back.42
Einstein’s next research proposal involved exploring the link between the ability of different materials to conduct heat and to conduct electricity, something that was suggested by the electron theory. Weber apparently did not like that idea either, so Einstein was reduced, along with Mari, to doing a study purely on heat conduction, which was one of Weber’s specialties.
Einstein later dismissed their graduation research papers as being of “no interest to me.” Weber gave Einstein and Mari the two lowest essay grades in the class, a 4.5 and a 4.0, respectively; Grossmann, by comparison, got a 5.5. Adding annoyance to that injury, Weber said that Einstein had not written his on the proper regulation paper, and he forced him to copy the entire essay over again.43
Despite the low mark on his essay, Einstein was able to eke by with a 4.9 average in his final set of grades, placing him fourth in his class of five. Although history refutes the delicious myth that he flunked math in high school, at least it does offer as a consolation the amusement that he graduated college near the bottom of his class.
At least he graduated. His 4.9 average was just enough to let him get his diploma, which he did officially in July 1900. Mileva Mari, however, managed only a 4.0, by far the lowest in the class, and was not allowed to graduate. She determined that she would try again the following year.44
Not surprisingly, Einstein’s years at the Polytechnic were marked by his pride at casting himself as a nonconformist. “His spirit of independence asserted itself one day in class when the professor mentioned a mild disciplinary measure just taken by the school’s authorities,” a classmate recalled. Einstein protested. The fundamental requirement of education, he felt, was the “need for intellectual freedom.”45
Throughout his life, Einstein would speak lovingly of the Zurich Polytechnic, but he also would note that he did not like the discipline that was inherent in the system of examinations. “The hitch in this was, of course, that one had to cram all this stuff into one’s mind for the examinations, whether one liked it or not,” he said. “This coercion had such a deterring effect that, after I had passed the final examination, I found the consideration of any scientific problems distasteful to me for an entire year.”46
In reality, that was neither possible nor true. He was cured within weeks, and he ended up taking with him some science books, including texts by Gustav Kirchhoff and Ludwig Boltzmann, when he joined his mother and sister later that July for their summer holiday in the Swiss Alps. “I’ve been studying a great deal,” he wrote Mari, “mainly Kirch-hoff ’s notorious investigations of the motion of the rigid body.” He admitted that his resentment over the exams had already worn off. “My nerves have calmed down enough so that I’m able to work happily again,” he said. “How are yours?”47
With Mileva and Hans Albert Einstein, 1904
Summer Vacation, 1900
Newly graduated, carrying his Kirchhoff and other physics books, Einstein arrived at the end of July 1900 for his family’s summer vacation in Melchtal, a village nestled in the Swiss Alps between Lake Lucerne and the border with northern Italy. In tow was his “dreadful aunt,” Julia Koch. They were met at the train station by his mother and sister, who smothered him with kisses, and then all piled into a carriage for the ride up the mountain.
As they neared the hotel, Einstein and his sister got off to walk. Maja confided that she had not dared to discuss with their mother his relationship with Mileva Mari, known in the family as “the Dollie affair” after his nickname for her, and she asked him to “go easy on Mama.” It was not in Einstein’s nature, however, “to keep my big mouth shut,” as he later put it in his letter to Mari about the scene, nor was it in his nature to protect Mari’s feelings by sparing her all the dramatic details about what ensued.1
He went to his mother’s room and, after hearing about his exams, she asked him, “So, what will become of your Dollie now?”
“My wife,” Einstein answered, trying to affect the same nonchalance that his mother had used in her question.
His mother, Einstein recalled, “threw herself on the bed, buried her head in the pillow, and wept like a child.” She was finally able to regain her composure and proceeded to go on the attack. “You are ruining your future and destroying your opportunities,” she said. “No decent family will have her. If she gets pregnant you’ll really be in a mess.”
At that point, it was Einstein’s turn to lose his composure. “I vehemently denied we had been living in sin,” he reported to Mari, “and scolded her roundly.”
Just as he was about to storm out, a friend of his mother’s came in, “a small, vivacious lady, an old hen of the most pleasant variety.” They promptly segued into the requisite small talk: about the weather, the new guests at the spa, the ill-mannered children. Then they went off to eat and play music.
Such periods of storm and calm alternated throughout the vacation. Every now and then, just when Einstein thought that the crisis had receded, his mother would revisit the topic.“Like you, she’s a book, but you ought to have a wife,” she scolded at one point. Another time she brought up the fact that Mari was 24 and he was then only 21. “By the time you’re 30, she’ll be an old witch.”
Einstein’s father, still working back in Milan, weighed in with “a moralistic letter.” The thrust of his parents’ views—at least when applied to the situation of Mileva Mari rather than Marie Winteler—was that a wife was “a luxury” affordable only when a man was making a comfortable living. “I have a low opinion of that view of a relationship between a man and wife,” he told Mari,“because it makes the wife and the prostitute distinguishable only insofar as the former is able to secure a lifelong contract.”2
Over the ensuing months, there would be times when it seemed as if his parents had decided to accept their relationship. “Mama is slowly resigning herself,” Einstein wrote Mari in August. Likewise in September: “They seem to have reconciled themselves to the inevitable. I think they will both come to like you very much once they get to know you.” And once again in October: “My parents have retreated, grudgingly and with hesitation, from the battle of Dollie—now that they have seen that they’ll lose it.”3
But repeatedly, after each period of acceptance, their resistance would flare up anew, randomly leaping into a higher state of frenzy. “Mama often cries bitterly and I don’t have a single moment of peace,” he wrote at the end of August. “My parents weep for me almost as if I had died. Again and again they complain that I have brought misfortune upon myself by my devotion to you. They think you are not healthy.”4
His parents’ dismay had little to do with the fact that Mari was not Jewish, for neither was Marie Winteler, nor that she was Serbian, although that certainly didn’t help her cause. Primarily, it seems, they considered her an unsuitable wife for many of the reasons that some of Einstein’s friends did: she was older, somewhat sickly, had a limp, was plain looking, and was an intense but not a star intellectual.
All of this emotional pressure stoked Einstein’s rebellious instincts and his passion for his “wild street urchin,” as he called her. “Only now do I see how madly in love with you I am!”The relationship, as expressed in their letters, remained equal parts intellectual and emotional, but the emotional part was now filled with a fire unexpected from a self-proclaimed loner. “I just realized that I haven’t been able to kiss you for an entire month, and I long for you so terribly much,” he wrote at one point.
During a quick trip to Zurich in August to check on his job prospects, he found himself walking around in a daze. “Without you, I lack self-confidence, pleasure in my work, pleasure in life—in short, without you my life is not life.” He even tried his hand at a poem for her, which began: “Oh my! That Johnnie boy! / So crazy with desire / While thinking of his Dollie / His pillow catches fire.”5
Their passion, however, was an elevated one, at least in their minds. With the lonely elitism of young German coffeehouse denizens who have read the philosophy of Schopenhauer once too often, they un-abashedly articulated the mystical distinction between their own rarefied spirits and the baser instincts and urges of the masses. “In the case of my parents, as with most people, the senses exercise a direct control over the emotions,” he wrote her amid the family wars of August. “With us, thanks to the fortunate circumstances in which we live, the enjoyment of life is vastly broadened.”
To his credit, Einstein reminded Mari (and himself) that “we mustn’t forget that many existences like my parents’ make our existence possible.” The simple and honest instincts of people like his parents had ensured the progress of civilization. “Thus I am trying to protect my parents without compromising anything that is important to me—and that means you, sweetheart!”
In his attempt to please his mother, Einstein became a charming son at their grand hotel in Melchtal. He found the endless meals excessive and the “overdressed” patrons to be “indolent and pampered,” but he dutifully played his violin for his mother’s friends, made polite conversation, and feigned a cheerful mood. It worked. “My popularity among the guests here and my music successes act as a balm on my mother’s heart.”6
As for his father, Einstein decided that the best way to assuage him, as well as to draw off some of the emotional charge generated by his relationship with Mari, was to visit him back in Milan, tour some of his new power plants, and learn about the family firm “so I can take Papa’s place in an emergency.” Hermann Einstein seemed so pleased that he promised to take his son to Venice after the inspection tour. “I’m leaving for Italy on Saturday to partake of the ‘holy sacraments’ administered by my father, but the valiant Swabian* is not afraid.”
Einstein’s visit with his father went well, for the most part. A distant yet dutiful son, he had fretted mightily about each family financial crisis, perhaps even more than his father did. But business was good for the moment, and that lifted Hermann Einstein’s spirits. “My father is a completely different man now that he has no more financial worries,” Einstein wrote Mari. Only once did the “Dollie affair” intrude enough to make him consider cutting short his visit, but this threat so alarmed his father that Einstein stuck to the original plans. He seemed flattered that his father appreciated both his company and his willingness to pay attention to the family business.7
Even though Einstein occasionally denigrated the idea of being an engineer, it was possible that he could have followed that course at the end of the summer of 1900—especially if, on their trip to Venice, his father had asked him to, or if fate intervened so that he was needed to take his father’s place. He was, after all, a low-ranked graduate of a teaching college without a teaching job, without any research accomplishments, and certainly without academic patrons.
Had he made such a choice in 1900, Einstein would have likely become a good enough engineer, but probably not a great one. Over the ensuing years he would dabble with inventions as a hobby and come up with some good concepts for devices ranging from noiseless refrigerators to a machine that measured very low voltage electricity. But none resulted in a significant engineering breakthrough or marketplace success. Though he would have been a more brilliant engineer than his father or uncle, it is not clear that he would have been any more financially successful.
Among the many surprising things about the life of Albert Einstein was the trouble he had getting an academic job. Indeed, it would be an astonishing nine years after his graduation from the Zurich Polytechnic in 1900—and four years after the miracle year in which he not only upended physics but also finally got a doctoral dissertation accepted—before he would be offered a job as a junior professor.
The delay was not due to a lack of desire on his part. In the middle of August 1900, between his family vacation in Melchtal and his visit to his father in Milan, Einstein stopped back in Zurich to see about getting a post as an assistant to a professor at the Polytechnic. It was typical that each graduate would find, if he wanted, some such role, and Einstein was confident it would happen. In the meantime, he rejected a friend’s offer to help him get a job at an insurance company, dismissing it as “an eight hour day of mindless drudgery.” As he told Mari, “One must avoid stultifying affairs.”8
The problem was that the two physics professors at the Polytechnic were acutely aware of his impudence but not of his genius. Getting a job with Professor Pernet, who had reprimanded him, was not even a consideration. As for Professor Weber, he had developed such an allergy to Einstein that, when no other graduates of the physics and math department were available to become his assistant, he instead hired two students from the engineering division.
That left math professor Adolf Hurwitz. When one of Hurwitz’s assistants got a job teaching at a high school, Einstein exulted to Mari: “This means I will become Hurwitz’s servant, God willing.” Unfortunately, he had skipped most of Hurwitz’s classes, a slight that apparently had not been forgotten.9
By late September, Einstein was still staying with his parents in Milan and had not received an offer. “I plan on going to Zurich on October 1 to talk with Hurwitz personally about the position,” he said. “It’s certainly better than writing.”
While there, he also planned to look for possible tutoring jobs that could tide them over while Mari prepared to retake her final exams. “No matter what happens, we’ll have the most wonderful life in the world. Pleasant work and being together—and what’s more, we now answer to no one, can stand on our own two feet, and enjoy our youth to the utmost. Who could have it any better? When we have scraped together enough money, we can buy bicycles and take a bike tour every couple of weeks.”10
Einstein ended up deciding to write Hurwitz instead of visiting him, which was probably a mistake. His two letters do not stand as models for future generations seeking to learn how to write a job application. He readily conceded that he did not show up at Hurwitz’s calculus classes and was more interested in physics than math. “Since lack of time prevented me from taking part in the mathematics seminar,” he rather lamely said, “there is nothing in my favor except the fact that I attended most of the lectures offered.” Rather presumptuously, he said he was eager for an answer because “the granting of citizenship in Zurich, for which I have applied, has been made conditional upon my proving that I have a permanent job.”11
Einstein’s impatience was matched by his confidence. “Hurwitz still hasn’t written me more,” he said only three days after sending his letter, “but I have hardly any doubt that I will get the position.” He did not. Indeed, he managed to become the only person graduating in his section of the Polytechnic who was not offered a job. “I was suddenly abandoned by everyone,” he later recalled.12
By the end of October 1900 he and Mari were both back in Zurich, where he spent most of his days hanging out at her apartment, reading and writing. On his citizenship application that month, he wrote “none” on the question asking his religion, and for his occupation he wrote, “I am giving private lessons in mathematics until I get a permanent position.”
Throughout that fall, he was able to find only eight sporadic tutoring jobs, and his relatives had ended their financial support. But Einstein put up an optimistic front. “We support ourselves by private lessons, if we can ever pick up some, which is still very doubtful,” he wrote a friend of Mari’s. “Isn’t this a journeyman’s or even a gypsy’s life? But I believe that we will remain cheerful in it as ever.”13 What kept him happy, in addition to Mari’s presence, were the theoretical papers he was writing on his own.
Einstein’s First Published Paper
The first of these papers was on a topic familiar to most school kids: the capillary effect that, among other things, causes water to cling to the side of a straw and curve upward. Although he later called this essay “worthless,” it is interesting from a biographical perspective. Not only is it Einstein’s first published paper, but it shows him heartily embracing an important premise—one not yet fully accepted—that would be at the core of much of his work over the next five years: that molecules (and their constituent atoms) actually exist, and that many natural phenomena can be explained by analyzing how these particles interact with one another.
During his vacation in the summer of 1900, Einstein had been reading the work of Ludwig Boltzmann, who had developed a theory of gases based on the behavior of countless molecules bouncing around. “The Boltzmann is absolutely magnificent,” he enthused to Mari in September. “I am firmly convinced of the correctness of the principles of his theory, i.e., I am convinced that in the case of gases we are really dealing with discrete particles of definite finite size which move according to certain conditions.”14
To understand capillarity, however, required looking at the forces acting between molecules in a liquid, not a gas. Such molecules attract one another, which accounts for the surface tension of a liquid, or the fact that drops hold together, as well as for the capillary effect. Einstein’s idea was that these forces might be analogous to Newton’s gravitational forces, in which two objects are attracted to each other in proportion to their mass and in inverse proportion to their distance from one another.
Einstein looked at whether the capillary effect showed such a relationship to the atomic weight of various liquid substances. He was encouraged, so he decided to see if he could find some experimental data to test the theory further. “The results on capillarity I recently obtained in Zurich seem to be entirely new despite their simplicity,” he wrote Mari. “When we’re back in Zurich we’ll try to get some empirical data on this subject . . . If this yields a law of nature, we’ll send the results to the Annalen.”15
He did end up sending the paper in December 1900 to the Annalen der Physik, Europe’s leading physics journal, which published it the following March. Written without the elegance or verve of his later papers, it conveyed what is at best a tenuous conclusion. “I started from the simple idea of attractive forces among the molecules, and I tested the consequences experimentally,” he wrote. “I took gravitational forces as an analogy.” At the end of the paper, he declares limply, “The question of whether and how our forces are related to gravitational forces must therefore be left completely open for the time being.”16
The paper elicited no comments and contributed nothing to the history of physics. Its basic conjecture was wrong, as the distance dependence is not the same for differing pairs of molecules.17 But it did get him published for the first time. That meant that he now had a printed article to attach to the job-seeking letters with which he was beginning to spam professors all over Europe.
In his letter to Mari, Einstein had used the term “we” when discussing plans to publish the paper. In two letters written the month after it appeared, Einstein referred to “our theory of molecular forces” and “our investigation.”Thus was launched a historical debate over how much credit Mari deserves for helping Einstein devise his theories.
In this case, she mainly seemed to be involved in looking up some data for him to use. His letters conveyed his latest thoughts on molecular forces, but hers contained no substantive science. And in a letter to her best friend, Mari sounded as if she had settled into the role of supportive lover rather than scientific partner. “Albert has written a paper in physics that will probably be published very soon in the Annalen der Physik,” she wrote. “You can imagine how very proud I am of my darling. This is not just an everyday paper, but a very significant one. It deals with the theory of liquids.”18
It had been almost four years since Einstein had renounced his German citizenship, and ever since then he had been stateless. Each month, he put aside some money toward the fee he would need to pay to become a Swiss citizen, a status he deeply desired. One reason was that he admired the Swiss system, its democracy, and its gentle respect for individuals and their privacy. “I like the Swiss because, by and large, they are more humane than the other people among whom I have lived,” he later said.19 There were also practical reasons; in order to work as a civil servant or a teacher in a state school, he would have to be a Swiss citizen.
The Zurich authorities examined him rather thoroughly, and they even sent to Milan for a report on his parents. By February 1901, they were satisfied, and he was made a citizen. He would retain that designation his entire life, even as he accepted citizenships in Germany (again), Austria, and the United States. Indeed, he was so eager to be a Swiss citizen that he put aside his antimilitary sentiments and presented himself, as required, for military service. He was rejected for having sweaty feet (“hyperidrosis ped”), flat feet (“pes planus”), and varicose veins (“varicosis”). The Swiss Army was, apparently, quite discriminating, and so his military service book was stamped “unfit.”20
A few weeks after he got his citizenship, however, his parents insisted that he come back to Milan and live with them. They had decreed, at the end of 1900, that he could not stay in Zurich past Easter unless he got a job there. When Easter came, he was still unemployed.
Mari, not unreasonably, assumed that his summons to Milan was due to his parents’ antipathy toward her. “What utterly depressed me was the fact that our separation had to come about in such an unnatural way, on account of slanders and intrigues,” she wrote her friend. With an absentmindedness he was later to make iconic, Einstein left behind in Zurich his nightshirt, toothbrush, comb, hairbrush (back then he used one), and other toiletries. “Send everything along to my sister,” he instructed Mari, “so she can bring them home with her.” Four days later, he added, “Hold on to my umbrella for the time being. We’ll figure out something to do with it later.”21
Both in Zurich and then in Milan, Einstein churned out job-seeking letters, ever more pleading, to professors around Europe. They were accompanied by his paper on the capillary effect, which proved not particularly impressive; he rarely even received the courtesy of a response. “I will soon have graced every physicist from the North Sea to the southern tip of Italy with my offer,” he wrote Mari.22
By April 1901, Einstein was reduced to buying a pile of postcards with postage-paid reply attachments in the forlorn hope that he would, at least, get an answer. In the two cases where these postcard pleas have survived, they have become, rather amusingly, prized collectors’ items. One of them, to a Dutch professor, is now on display in the Leiden Museum for the History of Science. In both cases, the return-reply attachment was not used; Einstein did not even get the courtesy of a rejection. “I leave no stone unturned and do not give up my sense of humor,” he wrote his friend Marcel Grossmann. “God created the donkey and gave him a thick skin.”23
Among the great scientists Einstein wrote was Wilhelm Ostwald, professor of chemistry in Leipzig, whose contributions to the theory of dilution were to earn him a Nobel Prize. “Your work on general chemistry inspired me to write the enclosed article,” Einstein said. Then flattery turned to plaintiveness as he asked “whether you might have use for a mathematical physicist.” Einstein concluded by pleading: “I am without money, and only a position of this kind would enable me to continue my studies.” He got no answer. Einstein wrote again two weeks later using the pretext “I am not sure whether I included my address” in the earlier letter. “Your judgment of my paper matters very much to me.” There was still no answer.24
Einstein’s father, with whom he was living in Milan, quietly shared his son’s anguish and tried, in a painfully sweet manner, to help. When no answer came after the second letter to Ostwald, Hermann Einstein took it upon himself, without his son’s knowledge, to make an unusual and awkward effort, suffused with heart-wrenching emotion, to prevail upon Ostwald himself:
Please forgive a father who is so bold as to turn to you, esteemed Herr Professor, in the interest of his son. Albert is 22 years old, he studied at the Zurich Polytechnic for four years, and he passed his exam with flying colors last summer. Since then he has been trying unsuccessfully to get a position as a teaching assistant, which would enable him to continue his education in physics. All those in a position to judge praise his talents; I can assure you that he is extraordinarily studious and diligent and clings with great love to his science. He therefore feels profoundly unhappy about his current lack of a job, and he becomes more and more convinced that he has gone off the tracks with his career. In addition, he is oppressed by the thought that he is a burden on us, people of modest means. Since it is you whom my son seems to admire and esteem more than any other scholar in physics, it is you to whom I have taken the liberty of turning with the humble request to read his paper and to write to him, if possible, a few words of encouragement, so that he might recover his joy in living and working. If, in addition, you could secure him an assistant’s position, my gratitude would know no bounds. I beg you to forgive me for my impudence in writing you, and my son does not know anything about my unusual step.
Ostwald still did not answer. However, in one of history’s nice ironies, he would become, nine years later, the first person to nominate Einstein for the Nobel Prize.
Einstein was convinced that his nemesis at the Zurich Polytechnic, physics professor Heinrich Weber, was behind the difficulties. Having hired two engineers rather than Einstein as his own assistant, he was apparently now giving him unfavorable references. After applying for a job with Göttingen professor Eduard Riecke, Einstein despaired to Mari: “I have more or less given up the position as lost. I cannot believe that Weber would let such a good opportunity pass without doing some mischief.” Mari advised him to write Weber, confronting him directly, and Einstein reported back that he had. “He should at least know that he cannot do these things behind my back. I wrote to him that I know that my appointment now depends on his report alone.”
It didn’t work. Einstein again got turned down. “Riecke’s rejection hasn’t surprised me,” he wrote Mari. “I’m completely convinced that Weber is to blame.” He became so discouraged that, at least for the moment, he felt it futile to continue his search. “Under these circumstances it no longer makes sense to write further to professors, since, should things get far enough along, it is certain they would all enquire with Weber, and he would again give a poor reference.” To Grossmann he lamented, “I could have found a job long ago had it not been for Weber’s underhandedness.”26
To what extent did anti-Semitism play a role? Einstein came to believe that it was a factor, which led him to seek work in Italy, where he felt it was not so pronounced. “One of the main obstacles in getting a position is absent here, namely anti-Semitism, which in German-speaking countries is as unpleasant as it is a hindrance,” he wrote Mari. She, in turn, lamented to her friend about her lover’s difficulties. “You know my sweetheart has a sharp tongue and moreover he is a Jew.”27
In his effort to find work in Italy, Einstein enlisted one of the friends he had made while studying in Zurich, an engineer named Michele Angelo Besso. Like Einstein, Besso was from a middle-class Jewish family that had wandered around Europe and eventually settled in Italy. He was six years older than Einstein, and by the time they met he had already graduated from the Polytechnic and was working for an engineering firm. He and Einstein forged a close friendship that would last for the rest of their lives (they died within weeks of each other in 1955).
Over the years, Besso and Einstein would share both the most intimate personal confidences and the loftiest scientific notions. As Einstein wrote in one of the 229 extant letters they exchanged, “Nobody else is so close to me, nobody knows me so well, nobody is so kindly disposed to me as you are.”28
Besso had a delightful intellect, but he lacked focus, drive, and diligence. Like Einstein, he had once been asked to leave high school because of his insubordinate attitude (he sent a petition complaining about a math teacher). Einstein called Besso “an awful weakling . . . who cannot rouse himself to any action in life or scientific creation, but who has an extraordinarily fine mind whose working, though disorderly, I watch with great delight.”
Einstein had introduced Besso to Anna Winteler of Aarau, Marie’s sister, whom he ended up marrying. By 1901 he had moved to Trieste with her. When Einstein caught up with him, he found Besso as smart, as funny, and as maddeningly unfocused as ever. He had recently been asked by his boss to inspect a power station, and he decided to leave the night before to make sure that he arrived on time. But he missed his train, then failed to get there the next day, and finally arrived on the third day—“but to his horror realizes that he has forgotten what he’s supposed to do.” So he sent a postcard back to the office asking them to resend his instructions. It was the boss’s assessment that Besso was “completely useless and almost unbalanced.”
Einstein’s assessment of Besso was more loving. “Michele is an awful schlemiel,” he reported to Mari, using the Yiddish word for a hapless bumbler. One evening, Besso and Einstein spent almost four hours talking about science, including the properties of the mysterious ether and “the definition of absolute rest.”These ideas would burst into bloom four years later, in the relativity theory that he would devise with Besso as his sounding board. “He’s interested in our research,” Einstein wrote Mari, “though he often misses the big picture by worrying about petty considerations.”
Besso had some connections that could, Einstein hoped, be useful. His uncle was a mathematics professor at the polytechnic in Milan, and Einstein’s plan was to have Besso provide an introduction: “I’ll grab him by the collar and drag him to his uncle, where I’ll do the talking myself.” Besso was able to persuade his uncle to write letters on Einstein’s behalf, but nothing came of the effort. Instead, Einstein spent most of 1901 juggling temporary teaching assignments and some tutoring.29
It was Einstein’s other close friend from Zurich, his classmate and math note-taker Marcel Grossmann, who ended up finally getting Einstein a job, though not one that would have been expected. Just when Einstein was beginning to despair, Grossmann wrote that there was likely to be an opening for an examiner at the Swiss Patent Office, located in Bern. Grossmann’s father knew the director and was willing to recommend Einstein.
“I was deeply moved by your devotion and compassion, which did not let you forget your luckless friend,” Einstein replied. “I would be delighted to get such a nice job and that I would spare no effort to live up to your recommendation.” To Mari he exulted: “Just think what a wonderful job this would be for me! I’ll be mad with joy if something should come of that.”
It would take months, he knew, before the patent-office job would materialize, assuming that it ever did. So he accepted a temporary post at a technical school in Winterthur for two months, filling in for a teacher on military leave. The hours would be long and, worse yet, he would have to teach descriptive geometry, neither then nor later his strongest field. “But the valiant Swabian is not afraid,” he proclaimed, repeating one of his favorite poetic phrases.30
In the meantime, he and Mari would have the chance to take a romantic vacation together, one that would have fateful consequences.
Lake Como, May 1901
“You absolutely must come see me in Como, you little witch,” Einstein wrote Mari at the end of April 1901. “You’ll see for yourself how bright and cheerful I’ve become and how all my brow-knitting is gone.”
The family disputes and frustrating job search had caused him to be snappish, but he promised that was now over. “It was only out of nervousness that I was mean to you,” he apologized. To make it up to her, he proposed that they should have a romantic and sensuous tryst in one of the world’s most romantic and sensuous places: Lake Como, the grandest of the jewel-like Alpine finger lakes high on the border of Italy and Switzerland, where in early May the lush foliage bursts forth under majestic snow-capped peaks.
“Bring my blue dressing-gown so we can wrap ourselves up in it,” he said. “I promise you an outing the likes of which you’ve never seen.”31
Mari quickly accepted, but then changed her mind; she had received a letter from her family in Novi Sad “that robs me of all desire, not only for having fun, but for life itself.” He should make the trip on his own, she sulked.“It seems I can have nothing without being punished.” But the next day she changed her mind again. “I wrote you a little card yesterday while in the worst of moods because of a letter I received. But when I read your letter today I became a bit more cheerful, since I see how much you love me, so I think we’ll take that trip after all.”32
And thus it was that early on the morning of Sunday, May 5, 1901, Albert Einstein was waiting for Mileva Mari at the train station in the village of Como, Italy, “with open arms and a pounding heart.” They spent the day there, admiring its gothic cathedral and walled old town, then took one of the stately white steamers that hop from village to village along the banks of the lake.
They stopped to visit Villa Carlotta, the most luscious of all the famous mansions that dot the shore, with its frescoed ceilings, a version of Antonio Canova’s erotic sculpture Cupid and Psyche, and five hundred species of plants. Mari later wrote a friend how much she admired “the splendid garden, which I preserved in my heart, the more so because we were not allowed to swipe a single flower.”
After spending the night in an inn, they decided to hike through the mountain pass to Switzerland, but found it still covered with up to twenty feet of snow. So they hired a small sleigh,“the kind they use that has just enough room for two people in love with each other, and a coachman stands on a little plank in the rear and prattles all the time and calls you ‘signora,’ ” Mari wrote. “Could you think of anything more beautiful?”
The snow was falling merrily, as far as the eye could see, “so that this cold, white infinity gave me the shivers and I held my sweetheart firmly in my arms under the coats and shawls covering us.” On the way down, they stomped and kicked at the snow to produce little avalanches, “so as to properly scare the world below.”33
A few days later, Einstein recalled “how beautiful it was the last time you let me press your dear little person against me in that most natural way.”34 And in that most natural way, Mileva Mari became pregnant with Albert Einstein’s child.
After returning to Winterthur, where he was a substitute teacher, Einstein wrote Mari a letter that made reference to her pregnancy. Oddly—or perhaps not oddly at all—he began by delving into matters scientific rather than personal.“I just read a wonderful paper by Lenard on the generation of cathode rays by ultraviolet light,” he started. “Under the influence of this beautiful piece I am filled with such happiness and joy that I must share some of it with you.” Einstein would soon revolutionize science by building on Lenard’s paper to produce a theory of light quanta that explained this photoelectric effect. Even so, it is rather surprising, or at least amusing, that when he rhapsodized about sharing “happiness and joy” with his newly pregnant lover, he was referring to a paper on beams of electrons.
Only after this scientific exultation came a brief reference to their expected child, whom Einstein referred to as a boy: “How are you darling? How’s the boy?” He went on to display an odd notion of what parenting would be like: “Can you imagine how pleasant it will be when we’re able to work again, completely undisturbed, and with no one around to tell us what to do!”
Most of all, he tried to be reassuring. He would find a job, he pledged, even if it meant going into the insurance business. They would create a comfortable home together. “Be happy and don’t fret, darling. I won’t leave you and will bring everything to a happy conclusion. You just have to be patient! You will see that my arms are not so bad to rest in, even if things are beginning a little awkwardly.”35
Mari was preparing to retake her graduation exams, and she was hoping to go on to get a doctorate and become a physicist. Both she and her parents had invested enormous amounts, emotionally and financially, in that goal over the years. She could have, if she had wished, terminated her pregnancy. Zurich was then a center of a burgeoning birth control industry, which included a mail-order abortion drug firm based there.
Instead, she decided that she wanted to have Einstein’s child—even though he was not yet ready or willing to marry her. Having a child out of wedlock was rebellious, given their upbringings, but not uncommon. The official statistics for Zurich in 1901 show that 12 percent of births were illegitimate. Residents who were Austro-Hungarian, moreover, were much more likely to get pregnant while unmarried. In southern Hungary, 33 percent of births were illegitimate. Serbs had the highest rate of illegitimate births, Jews by far the lowest.36
The decision caused Einstein to focus on the future. “I will look for a position immediately, no matter how humble it is,” he told her. “My scientific goals and my personal vanity will not prevent me from accepting even the most subordinate position.” He decided to call Besso’s father as well as the director of the local insurance company, and he promised to marry her as soon as he settled into a job. “Then no one can cast a stone on your dear little head.”
The pregnancy could also resolve, or so he hoped, the issues they faced with their families. “When your parents and mine are presented with a fait accompli, they’ll just have to reconcile themselves to it as best they can.”37
Mari, bedridden in Zurich with pregnancy sickness, was thrilled. “So, sweetheart, you want to look for a job immediately? And have me move in with you!” It was a vague proposal, but she immediately pronounced herself “happy” to agree. “Of course it mustn’t involve accepting a really bad position, darling,” she added. “That would make me feel terrible.” At her sister’s suggestion she tried to convince Einstein to visit her parents in Serbia for the summer vacation. “It would make me so happy,” she begged. “And when my parents see the two of us physically in front of them, all their doubts will evaporate.”38
But Einstein, to her dismay, decided to spend the summer vacation again with his mother and sister in the Alps. As a result, he was not there to help and encourage her at the end of July 1901 when she re-took her exams. Perhaps as a consequence of her pregnancy and personal situation, Mileva ended up failing for the second time, once again getting a 4.0 out of 6 and once again being the only one in her group not to pass.
Thus it was that Mileva Mari found herself resigned to giving up her dream of being a scientific scholar. She visited her home in Serbia—alone—and told her parents about her academic failure and her pregnancy. Before leaving, she asked Einstein to send her father a letter describing their plans and, presumably, pledging to marry her. “Will you send me the letter so I can see what you’ve written?” she asked. “By and by I’ll give him the necessary information, the unpleasant news as well.”39
Disputes with Drude and Others
Einstein’s impudence and contempt for convention, traits that were abetted by Mari, were evident in his science as well as in his personal life in 1901. That year, the unemployed enthusiast engaged in a series of tangles with academic authorities.
The squabbles show that Einstein had no qualms about challenging those in power. In fact, it seemed to infuse him with glee. As he proclaimed to Jost Winteler in the midst of his disputes that year, “Blind respect for authority is the greatest enemy of truth.” It would prove a worthy credo, one suitable for being carved on his coat of arms if he had ever wanted such a thing.
His struggles that year also reveal something more subtle about Einstein’s scientific thinking: he had an urge—indeed, a compulsion—to unify concepts from different branches of physics. “It is a glorious feeling to discover the unity of a set of phenomena that seem at first to be completely separate,” he wrote to his friend Grossmann as he embarked that spring on an attempt to tie his work on capillarity to Boltzmann’s theory of gases. That sentence, more than any other, sums up the faith that underlay Einstein’s scientific mission, from his first paper until his last scribbled field equations, guiding him with the same sure sense that was displayed by the needle of his childhood compass.40
Among the potentially unifying concepts that were mesmerizing Einstein, and much of the physics world, were those that sprang from kinetic theory, which had been developed in the late nineteenth century by applying the principles of mechanics to phenomena such as heat transfer and the behavior of gases. This involved regarding a gas, for example, as a collection of a huge number of tiny particles—in this case, molecules made up of one or more atoms—that careen around freely and occasionally collide with one another.
Kinetic theory spurred the growth of statistical mechanics, which describes the behavior of a large number of particles using statistical calculations. It was, of course, impossible to trace each molecule and each collision in a gas, but knowing the statistical behavior gave a workable theory of how billions of molecules behaved under varying conditions.
Scientists proceeded to apply these concepts not only to the behavior of gases, but also to phenomena that occurred in liquids and solids, including electrical conductivity and radiation. “The opportunity arose to apply the methods of the kinetic theory of gases to completely different branches of physics,” Einstein’s close friend Paul Ehrenfest, himself an expert in the field, later wrote.“Above all, the theory was applied to the motion of electrons in metals, to the Brownian motion of microscopically small particles in suspensions, and to the theory of blackbody radiation.”41
Although many scientists were using atomism to explore their own specialties, for Einstein it was a way to make connections, and develop unifying theories, between a variety of disciplines. In April 1901, for example, he adapted the molecular theories he had used to explain the capillary effect in liquids and applied them to the diffusion of gas molecules. “I’ve got an extremely lucky idea, which will make it possible to apply our theory of molecular forces to gases as well,” he wrote Mari. To Grossmann he noted, “I am now convinced that my theory of atomic attractive forces can also be extended to gases.”42
Next he became interested in the conduction of heat and electricity, which led him to study Paul Drude’s electron theory of metals. As the Einstein scholar Jürgen Renn notes, “Drude’s electron theory and Boltzmann’s kinetic theory of gas do not just happen to be two arbitrary subjects of interest to Einstein, but rather they share an important common property with several other of his early research topics: they are two examples of the application of atomistic ideas to physical and chemical problems.”43
Drude’s electron theory posited that there are particles in metal that move freely, as molecules of gas do, and thereby conduct both heat and electricity. When Einstein looked into it, he was pleased with it in parts. “I have a study in my hands by Paul Drude on the electron theory, which is written to my heart’s desire, even though it contains some very sloppy things,” he told Mari. A month later, with his usual lack of deference to authority, he declared, “Perhaps I’ll write to Drude privately to point out his mistakes.”
And so he did. In a letter to Drude in June,Einstein pointed out what he thought were two mistakes.“He will hardly have anything sensible to refute me with,” Einstein gloated to Mari, “because my objections are very straightforward.” Perhaps under the charming illusion that showing an eminent scientist his purported lapses is a good method for getting a job, Einstein included a request for one in his letter.44
Surprisingly, Drude replied. Not surprisingly, he dismissed Einstein’s objections. Einstein was outraged. “It is such manifest proof of the wretchedness of its author that no further comment by me is necessary,” Einstein said when forwarding Drude’s reply to Mari. “From now on I’ll no longer turn to such people, and will instead attack them mercilessly in the journals, as they deserve. It is no wonder that little by little one becomes a misanthrope.”
Einstein also vented his frustration to Jost Winteler, his father figure from Aarau, in a letter that included his declaration about a blind respect for authority being the greatest enemy of truth. “He responds by pointing out that another ‘infallible’ colleague of his shares his opinion. I’ll soon make it hot for the man with a masterly publication.”45
The published papers of Einstein do not identify this “infallible” colleague cited by Drude, but some sleuthing by Renn has turned up a letter from Mari that declares it to be Ludwig Boltzmann.46 That explains why Einstein proceeded to immerse himself in Boltzmann’s writings. “I have been engrossed in Boltzmann’s works on the kinetic theory of gases,” he wrote Grossmann in September, “and these last few days I wrote a short paper myself that provides the missing key-stone in the chain of proofs that he started.”47
Boltzmann, then at the University of Leipzig, was Europe’s master of statistical physics. He had helped to develop the kinetic theory and defend the faith that atoms and molecules actually exist. In doing so, he found it necessary to reconceive the great Second Law of Thermodynamics. This law has many equivalent formulations. It says that heat flows naturally from hot to cold, but not the reverse. Another way to describe the Second Law is in terms of entropy, the degree of disorder and randomness in a system. Any spontaneous process tends to increase the entropy of a system. For example, perfume molecules drift out of an open bottle and into a room but don’t, at least in our common experience, spontaneously gather themselves together and all drift back into the bottle.
The problem for Boltzmann was that mechanical processes, such as molecules bumping around, could each be reversed, according to Newton. So a spontaneous decrease in entropy would, at least in theory, be possible. The absurdity of positing that diffused perfume molecules could gather back into a bottle, or that heat could flow from a cold body to a hot one spontaneously, was flung against Boltzmann by opponents, such as Wilhelm Ostwald, who did not believe in the reality of atoms and molecules. “The proposition that all natural phenomena can ultimately be reduced to mechanical ones cannot even be taken as a useful working hypothesis: it is simply a mistake,” Ostwald declared. “The irreversibility of natural phenomena proves the existence of processes that cannot be described by mechanical equations.”
Boltzmann responded by revising the Second Law so that it was not absolute but merely a statistical near-certainty. It was theoretically possible that millions of perfume molecules could randomly bounce around in a way that they all put themselves back into a bottle at a certain moment, but that was exceedingly unlikely, perhaps trillions of times less likely than that a new deck of cards shuffled a hundred times would end up back in its pristine rank-and-suit precise order.48
When Einstein rather immodestly declared in September 1901 that he was filling in a “keystone” that was missing in Boltzmann’s chain of proofs, he said he planned to publish it soon. But first, he sent a paper to the Annalen der Physik that involved an electrical method for investigating molecular forces, which used calculations derived from experiments others had done using salt solutions and an electrode.49
Then he published his critique of Boltzmann’s theories. He noted that they worked well in explaining heat transfer in gases but had not yet been properly generalized for other realms. “Great as the achievements of the kinetic theory of heat have been in the domain of gas theory,” he wrote, “the science of mechanics has not yet been able to produce an adequate foundation for the general theory of heat.” His aim was “to close this gap.”50
This was all quite presumptuous for an undistinguished Polytechnic student who had not been able to get either a doctorate or a job. Einstein himself later admitted that these papers added little to the body of physics wisdom. But they do indicate what was at the heart of his 1901 challenges to Drude and Boltzmann. Their theories, he felt, did not live up to the maxim he had proclaimed to Grossmann earlier that year about how glorious it was to discover an underlying unity in a set of phenomena that seem completely separate.
In the meantime, in November 1901, Einstein had submitted an attempt at a doctoral dissertation to Professor Alfred Kleiner at the University of Zurich. The dissertation has not survived, but Mari told a friend that “it deals with research into the molecular forces in gases using various known phenomena.” Einstein was confident. “He won’t dare reject my dissertation,” he said of Kleiner, “otherwise the shortsighted man is of little use to me.”51
By December Kleiner had not even responded, and Einstein started worrying that perhaps the professor’s “fragile dignity” might make him uncomfortable accepting a dissertation that denigrated the work of such masters as Drude and Boltzmann. “If he dares to reject my dissertation, then I’ll publish his rejection along with my paper and make a fool of him,” Einstein said. “But if he accepts it, then we’ll see what good old Herr Drude has to say.”
Eager for a resolution, he decided to go see Kleiner personally. Rather surprisingly, the meeting went well. Kleiner admitted he had not yet read the dissertation, and Einstein told him to take his time. They then proceeded to discuss various ideas that Einstein was developing, some of which would eventually bear fruit in his relativity theory. Kleiner promised Einstein that he could count on him for a recommendation the next time a teaching job came up. “He’s not quite as stupid as I’d thought,” was Einstein’s verdict.“Moreover, he’s a good fellow.”52
Kleiner may have been a good fellow, but he did not like Einstein’s dissertation when he finally got around to reading it. In particular, he was unhappy about Einstein’s attack on the scientific establishment. So he rejected it; more precisely, he told Einstein to withdraw it voluntarily, which permitted him to get back his 230 franc fee. According to a book written by Einstein’s stepson-in-law, Kleiner’s action was “out of consideration to his colleague Ludwig Boltzmann, whose train of reasoning Einstein had sharply criticized.” Einstein, lacking such sensitivity, was persuaded by a friend to send the attack directly to Boltzmann.53
Marcel Grossmann had mentioned to Einstein that there was likely to be a job at the patent office for him, but it had not yet materialized. So five months later, he gently reminded Grossmann that he still needed help. Noticing in the newspaper that Grossmann had won a job teaching at a Swiss high school, Einstein expressed his “great joy” and then plaintively added, “I, too, applied for that position, but I did it only so that I wouldn’t have to tell myself that I was too faint-hearted to apply.”54
In the fall of 1901, Einstein took an even humbler job as a tutor at a little private academy in Schaffhausen, a village on the Rhine twenty miles north of Zurich. The work consisted solely of tutoring a rich English schoolboy who was there. To be taught by Einstein would someday seem a bargain at any price. But at the time, the proprietor of the school, Jacob Nüesch, was getting the bargain. He was charging the child’s family 4,000 francs a year, while paying Einstein only 150 francs a month, plus providing room and board.
Einstein continued to promise Mari that she would “get a good husband as soon as this becomes feasible,” but he was now despairing about the patent job. “The position in Bern has not yet been advertised so that I am really giving up hope for it.”55
Mari was eager to be with him, but her pregnancy made it impossible for them to be together in public. So she spent most of November at a small hotel in a neighboring village. Their relationship was becoming strained. Despite her pleas, Einstein came only infrequently to visit her, often claiming that he did not have the spare money. “You’ll surely surprise me, right?” she begged after getting yet another note canceling a visit. Her pleadings and anger alternated, often in the same letter:
If you only knew how terribly homesick I am, you would surely come. Are you really out of money? That’s nice! The man earns 150 francs, has room and board provided, and at the end of the month doesn’t have a cent to his name! ... Don’t use that as an excuse for Sunday, please. If you don’t get any money by then, I will send you some . . . If you only knew how much I want to see you again! I think about you all day long, and even more at night.
Einstein’s impatience with authority soon pitted him against the proprietor of the academy. He tried to cajole his tutee to move to Bern with him and pay him directly, but the boy’s mother balked. Then Einstein asked Nüesch to give him his meal money in cash so that he would not have to eat with his family. “You know what our conditions are,” Nüesch replied. “There is no reason to deviate from them.”
A surly Einstein threatened to find new arrangements, and Nüesch backed down in a rage. In a line that could be considered yet another maxim for his life, Einstein recounted the scene to Mari and exulted, “Long live impudence! It is my guardian angel in this world.”
That night, as he sat down for his last meal at the Nüesch household, he found a letter for him next to his soup plate. It was from his real-life guardian angel, Marcel Grossmann. The position at the patent office, Grossmann wrote, was about to be advertised, and Einstein was sure to get it. Their lives were soon to be “brilliantly changed for the better,” an excited Einstein wrote Mari. “I’m dizzy with joy when I think about it,” he said. “I’m even happier for you than for myself. Together we’d surely be the happiest people on the earth.”
That still left the issue of what to do about their baby, who was due to be born in less than two months, by early February 1902. “The only problem that would remain to be solved would be how to keep our Lieserl with us,” Einstein (who had begun referring to their unborn child as a girl) wrote to Mari, who had returned home to have the baby at her parents’ house in Novi Sad. “I wouldn’t want to have to give her up.” It was a noble intention on his part, yet he knew that it would be difficult for him to show up for work in Bern with an illegitimate child. “Ask your Papa; he’s an experienced man, and knows the world better than your overworked, impractical Johnnie.” For good measure, he declared that the baby, when born, “shouldn’t be stuffed with cow milk, because it might make her stupid.” Mari’s milk would be more nourishing, he said.57
Although he was willing to consult Mari’s family, Einstein had no intention of letting his own family know that his mother’s worst fears about his relationship—a pregnancy and possible marriage—were materializing. His sister seemed to realize that he and Mari were secretly planning to be married, and she told this to members of the Winteler family in Aarau. But none of them showed any sign of suspecting that a child was involved. Einstein’s mother learned about the purported engagement from Mrs. Winteler. “We are resolutely against Albert’s relationship with Fraulein Mari, and we don’t ever wish to have anything to do with her,” Pauline Einstein lamented.58
Einstein’s mother even took the extraordinary step of writing a nasty letter, signed also by her husband, to Mari’s parents. “This lady,” Mari lamented to a friend about Einstein’s mother, “seems to have set as her life’s goal to embitter as much as possible not only my life but also that of her son. I could not have thought it possible that there could exist such heartless and outright wicked people! They felt no compunctions about writing a letter to my parents in which they reviled me in a manner that was a disgrace.”59
The official advertisement announcing the patent office opportunity finally appeared in December 1901. The director, Friedrich Haller, apparently tailored the specifications so that Einstein would get the job. Candidates did not need a doctorate, but they must have mechanical training and also know physics. “Haller put this in for my sake,” Einstein told Mari.
Haller wrote Einstein a friendly letter making it clear that he was the prime candidate, and Grossmann called to congratulate him. “There’s no doubt anymore,” Einstein exulted to Mari. “Soon you’ll be my happy little wife, just watch. Now our troubles are over. Only now that this terrible weight is off my shoulders do I realize how much I love you... Soon I’ll be able to take my Dollie in my arms and call her my own in front of the whole world.”60
He made her promise, however, that marriage would not turn them into a comfortable bourgeois couple: “We’ll diligently work on science together so we don’t become old philistines, right?” Even his sister, he felt, was becoming “so crass” in her approach to creature comforts. “You’d better not get that way,” he told Mari. “It would be terrible. You must always be my witch and street urchin. Everyone but you seems foreign to me, as if they were separated from me by an invisible wall.”
In anticipation of getting the patent-office job, Einstein abandoned the student he had been tutoring in Schaffhausen and moved to Bern in late January 1902. He would be forever grateful to Grossmann, whose aid would continue in different ways over the next few years. “Grossmann is doing his dissertation on a subject that is related to non-Euclidean geometry,” Einstein noted to Mari. “I don’t know exactly what it is.”61
A few days after Einstein arrived in Bern, Mileva Mari, staying at her parents’ home in Novi Sad, gave birth to their baby, a girl whom they called Lieserl. Because the childbirth was so difficult, Mari was unable to write to him. Her father sent Einstein the news.
“Is she healthy, and does she cry properly?” Einstein wrote Mari. “What are her eyes like? Which one of us does she more resemble? Who is giving her milk? Is she hungry? She must be completely bald. I love her so much and don’t even know her yet!” Yet his love for their new baby seemed to exist mainly in the abstract, for it was not quite enough to induce him to make the train trip to Novi Sad.62
Einstein did not tell his mother, sister, or any of his friends about the birth of Lieserl. In fact, there is no indication that he ever told them about her. Never once did he publicly speak of her or acknowledge that she even existed. No mention of her survives in any correspondence, except for a few letters between Einstein and Mari, and these were suppressed and hidden until 1986, when scholars and the editors of his papers were completely surprised to learn of Lieserl’s existence.*
But in his letter to Mari right after Lieserl’s birth, the baby brought out Einstein’s wry side. “She’s certainly able to cry already, but won’t know how to laugh until much later,” he said. “Therein lies a profound truth.”
Fatherhood also focused him on the need to make some money while he waited to get the patent-office job. So the next day an ad appeared in the newspaper: “Private lessons in Mathematics and Physics . . . given most thoroughly by Albert Einstein, holder of the federal Polytechnic teacher’s diploma ... Trial lessons free.”
Lieserl’s birth even caused Einstein to display a domestic, nesting instinct not previously apparent. He found a large room in Bern and drew for Mari a sketch of it, complete with diagrams showing the bed, six chairs, three cabinets, himself (“Johnnie”), and a couch marked “look at that!”63 However, Mari was not going to be moving into it with him. They were not married, and an aspiring Swiss civil servant could not be seen cohabitating in such a way. Instead, after a few months, Mari moved back to Zurich to wait for him to get a job and, as promised, marry her. She did not bring Lieserl with her.
Einstein and his daughter apparently never laid eyes on each other. She would merit, as we shall see, just one brief mention in their surviving correspondence less than two years later, in September 1903, and then not be referred to again. In the meantime, she was left back in Novi Sad with her mother’s relatives or friends so that Einstein could maintain both his unencumbered lifestyle and the bourgeois respectability he needed to become a Swiss official.
There is a cryptic hint that the person who took custody of Lieserl may have been Mari’s close friend, Helene Kaufler Savi, whom she had met in 1899 when they lived in the same rooming house in Zurich. Savi was from a Viennese Jewish family and had married an engineer from Serbia in 1900. During her pregnancy, Mari had written her a letter pouring out all of her woes, but she tore it up before mailing it. She was glad she had done so, she explained to Einstein two months before Lieserl’s birth, because “I don’t think we should say anything about Lieserl yet.” Mari added that Einstein should write Savi a few words now and then. “We must now treat her very nicely. She’ll have to help us in something important, after all.”64
The Patent Office
As he was waiting to be offered the job at the patent office, Einstein ran into an acquaintance who was working there. The job was boring, the person complained, and he noted that the position Einstein was waiting to get was “the lowest rank,” so at least he didn’t have to worry that anyone else would apply for it. Einstein was unfazed. “Certain people find everything boring,” Einstein told Mari. As for the disdain about being on the lowest rung, Einstein told her that they should feel just the opposite: “We couldn’t care less about being on top!”65
The job finally came through on June 16, 1902, when a session of the Swiss Council officially elected him “provisionally as a Technical Expert Class 3 of the Federal Office for Intellectual Property with an annual salary of 3,500 francs,” which was actually more than what a junior professor would make.66
His office in Bern’s new Postal and Telegraph Building was near the world-famous clock tower over the old city gate (see p. 107). As he turned left out of his apartment on his way to work, Einstein walked past it every day. The clock was originally built shortly after the city was founded in 1191, and an astronomical contraption featuring the positions of the planets was added in 1530. Every hour, the clock would put on its show: out would come a dancing jester ringing bells, then a parade of bears, a crowing rooster, and an armored knight, followed by Father Time with his scepter and hourglass.
The clock was the official timekeeper for the nearby train station, the one from which all of the other clocks that lined the platform were synchronized. The moving trains arriving from other cities, where the local time was not always standardized, would reset their own clocks by looking up at the Bern clock tower as they sped into town.67
So it was that Albert Einstein would end up spending the most creative seven years of his life—even after he had written the papers that reoriented physics—arriving at work at 8 a.m., six days a week, and examining patent applications. “I am frightfully busy,” he wrote a friend a few months later. “Every day I spend eight hours at the office and at least one hour of private lessons, and then, in addition, I do some scientific work.” Yet it would be wrong to think that poring over applications for patents was drudgery. “I enjoy my work at the office very much, because it is uncommonly diversified.”68
He soon learned that he could work on the patent applications so quickly that it left time for him to sneak in his own scientific thinking during the day. “I was able to do a full day’s work in only two or three hours,” he recalled. “The remaining part of the day, I would work out my own ideas.” His boss, Friedrich Haller, was a man of good-natured, growling skepticism and genial humor who graciously ignored the sheets of paper that cluttered Einstein’s desk and vanished into his drawer when people came to see him. “Whenever anybody would come by, I would cram my notes into my desk drawer and pretend to work on my office work.”69
Indeed, we should not feel sorry for Einstein that he found himself exiled from the cloisters of academe. He came to believe that it was a benefit to his science, rather than a burden, to work instead in “that worldly cloister where I hatched my most beautiful ideas.”70
Every day, he would do thought experiments based on theoretical premises, sniffing out the underlying realities. Focusing on real-life questions, he later said,“stimulated me to see the physical ramifications of theoretical concepts.”71 Among the ideas that he had to consider for patents were dozens of new methods for synchronizing clocks and coordinating time through signals sent at the speed of light.72
In addition, his boss Haller had a credo that was as useful for a creative and rebellious theorist as it was for a patent examiner: “You have to remain critically vigilant.” Question every premise, challenge conventional wisdom, and never accept the truth of something merely because everyone else views it as obvious. Resist being credulous. “When you pick up an application,” Haller instructed, “think that everything the inventor says is wrong.”73
Einstein had grown up in a family that created patents and tried to apply them in business, and he found the process to be fulfilling. It reinforced one of his ingenious talents: the ability to conduct thought experiments in which he could visualize how a theory would play out in practice. It also helped him peel off the irrelevant facts that surrounded a problem.74
Had he been consigned instead to the job of an assistant to a professor, he might have felt compelled to churn out safe publications and be overly cautious in challenging accepted notions. As he later noted, originality and creativity were not prime assets for climbing academic ladders, especially in the German-speaking world, and he would have felt pressure to conform to the prejudices or prevailing wisdom of his patrons. “An academic career in which a person is forced to produce scientific writings in great amounts creates a danger of intellectual superficiality,” he said.75
As a result, the happenstance that landed him on a stool at the Swiss Patent Office, rather than as an acolyte in academia, likely reinforced some of the traits destined to make him successful: a merry skepticism about what appeared on the pages in front of him and an independence of judgment that allowed him to challenge basic assumptions. There were no pressures or incentives among the patent examiners to behave otherwise.
The Olympia Academy
Maurice Solovine, a Romanian studying philosophy at the University of Bern, bought a newspaper while on a stroll one day during Easter vacation of 1902 and noticed Einstein’s advertisement offering tutorials in physics (“trial lessons free”). A dapper dilettante with close-cropped hair and a raffish goatee, Solovine was four years older than Einstein, but he had yet to decide whether he wanted to be a philosopher, a physicist, or something else. So he went to the address, rang the bell, and a moment later a loud voice thundered “In here!” Einstein made an immediate impression. “I was struck by the extraordinary brilliance of his large eyes,” Solovine recalled.76
Their first discussion lasted almost two hours, after which Einstein followed Solovine into the street, where they talked for a half-hour more. They agreed to meet the next day. At the third session, Einstein announced that conversing freely was more fun than tutoring for pay. “You don’t have to be tutored in physics,” he said. “Just come see me when you want and I will be glad to talk with you.” They decided to read the great thinkers together and then discuss their ideas.
Their sessions were joined by Conrad Habicht, a banker’s son and former student of mathematics at the Zurich Polytechnic. Poking a little fun at pompous scholarly societies, they dubbed themselves the Olympia Academy. Einstein, even though he was the youngest, was designated the president, and Solovine prepared a certificate with a drawing of an Einstein bust in profile beneath a string of sausages. “A man perfectly and clearly erudite, imbued with exquisite, subtle and elegant knowledge, steeped in the revolutionary science of the cosmos,” the dedication declared.77
Generally their dinners were frugal repasts of sausage, Gruyère cheese, fruit, and tea. But for Einstein’s birthday, Solovine and Habicht decided to surprise him by putting three plates of caviar on the table. Einstein was engrossed in analyzing Galileo’s principle of inertia, and as he talked he took mouthful after mouthful of his caviar without seeming to notice. Habicht and Solovine exchanged furtive glances. “Do you realize what you’ve been eating?” Solovine finally asked.
“For goodness’ sake,” Einstein exclaimed. “So that was the famous caviar!” He paused for a moment, then added, “Well, if you offer gourmet food to peasants like me, you know they won’t appreciate it.”
After their discussions, which could last all night, Einstein would sometimes play the violin and, in the summertime, they occasionally climbed a mountain on the outskirts of Bern to watch the sunrise. “The sight of the twinkling stars made a strong impression on us and led to discussions of astronomy,” Solovine recalled. “We would marvel at the sun as it came slowly toward the horizon and finally appeared in all of its splendor to bathe the Alps in a mystic rose.” Then they would wait for the mountain café to open so they could drink dark coffee before hiking down to start work.
Solovine once skipped a session scheduled for his apartment because he was enticed instead to a concert by a Czech quartet. As a peace offering he left behind, as his note written in Latin proclaimed, “hard boiled eggs and a salutation.” Einstein and Habicht, knowing how much Solovine hated tobacco, took revenge by smoking pipes and cigars in Solovine’s room and piling his furniture and dishes on the bed. “Thick smoke and a salutation,” they wrote in Latin. Solovine says he was “almost overwhelmed” by the fumes when he returned.“I thought I would suffocate. I opened the window wide and began to remove from the bed the mound of things that reached almost to the ceiling.”78
Solovine and Habicht would become Einstein’s lifelong friends, and he would later reminisce with them about “our cheerful ‘Academy,’ which was less childish than those respectable ones which I later got to know at close quarters.” In response to a joint postcard sent from Paris by his two colleagues on his seventy-fourth birthday, he paid tribute to it: “Your members created you to make fun of your long-established sister Academies. How well their mockery hit the mark I have learned to appreciate fully through long years of careful observation.”79
The Academy’s reading list included some classics with themes that Einstein could appreciate, such as Sophocles’ searing play about the defiance of authority, Antigone, and Cervantes’ epic about stubbornly tilting at windmills, Don Quixote. But mostly the three academicians read books that explored the intersection of science and philosophy: David Hume’s A Treatise of Human Nature, Ernst Mach’s Analysis of the Sensations and Mechanics and Its Development, Baruch Spinoza’s Ethics, and Henri Poincaré’s Science and Hypothesis.80 It was from reading these authors that the young patent examiner began to develop his own philosophy of science.
The most influential of these, Einstein later said, was the Scottish empiricist David Hume (1711–1776). In the tradition of Locke and Berkeley, Hume was skeptical about any knowledge other than what could be directly perceived by the senses. Even the apparent laws of causality were suspect to him, mere habits of the mind; a ball hitting another may behave the way that Newton’s laws predict time after time after time, yet that was not, strictly speaking, a reason to believe that it would happen that way the next time. “Hume saw clearly that certain concepts, for example that of causality, cannot be deduced from our perceptions of experience by logical methods,” Einstein noted.
A version of this philosophy, sometimes called positivism, denied the validity of any concepts that went beyond descriptions of phenomena that we directly experience. It appealed to Einstein, at least initially. “The theory of relativity suggests itself in positivism,” he said. “This line of thought had a great influence on my efforts, most specifically Mach and even more so Hume, whose Treatise of Human Nature I studied avidly and with admiration shortly before discovering the theory of relativity.”81
Hume applied his skeptical rigor to the concept of time. It made no sense, he said, to speak of time as having an absolute existence that was independent of observable objects whose movements permitted us to define time.“From the succession of ideas and impressions we form the idea of time,” Hume wrote. “It is not possible for time alone ever to make its appearance.” This idea that there is no such thing as absolute time would later echo in Einstein’s theory of relativity. Hume’s specific thoughts about time, however, had less influence on Einstein than his more general insight that it is dangerous to talk about concepts that are not definable by perceptions and observations.82
Einstein’s views on Hume were tempered by his appreciation for Immanuel Kant (1724–1804), the German metaphysician he had been introduced to, back when he was a schoolboy, by Max Talmud. “Kant took the stage with an idea that signified a step towards the solution of Hume’s dilemma,” Einstein said. Some truths fit into a category of “definitely assured knowledge” that was “grounded in reason itself.”
In other words, Kant distinguished between two types of truths: (1) analytic propositions, which derive from logic and “reason itself ” rather than from observing the world; for example, all bachelors are unmarried, two plus two equals four, and the angles of a triangle always add up to 180 degrees; and (2) synthetic propositions, which are based on experience and observations; for example, Munich is bigger than Bern, all swans are white. Synthetic propositions could be revised by new empirical evidence, but not analytic ones. We may discover a black swan but not a married bachelor or (at least so Kant thought) a triangle with 181 degrees. As Einstein said of Kant’s first category of truths: “This is held to be the case, for example, in the propositions of geometry and in the principle of causality. These and certain other types of knowledge . . . do not previously have to be gained from sense data, in other words they are a priori knowledge.”
Einstein initially found it wondrous that certain truths could be discovered by reason alone. But he soon began to question Kant’s rigid distinction between analytic and synthetic truths. “The objects with which geometry deals seemed to be of no different type than the objects of sensory perception,” he recalled. And later he would reject outright this Kantian distinction. “I am convinced that this differentiation is erroneous,” he wrote. A proposition that seems purely analytic—such as the angles of a triangle adding up to 180 degrees—could turn out to be false in a non-Euclidean geometry or in a curved space (such as would be the case in the general theory of relativity). As he later said of the concepts of geometry and causality, “Today everyone knows, of course, that the mentioned concepts contain nothing of the certainty, of the inherent necessity, which Kant had attributed to them.”83
Hume’s empiricism was carried a step further by Ernst Mach (1838–1916), the Austrian physicist and philosopher whose writings Einstein read at the urging of Michele Besso. He became one of the favorite authors of the Olympia Academy, and he helped to instill in Einstein the skepticism about received wisdom and accepted conventions that would become a hallmark of his creativity. Einstein would later proclaim, in words that could be used to describe himself as well, that Mach’s genius was partly due to his “incorruptible skepticism and independence.”84
The essence of Mach’s philosophy was this, in Einstein’s words: “Concepts have meaning only if we can point to objects to which they refer and to the rules by which they are assigned to these objects.”85 In other words, for a concept to make sense you need an operational definition of it, one that describes how you would observe the concept in operation. This would bear fruit for Einstein when, a few years later, he and Besso would talk about what observation would give meaning to the apparently simple concept that two events happened “simultaneously.”
The most influential thing that Mach did for Einstein was to apply this approach to Newton’s concepts of “absolute time” and “absolute space.” It was impossible to define these concepts, Mach asserted, in terms of observations you could make. Therefore they were meaningless. Mach ridiculed Newton’s “conceptual monstrosity of absolute space”; he called it “purely a thought-thing which cannot be pointed to in experience.”86
The final intellectual hero of the Olympia Academy was Baruch Spinoza (1632–1677), the Jewish philosopher from Amsterdam. His influence was primarily religious: Einstein embraced his concept of an amorphous God reflected in the awe-inspiring beauty, rationality, and unity of nature’s laws. But like Spinoza, Einstein did not believe in a personal God who rewarded and punished and intervened in our daily lives.
In addition, Einstein drew from Spinoza a faith in determinism: a sense that the laws of nature, once we could fathom them, decreed immutable causes and effects, and that God did not play dice by allowing any events to be random or undetermined. “All things are determined by the necessity of divine nature,” Spinoza declared, and even when quantum mechanics seemed to show that was wrong, Einstein steadfastly believed it was right.87
Hermann Einstein was not destined to see his son become anything more successful than a third-class patent examiner. In October 1902, when Hermann’s health began to decline, Einstein traveled to Milan to be with him at the end. Their relationship had long been a mix of alienation and affection, and it concluded on that note as well. “When the end came,” Einstein’s assistant Helen Dukas later said, “Hermann asked all of them to leave the room, so he could die on his own.”
Einstein felt, for the rest of his life, a sense of guilt about that moment, which encapsulated his inability to forge a true bond with his father. For the first time, he was thrown into a daze, “overwhelmed by a feeling of desolation.” He later called his father’s death the deepest shock he had ever experienced. The event did, however, solve one important issue. On his deathbed, Hermann Einstein gave his permission, finally, for his son to marry Mileva Mari.88
Einstein’s Olympia Academy colleagues, Maurice Solovine and Conrad Habicht, convened in special session on January 6, 1903, to serve as witnesses at the tiny civil ceremony in the Bern registrar’s office where Albert Einstein married Mileva Mari. No family members—not Einstein’s mother or sister, nor Mari’s parents—came to Bern. The tight group of intellectual comrades celebrated together at a restaurant that evening, and then Einstein and Mari went back to his apartment together. Not surprisingly, he had forgotten his key and had to wake his landlady.89
“Well, now I am a married man and I am living a very pleasant cozy life with my wife,” he reported to Michele Besso two weeks later. “She takes excellent care of everything, cooks well, and is always cheerful.” For her part, Mari* reported to her own best friend, “I am even closer to my sweetheart, if it is at all possible, than I was in our Zurich days.” Occasionally she would attend sessions of the Olympia Academy, but mainly as an observer. “Mileva, intelligent and reserved, listened intently but never intervened in our discussions,” Solovine recalled.
Nevertheless, clouds began to form. “My new duties are taking their toll,” Mari said of her housekeeping chores and role as a mere onlooker when science was discussed. Einstein’s friends felt that she was becoming even more gloomy. At times she seemed laconic, and distrustful as well. And Einstein, at least so he claimed in retrospect, had already become wary. He had felt an “inner resistance” to marrying Mari, he later claimed, but had overcome it out of a “sense of duty.”
Mari soon began to look for ways to restore the magic to their relationship. She hoped that they would escape the bourgeois drudgery that seemed inherent in the household of a Swiss civil servant and, instead, find some opportunity to recapture their old bohemian academic life. They decided—or at least so Mari hoped—that Einstein would find a teaching job somewhere far away, perhaps near their forsaken daughter. “We will try anywhere,” she wrote to her friend in Serbia. “Do you think, for example, that in Belgrade people of our kind could find something?” Mari said they would do anything academic, even teaching German in a high school. “You see, we still have that old enterprising spirit.”90
As far as we know, Einstein never went to Serbia to seek a job or to see his baby. A few months into their marriage, in August 1903, the secret cloud hovering over their lives suddenly cast a new pall. Mari received word that Lieserl, then 19 months old, had come down with scarlet fever. She boarded a train for Novi Sad. When it stopped in Salzburg, she bought a postcard of a local castle and jotted a note, which she mailed from the stop in Budapest: “It is going quickly, but it is hard. I don’t feel at all well. What are you doing, little Jonzile, write me soon, will you? Your poor Dollie.”91
Apparently, the child was given up for adoption. The only clue we have is a cryptic letter Einstein wrote Mari in September, after she had been in Novi Sad for a month: “I am very sorry about what happened with Lieserl. Scarlet fever often leaves some lasting trace behind. If only everything passes well. How is Lieserl registered? We must take great care, lest difficulties arise for the child in the future.”92
Whatever the motivation Einstein may have had for asking the question, neither Lieserl’s registration documents nor any other paper trace of her existence is known to have survived. Various researchers, Serbian and American, including Robert Schulmann of the Einstein Papers Project and Michele Zackheim, who wrote a book about searching for Lieserl, have fruitlessly scoured churches, registries, synagogues, and cemeteries.
All evidence about Einstein’s daughter was carefully erased. Almost every one of the letters between Einstein and Mari in the summer and fall of 1902, many of which presumably dealt with Lieserl, were destroyed. Those between Mari and her friend Helene Savi during that period were intentionally burned by Savi’s family. For the rest of their lives, even after they divorced, Einstein and his wife did all they could, with surprising success, to cover up not only the fate of their first child but her very existence.
One of the few facts that have escaped this black hole of history is that Lieserl was still alive in September 1903. Einstein’s expression of worry, in his letter to Mari that month, about potential difficulties “for the child in the future,” makes this clear. The letter also indicates that she had been given up for adoption by then, because in it Einstein spoke of the desirability of having a “replacement” child.
There are two plausible explanations about the fate of Lieserl. The first is that she survived her bout of scarlet fever and was raised by an adoptive family. On a couple of occasions later in his life, when women came forward claiming (falsely, it turned out) to be illegitimate children of his, Einstein did not dismiss the possibility out of hand, although given the number of affairs he had, this is no indication that he thought they might be Lieserl.
One possibility, favored by Schulmann, is that Mari’s friend Helene Savi adopted Lieserl. She did in fact raise a daughter Zorka, who was blind from early childhood (perhaps a result of scarlet fever), was never married, and was shielded by her nephew from people who sought to interview her. Zorka died in the 1990s.
The nephew who protected Zorka, Milan Popovi, rejects this possibility. In a book he wrote on the friendship and correspondence between Mari and his grandmother Helene Savi, In Albert’s Shadow, Popovi asserted, “A theory has been advanced that my grandmother adopted Lieserl, but an examination of my family’s history renders this groundless.” He did not, however, produce any documentary evidence, such as his aunt’s birth certificate, to back up this contention. His mother burned most of Helene Savi’s letters, including any that had dealt with Lieserl. Popovi’s own theory, based partly on the family stories recalled by a Serbian writer named Mira Alekovi, is that Lieserl died of scarlet fever in September 1903, after Einstein’s letter of that month. Michele Zackheim, in her book describing her hunt for Lieserl, comes to a similar conclusion.93
Whatever happened added to Mari’s gloom. Shortly after Einstein died, a writer named Peter Michelmore, who knew nothing of Lieserl, published a book that was based in part on conversations with Einstein’s son Hans Albert Einstein. Referring to the year right after their marriage, Michelmore noted, “Something had happened between the two, but Mileva would say only that it was ‘intensely personal.’ Whatever it was, she brooded about it, and Albert seemed to be in some ways responsible. Friends encouraged Mileva to talk about her problem and get it out in the open. She insisted that it was too personal and kept it a secret all her life—a vital detail in the story of Albert Einstein that still remains shrouded in mystery.”94
The illness that Mari complained about in her postcard from Budapest was likely because she was pregnant again. When she found out that indeed she was, she worried that this would anger her husband. But Einstein expressed happiness on hearing the news that there would soon be a replacement for their daughter. “I’m not the least bit angry that poor Dollie is hatching a new chick,” he wrote. “In fact, I’m happy about it and had already given some thought to whether I shouldn’t see to it that you get a new Lieserl. After all, you shouldn’t be denied that which is the right of all women.”95
Hans Albert Einstein was born on May 14, 1904. The new child lifted Mari’s spirits and restored some joy to her marriage, or so at least she told her friend Helene Savi: “Hop over to Bern so I can see you again and I can show you my dear little sweetheart, who is also named Albert. I cannot tell you how much joy he gives me when he laughs so cheerfully on waking up or when he kicks his legs while taking a bath.”
Einstein was “behaving with fatherly dignity,” Mari noted, and he spent time making little toys for his baby son, such as a cable car he constructed from matchboxes and string. “That was one of the nicest toys I had at the time and it worked,” Hans Albert could still recall when he was an adult. “Out of little string and matchboxes and so on, he could make the most beautiful things.”96
Milos Mari was so overjoyed with the birth of a grandson that he came to visit and offered a sizable dowry, reported in family lore (likely with some exaggeration) to be 100,000 Swiss francs. But Einstein declined it, saying he had not married his daughter for money, Milos Mari later recounted with tears in his eyes. In fact, Einstein was beginning to do well enough on his own. After more than a year at the patent office, he had been taken off probationary status.97
THE MIRACLE YEAR: Quanta and Molecules, 1905
At the Patent Office, 1905
Turn of the Century
“There is nothing new to be discovered in physics now,” the revered Lord Kelvin reportedly told the British Association for the Advancement of Science in 1900. “All that remains is more and more precise measurement.”1 He was wrong.
The foundations of classical physics had been laid by Isaac Newton (1642–1727) in the late seventeenth century. Building on the discoveries of Galileo and others, he developed laws that described a very comprehensible mechanical universe: a falling apple and an orbiting moon were governed by the same rules of gravity, mass, force, and motion. Causes produced effects, forces acted upon objects, and in theory everything could be explained, determined, and predicted. As the mathematician and astronomer Laplace exulted about Newton’s universe, “An intelligence knowing all the forces acting in nature at a given instant, as well as the momentary positions of all things in the universe, would be able to comprehend in one single formula the motions of the largest bodies as well as the lightest atoms in the world; to him nothing would be uncertain, the future as well as the past would be present to his eyes.”2
Einstein admired this strict causality, calling it “the profoundest characteristic of Newton’s teaching.”3 He wryly summarized the history of physics: “In the beginning (if there was such a thing) God created Newton’s laws of motion together with the necessary masses and forces.” What especially impressed Einstein were “the achievements of mechanics in areas that apparently had nothing to do with mechanics,” such as the kinetic theory he had been exploring, which explained the behavior of gases as being caused by the actions of billions of molecules bumping around.4
In the mid-1800s, Newtonian mechanics was joined by another great advance. The English experimenter Michael Faraday (1791– 1867), the self-taught son of a blacksmith, discovered the properties of electrical and magnetic fields. He showed that an electric current produced magnetism, and then he showed that a changing magnetic field could produce an electric current. When a magnet is moved near a wire loop, or vice versa, an electric current is produced.5
Faraday’s work on electromagnetic induction permitted inventive entrepreneurs like Einstein’s father and uncle to create new ways of combining spinning wire coils and moving magnets to build electricity generators. As a result, young Albert Einstein had a profound physical feel for Faraday’s fields and not just a theoretical understanding of them.
The bushy-bearded Scottish physicist James Clerk Maxwell (1831–1879) subsequently devised wonderful equations that specified, among other things, how changing electric fields create magnetic fields and how changing magnetic fields create electrical ones. A changing electric field could, in fact, produce a changing magnetic field that could, in turn, produce a changing electric field, and so on. The result of this coupling was an electromagnetic wave.
Just as Newton had been born the year that Galileo died, so Einstein was born the year that Maxwell died, and he saw it as part of his mission to extend the work of the Scotsman. Here was a theorist who had shed prevailing biases, let mathematical melodies lead him into unknown territories, and found a harmony that was based on the beauty and simplicity of a field theory.
All of his life, Einstein was fascinated by field theories, and he described the development of the concept in a textbook he wrote with a colleague:
A new concept appeared in physics, the most important invention since Newton’s time: the field. It needed great scientific imagination to realize that it is not the charges nor the particles but the field in the space between the charges and the particles that is essential for the description of physical phenomena. The field concept proved successful when it led to the formulation of Maxwell’s equations describing the structure of the electromagnetic field.
At first, the electromagnetic field theory developed by Maxwell seemed compatible with the mechanics of Newton. For example, Maxwell believed that electromagnetic waves, which include visible light, could be explained by classical mechanics—if we assume that the universe is suffused with some unseen, gossamer “light-bearing ether” that serves as the physical substance that undulates and oscillates to propagate the electromagnetic waves, comparable to the role water plays for ocean waves and air plays for sound waves.
By the end of the nineteenth century, however, fissures had begun to develop in the foundations of classical physics. One problem was that scientists, as hard as they tried, could not find any evidence of our motion through this supposed light-propagating ether. The study of radiation—how light and other electromagnetic waves emanate from physical bodies—exposed another problem: strange things were happening at the borderline where Newtonian theories, which described the mechanics of discrete particles, interacted with field theory, which described all electromagnetic phenomena.
Up until then, Einstein had published five little-noted papers. They had earned him neither a doctorate nor a teaching job, even at a high school. Had he given up theoretical physics at that point, the scientific community would not have noticed, and he might have moved up the ladder to become the head of the Swiss Patent Office, a job in which he would likely have been very good indeed.
There was no sign that he was about to unleash an annus mirabilis the like of which science had not seen since 1666, when Isaac Newton, holed up at his mother’s home in rural Woolsthorpe to escape the plague that was devastating Cambridge, developed calculus, an analysis of the light spectrum, and the laws of gravity.
But physics was poised to be upended again, and Einstein was poised to be the one to do it. He had the brashness needed to scrub away the layers of conventional wisdom that were obscuring the cracks in the foundation of physics, and his visual imagination allowed him to make conceptual leaps that eluded more traditional thinkers.
The breakthroughs that he wrought during a four-month frenzy from March to June 1905 were heralded in what would become one of the most famous personal letters in the history of science. Conrad Habicht, his fellow philosophical frolicker in the Olympia Academy, had just moved away from Bern, which, happily for historians, gave a reason for Einstein to write to him in late May.
Such a solemn air of silence has descended between us that I almost feel as if I am committing a sacrilege when I break it now with some inconsequential babble . . .
So, what are you up to, you frozen whale, you smoked, dried, canned piece of soul ...? Why have you still not sent me your dissertation? Don’t you know that I am one of the 1½ fellows who would read it with interest and pleasure, you wretched man? I promise you four papers in return. The first deals with radiation and the energy properties of light and is very revolutionary, as you will see if you send me your work first. The second paper is a determination of the true sizes of atoms ... The third proves that bodies on the order of magnitude 1/1000 mm, suspended in liquids, must already perform an observable random motion that is produced by thermal motion. Such movement of suspended bodies has actually been observed by physiologists who call it Brownian molecular motion. The fourth paper is only a rough draft at this point, and is an electrodynamics of moving bodies which employs a modification of the theory of space and time.
Light Quanta, March 1905
As Einstein noted to Habicht, it was the first of these 1905 papers, not the famous final one expounding a theory of relativity, that deserved the designation “revolutionary.” Indeed, it may contain the most revolutionary development in the history of physics. Its suggestion that light comes not just in waves but in tiny packets—quanta of light that were later dubbed “photons”—spirits us into strange scientific mists that are far murkier, indeed more spooky, than even the weirdest aspects of the theory of relativity.
Einstein recognized this in the slightly odd title he gave to the paper, which he submitted on March 17, 1905, to the Annalen der Physik: “On a Heuristic Point of View Concerning the Production and Transformation of Light.”8 Heuristic? It means a hypothesis that serves as a guide and gives direction in solving a problem but is not considered proven. From this first sentence he ever published about quantum theory until his last such sentence, which came in a paper exactly fifty years later, just before he died, Einstein regarded the concept of the quanta and all of its unsettling implications as heuristic at best: provisional and incomplete and not fully compatible with his own intimations of underlying reality.
At the heart of Einstein’s paper were questions that were bedeviling physics at the turn of the century, and in fact have done so from the time of the ancient Greeks until today: Is the universe made up of particles, such as atoms and electrons? Or is it an unbroken continuum, as a gravitational or electromagnetic field seems to be? And if both methods of describing things are valid at times, what happens when they intersect?
Since the 1860s, scientists had been exploring just such a point of intersection by analyzing what was called “blackbody radiation.” As anyone who has played with a kiln or a gas burner knows, the glow from a material such as iron changes color as it heats up. First it appears to radiate mainly red light; as it gets hotter, it glows more orange, and then white and then blue. To study this radiation, Gustav Kirchhoff and others devised a closed metal container with a tiny hole to let a little light escape. Then they drew a graph of the intensity of each wavelength when the device reached equilibrium at a certain temperature. No matter what the material or shape of the container’s walls, the results were the same; the shape of the graphs depended only on the temperature.
There was, alas, a problem. No one could fully account for the basis of the mathematical formula that would produce the hill-like shape of these graphs.
When Kirchhoff died, his professorship at the University of Berlin was given to Max Planck. Born in 1858 into an ancient German family of great scholars, theologians, and lawyers, Planck was many things that Einstein was not: with his pince-nez glasses and meticulous dress, he was very proudly German, somewhat shy, steely in his resolve, conservative by instinct, and formal in his manner. “It is difficult to imagine two men of more different attitudes,” their mutual friend Max Born later said. “Einstein a citizen of the whole world, little attached to the people around him, independent of the emotional background of the society in which he lived—Planck deeply rooted in the traditions of his family and nation, an ardent patriot, proud of the greatness of German history and consciously Prussian in his attitude to the state.”9
His conservatism made Planck skeptical about the atom, and of particle (rather than wave and continuous field) theories in general. As he wrote in 1882, “Despite the great success that the atomic theory has so far enjoyed, ultimately it will have to be abandoned in favor of the assumption of continuous matter.” In one of our planet’s little ironies, Planck and Einstein would share the fate of laying the groundwork for quantum mechanics, and then both would flinch when it became clear that it undermined the concepts of strict causality and certainty they both worshipped.10
In 1900, Planck came up with an equation, partly using what he called “a fortuitous guess,” that described the curve of radiation wavelengths at each temperature. In doing so he accepted that Boltzmann’s statistical methods, which he had resisted, were correct after all. But the equation had an odd feature: it required the use of a constant, which was an unexplained tiny quantity (approximately 6.62607 x 10–34 joule-seconds), that needed to be included for it to come out right. It was soon dubbed Planck’s constant, h, and is now known as one of the fundamental constants of nature.
At first Planck had no idea what, if any, physical meaning this mathematical constant had. But then he came up with a theory that, he thought, applied not to the nature of light itself but to the action that occurred when the light was absorbed or emitted by a piece of matter. He posited that the surface of anything that was radiating heat and light—such as the walls in a blackbody device—contained “vibrating molecules” or “harmonic oscillators,” like little vibrating springs.11 These harmonic oscillators could absorb or emit energy only in the form of discrete packets or bundles. These packets or bundles of energy came only in fixed amounts, determined by Planck’s constant, rather than being divisible or having a continuous range of values.
Planck considered his constant a mere calculational contrivance that explained the process of emitting or absorbing light but did not apply to the fundamental nature of light itself. Nevertheless, the declaration he made to the Berlin Physical Society in December 1900 was momentous: “We therefore regard—and this is the most essential point of the entire calculation—energy to be composed of a very definite number of equal finite packages.”12
Einstein quickly realized that quantum theory could undermine classical physics. “All of this was quite clear to me shortly after the appearance of Planck’s fundamental work,” he wrote later. “All of my attempts to adapt the theoretical foundation of physics to this knowledge failed completely. It was as if the ground had been pulled out from under us, with no firm foundation to be seen anywhere.”13
In addition to the problem of explaining what Planck’s constant was really all about, there was another curiosity about radiation that needed to be explained. It was called the photoelectric effect, and it occurs when light shining on a metal surface causes electrons to be knocked loose and emitted. In the letter he wrote to Mari right after he learned of her pregnancy in May 1901, Einstein enthused over a “beautiful piece” by Philipp Lenard that explored this topic.
Lenard’s experiments found something unexpected. When he increased the frequency of the light—moving from infrared heat and red light up in frequency to violet and ultraviolet—the emitted electrons sped out with much more energy. Then, he increased the intensity of the light by using a carbon arc light that could be made brighter by a factor of 1,000. The brighter, more intense light had a lot more energy, so it seemed logical that the electrons emitted would have more energy and speed away faster. But that did not occur. More intense light produced more electrons, but the energy of each remained the same. This was something that the wave theory of light did not explain.
Einstein had been pondering the work of Planck and Lenard for four years. In his final paper of 1904, “On the General Molecular Theory of Heat,” he discussed how the average energy of a system of molecules fluctuates. He then applied this to a volume filled with radiation, and found that experimental results were comparable. His concluding phrase was, “I believe that this agreement must not be ascribed to chance.”14 As he wrote to his friend Conrad Habicht just after finishing that 1904 paper, “I have now found in a most simple way the relation between the size of elementary quanta of matter and the wavelengths of radiation.” He was thus primed, so it seems, to form a theory that the radiation field was made up of quanta.15
In his 1905 light quanta paper, published a year later, he did just that. He took the mathematical quirk that Planck had discovered, interpreted it literally, related it to Lenard’s photoelectric results, and analyzed light as if it really was made up of pointlike particles—light quanta, he called them—rather than being a continuous wave.
Einstein began his paper by describing the great distinction between theories based on particles (such as the kinetic theory of gases) and theories that involve continuous functions (such as the electromagnetic fields of the wave theory of light). “There exists a profound formal difference between the theories that physicists have formed about gases and other ponderable bodies, and Maxwell’s theory of electromagnetic processes in so-called empty space,” he noted. “While we consider the state of a body to be completely determined by the positions and velocities of a very large, yet finite, number of atoms and electrons, we make use of continuous spatial functions to describe the electromagnetic state of a given volume.”16
Before he made his case for a particle theory of light, he emphasized that this would not make it necessary to scrap the wave theory, which would continue to be useful as well. “The wave theory of light, which operates with continuous spatial functions, has worked well in the representation of purely optical phenomena and will probably never be replaced by another theory.”
His way of accommodating both a wave theory and a particle theory was to suggest, in a “heuristic” way, that our observation of waves involve statistical averages of the positions of what could be countless particles. “It should be kept in mind,” he said, “that the optical observations refer to time averages rather than instantaneous values.”
Then came what may be the most revolutionary sentence that Einstein ever wrote. It suggests that light is made up of discrete particles or packets of energy: “According to the assumption to be considered here, when a light ray is propagated from a point, the energy is not continuously distributed over an increasing space but consists of a finite number of energy quanta which are localized at points in space and which can be produced and absorbed only as complete units.”
Einstein explored this hypothesis by determining whether a volume of blackbody radiation, which he was now assuming consisted of discrete quanta, might in fact behave like a volume of gas, which he knew consisted of discrete particles. First, he looked at the formulas that showed how the entropy of a gas changes when its volume changes. Then he compared this to how the entropy of blackbody radiation changes as its volume changes. He found that the entropy of the radiation “varies with volume according to the same law as the entropy of an ideal gas.”
He did a calculation using Boltzmann’s statistical formulas for entropy. The statistical mechanics that described a dilute gas of particles was mathematically the same as that for blackbody radiation. This led Einstein to declare that the radiation “behaves thermodynamically as if it consisted of mutually independent energy quanta.” It also provided a way to calculate the energy of a “particle” of light at a particular frequency, which turned out to be in accord with what Planck had found.17
Einstein went on to show how the existence of these light quanta could explain what he graciously called Lenard’s “pioneering work” on the photoelectric effect. If light came in discrete quanta, then the energy of each one was determined simply by the frequency of the light multiplied by Planck’s constant. If we assume, Einstein suggested, “that a light quantum transfers its entire energy to a single electron,” then it follows that light of a higher frequency would cause the electrons to emit with more energy. On the other hand, increasing the intensity of the light (but not the frequency) would simply mean that more electrons would be emitted, but the energy of each would be the same.
That was precisely what Lenard had found. With a trace of humility or tentativeness, along with a desire to show that his conclusions had been deduced theoretically rather than induced entirely from experimental data, Einstein declared of his paper’s premise that light consists of tiny quanta: “As far as I can see, our conception does not conflict with the properties of the photoelectric effect observed by Mr. Lenard.”
By blowing on Planck’s embers, Einstein had turned them into a flame that would consume classical physics. What precisely did Einstein produce that made his 1905 paper a discontinuous—one is tempted to say quantum—leap beyond the work of Planck?
In effect, as Einstein noted in a paper the following year, his role was that he figured out the physical significance of what Planck had discovered.18 For Planck, a reluctant revolutionary, the quantum was a mathematical contrivance that explained how energy was emitted and absorbed when it interacted with matter. But he did not see that it related to a physical reality that was inherent in the nature of light and the electromagnetic field itself. “One can interpret Planck’s 1900 paper to mean only that the quantum hypothesis is used as a mathematical convenience introduced in order to calculate a statistical distribution, not as a new physical assumption,” write science historians Gerald Holton and Steven Brush.19
Einstein, on the other hand, considered the light quantum to be a feature of reality: a perplexing, pesky, mysterious, and sometimes maddening quirk in the cosmos. For him, these quanta of energy (which in 1926 were named photons)20 existed even when light was moving through a vacuum. “We wish to show that Mr. Planck’s determination of the elementary quanta is to some extent independent of his theory of blackbody radiation,” he wrote. In other words, Einstein argued that the particulate nature of light was a property of the light itself and not just some description of how the light interacts with matter.21
Even after Einstein published his paper, Planck did not accept his leap. Two years later, Planck warned the young patent clerk that he had gone too far, and that quanta described a process that occurred during emission or absorption, rather than some real property of radiation in a vacuum. “I do not seek the meaning of the ‘quantum of action’ (light quantum) in the vacuum but at the site of absorption and emission,” he advised.22
Planck’s resistance to believing that the light quanta had a physical reality persisted. Eight years after Einstein’s paper was published, Planck proposed him for a coveted seat in the Prussian Academy of Sciences. The letter he and other supporters wrote was filled with praise, but Planck added: “That he might sometimes have overshot the target in his speculations, as for example in his light quantum hypothesis, should not be counted against him too much.”23
Just before he died, Planck reflected on the fact that he had long recoiled from the implications of his discovery. “My futile attempts to fit the elementary quantum of action somehow into classical theory continued for a number of years and cost me a great deal of effort,” he wrote. “Many of my colleagues saw in this something bordering on a tragedy.”
Ironically, similar words would later be used to describe Einstein. He became increasingly “aloof and skeptical” about the quantum discoveries he pioneered, Born said of Einstein. “Many of us regard this as a tragedy.”24
Einstein’s theory produced a law of the photoelectric effect that was experimentally testable: the energy of emitted electrons would depend on the frequency of the light according to a simple mathematical formula involving Planck’s constant. The formula was subsequently shown to be correct. The physicist who did the crucial experiment was Robert Millikan, who would later head the California Institute of Technology and try to recruit Einstein.
Yet even after he verified Einstein’s photoelectric formulas, Millikan still rejected the theory. “Despite the apparently complete success of the Einstein equation,” he declared, “the physical theory on which it was designed to be the symbolic expression is found so untenable that Einstein himself, I believe, no longer holds to it.”25
Millikan was wrong to say that Einstein’s formulation of the photo-electric effect had been abandoned. In fact, it was specifically for discovering the law of the photoelectric effect that Einstein would win his only Nobel Prize. With the advent of quantum mechanics in the 1920s, the reality of the photon became a fundamental part of physics.
However, on the larger point Millikan was right. Einstein would increasingly find the eerie implications of the quantum—and of the wave-particle duality of light—to be deeply unsettling. In a letter he wrote near the end of his life to his dear friend Michele Besso, after quantum mechanics had been accepted by almost every living physicist, Einstein would lament, “All these fifty years of pondering have not brought me any closer to answering the question, What are light quanta?”26
Doctoral Dissertation on the Size of Molecules, April 1905
Einstein had written a paper that would revolutionize science, but he had not yet been able to earn a doctorate. So he tried one more time to get a dissertation accepted.
He realized that he needed a safe topic, not a radical one like quanta or relativity, so he chose the second paper he was working on, titled “A New Determination of Molecular Dimensions,” which he completed on April 30 and submitted to the University of Zurich in July.27
Perhaps out of caution and deference to the conservative approach of his adviser, Alfred Kleiner, he generally avoided the innovative statistical physics featured in his previous papers (and in his Brownian motion paper completed eleven days later) and relied instead mainly on classical hydrodynamics.28 Yet he was still able to explore how the behavior of countless tiny particles (atoms, molecules) are reflected in observable phenomena, and conversely how observable phenomena can tell us about the nature of those tiny unseen particles.
Almost a century earlier, the Italian scientist Amedeo Avogadro (1776–1856) had developed the hypothesis—correct, as it turned out—that equal volumes of any gas, when measured at the same temperature and pressure, will have the same number of molecules. That led to a difficult quest: figuring out just how many this was.
The volume usually chosen is that occupied by a mole of the gas (its molecular weight in grams), which is 22.4 liters at standard temperature and pressure. The number of molecules under such conditions later became known as Avogadro’s number. Determining it precisely was, and still is, rather difficult. A current estimate is approximately 6.02214 x 1023. (This is a big number: that many unpopped popcorn kernels when spread across the United States would cover the country nine miles deep.)29
Most previous measurements of molecules had been done by studying gases. But as Einstein noted in the first sentence of his paper, “The physical phenomena observed in liquids have thus far not served for the determination of molecular sizes.” In this dissertation (after a few math and data corrections were later made), Einstein was the first person able to get a respectable result using liquids.
His method involved making use of data about viscosity, which is how much resistance a liquid offers to an object that tries to move through it. Tar and molasses, for example, are highly viscous. If you dissolve sugar in water, the solution’s viscosity increases as it gets more syrupy. Einstein envisioned the sugar molecules gradually diffusing their way through the smaller water molecules. He was able to come up with two equations, each containing the two unknown variables—the size of the sugar molecules and the number of them in the water—that he was trying to determine. He could then solve for these unknown variables. Doing so, he got a result for Avogadro’s number that was 2.1 x 1023.
That, unfortunately, was not very close. When he submitted his paper to the Annalen der Physik in August, right after it had been accepted by Zurich University, the editor Paul Drude (who was blissfully unaware of Einstein’s earlier desire to ridicule him) held up its publication because he knew of some better data on the properties of sugar solutions. Using this new data, Einstein came up with a result that was closer to correct: 4.15 x 1023.
A few years later, a French student tested the approach experimentally and discovered something amiss. So Einstein asked an assistant in Zurich to look at it all over again. He found a minor error, which when corrected produced a result of 6.56 x 1023, which ended up being quite respectable.30
Einstein later said, perhaps half-jokingly, that when he submitted his thesis, Professor Kleiner rejected it for being too short, so he added one more sentence and it was promptly accepted. There is no documentary evidence for this.31 Either way, his thesis actually became one of his most cited and practically useful papers, with applications in such diverse fields as cement mixing, dairy production, and aerosol products. And even though it did not help him get an academic job, it did make it possible for him to become known, finally, as Dr. Einstein.
Brownian Motion, May 1905
Eleven days after finishing his dissertation, Einstein produced another paper exploring evidence of things unseen. As he had been doing since 1901, he relied on statistical analysis of the random actions of invisible particles to show how they were reflected in the visible world.
In doing so, Einstein explained a phenomenon, known as Brownian motion, that had been puzzling scientists for almost eighty years: why small particles suspended in a liquid such as water are observed to jiggle around. And as a byproduct, he pretty much settled once and for all that atoms and molecules actually existed as physical objects.
Brownian motion was named after the Scottish botanist Robert Brown, who in 1828 had published detailed observations about how minuscule pollen particles suspended in water can be seen to wiggle and wander when examined under a strong microscope. The study was replicated with other particles, including filings from the Sphinx, and a variety of explanations was offered. Perhaps it had something to do with tiny water currents or the effect of light. But none of these theories proved plausible.
With the rise in the 1870s of the kinetic theory, which used the random motions of molecules to explain things like the behavior of gases, some tried to use it to explain Brownian motion. But because the suspended particles were 10,000 times larger than a water molecule, it seemed that a molecule would not have the power to budge the particle any more than a baseball could budge an object that was a half-mile in diameter.32
Einstein showed that even though one collision could not budge a particle, the effect of millions of random collisions per second could explain the jig observed by Brown. “In this paper,” he announced in his first sentence, “it will be shown that, according to the molecular-kinetic theory of heat, bodies of a microscopically visible size suspended in liquids must, as a result of thermal molecular motions, perform motions of such magnitudes that they can be easily observed with a microscope.”33
He went on to say something that seems, on the surface, somewhat puzzling: his paper was not an attempt to explain the observations of Brownian motion. Indeed, he acted as if he wasn’t even sure that the motions he deduced from his theory were the same as those observed by Brown: “It is possible that the motions to be discussed here are identical with so-called Brownian molecular motion; however, the data available to me on the latter are so imprecise that I could not form a judgment on the question.” Later, he distanced his work even further from intending to be an explanation of Brownian motion: “I discovered that, according to atomistic theory, there would have to be a movement of suspended microscopic particles open to observations, without knowing that observations concerning the Brownian motion were already long familiar.”34
At first glance his demurral that he was dealing with Brownian motion seems odd, even disingenuous. After all, he had written Conrad Habicht a few months earlier, “Such movement of suspended bodies has actually been observed by physiologists who call it Brownian molecular motion.” Yet Einstein’s point was both true and significant: his paper did not start with the observed facts of Brownian motion and build toward an explanation of it. Rather, it was a continuation of his earlier statistical analysis of how the actions of molecules could be manifest in the visible world.
In other words, Einstein wanted to assert that he had produced a theory that was deduced from grand principles and postulates, not a theory that was constructed by examining physical data (just as he had made plain that his light quanta paper had not started with the photo-electric effect data gathered by Philipp Lenard). It was a distinction he would also make, as we shall soon see, when insisting that his theory of relativity did not derive merely from trying to explain experimental results about the speed of light and the ether.
Einstein realized that a bump from a single water molecule would not cause a suspended pollen particle to move enough to be visible. However, at any given moment, the particle was being hit from all sides by thousands of molecules. There would be some moments when a lot more bumps happened to hit one particular side of the particle. Then, in another moment, a different side might get the heaviest barrage.
The result would be random little lurches that would result in what is known as a random walk. The best way for us to envision this is to imagine a drunk who starts at a lamppost and lurches one step in a random direction every second. After two such lurches he may have gone back and forth to return to the lamp. Or he may be two steps away in the same direction. Or he may be one step west and one step northeast. A little mathematical plotting and charting reveals an interesting thing about such a random walk: statistically, the drunk’s distance from the lamp will be proportional to the square root of the number of seconds that have elapsed.35
Einstein realized that it was neither possible nor necessary to measure each zig and zag of Brownian motion, nor to measure the particle’s velocity at any moment. But it was rather easy to measure the total distances of randomly lurching particles as these distances grew over time.
Einstein wanted concrete predictions that could be tested, so he used both his theoretical knowledge and experimental data about viscosity and diffusion rates to come up with precise predictions showing the distance a particle should move depending on its size and the temperature of the liquid. For example, he predicted, in the case of a particle with a diameter of one thousandth of a millimeter in water at 17 degrees centigrade, “the mean displacement in one minute would be about 6 microns.”
Here was something that could actually be tested, and with great consequence. “If the motion discussed here can be observed,” he wrote, “then classical thermodynamics can no longer be viewed as strictly valid.” Better at theorizing than at conducting experiments, Einstein ended his paper with a charming exhortation: “Let us hope that a researcher will soon succeed in solving the problem presented here, which is so important for the theory of heat.”
Within months, a German experimenter named Henry Seidentopf, using a powerful microscope, confirmed Einstein’s predictions. For all practical purposes, the physical reality of atoms and molecules was now conclusively proven. “At the time atoms and molecules were still far from being regarded as real,” the theoretical physicist Max Born later recalled. “I think that these investigations of Einstein have done more than any other work to convince physicists of the reality of atoms and molecules.”36
As lagniappe, Einstein’s paper also provided yet another way to determine Avogadro’s number. “It bristles with new ideas,” Abraham Pais said of the paper. “The final conclusion, that Avogadro’s number can essentially be determined from observations with an ordinary microscope, never fails to cause a moment of astonishment even if one has read the paper before and therefore knows the punch line.”
A strength of Einstein’s mind was that it could juggle a variety of ideas simultaneously. Even as he was pondering dancing particles in a liquid, he had been wrestling with a different theory that involved moving bodies and the speed of light. A day or so after sending in his Brownian motion paper, he was talking to his friend Michele Besso when a new brainstorm struck. It would produce, as he wrote Habicht in his famous letter of that month, “a modification of the theory of space and time.”
SPECIAL RELATIVITY 1905
The Bern Clock Tower
Relativity is a simple concept. It asserts that the fundamental laws of physics are the same whatever your state of motion.
For the special case of observers moving at a constant velocity, this concept is pretty easy to accept. Imagine a man in an armchair at home and a woman in an airplane gliding very smoothly above. Each can pour a cup of coffee, bounce a ball, shine a flashlight, or heat a muffin in a microwave and have the same laws of physics apply.
In fact, there is no way to determine which of them is “in motion” and which is “at rest.” The man in the armchair could consider himself at rest and the plane in motion. And the woman in the plane could consider herself at rest and the earth as gliding past. There is no experiment that can prove who is right.
Indeed, there is no absolute right. All that can be said is that each is moving relative to the other. And of course, both are moving very rapidly relative to other planets, stars, and galaxies.*
The special theory of relativity that Einstein developed in 1905 applies only to this special case (hence the name): a situation in which the observers are moving at a constant velocity relative to one another—uniformly in a straight line at a steady speed—referred to as an “inertial reference system.”1
It’s harder to make the more general case that a person who is accelerating or turning or rotating or slamming on the brakes or moving in an arbitrary manner is not in some form of absolute motion, because coffee sloshes and balls roll away in a different manner than for people on a smoothly gliding train, plane, or planet. It would take Einstein a decade more, as we shall see, to come up with what he called a general theory of relativity, which incorporated accelerated motion into a theory of gravity and attempted to apply the concept of relativity to it.2
The story of relativity best begins in 1632, when Galileo articulated the principle that the laws of motion and mechanics (the laws of electromagnetism had not yet been discovered) were the same in all constant-velocity reference frames. In his Dialogue Concerning the Two Chief World Systems, Galileo wanted to defend Copernicus’s idea that the earth does not rest motionless at the center of the universe with everything else revolving around it. Skeptics contended that if the earth was moving, as Copernicus said, we’d feel it. Galileo refuted this with a brilliantly clear thought experiment about being inside the cabin of a smoothly sailing ship:
Shut yourself up with some friend in the main cabin below decks on some large ship, and have with you there some flies, butterflies, and other small flying animals. Have a large bowl of water with some fish in it; hang up a bottle that empties drop by drop into a wide vessel beneath it. With the ship standing still, observe carefully how the little animals fly with equal speed to all sides of the cabin. The fish swim indifferently in all directions; the drops fall into the vessel beneath; and, in throwing something to your friend, you need throw it no more strongly in one direction than another, the distances being equal; jumping with your feet together, you pass equal spaces in every direction. When you have observed all these things carefully, have the ship proceed with any speed you like, so long as the motion is uniform and not fluctuating this way and that. You will discover not the least change in all the effects named, nor could you tell from any of them whether the ship was moving or standing still.
There is no better description of relativity, or at least of how that principle applies to systems that are moving at a constant velocity relative to each other.
Inside Galileo’s ship, it is easy to have a conversation, because the air that carries the sound waves is moving smoothly along with the people in the chamber. Likewise, if one of Galileo’s passengers dropped a pebble into a bowl of water, the ripples would emanate the same way they would if the bowl were resting on shore; that’s because the water propagating the ripples is moving smoothly along with the bowl and everything else in the chamber.
Sound waves and water waves are easily explained by classical mechanics. They are simply a traveling disturbance in some medium. That is why sound cannot travel through a vacuum. But it can travel through such things as air or water or metal. For example, sound waves move through room temperature air, as a vibrating disturbance that compresses and rarefies the air, at about 770 miles per hour.
Deep inside Galileo’s ship, sound and water waves behave as they do on land, because the air in the chamber and the water in the bowls are moving at the same velocity as the passengers. But now imagine that you go up on deck and look at the waves out in the ocean, or that you measure the speed of the sound waves from the horn of another boat. The speed at which these waves come toward you depends on your motion relative to the medium (the water or air) propagating them.
In other words, the speed at which an ocean wave reaches you will depend on how fast you are moving through the water toward or away from the source of the wave. The speed of a sound wave relative to you will likewise depend on your motion relative to the air that’s propagating the sound wave.
Those relative speeds add up. Imagine that you are standing in the ocean as the waves come toward you at 10 miles per hour. If you jump on a Jet Ski and head directly into the waves at 40 miles per hour, you will see them moving toward you and zipping past you at a speed (relative to you) of 50 miles per hour. Likewise, imagine that sound waves are coming at you from a distant boat horn, rippling through still air at 770 miles per hour toward the shore. If you jump on your Jet Ski and head toward the horn at 40 miles per hour, the sound waves will be moving toward you and zipping past you at a speed (relative to you) of 810 miles per hour.
All of this led to a question that Einstein had been pondering since age 16, when he imagined riding alongside a light beam: Does light behave the same way?
Newton had conceived of light as primarily a stream of emitted particles. But by Einstein’s day, most scientists accepted the rival theory, propounded by Newton’s contemporary Christiaan Huygens, that light should be considered a wave.
A wide variety of experiments had confirmed the wave theory by the late nineteenth century. For example, Thomas Young did a famous experiment, now replicated by high school students, showing how light passing through two slits produces an interference pattern that resembles that of water waves going through two slits. In each case, the crests and troughs of the waves emanating from each slit reinforce each other in some places and cancel each other out in some places.
James Clerk Maxwell helped to enshrine this wave theory when he successfully conjectured a connection between light, electricity, and magnetism. He came up with equations that described the behavior of electric and magnetic fields, and when they were combined they predicted electromagnetic waves. Maxwell found that these electromagnetic waves had to travel at a certain speed: approximately 186,000 miles per second.* That was the speed that scientists had already measured for light, and it was obviously not a mere coincidence.4
It became clear that light was the visible manifestation of a whole spectrum of electromagnetic waves. This includes what we now call AM radio signals (with a wavelength of 300 yards), FM radio signals (3 yards), and microwaves (3 inches). As the wavelengths get shorter (and the frequency of the wave cycles thus increases), they produce the spectrum of visible light, ranging from red (25 millionths of an inch) to violet (14 millionths of an inch). Even shorter wavelengths produce ultraviolet rays, X-rays, and gamma rays. When we speak of “light” and the “speed of light,” we mean all electromagnetic waves, not just the ones that are visible to our eyes.
That raised some big questions: What was the medium that was propagating these waves? And their speed of 186,000 miles per second was a speed relative to what?
The answer, it seemed, was that light waves are a disturbance of an unseen medium, which was called the ether, and that their speed is relative to this ether. In other words, the ether was for light waves something akin to what air was for sound waves. “It appeared beyond question that light must be interpreted as a vibratory process in an elastic, inert medium filling up universal space,” Einstein later noted.5
This ether, unfortunately, needed to have many puzzling properties. Because light from distant stars is able to reach the earth, the ether had to pervade the entire known universe. It had to be so gossamer and, shall we say, so ethereal that it had no effect on planets and feathers floating through it. Yet it had to be stiff enough to allow a wave to vibrate through it at an enormous speed.
All of this led to the great ether hunt of the late nineteenth century. If light was indeed a wave rippling through the ether, then you should see the waves going by you at a faster speed if you were moving through the ether toward the light source. Scientists devised all sorts of ingenious devices and experiments to detect such differences.
They used a variety of suppositions of how the ether might behave. They looked for it as if it were motionless and the earth passed freely through it. They looked for it as if the earth dragged parts of it along in a blob, the way it does its own atmosphere. They even considered the unlikely possibility that the earth was the only thing at rest with respect to the ether, and that everything else in the cosmos was spinning around, including the other planets, the sun, the stars, and presumably poor Copernicus in his grave.
One experiment, which Einstein later called “of fundamental importance in the special theory of relativity,”6 was by the French physicist Hippolyte Fizeau, who sought to measure the speed of light in a moving medium. He split a light beam with a half-silvered angled mirror that sent one part of the beam through water in the direction of the water’s flow and the other part against the flow. The two parts of the beam were then reunited. If one route took longer, then the crests and troughs of its waves would be out of sync with the waves of the other beam. The experimenters could tell if this happened by looking at the interference pattern that resulted when the waves were rejoined.
A different and far more famous experiment was done in Cleveland in 1887 by Albert Michelson and Edward Morley. They built a contraption that similarly split a light beam and sent one part back and forth to a mirror at the end of an arm facing in the direction of the earth’s movement and the other part back and forth along an arm at a 90-degree angle to it. Once again, the two parts of the beam were then rejoined and the interference pattern analyzed to see if the path that was going up against the supposed ether wind would take longer.
No matter who looked, or how they looked, or what suppositions they made about the behavior of the ether, no one was able to detect the elusive substance. No matter which way anything was moving, the speed of light was observed to be exactly the same.
So scientists, somewhat awkwardly, turned their attention to coming up with explanations about why the ether existed but was undetectable in any experiment. Most notably, in the early 1890s Hendrik Lorentz—the cosmopolitan and congenial Dutch father figure of theoretical physics—and, independently, the Irish physicist George Fitzgerald came up with the hypothesis that solid objects contracted slightly when they moved through the ether. The Lorentz-Fitzgerald contraction would shorten everything, including the measuring arms used by Michelson and Morley, and it would do so by just the exact amount to make the effect of the ether on light undetectable.
Einstein felt that the situation “was very depressing.” Scientists found themselves unable to explain electromagnetism using the Newtonian “mechanical view of nature,” he said, and this “led to a fundamental dualism which in the long run was insupportable.”7
Einstein’s Road to Relativity
“A new idea comes suddenly and in a rather intuitive way,” Einstein once said. “But,” he hastened to add, “intuition is nothing but the outcome of earlier intellectual experience.”8
Einstein’s discovery of special relativity involved an intuition based on a decade of intellectual as well as personal experiences.9 The most important and obvious, I think, was his deep understanding and knowledge of theoretical physics. He was also helped by his ability to visualize thought experiments, which had been encouraged by his education in Aarau. Also, there was his grounding in philosophy: from Hume and Mach he had developed a skepticism about things that could not be observed. And this skepticism was enhanced by his innate rebellious tendency to question authority.
Also part of the mix—and probably reinforcing his ability to both visualize physical situations and to cut to the heart of concepts—was the technological backdrop of his life: helping his uncle Jakob to refine the moving coils and magnets in a generator; working in a patent office that was being flooded with applications for new methods of coordinating clocks; having a boss who encouraged him to apply his skepticism; living near the clock tower and train station and just above the telegraph office in Bern just as Europe was using electrical signals to synchronize clocks within time zones; and having as a sounding board his engineer friend Michele Besso, who worked with him at the patent office, examining electromechanical devices.10
The ranking of these influences is, of course, a subjective judgment. After all, even Einstein himself could not be sure how the process unfolded. “It is not easy to talk about how I arrived at the theory of relativity,” he said. “There were so many hidden complexities to motivate my thought.”11
One thing we can note with some confidence is Einstein’s main starting point. He repeatedly said that his path toward the theory of relativity began with his thought experiment at age 16 about what it would be like to ride at the speed of light alongside a light beam. This produced a “paradox,” he said, and it troubled him for the next ten years:
If I pursue a beam of light with the velocity
(velocity of light in a vacuum), I should observe such a beam of light as an electromagnetic field at rest though spatially oscillating. There seems to be no such thing, however, neither on the basis of experience nor according to Maxwell’s equations. From the very beginning it appeared to me intuitively clear that, judged from the standpoint of such an observer, everything would have to happen according to the same laws as for an observer who, relative to the earth, was at rest. For how should the first observer know or be able to determine that he is in a state of fast uniform motion? One sees in this paradox the germ of the special relativity theory is already contained.
This thought experiment did not necessarily undermine the ether theory of light waves. An ether theorist could imagine a frozen light beam. But it violated Einstein’s intuition that the laws of optics should obey the principle of relativity. In other words, Maxwell’s equations, which specify the speed of light, should be the same for all observers in constant-velocity motion. The emphasis that Einstein placed on this memory indicates that the idea of a frozen light beam—or frozen electromagnetic waves—seemed instinctively wrong to him.13
In addition, the thought experiment suggests that he sensed a conflict between Newton’s laws of mechanics and the constancy of the speed of light in Maxwell’s equations. All of this instilled in him “a state of psychic tension” that he found deeply unnerving. “At the very beginning, when the special theory of relativity began to germinate in me, I was visited by all sorts of nervous conflicts,” he later recalled. “When young, I used to go away for weeks in a state of confusion.”14
There was also a more specific “asymmetry” that began to bother him. When a magnet moves relative to a wire loop, an electric current is produced. As Einstein knew from his experience with his family’s generators, the amount of this electric current is exactly the same whether the magnet is moving while the coil seems to be sitting still, or the coil is moving while the magnet seems to be sitting still. He also had studied an 1894 book by August Föppl, Introduction to Maxwell’s Theory of Electricity. It had a section specifically on “The Electrodynamics of Moving Conductors” that questioned whether, when induction occurs, there should be any distinction between whether the magnet or the conducting coil is said to be in motion.15
“But according to the Maxwell-Lorentz theory,” Einstein recalled, “the theoretical interpretation of the phenomenon is very different for the two cases.” In the first case, Faraday’s law of induction said that the motion of the magnet through the ether created an electric field. In the second case, Lorentz’s force law said a current was created by the motion of the conducting coil through the magnetic field. “The idea that these two cases should essentially be different was unbearable to me,” Einstein said.16
Einstein had been wrestling for years with the concept of the ether, which theoretically determined the definition of “at rest” in these electrical induction theories. As a student at the Zurich Polytechnic in 1899, he had written to Mileva Mari that “the introduction of the term ‘ether’ into theories of electricity has led to the conception of a medium whose motion can be described without, I believe, being able to ascribe physical meaning to it.”17 Yet that very month he was on vacation in Aarau working with a teacher at his old school on ways to detect the ether. “I had a good idea for investigating the way in which a body’s relative motion with respect to the ether affects the velocity of the propagation of light,” he told Mari.
Professor Weber told Einstein that his approach was impractical. Probably at Weber’s suggestion, Einstein then read a paper by Wilhelm Wien that described the null results of thirteen ether-detection experiments, including those by Michelson and Morley and by Fizeau.18 He also learned about the Michelson-Morley experiment by reading, sometime before 1905, Lorentz’s 1895 book, Attempt at a Theory of Electrical and Optical Phenomena in Moving Bodies. In this book, Lorentz goes through various failed attempts to detect the ether as a prelude to developing his theory of contractions.19
“Induction and Deduction in Physics”
So what effect did the Michelson-Morley results—which showed no evidence of the ether and no difference in the observed speed of light no matter in what direction the observer was moving—have on Einstein as he was incubating his ideas on relativity? To hear him tell it, almost none at all. In fact, at times he would even recollect (incorrectly) that he had not even known of the experiment before 1905. Einstein’s inconsistent statements over the next fifty years about the influence of Michelson-Morley are useful in that they remind us of the caution needed when writing history based on dimming recollections.20
Einstein’s trail of contradictory statements begins with an address he gave in Kyoto, Japan, in 1922, when he noted that Michelson’s failure to detect an ether was “the first path that led me to what we call the principle of special relativity.” In a toast at a 1931 dinner in Pasadena honoring Michelson, Einstein was gracious to the eminent experimenter, yet subtly circumspect: “You uncovered an insidious defect in the ether theory of light, as it then existed, and stimulated the ideas of Lorentz and Fitzgerald, out of which the Special Theory of Relativity developed.”21
Einstein described his thought process in a series of talks with the Gestalt psychology pioneer Max Wertheimer, who later called the Michelson-Morley results “crucial” to Einstein’s thinking. But as Arthur I. Miller has shown, this assertion was probably motivated by Wertheimer’s goal of using Einstein’s tale as a way to illustrate the tenets of Gestalt psychology.22
Einstein further confused the issue in the last few years of his life by giving a series of statements on the subject to a physicist named Robert Shankland. At first he said he had read of Michelson-Morley only after 1905, then he said he had read about it in Lorentz’s book before 1905, and finally he added, “I guess I just took it for granted that it was true.”23
That final point is the most significant one because Einstein made it often. He simply took for granted, by the time he started working seriously on relativity, that there was no need to review all the ether-drift experiments because, based on his starting assumptions, all attempts to detect the ether were doomed to failure.24 For him, the significance of these experimental results was to reinforce what he already believed: that Galileo’s relativity principle applied to light waves.25
This may account for the scant attention he gave to the experiments in his 1905 paper. He never mentioned the Michelson-Morley experiment by name, even where it would have been relevant, nor the Fizeau experiment using moving water. Instead, right after discussing the relativity of the magnet-and-coil movements, he merely flicked in a phrase about “the unsuccessful attempts to detect a motion of the earth relative to the light medium.”
Some scientific theories depend primarily on induction: analyzing a lot of experimental findings and then finding theories that explain the empirical patterns. Others depend more on deduction: starting with elegant principles and postulates that are embraced as holy and then deducing the consequences from them. All scientists blend both approaches to differing degrees. Einstein had a good feel for experimental findings, and he used this knowledge to find certain fixed points upon which he could construct a theory.26 But his emphasis was primarily on the deductive approach.27
Remember how in his Brownian motion paper he so oddly, yet accurately, downplayed the role that experimental findings played in what was essentially a theoretical deduction? There was a similar situation with his relativity theory. What he implied about Brownian motion he said explicitly about relativity and Michelson-Morley: “I was pretty much convinced of the validity of the principle before I knew of this experiment and its results.”
Indeed, all three of his epochal papers in 1905 begin by asserting his intention to pursue a deductive approach. He opens each one by pointing out some oddity caused by jostling theories, rather than some unexplained set of experimental data. He then postulates grand principles while minimizing the role played by data, be it on Brownian motion or blackbody radiation or the speed of light.28
In a 1919 essay called “Induction and Deduction in Physics,” he described his preference for the latter approach:
The simplest picture one can form about the creation of an empirical science is along the lines of an inductive method. Individual facts are selected and grouped together so that the laws that connect them become apparent ... However, the big advances in scientific knowledge originated in this way only to a small degree . . . The truly great advances in our understanding of nature originated in a way almost diametrically opposed to induction. The intuitive grasp of the essentials of a large complex of facts leads the scientist to the postulation of a hypothetical basic law or laws. From these laws, he derives his conclusions.
His appreciation for this approach would grow. “The deeper we penetrate and the more extensive our theories become,” he would declare near the end of his life, “the less empirical knowledge is needed to determine those theories.”30
By the beginning of 1905, Einstein had begun to emphasize deduction rather than induction in his attempt to explain electrodynamics. “By and by, I despaired of the possibility of discovering the true laws by means of constructive efforts based on experimentally known facts,” he later said. “The longer and the more despairingly I tried, the more I came to the conviction that only the discovery of a universal formal principle could lead us to assured results.”31
The Two Postulates
Now that Einstein had decided to pursue his theory from the top down, by deriving it from grand postulates, he had a choice to make: What postulates—what basic assumptions of general principle—would he start with?32
His first postulate was the principle of relativity, which asserted that all of the fundamental laws of physics, even Maxwell’s equations governing electromagnetic waves, are the same for all observers moving at constant velocity relative to each other. Put more precisely, they are the same for all inertial reference systems, the same for someone at rest relative to the earth as for someone traveling at a uniform velocity on a train or spaceship. He had nurtured his faith in this postulate beginning with his thought experiment about riding alongside a light beam: “From the very beginning it appeared to me intuitively clear that, judged from the standpoint of such an observer, everything would have to happen according to the same laws as for an observer who, relative to the earth, was at rest.”
For a companion postulate, involving the velocity of light, Einstein had at least two options:
1. He could go with an emission theory, in which light would shoot from its source like particles from a gun. There would be no need for an ether. The light particles could zoom through emptiness. Their speed would be relative to the source. If this source was racing toward you, its emissions would come at you faster than if it was racing away. (Imagine a pitcher who can throw a ball at 100 miles per hour. If he throws it at you from a car racing toward you it will come at you faster than if he throws it from a car racing away.) In other words, starlight would be emitted from a star at 186,000 miles per second; but if that star was heading toward earth at 10,000 miles per second, the speed of its light would be 196,000 miles per second relative to an observer on earth.
2. An alternative was to postulate that the speed of light was a constant 186,000 miles per second irrespective of the motion of the source that emitted it, which was more consistent with a wave theory. By analogy with sound waves, a fire truck siren does not throw its sound at you faster when it’s rushing toward you than it does when it’s standing still. In either case, the sound travels through the air at 770 miles per hour.
For a while, Einstein explored the emission theory route. This approach was particularly appealing if you conceived of light as behaving like a stream of quanta. And as noted in the previous chapter, that concept of light quanta was precisely what Einstein had propounded in March 1905, just when he was wrestling with his relativity theory.33
But there were problems with this approach. It seemed to entail abandoning Maxwell’s equations and the wave theory. If the velocity of a light wave depended on the velocity of the source that emitted it, then the light wave must somehow encode within it this information. But experiments and Maxwell’s equations indicated that was not the case.34
Einstein tried to find ways to modify Maxwell’s equations so that they would fit an emission theory, but the quest became frustrating. “This theory requires that everywhere and in each fixed direction light waves of a different velocity of propagation should be possible,” he later recalled. “It may be impossible to set up a reasonable electromagnetic theory that accomplishes such a feat.”35
In addition, scientists had not been able to find any evidence that the velocity of light depended on that of its source. Light coming from any star seemed to arrive at the same speed.36
The more Einstein thought about an emission theory, the more problems he encountered. As he explained to his friend Paul Ehrenfest, it was hard to figure out what would happen when light from a “moving” source was refracted or reflected by a screen at rest. Also, in an emission theory, light from an accelerating source might back up on itself.
So Einstein rejected the emission theory in favor of postulating that the speed of a light beam was constant no matter how fast its source was moving. “I came to the conviction that all light should be defined by frequency and intensity alone, completely independently of whether it comes from a moving or from a stationary light source,” he told Ehrenfest.37
Now Einstein had two postulates: “the principle of relativity” and this new one, which he called “the light postulate.” He defined it carefully: “Light always propagates in empty space with a definite velocity V that is independent of the state of motion of the emitting body.”38For example, when you measure the velocity of light coming from the headlight of a train, it will always be a constant 186,000 miles per second, even if the train is rushing toward you or backing away from you.
Unfortunately, this light postulate seemed to be incompatible with the principle of relativity. Why? Einstein later used the following thought experiment to explain his apparent dilemma.
Imagine that “a ray of light is sent along the embankment” of a railway track, he said. A man standing on the embankment would measure its speed as 186,000 miles per second as it zipped past him. But now imagine a woman who is riding in a very fast train carriage that is racing away from the light source at 2,000 miles per second. We would assume that she would observe the beam to be zipping past her at only 184,000 miles per second. “The velocity of propagation of a ray of light relative to the carriage thus comes out smaller,” Einstein wrote.
“But this result comes into conflict with the principle of relativity,” he added. “For, like every other general law of nature, the law of the transmission of light must, according to the principle of relativity, be the same when the railway carriage is the reference body as it is when the embankment is the reference body.” In other words, Maxwell’s equations, which determine the speed at which light propagates, should operate the same way in the moving carriage as on the embankment. There should be no experiment you can do, including measuring the speed of light, to distinguish which inertial frame of reference is “at rest” and which is moving at a constant velocity.39
This was an odd result. A woman racing along the tracks toward or away from the source of a light beam should see that beam zip by her with the exact same speed as an observer standing on the embankment would see that same beam zip by him. The woman’s speed relative to the train would vary, depending on whether she was running toward it or away from it. But her speed relative to the light beam coming from the train’s headlight would be invariant. All of this made the two postulates, Einstein thought, “seemingly incompatible.” As he later explained in a lecture on how he came to his theory, “the constancy of the velocity of light is not consistent with the law of the addition of velocities. The result was that I had to spend almost one year in fruitless thoughts.”40
By combining the light postulate with the principle of relativity, it meant that an observer would measure the speed of light as the same whether the source was moving toward or away from him, or whether he was moving toward or away from the source, or both, or neither. The speed of light would be the same whatever the motion of the observer and the source.
That is where matters stood in early May 1905. Einstein had embraced the relativity principle and elevated it to a postulate. Then, with a bit more trepidation, he had adopted as a postulate that the velocity of light was independent of the motion of its source. And he puzzled over the apparent dilemma that an observer racing up a track toward a light would see the beam coming at him with the same velocity as when he was racing away from the light—and with the same velocity as someone standing still on the embankment would observe the same beam.
“In view of this dilemma, there appears to be nothing else to do than to abandon either the principle of relativity or the simple law of the propagation of light,” Einstein wrote.41
Then something delightful happened. Albert Einstein, while talking with a friend, took one of the most elegant imaginative leaps in the history of physics.
It was a beautiful day in Bern, Einstein later remembered, when he went to visit his best friend Michele Besso, the brilliant but unfocused engineer he had met while studying in Zurich and then recruited to join him at the Swiss Patent Office. Many days they would walk to work together, and on this occasion Einstein told Besso about the dilemma that was dogging him.
“I’m going to give it up,” Einstein said at one point. But as they discussed it, Einstein recalled, “I suddenly understood the key to the problem.” The next day, when he saw Besso, Einstein was in a state of great excitement. He skipped any greeting and immediately declared, “Thank you. I’ve completely solved the problem.”42
Only five weeks elapsed between that eureka moment and the day that Einstein sent off his most famous paper, “On the Electrodynamics of Moving Bodies.” It contained no citations of other literature, no mention of anyone else’s work, and no acknowledgments except for the charming one in the last sentence: “Let me note that my friend and colleague M. Besso steadfastly stood by me in my work on the problem discussed here, and that I am indebted to him for several valuable suggestions.”
So what was the insight that struck him while talking to Besso? “An analysis of the concept of time was my solution,” Einstein said. “Time cannot be absolutely defined, and there is an inseparable relation between time and signal velocity.”
More specifically, the key insight was that two events that appear to be simultaneous to one observer will not appear to be simultaneous to another observer who is moving rapidly. And there is no way to declare that one of the observers is really correct. In other words, there is no way to declare that the two events are truly simultaneous.
Einstein later explained this concept using a thought experiment involving moving trains. Suppose lightning bolts strike the train track’s embankment at two distant places, A and B. If we declare that they struck simultaneously, what does that mean?
Einstein realized that we need an operational definition, one we can actually apply, and that would require taking into account the speed of light. His answer was that we would define the two strikes as simultaneous if we were standing exactly halfway between them and the light from each reached us at the exact same time.
But now let us imagine how the event looks to a train passenger who is moving rapidly along the track. In a 1916 book written to explain this to nonscientists, he used the following drawing, in which the long train is the line on the top:
Suppose that at the exact instant (from the viewpoint of the person on the embankment) when lightning strikes at points A and B, there is a passenger at the midpoint of the train, Mt, just passing the observer who is at the midpoint alongside the tracks, M. If the train was motionless relative to the embankment, the passenger inside would see the lightning flashes simultaneously, just as the observer on the embankment would.
But if the train is moving to the right relative to the embankment, the observer inside will be rushing closer toward place B while the light signals are traveling. Thus he will be positioned slightly to the right by the time the light arrives; as a result, he will see the light from the strike at place B before he will see the light from the strike at place A. So he will assert that lightning hit at B before it did so at A, and the strikes were not simultaneous.
“We thus arrive at the important result: Events that are simultaneous with reference to the embankment are not simultaneous with respect to the train,” said Einstein. The principle of relativity says that there is no way to decree that the embankment is “at rest” and the train “in motion.” We can say only that they are in motion relative to each other. So there is no “real” or “right” answer. There is no way to say that any two events are “absolutely” or “really” simultaneous.43
This is a simple insight, but also a radical one. It means that there is no absolute time. Instead, all moving reference frames have their own relative time. Although Einstein refrained from saying that this leap was as truly “revolutionary” as the one he made about light quanta, it did in fact transform science. “This was a change in the very foundation of physics, an unexpected and very radical change that required all the courage of a young and revolutionary genius,” noted Werner Heisenberg, who later contributed to a similar feat with his principle of quantum uncertainty.44
In his 1905 paper, Einstein used a vivid image, which we can imagine him conceiving as he watched the trains moving into the Bern station past the rows of clocks that were synchronized with the one atop the town’s famed tower. “Our judgments in which time plays a part are always judgments of simultaneous events,” he wrote. “If, for instance, I say, ‘That train arrives here at 7 o’clock,’ I mean something like this: ‘The pointing of the small hand of my watch to 7 and the arrival of the train are simultaneous events.’ ” Once again, however, observers who are moving rapidly relative to one another will have a different view on whether two distant events are simultaneous.
The concept of absolute time—meaning a time that exists in “reality” and tick-tocks along independent of any observations of it—had been a mainstay of physics ever since Newton had made it a premise of his Principia 216 years earlier. The same was true for absolute space and distance.“Absolute, true, and mathematical time, of itself and from its own nature, flows equably without relation to anything external,” he famously wrote in Book 1 of the Principia. “Absolute space, in its own nature, without relation to anything external, remains always similar and immovable.”
But even Newton seemed discomforted by the fact that these concepts could not be directly observed. “Absolute time is not an object of perception,” he admitted. He resorted to relying on the presence of God to get him out of the dilemma. “The Deity endures forever and is everywhere present, and by existing always and everywhere, He constitutes duration and space.”45
Ernst Mach, whose books had influenced Einstein and his fellow members of the Olympia Academy, lambasted Newton’s notion of absolute time as a “useless metaphysical concept” that “cannot be produced in experience.” Newton, he charged, “acted contrary to his expressed intention only to investigate actual facts.”46
Henri Poincaré also pointed out the weakness of Newton’s concept of absolute time in his book Science and Hypothesis, another favorite of the Olympia Academy. “Not only do we have no direct intuition of the equality of two times, we do not even have one of the simultaneity of two events occurring in different places,” he wrote.47
Both Mach and Poincaré were, it thus seems, useful in providing a foundation for Einstein’s great breakthrough. But he owed even more, he later said, to the skepticism he learned from the Scottish philosopher David Hume regarding mental constructs that were divorced from purely factual observations.
Given the number of times in his papers that he uses thought experiments involving moving trains and distant clocks, it is also logical to surmise that he was helped in visualizing and articulating his thoughts by the trains that moved past Bern’s clock tower and the rows of synchronized clocks on the station platform. Indeed, there is a tale that involves him discussing his new theory with friends by pointing to (or at least referring to) the synchronized clocks of Bern and the unsynchronized steeple clock visible in the neighboring village of Muni.48
Peter Galison provides a thought-provoking study of the technological ethos in his book Einstein’s Clocks, Poincaré’s Maps. Clock coordination was in the air at the time. Bern had inaugurated an urban time network of electrically synchronized clocks in 1890, and a decade later, by the time Einstein had arrived, finding ways to make them more accurate and coordinate them with clocks in other cities became a Swiss passion.
In addition, Einstein’s chief duty at the patent office, in partnership with Besso, was evaluating electromechanical devices. This included a flood of applications for ways to synchronize clocks by using electric signals. From 1901 to 1904, Galison notes, there were twenty-eight such patents issued in Bern.
One of them, for example, was called “Installation with Central Clock for Indicating the Time Simultaneously in Several Places Separated from One Another.” A similar application arrived on April 25, just three weeks before Einstein had his breakthrough conversation with Besso; it involved a clock with an electromagnetically controlled pendulum that could be coordinated with another such clock through an electric signal. What these applications had in common was that they used signals that traveled at the speed of light.49
We should be careful not to overemphasize the role played by the technological backdrop of the patent office. Although clocks are part of Einstein’s description of his theory, his point is about the difficulties that observers in relative motion have in using light signals to synchronize them, something that was not an issue for the patent applicants.50
Nevertheless, it is interesting to note that almost the entire first two sections of his relativity paper deal directly and in vivid practical detail (in a manner so different from the writings of, say, Lorentz and Maxwell) with the two real-world technological phenomena he knew best. He writes about the generation of “electric currents of the same magnitude” due to the “equality of relative motion” of coils and magnets, and the use of “a light signal” to make sure that “two clocks are synchronous.”
As Einstein himself stated, his time in the patent office “stimulated me to see the physical ramifications of theoretical concepts.”51 And Alexander Moszkowski, who compiled a book in 1921 based on conversations with Einstein, noted that Einstein believed there was “a definite connection between the knowledge acquired at the patent office and the theoretical results.”52
“On the Electrodynamics of Moving Bodies”
Now let’s look at how Einstein articulated all of this in the famous paper that the Annalen der Physik received on June 30, 1905. For all its momentous import, it may be one of the most spunky and enjoyable papers in all of science. Most of its insights are conveyed in words and vivid thought experiments, rather than in complex equations. There is some math involved, but it is mainly what a good high school senior could comprehend. “The whole paper is a testament to the power of simple language to convey deep and powerfully disturbing ideas,” says the science writer Dennis Overbye.53
The paper starts with the “asymmetry” that a magnet and wire loop induce an electric current based only on their relative motion to one another, but since the days of Faraday there had been two different theoretical explanations for the current produced depending on whether it was the magnet or the loop that was in motion.54 “The observable phenomenon here depends only on the relative motion of the conductor and the magnet,” Einstein writes, “whereas the customary view draws a sharp distinction between the two cases in which either the one or the other of these bodies is in motion.”55
The distinction between the two cases was based on the belief, which most scientists still held, that there was such a thing as a state of “rest” with respect to the ether. But the magnet-and-coil example, along with every observation made on light, “suggest that the phenomena of electrodynamics as well as of mechanics possess no properties corresponding to the idea of absolute rest.” This prompts Einstein to raise “to the status of a postulate” the principle of relativity, which holds that the laws of mechanics and electrodynamics are the same in all reference systems moving at constant velocity relative to one another.
Einstein goes on to propound the other postulate upon which his theory was premised: the constancy of the speed of light “independent of the state of motion of the emitting body.” Then, with the casual stroke of a pen, and the marvelously insouciant word “superfluous,” the rebellious patent examiner dismissed two generations’ worth of accrued scientific dogma: “The introduction of a ‘light ether’ will prove to be superfluous, inasmuch as the view to be developed here will not require a ‘space at absolute rest.’ ”
Using these two postulates, Einstein explained the great conceptual step he had taken during his talk with Besso. “Two events which, viewed from a system of coordinates, are simultaneous, can no longer be looked upon as simultaneous events when envisaged from a system which is in motion relative to that system.” In other words, there is no such thing as absolute simultaneity.
In phrases so simple as to be seductive, Einstein pointed out that time itself can be defined only by referring to simultaneous events, such as the small hand of a watch pointing to 7 as a train arrives. The obvious yet still astonishing conclusion: with no such thing as absolute simultaneity, there is no such thing as “real” or absolute time. As he later put it, “There is no audible tick-tock everywhere in the world that can be considered as time.”56
Moreover, this realization also meant overturning the other assumption that Newton made at the beginning of his Principia. Einstein showed that if time is relative, so too are space and distance: “If the man in the carriage covers the distance w in a unit of time—measured from the train—then this distance—as measured from the embankment—is not necessarily also equal to w.”57
Einstein explained this by asking us to picture a rod that has a certain length when it is measured while it is stationary relative to the observer. Now imagine that the rod is moving. How long is the rod?
One way to determine this is by moving alongside the rod, at the same speed, and superimposing a measuring stick on it. But how long would the rod be if measured by someone not in motion with it? In that case, a way to measure the moving rod would be to determine, based on synchronized stationary clocks, the precise location of each end of the rod at a specific moment, and then use a stationary ruler to measure the distance between these two points. Einstein shows that these methods will produce different results.
Why? Because the two stationary clocks have been synchronized by a stationary observer. But what happens if an observer who is moving as fast as the rod tries to synchronize those clocks? She would synchronize them differently, because she would have a different perception of simultaneity. As Einstein put it, “Observers moving with the moving rod would thus find that the two clocks were not synchronous, while observers in the stationary system would declare the clocks to be synchronous.”
Another consequence of special relativity is that a person standing on the platform will observe that time goes more slowly on a train speeding past. Imagine that on the train there is a “clock” made up of a mirror on the floor and one on the ceiling and a beam of light that bounces up and down between them. From the perspective of a woman on the train, the light goes straight up and then straight down. But from the perspective of a man standing on the platform, it appears that the light is starting at the bottom but moving on a diagonal to get to the ceiling mirror, which has zipped ahead a tiny bit, then bouncing down on a diagonal back to the mirror on the floor, which has in turn zipped ahead a tiny bit. For both observers, the speed of the light is the same (that is Einstein’s great given). The man on the track observes the distance the light has to travel as being longer than the woman on the train observes it to be. Thus, from the perspective of the man on the track, time is going by more slowly inside the speeding train.58
Another way to picture this is to use Galileo’s ship. Imagine a light beam being shot down from the top of the mast to the deck. To an observer on the ship, the light beam will travel the exact length of the mast. To an observer on land, however, the light beam will travel a diagonal formed by the length of the mast plus the distance (it’s a fast ship) that the ship has traveled forward during the time it took the light to get from the top to the bottom of the mast. To both observers, the speed of light is the same. To the observer on land, it traveled farther before it reached the deck. In other words, the exact same event (a light beam sent from the top of the mast hitting the deck) took longer when viewed by a person on land than by a person on the ship.59
This phenomenon, called time dilation, leads to what is known as the twin paradox. If a man stays on the platform while his twin sister takes off in a spaceship that travels long distances at nearly the speed of light, when she returns she would be younger than he is. But because motion is relative, this seems to present a paradox. The sister on the spaceship might think it’s her brother on earth who is doing the fast traveling, and when they are rejoined she would expect to observe that it was he who did not age much.
Could they each come back younger than the other one? Of course not. The phenomenon does not work in both directions. Because the spaceship does not travel at a constant velocity, but instead must turn around, it’s the twin on the spaceship, not the one on earth, who would age more slowly.
The phenomenon of time dilation has been experimentally confirmed, even by using test clocks on commercial planes. But in our normal life, it has no real impact, because our motion relative to any other observer is never anything near the speed of light. In fact, if you spent almost your entire life on an airplane, you would have aged merely 0.00005 seconds or so less than your twin on earth when you returned, an effect that would likely be counteracted by a lifetime spent eating airline food.60
Special relativity has many other curious manifestations. Think again about that light clock on the train. What happens as the train approaches the speed of light relative to an observer on the platform? It would take almost forever for a light beam in the train to bounce from the floor to the moving ceiling and back to the moving floor. Thus time on the train would almost stand still from the perspective of an observer on the platform.
As an object approaches the speed of light, its apparent mass also increases. Newton’s law that force equals mass times acceleration still holds, but as the apparent mass increases, more and more force will produce less and less acceleration. There is no way to apply enough force to push even a pebble faster than the speed of light. That’s the ultimate speed limit of the universe, and no particle or piece of information can go faster than that, according to Einstein’s theory.
With all this talk of distance and duration being relative depending on the observer’s motion, some may be tempted to ask: So which observer is “right”? Whose watch shows the “actual” time elapsed? Which length of the rod is “real”? Whose notion of simultaneity is “correct”?
According to the special theory of relativity, all inertial reference frames are equally valid. It is not a question of whether rods actually shrink or time really slows down; all we know is that observers in different states of motion will measure things differently. And now that we have dispensed with the ether as “superfluous,” there is no designated “rest” frame of reference that has preference over any other.
One of Einstein’s clearest explanations of what he had wrought was in a letter to his Olympia Academy colleague Solovine:
The theory of relativity can be outlined in a few words. In contrast to the fact, known since ancient times, that movement is perceivable only as
movement, physics was based on the notion of
movement. The study of light waves had assumed that one state of movement, that of the light-carrying ether, is distinct from all others. All movements of bodies were supposed to be relative to the light-carrying ether, which was the incarnation of absolute rest. But after efforts to discover the privileged state of movement of this hypothetical ether through experiments had failed, it seemed that the problem should be restated. That is what the theory of relativity did. It assumed that there are no privileged physical states of movement and asked what consequences could be drawn from this.
Einstein’s insight, as he explained it to Solovine, was that we must discard concepts that “have no link with experience,” such as “absolute simultaneity” and “absolute speed.”61
It is very important to note, however, that the theory of relativity does not mean that “everything is relative.” It does not mean that everything is subjective.
Instead, it means that measurements of time, including duration and simultaneity, can be relative, depending on the motion of the observer. So can the measurements of space, such as distance and length. But there is a union of the two, which we call spacetime, and that remains invariant in all inertial frames. Likewise, there are things such as the speed of light that remain invariant.
In fact, Einstein briefly considered calling his creation Invariance Theory, but the name never took hold. Max Planck used the term Relativtheorie in 1906, and by 1907 Einstein, in an exchange with his friend Paul Ehrenfest, was calling it Relativitätstheorie.
One way to understand that Einstein was talking about invariance, rather than declaring everything to be relative, is to think about how far a light beam would travel in a given period of time. That distance would be the speed of light multiplied by the amount of time it traveled. If we were on a platform observing this happening on a train speeding by, the elapsed time would appear shorter (time seems to move more slowly on the moving train), and the distance would appear shorter (rulers seem to be contracted on the moving train). But there is a relationship between the two quantities—a relationship between the measurements of space and of time—that remains invariant, whatever your frame of reference.62
A more complex way to understand this is the method used by Hermann Minkowski, Einstein’s former math teacher at the Zurich Polytechnic. Reflecting on Einstein’s work, Minkowski uttered the expression of amazement that every beleaguered student wants to elicit someday from condescending professors. “It came as a tremendous surprise, for in his student days Einstein had been a lazy dog,” Minkowski told physicist Max Born. “He never bothered about mathematics at all.”63
Minkowski decided to give a formal mathematical structure to the theory. His approach was the same one suggested by the time traveler on the first page of H. G. Wells’s great novel The Time Machine, published in 1895: “There are really four dimensions, three which we call the three planes of Space, and a fourth, Time.” Minkowski turned all events into mathematical coordinates in four dimensions, with time as the fourth dimension. This permitted transformations to occur, but the mathematical relationships between the events remained invariant.
Minkowski dramatically announced his new mathematical approach in a lecture in 1908. “The views of space and time which I wish to lay before you have sprung from the soil of experimental physics, and therein lies their strength,” he said. “They are radical. Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality.”64
Einstein, who was still not yet enamored of math, at one point described Minkowski’s work as “superfluous learnedness” and joked, “Since the mathematicians have grabbed hold of the theory of relativity, I myself no longer understand it.” But he in fact came to admire Minkowski’s handiwork and wrote a section about it in his popular 1916 book on relativity.
What a wonderful collaboration it could have been! But at the end of 1908, Minkowski was taken to the hospital, fatally stricken with peritonitis. Legend has it that he declared, “What a pity that I have to die in the age of relativity’s development.”65
Once again, it’s worth asking why Einstein discovered a new theory and his contemporaries did not. Both Lorentz and Poincaré had already come up with many of the components of Einstein’s theory. Poincaré even questioned the absolute nature of time.
But neither Lorentz nor Poincaré made the full leap: that there is no need to posit an ether, that there is no absolute rest, that time is relative based on an observer’s motion, and so is space. Both men, the physicist Kip Thorne says, “were groping toward the same revision of our notions of space and time as Einstein, but they were groping through a fog of misperceptions foisted on them by Newtonian physics.”
Einstein, by contrast, was able to cast off Newtonian misconceptions. “His conviction that the universe loves simplification and beauty, and his willingness to be guided by this conviction, even if it meant destroying the foundations of Newtonian physics, led him, with a clarity of thought that others could not match, to his new description of space and time.”66
Poincaré never made the connection between the relativity of simultaneity and the relativity of time, and he “drew back when on the brink” of understanding the full ramifications of his ideas about local time. Why did he hesitate? Despite his interesting insights, he was too much of a traditionalist in physics to display the rebellious streak in-grained in the unknown patent examiner.67 “When he came to the decisive step, his nerve failed him and he clung to old habits of thought and familiar ideas of space and time,” Banesh Hoffmann said of Poincaré. “If this seems surprising, it is because we underestimate the boldness of Einstein in stating the principle of relativity as an axiom and, by keeping faith with it, changing our notion of space and time.”68
A clear explanation of Poincaré’s limitations and Einstein’s boldness comes from one of Einstein’s successors as a theoretical physicist at the Institute for Advanced Studies in Princeton, Freeman Dyson:
The essential difference between Poincaré and Einstein was that Poincaré was by temperament conservative and Einstein was by temperament revolutionary. When Poincaré looked for a new theory of electromagnetism, he tried to preserve as much as he could of the old. He loved the ether and continued to believe in it, even when his own theory showed that it was unobservable. His version of relativity theory was a patchwork quilt. The new idea of local time, depending on the motion of the observer, was patched onto the old framework of absolute space and time defined by a rigid and immovable ether. Einstein, on the other hand, saw the old framework as cumbersome and unnecessary and was delighted to be rid of it. His version of the theory was simpler and more elegant. There was no absolute space and time and there was no ether. All the complicated explanations of electric and magnetic forces as elastic stresses in the ether could be swept into the dustbin of history, together with the famous old professors who still believed in them.
As a result, Poincaré expressed a principle of relativity that contained certain similarities to Einstein’s, but it had a fundamental difference. Poincaré retained the existence of the ether, and the speed of light was, for him, constant only when measured by those at rest to this presumed ether’s frame of reference.70
Even more surprising, and revealing, is the fact that Lorentz and Poincaré never were able to make Einstein’s leap even after they read his paper. Lorentz still clung to the existence of the ether and its “at rest” frame of reference. In a lecture in 1913, which he reprinted in his 1920 book The Relativity Principle, Lorentz said, “According to Einstein, it is meaningless to speak of motion relative to the ether. He likewise denies the existence of absolute simultaneity. As far as this lecturer is concerned, he finds a certain satisfaction in the older interpretations, according to which the ether possesses at least some substantiality, space and time can be sharply separated, and simultaneity without further specification can be spoken of.”71
For his part, Poincaré seems never to have fully understood Einstein’s breakthrough. Even in 1909, he was still insisting that relativity theory required a third postulate, which was that “a body in motion suffers a deformation in the direction in which it was displaced.” In fact, the contraction of rods is not, as Einstein showed, some separate hypothesis involving a real deformation, but rather the consequence of accepting Einstein’s theory of relativity.
Until his death in 1912, Poincaré never fully gave up the concept of the ether or the notion of absolute rest. Instead, he spoke of the adoption of “the principle of relativity according to Lorentz.” He never fully understood or accepted the basis of Einstein’s theory. “Poincaré stood steadfast and held to his position that in the world of perceptions there was an absoluteness of simultaneity,” notes the science historian Arthur I. Miller.72
“How happy and proud I will be when the two of us together will have brought our work on the relative motion to a conclusion!” Einstein had written his lover Mileva Mari back in 1901.73 Now it had been brought to that conclusion, and Einstein was so exhausted when he finished a draft in June that “his body buckled and he went to bed for two weeks,” while Mari “checked the article again and again.”74
Then they did something unusual: they celebrated together. As soon as he finished all four of the papers that he had promised in his memorable letter to Conrad Habicht, he sent his old colleague from the Olympia Academy another missive, this one a postcard signed by his wife as well. It read in full: “Both of us, alas, dead drunk under the table.”75
All of which raises a question more subtle and contentious than that posed by the influences of Lorentz and Poincaré: What was Mileva Mari’s role?
That August, they took a vacation together in Serbia to see her friends and family. While there, Mari was proud and also willing to accept part of the credit. “Not long ago we finished a very significant work that will make my husband world famous,” she told her father, according to stories later recorded there. Their relationship seemed restored, for the time being, and Einstein happily praised his wife’s help. “I need my wife,” he told her friends in Serbia.“She solves all the mathematical problems for me.”76
Some have contended that Mari was a full-fledged collaborator, and there was even a report, later discredited,77 that an early draft version of his relativity paper had her name on it as well. At a 1990 conference in New Orleans, the American Association for the Advancement of Science held a panel on the issue at which Evan Walker, a physicist and cancer researcher from Maryland, debated John Stachel, the leader of the Einstein Papers Project. Walker presented the various letters referring to “our work,” and Stachel replied that such phrases were clearly romantic politeness and that there was “no evidence at all that she contributed any ideas of her own.”
The controversy, understandably, fascinated both scientists and the press. Columnist Ellen Goodman wrote a wry commentary in the Boston Globe, in which she judiciously laid out the evidence, and the Economist did a story headlined “The Relative Importance of Mrs. Einstein.” Another conference followed in 1994 at the University of Novi Sad, where organizer Professor Rastko Magli contended that it was time “to emphasize Mileva’s merit in order to ensure a deserved place in the history of science for her.” The public discussion culminated with a PBS documentary, Einstein’s Wife, in 2003, that was generally balanced, although it gave unwarranted credence to the report that her name had been on the original manuscript.78
From all the evidence, Mari was a sounding board, though not as important in that role as Besso. She also helped check his math, although there is no evidence that she came up with any of the mathematical concepts. In addition, she encouraged him and (what at times was more difficult) put up with him.
For both the sake of colorful history and the emotional resonance it would have, it would be fun if we could go even further than this. But instead, we must follow the less exciting course of being confined to the evidence. None of their many letters, to each other or to friends, mentions a single instance of an idea or creative concept relating to relativity that came from Mari.
Nor did she ever—even to her family and close friends while in the throes of their bitter divorce—claim to have made any substantive contributions to Einstein’s theories. Her son Hans Albert, who remained devoted to her and lived with her during the divorce, gave his own version that was reflected in a book by Peter Michelmore, and it seems to reflect what Mari told her son: “Mileva helped him solve certain mathematical problems, but no one could assist with the creative work, the flow of ideas.”79
There is, in fact, no need to exaggerate Mari’s contributions in order to admire, honor, and sympathize with her as a pioneer. To give her credit beyond what she ever claimed, says the science historian Gerald Holton, “only detracts both from her real and significant place in history and from the tragic unfulfillment of her early hopes and promise.”
Einstein admired the pluck and courage of a feisty female physicist who had emerged from a land where women were generally not allowed to go into that field. Nowadays, when the same issues still reverberate across a century of time, the courage that Mari displayed by entering and competing in the male-dominated world of physics and math is what should earn her an admired spot in the annals of scientific history. This she deserves without inflating the importance of her collaboration on the special theory of relativity.80
The E=mc2Coda, September 1905
Einstein had raised the curtain on his miracle year in his letter to his Olympia Academy mate Conrad Habicht, and he celebrated its climax with his one-sentence drunken postcard to him. In September, he wrote yet another letter to Habicht, this one trying to entice him to come work at the patent office. Einstein’s reputation as a lone wolf was somewhat artificial. “Perhaps it would be possible to smuggle you in among the patent slaves,” he said. “You probably would find it relatively pleasant. Would you actually be ready and willing to come? Keep in mind that besides the eight hours of work, each day also has eight hours for fooling around, and then there’s also Sunday. I would love to have you here.”
As with his letter six months earlier, Einstein went on to reveal quite casually a momentous scientific breakthrough, one that would be expressed by the most famous equation in all of science:
One more consequence of the electrodynamics paper has also crossed my mind. Namely, the relativity principle, together with Maxwell’s equations, requires that mass be a direct measure of the energy contained in a body. Light carries mass with it. With the case of radium there should be a noticeable reduction of mass. The thought is amusing and seductive; but for all I know, the good Lord might be laughing at the whole matter and might have been leading me up the garden path.
Einstein developed the idea with a beautiful simplicity. The paper that the Annalen der Physik received from him on September 27, 1905, “Does the Inertia of a Body Depend on Its Energy Content?,” involved only three steps that filled merely three pages. Referring back to his special relativity paper, he declared, “The results of an electrodynamic investigation recently published by me in this journal lead to a very interesting conclusion, which will be derived here.”82
Once again, he was deducing a theory from principles and postulates, not trying to explain the empirical data that experimental physicists studying cathode rays had begun to gather about the relation of mass to the velocity of particles. Coupling Maxwell’s theory with the relativity theory, he began (not surprisingly) with a thought experiment. He calculated the properties of two light pulses emitted in opposite directions by a body at rest. He then calculated the properties of these light pulses when observed from a moving frame of reference. From this he came up with equations regarding the relationship between speed and mass.
The result was an elegant conclusion: mass and energy are different manifestations of the same thing. There is a fundamental interchangeability between the two. As he put it in his paper, “The mass of a body is a measure of its energy content.”
The formula he used to describe this relationship was also strikingly simple: “If a body emits the energy L in the form of radiation, its mass decreases by L/V 2.” Or, to express the same equation in a different manner:L=mV 2. Einstein used the letter L to represent energy until 1912, when he crossed it out in a manuscript and replaced it with the more common E. He also used V to represent the velocity of light, before changing to the more common c. So, using the letters that soon became standard, Einstein had come up with his memorable equation:
Energy equals mass times the square of the speed of light. The speed of light, of course, is huge. Squared it is almost inconceivably bigger. That is why a tiny amount of matter, if converted completely into energy, has an enormous punch. A kilogram of mass would convert into approximately 25 billion kilowatt hours of electricity. More vividly: the energy in the mass of one raisin could supply most of New York City’s energy needs for a day.83
As usual, Einstein ended by proposing experimental ways to confirm the theory he had just derived. “Perhaps it will prove possible,” he wrote,“to test this theory using bodies whose energy content is variable to a high degree, e.g., salts of radium.”
THE HAPPIEST THOUGHT
Einstein’s 1905 burst of creativity was astonishing. He had devised a revolutionary quantum theory of light, helped prove the existence of atoms, explained Brownian motion, upended the concept of space and time, and produced what would become science’s best known equation. But not many people seemed to notice at first. According to his sister, Einstein had hoped that his flurry of essays in a preeminent journal would lift him from the obscurity of a third-class patent examiner and provide some academic recognition, perhaps even an academic job. “But he was bitterly disappointed,” she noted. “Icy silence followed the publication.”1
That was not exactly true. A small but respectable handful of physicists soon took note of Einstein’s papers, and one of these turned out to be, as good fortune would have it, the most important possible admirer he could attract: Max Planck, Europe’s revered monarch of theoretical physics, whose mysterious mathematical constant explaining black-body radiation Einstein had transformed into a radical new reality of nature. As the editorial board member of Annalen der Physik responsible for theoretical submissions, Planck had vetted Einstein’s papers, and the one on relativity had “immediately aroused my lively attention,” he later recalled. As soon as it was published, Planck gave a lecture on relativity at the University of Berlin.2
Planck became the first physicist to build on Einstein’s theory. In an article published in the spring of 1906, he argued that relativity conformed to the principle of least action, a foundation of physics that holds that light or any object moving between two points should follow the easiest path.3
Planck’s paper not only contributed to the development of relativity theory; it also helped to legitimize it among other physicists. Whatever disappointment Maja Einstein had detected in her brother dissipated. “My papers are much appreciated and are giving rise to further investigations,” he exulted to Solovine. “Professor Planck has recently written to me about that.”4
The proud patent examiner was soon exchanging letters with the eminent professor. When another theorist challenged Planck’s contention that relativity theory conformed to the principle of least action, Einstein took Planck’s side and sent him a card saying so. Planck was pleased. “As long as the proponents of the principle of relativity constitute such a modest little band as is now the case,” he replied to Einstein, “it is doubly important that they agree among themselves.” He added that he hoped to visit Bern the following year and meet Einstein personally.5
Planck did not end up coming to Bern, but he did send his earnest assistant, Max Laue.* He and Einstein had already been corresponding about Einstein’s light quanta paper, with Laue saying that he agreed with “your heuristic view that radiation can be absorbed and emitted only in specific finite quanta.”
However, Laue insisted, just as Planck had, that Einstein was wrong to assume that these quanta were a characteristic of the radiation itself. Instead, Laue contended that the quanta were merely a description of the way that radiation was emitted or absorbed by a piece of matter. “This is not a characteristic of electromagnetic processes in a vacuum but rather of the emitting or absorbing matter,” Laue wrote, “and hence radiation does not consist of light quanta as it says in section six of your first paper.”6 (In that section, Einstein had said that the radiation “behaves thermodynamically as if it consisted of mutually independent energy quanta.”)
When Laue was preparing to visit in the summer of 1907, he was surprised to discover that Einstein was not at the University of Bern but was working at the patent office on the third floor of the Post and Telegraph Building. Meeting Einstein there did not lessen his wonder. “The young man who came to meet me made so unexpected an impression on me that I did not believe he could possibly be the father of the relativity theory,” Laue said, “so I let him pass.” After a while, Einstein came wandering through the reception area again, and Laue finally realized who he was.
They walked and talked for hours, with Einstein at one point offering a cigar that, Laue recalled, “was so unpleasant that I ‘accidentally’ dropped it into the river.” Einstein’s theories, on the other hand, made a pleasing impression. “During the first two hours of our conversation he overthrew the entire mechanics and electrodynamics,” Laue noted. Indeed, he was so enthralled that over the next four years he would publish eight papers on Einstein’s relativity theory and become a close friend.7
Some theorists found the amazing flurry of papers from the patent office to be uncomfortably abstract. Arnold Sommerfeld, later a friend, was among the first to suggest there was something Jewish about Einstein’s theoretical approach, a theme later picked up by anti-Semites. It lacked due respect for the notion of order and absolutes, and it did not seem solidly grounded. “As remarkable as Einstein’s papers are,” he wrote Lorentz in 1907, “it still seems to me that something almost unhealthy lies in this unconstruable and impossible to visualize dogma. An Englishman would hardly have given us this theory. It might be here too, as in the case of Cohn, the abstract conceptual character of the Semite expresses itself.”8
None of this interest made Einstein famous, nor did it get him any job offers. “I was surprised to read that you must sit in an office for eight hours a day,” wrote yet another young physicist who was planning to visit. “History is full of bad jokes.”9 But because he had finally earned his doctorate, he had at least gotten promoted from a third-class to a second-class technical expert at the patent office, which came with a hefty 1,000-franc raise to an annual salary of 4,500 francs.10
His productivity was startling. In addition to working six days a week at the patent office, he continued his torrent of papers and reviews: six in 1906 and ten more in 1907. At least once a week he played in a string quartet. And he was a good father to the 3-year-old son he proudly labeled “impertinent.” As Mari wrote to her friend Helene Savi, “My husband often spends his free time at home just playing with the boy.”11
Beginning in the summer of 1907, Einstein also found time to dabble in what might have become, if the fates had been more impish, a new career path: as an inventor and salesman of electrical devices like his uncle and father. Working with Olympia Academy member Conrad Habicht and his brother Paul, Einstein developed a machine to amplify tiny electrical charges so they could be measured and studied. It had more academic than practical purpose; the idea was to create a lab device that would permit the study of small electrical fluctuations.
The concept was simple. When two strips of metal move close to each other, an electric charge on one will induce an opposite charge on the other. Einstein’s idea was to use a series of strips that would induce the charge ten times and then transfer that to another disc. The process would be repeated until the original minuscule charge would be multiplied by a large number and thus be easily measurable. The trick was making the contraption actually work.12
Given his heritage, breeding, and years in the patent office, Einstein had the background to be an engineering genius. But as it turned out, he was better suited to theorizing. Fortunately, Paul Habicht was a good machinist, and by August 1907 he had a prototype of the Maschinchen, or little machine, ready to be unveiled. “I am astounded at the lightning speed with which you built the Maschinchen,” Einstein wrote. “I’ll show up on Sunday.” Unfortunately, it didn’t work. “I am driven by murderous curiosity as to what you’re up to,” Einstein wrote a month later as they tried to fix things.
Throughout 1908, letters flew back and forth between Einstein and the Habichts, filled with complex diagrams and a torrent of ideas for how to make the device work. Einstein published a description in a journal, which produced, for a while, a potential sponsor. Paul Habicht was able to build a better version by October, but it had trouble keeping a charge. He brought the machine to Bern, where Einstein commandeered a lab in one of the schools and dragooned a local mechanic. By November the machine seemed to be working. It took another year or so to get a patent and begin to make some versions for sale. But even then, it never truly caught hold or found a market, and Einstein eventually lost interest.13
These practical exploits may have been fun, but Einstein’s glorious isolation from the priesthood of academic physicists was starting to have more drawbacks than advantages. In a paper he wrote in the spring of 1907, he began by exuding a joyful self-assurance about having neither the library nor the inclination to know what other theorists had written on the topic. “Other authors might have already clarified part of what I am going to say,” he wrote. “I felt I could dispense with doing a literature search (which would have been very troublesome for me), especially since there is good reason to hope that others will fill this gap.” However, when he was commissioned to write a major year-book piece on relativity later that year, there was slightly less cockiness in his warning to the editor that he might not be aware of all the literature. “Unfortunately I am not in a position to acquaint myself about everything that has been published on this subject,” he wrote, “because the library is closed in my free time.”14
That year he applied for a position at the University of Bern as a privatdozent, a starter rung on the academic ladder, which involved giving lectures and collecting a small fee from anyone who felt like showing up. To become a professor at most European universities, it helped to serve such an apprenticeship. With his application Einstein enclosed seventeen papers he had published, including the ones on relativity and light quanta. He was also expected to include an unpublished paper known as a habilitation thesis, but he decided not to bother writing one, as this requirement was sometimes waived for those who had “other outstanding achievements.”
Only one professor on the faculty committee supported hiring him without requiring him to write a new thesis, “in view of the important scientific achievements of Herr Einstein.” The others disagreed, and the requirement was not waived. Not surprisingly, Einstein considered the matter “amusing.” He did not write the special habilitation or get the post.15
The Equivalence of Gravity and Acceleration
Einstein’s road to the general theory of relativity began in November 1907, when he was struggling against a deadline to finish an article for a science yearbook explaining his special theory of relativity. Two limitations of that theory still bothered him: it applied only to uniform constant-velocity motion (things felt and behaved differently if your speed or direction was changing), and it did not incorporate Newton’s theory of gravity.
“I was sitting in a chair in the patent office at Bern when all of a sudden a thought occurred to me,” he recalled. “If a person falls freely, he will not feel his own weight.”That realization, which “startled” him, launched him on an arduous eight-year effort to generalize his special theory of relativity and “impelled me toward a theory of gravitation.”16 Later, he would grandly call it “the happiest* thought in my life.”17
The tale of the falling man has become an iconic one, and in some accounts it actually involves a painter who fell from the roof of an apartment building near the patent office.18 In fact, probably like other great tales of gravitational discovery—Galileo dropping objects from the Tower of Pisa and the apple falling on Newton’s head19—it was embellished in popular lore and was more of a thought experiment than a real occurrence. Despite Einstein’s propensity to focus on science rather than the merely personal, even he was not likely to watch a real human plunging off a roof and think of gravitational theory, much less call it the happiest thought in his life.
Einstein refined his thought experiment so that the falling man was in an enclosed chamber, such as an elevator in free fall above the earth. In this falling chamber (at least until it crashed), the man would feel weightless. Any objects he emptied from his pocket and let loose would float alongside him.
Looking at it another way, Einstein imagined a man in an enclosed chamber floating in deep space “far removed from stars and other appreciable masses.” He would experience the same perceptions of weightlessness. “Gravitation naturally does not exist for this observer. He must fasten himself with strings to the floor, otherwise the slightest impact against the floor will cause him to rise slowly towards the ceiling.”
Then Einstein imagined that a rope was hooked onto the roof of the chamber and pulled up with a constant force. “The chamber together with the observer then begin to move ‘upwards’ with a uniformly accelerated motion.”The man inside will feel himself pressed to the floor. “He is then standing in the chest in exactly the same way as anyone stands in a room of a house on our earth.” If he pulls something from his pocket and lets go, it will fall to the floor “with an accelerated relative motion” that is the same no matter the weight of the object—just as Galileo discovered to be the case for gravity. “The man in the chamber will thus come to the conclusion that he and the chest are in a gravitational field. Of course he will be puzzled for a moment as to why the chest does not fall in this gravitational field. Just then, however, he discovers the hook in the middle of the lid of the chest and the rope which is attached to it, and he consequently comes to the conclusion that the chamber is suspended at rest in the gravitational field.”
“Ought we to smile at the man and say that he errs in his conclusion?” Einstein asked. Just as with special relativity, there was no right or wrong perception. “We must rather admit that his mode of grasping the situation violates neither reason nor known mechanical laws.”20
A related way that Einstein addressed this same issue was typical of his ingenuity: he examined a phenomenon that was so very well-known that scientists rarely puzzled about it. Every object has a “gravitational mass,” which determines its weight on the earth’s surface or, more generally, the tug between it and any other object. It also has an “inertial mass,” which determines how much force must be applied to it in order to make it accelerate. As Newton noted, the inertial mass of an object is always the same as its gravitational mass, even though they are defined differently. This was obviously more than a mere coincidence, but no one had fully explained why.
Uncomfortable with two explanations for what seemed to be one phenomenon, Einstein probed the equivalence of inertial mass and gravitational mass using his thought experiment. If we imagine that the enclosed elevator is being accelerated upward in a region of outer space where there is no gravity, then the downward force felt by the man inside (or the force that tugs downward on an object hanging from the ceiling by a string) is due to inertial mass. If we imagine that the enclosed elevator is at rest in a gravitational field, then the downward force felt by the man inside (or the force that tugs downward on an object hanging from the ceiling by a string) is due to gravitational mass. But inertial mass always equals gravitational mass. “From this correspondence,” said Einstein, “it follows that it is impossible to discover by experiment whether a given system of coordinates is accelerated, or whether . . . the observed effects are due to a gravitational field.”21
Einstein called this “the equivalence principle.”22 The local effects of gravity and of acceleration are equivalent. This became a foundation for his attempt to generalize his theory of relativity so that it was not restricted just to systems that moved with a uniform velocity. The basic insight that he would develop over the next eight years was that “the effects we ascribe to gravity and the effects we ascribe to acceleration are both produced by one and the same structure.”23
Einstein’s approach to general relativity again showed how his mind tended to work:
• He was disquieted when there were two seemingly unrelated theories for the same observable phenomenon. That had been the case with the moving coil or moving magnet producing the same observable electric current, which he resolved with the special theory of relativity. Now it was the case with the differing definitions of inertial mass and gravitational mass, which he began to resolve by building on the equivalence principle.
• He was likewise uncomfortable when a theory made distinctions
that could not be observed in nature. That had been the case with observers in uniform motion: there was no way of determining who was at rest and who was in motion. Now it was also, apparently, the case for observers in accelerated motion: there was no way of telling who was accelerating and who was in a gravitational field.
• He was eager to generalize theories rather than settling for having them restricted to a special case. There should not, he felt, be one set of principles for the special case of constant-velocity motion and a different set for all other types of motion. His life was a constant quest for unifying theories.
In November 1907, working against the deadline imposed by the Yearbook of Radioactivity and Electronics, Einstein tacked on a fifth section to his article on relativity that sketched out his new ideas. “So far we have applied the principle of relativity ...only to nonaccelerated reference systems,” he began. “Is it conceivable that the principle of relativity applies to systems that are accelerated relative to each other?”
Imagine two environments, he said, one being accelerated and the other resting in a gravitational field.24 There is no physical experiment you can do that would tell these situations apart. “In the discussion that follows, we shall therefore assume the complete physical equivalence of a gravitational field and a corresponding acceleration of the reference system.”
Using various mathematical calculations that can be made about an accelerated system, Einstein proceeded to show that, if his notions were correct, clocks would run more slowly in a more intense gravitational field. He also came up with many predictions that could be tested, including that light should be bent by gravity and that the wavelength of light emitted from a source with a large mass, such as the sun, should increase slightly in what has become known as the gravitational redshift. “On the basis of some ruminating, which, though daring, does have something going for it, I have arrived at the view that the gravitational difference might be the cause of the shift to the red end of the spectrum,” he explained to a colleague. “A bending of light rays by gravity also follows from these arguments.”25
It would take Einstein another eight years, until November 1915, to work out the fundamentals of this theory and find the math to express it. Then it would take another four years before the most vivid of his predictions, the extent to which gravity would bend light, was verified by dramatic observations. But at least Einstein now had a vision, one that started him on the road toward one of the most elegant and impressive achievements in the history of physics: the general theory of relativity.
Winning a Professorship
By the beginning of 1908, even as such academic stars as Max Planck and Wilhelm Wien were writing to ask for his insights, Einstein had tempered his aspirations to be a university professor. Instead, he had begun, believe it or not, to seek work as a high school teacher. “This craving,” he told Marcel Grossmann, who had helped him get the patent-office job, “comes only from my ardent wish to be able to continue my private scientific work under easier conditions.”
He was even eager to go back to the Technical School in Winter-hur, where he had briefly been a substitute teacher. “How does one go about this?” he asked Grossmann. “Could I possibly call on somebody and talk him into the great worth of my admirable person as a teacher and a citizen? Wouldn’t I make a bad impression on him (no Swiss-German dialect, my Semitic appearance, etc.)?” He had written papers that were transforming physics, but he did not know if that would help. “Would there be any point in my stressing my scientific papers on that occasion?”26
He also responded to an advertisement for a “teacher of mathematics and descriptive geometry” at a high school in Zurich, noting in his application “that I would be ready to teach physics as well.” He ended up deciding to enclose all of the papers he had written thus far, including the special theory of relativity. There were twenty-one applicants. Einstein did not even make the list of three finalists.27
So Einstein finally overcame his pride and decided to write a thesis in order to become a privatdozent at Bern. As he explained to the patron there who had supported him, “The conversation I had with you in the city library, as well as the advice of several friends, has induced me to change my decision for the second time and to try my luck with a habilitation at the University of Bern after all.”28
The paper he submitted, an extension of his revolutionary work on light quanta, was promptly accepted, and at the end of February 1908, he was made a privatdozent. He had finally scaled the walls, or at least the outer wall, of academe. But his post neither paid enough nor was important enough for him to give up his job at the patent office. His lectures at the University of Bern thus became simply one more thing for him to do.
His topic for the summer of 1908 was the theory of heat, held on Tuesday and Saturday at 7 a.m., and he initially attracted only three attendees: Michele Besso and two other colleagues who worked at the postal building. In the winter session he switched to the theory of radiation, and his three coworkers were joined by an actual student named Max Stern. By the summer of 1909, Stern was the only attendee, and Einstein canceled his lecturing. He had, in the meantime, begun to adopt his professorial look: both his hair and clothing became a victim of nature’s tendency toward randomness.29
Alfred Kleiner, the University of Zurich physics professor who helped Einstein get his doctorate, had encouraged him to pursue the privatdozent position.30 He also had waged a long effort, which succeeded in 1908, to convince the Zurich authorities to increase the university’s stature by creating a new position in theoretical physics. It was not a full professorship; instead, it was an associate professorship under Kleiner.
It was the obvious post for Einstein, but there was one obstacle. Kleiner had another candidate in mind: his assistant Friedrich Adler, a pale and passionate political activist who had become friends with Einstein when they were both at the Polytechnic. Adler, whose father was the leader of the Social Democratic Party in Austria, was more disposed to political philosophy than theoretical physics. So he went to see Kleiner one morning in June 1908, and the two of them concluded that Adler was not right for the job and Einstein was.
In a letter to his father, Adler recounted the conversation and said that Einstein “had no understanding how to relate to people” and had been “treated by the professors at the Polytechnic with outright contempt.” But Adler said he deserved the job because of his genius and was likely to get it. “They have a bad conscience over how they treated him earlier. The scandal is being felt not only here but in Germany that such a man would have to sit in the patent office.”31
Adler made sure that the Zurich authorities, and for that matter everyone else, knew that he was officially stepping aside for his friend. “If it is possible to get a man like Einstein for our university, it would be absurd to appoint me,” he wrote. That resolved the political issue for the councilor in charge of education, who was a partisan Social Democrat. “Ernst would have liked Adler, since he was a fellow party member,” Einstein explained to Michele Besso. “But Adler’s statements about himself and me made it impossible.”32
So, at the end of June 1908, Kleiner traveled from Zurich to Bern to audit one of Einstein’s privatdozent lectures and, as Einstein put it, “size up the beast.” Alas, it was not a great show. “I really did not lecture divinely,” Einstein lamented to a friend, “partly because I was not well prepared, partly because being investigated got on my nerves a bit.” Kleiner sat listening with a wrinkled brow, and after the lecture he informed Einstein that his teaching style was not good enough to qualify him for the professorship. Einstein calmly claimed that he considered the job “quite unnecessary.”33
Kleiner went back to Zurich and reported that Einstein “holds monologues” and was “a long way from being a teacher.” That seemed to end his chances. As Adler informed his powerful father, “The situation has therefore changed, and the Einstein business is closed.” Einstein pretended to be sanguine. “The business with the professorship fell through, but that’s all right with me,” he wrote a friend. “There are enough teachers even without me.”34
In fact Einstein was upset, and he became even more so when he heard that Kleiner’s criticism of his teaching skills was being widely circulated, even in Germany. So he wrote to Kleiner, angrily reproaching him “for spreading unfavorable rumors about me.” He was already finding it difficult to get a proper academic job, and Kleiner’s assessment would make it impossible.
There was some validity to Kleiner’s criticism. Einstein was never an inspired teacher, and his lectures tended to be regarded as disorganized until his celebrity ensured that every stumble he made was transformed into a charming anecdote. Nevertheless, Kleiner relented. He said that he would be pleased to help him get the Zurich job if he could only show “some teaching ability.”
Einstein replied by suggesting that he come to Zurich to give a full-fledged (and presumably well-prepared) lecture to the physics society there, which he did in February 1909. “I was lucky,” Einstein reported soon after. “Contrary to my habit, I lectured well on that occasion.”35 When he went to call on Kleiner afterward, the professor intimated that a job offer would soon follow.
A few days after Einstein returned to Bern, Kleiner provided his official recommendation to the University of Zurich faculty. “Einstein ranks among the most important theoretical physicists and has been recognized as such since his work on the relativity principle,” he wrote. As for Einstein’s teaching skills, he said as politely as possible that they were ripe for improvement: “Dr. Einstein will prove his worth also as a teacher, because he is too intelligent and too conscientious not to be open to advice when necessary.”36
One issue was Einstein’s Jewishness. Some faculty members considered this a potential problem, but they were assured by Kleiner that Einstein did not exhibit the “unpleasant peculiarities” supposedly associated with Jews. Their conclusion is a revealing look at both the anti-Semitism of the time and the attempts to rise above it:
The expressions of our colleague Kleiner, based on several years of personal contact, were all the more valuable for the committee as well as for the faculty as a whole since Herr Dr. Einstein is an Israelite and since precisely to the Israelites among scholars are inscribed (in numerous cases not entirely without cause) all kinds of unpleasant peculiarities of character, such as intrusiveness, impudence, and a shopkeeper’s mentality in the perception of their academic position. It should be said, however, that also among the Israelites there exist men who do not exhibit a trace of these disagreeable qualities and that it is not proper, therefore, to disqualify a man only because he happens to be a Jew. Indeed, one occasionally finds people also among non-Jewish scholars who in regard to a commercial perception and utilization of their academic profession develop qualities that are usually considered as specifically Jewish. Therefore, neither the committee nor the faculty as a whole considered it compatible with its dignity to adopt anti-Semitism as a matter of policy.
The secret faculty vote in late March 1909 was ten in favor and one abstention. Einstein was offered his first professorship, four years after he had revolutionized physics. Unfortunately, his proposed salary was less than what he was making at the patent office, so he declined. Finally, the Zurich authorities raised their offer, and Einstein accepted. “So, now I too am an official member of the guild of whores,” he exulted to a colleague.38
One person who saw a newspaper notice about Einstein’s appointment was a Basel housewife named Anna Meyer-Schmid. Ten years earlier, when she was an unmarried girl of 17, they had met during one of Einstein’s vacations with his mother at the Hotel Paradies. Most of the guests had seemed to him “philistines,” but he took a liking to Anna and even wrote a poem in her album: “What should I inscribe for you here? / I could think of many things / Including a kiss / On your tiny little mouth / If you’re angry about it / Do not start to cry / The best punishment / Is to give me one too.” He signed it, “Your rascally friend.”39
In response to a congratulatory postcard from her, Einstein replied with a polite and mildly suggestive letter. “I probably cherish the memory of the lovely weeks that I was allowed to spend near you in the Paradies more than you do,” he wrote. “So now I’ve become such a big schoolmaster that my name is even mentioned in the newspapers. But I have remained a simple fellow.” He noted that he had married his college friend Mari, but he gave her his office address. “If you ever happen to be in Zurich and have time, look me up there; it would give me great pleasure.”40
Whether or not Einstein intended his response to hover uncertainly between innocence and suggestiveness, Anna’s eyes apparently snapped it into the latter position. She wrote a letter back, which Mari intercepted. Her jealousy aroused, Mari then wrote a letter to Anna’s husband claiming (wishfully more than truthfully) that Einstein was outraged by Anna’s “inappropriate letter” and brazen attempt to rekindle a relationship.
Einstein ended up having to calm matters with an apology to the husband. “I am very sorry if I have caused you distress by my careless behavior,” he wrote. “I answered the congratulatory card your wife sent me on the occasion of my appointment too heartily and thereby re-awakened the old affection we had for each other. But this was not done with impure intentions. The behavior of your wife, for whom I have the greatest respect, was totally honorable. It was wrong of my wife—and excusable only on account of extreme jealousy—to behave—without my knowledge—the way she did.”
Although the incident itself was of no consequence, it marked a turn in Einstein’s relationship with Mari. In his eyes, her brooding jealousy was making her darker. Decades later, still rankling at Mari’s behavior, he wrote to Anna’s daughter asserting, with a brutal bluntness, that his wife’s jealousy had been a pathological flaw typical of a woman of such “uncommon ugliness.”41
Mari indeed had a jealous streak. She resented not only her husband’s flirtations with other women but also the time he spent with male colleagues. Now that he had become a professor, she succumbed to a professional envy that was understandable given her own curtailed scientific career. “With that kind of fame, he does not have much time left for his wife,” she told her friend Helene Savi. “You wrote that I must be jealous of science. But what can you do? One gets the pearl, the other the box.”
In particular, Mari worried that her husband’s fame would make him colder and more self-centered. “I am very happy for his success, because he really does deserve it,” she wrote in another letter. “I only hope that fame does not exert a detrimental influence on his human side.”42
In one sense, Mari’s worries proved unwarranted. Even as his fame increased exponentially, Einstein would retain a personal simplicity, an unaffected style, and at least a veneer of genial humility. But viewed from a different reference frame, there were transformations to his human side. Sometime around 1909, he began drifting apart from his wife. His resistance to chains and bonds increasingly led him to escape into his work while taking a detached approach to the realm he dismissed as “the merely personal.”
On one of his last days working at the patent office, he received a large envelope with an elegant sheet covered in what seemed to be Latin calligraphy. Because it seemed odd and impersonal, he threw it in the wastebasket. It was, in fact, an invitation to be one of those receiving an honorary doctorate at the July 1909 commemoration of the founding of Geneva’s university, and authorities there finally got a friend of Einstein to persuade him to attend. Einstein brought only a straw hat and an informal suit, so he stood out rather strangely, both in the parade and at the opulent formal dinner that night. Amused by the whole situation, he turned to the patrician seated next to him and speculated about the austere Protestant Reformation leader who had founded the university: “Do you know what Calvin would have done had he been here?” The gentleman, befuddled, said no. Einstein replied, “He would have erected an enormous stake and had us all burnt for our sinful extravagance.” As Einstein later recalled,“The man never addressed another word to me.”43
Light Can Be Wave and Particle
Also at the end of the summer of 1909, Einstein was invited to address the annual Naturforscher conference, the preeminent meeting of German-speaking scientists, which was held that year in Salzburg. Organizers had put both relativity and the quantum nature of light on the agenda, and they expected him to speak on the former. Instead, Einstein decided that he preferred to emphasize what he considered the more pressing issue: how to interpret quantum theory and reconcile it with the wave theory of light that Maxwell had so elegantly formulated.
After his “happiest thought” at the end of 1907 about how the equivalence of gravity and acceleration might lead to a generalization of relativity theory, Einstein had put that subject aside to focus instead on what he called “the radiation problem” (i.e., quantum theory). The more he thought about his “heuristic” notion that light was made up of quanta, or indivisible packets, the more he worried that he and Planck had wrought a revolution that would destroy the classical foundations of physics, especially Maxwell’s equations. “I have come to this pessimistic view mainly as a result of endless, vain efforts to interpret . . . Planck’s constant in an intuitive way,” he wrote a fellow physicist early in 1908. “I even seriously doubt that it will be possible to maintain the general validity of Maxwell’s equations.”44 (As it turned out, his love of Maxwell’s equations was well placed. They are among the few elements of theoretical physics to remain unchanged by both the relativity and quantum revolutions that Einstein helped launch.)
When Einstein, still not officially a professor, arrived at the Salzburg conference in September 1909, he finally met Max Planck and other giants that he had known only through letters. On the afternoon of the third day, he stepped in front of more than a hundred famed scientists and delivered a speech that Wolfgang Pauli, who was to become a pioneer of quantum mechanics, later pronounced “one of the landmarks in the development of theoretical physics.”
Einstein began by explaining how the wave theory of light was no longer complete. Light (or any radiation) could also be regarded, he said, as a beam of particles or packets of energy, which he said was akin to what Newton had posited. “Light has certain basic properties that can be understood more readily from the standpoint of the Newtonian emission theory than from the standpoint of the wave theory,” he declared. “I thus believe that the next phase of theoretical physics will bring us a theory of light that can be interpreted as a kind of fusion of the wave and of the emission theories of light.”
Combining particle theory with wave theory, he warned, would bring “a profound change.” This was not a good thing, he feared. It could undermine the certainties and determinism inherent in classical physics.
For a moment, Einstein mused that perhaps such a fate could be avoided by accepting Planck’s more limited interpretation of quanta: that they were features only of how radiation was emitted and absorbed by a surface rather than a feature of the actual light wave as it propagated through space. “Would it not be possible,” he asked, “to retain at least the equations for the propagation of radiation and conceive only the processes of emission and absorption differently?” But after comparing the behavior of light to the behavior of gas molecules, as he had done in his 1905 light quanta paper, Einstein concluded that, alas, this was not possible.
As a result, Einstein said, light must be regarded as behaving like both an undulating wave and a stream of particles. “These two structural properties simultaneously displayed by radiation,” he declared at the end of his talk, “should not be considered as mutually incompatible.”45
It was the first well-conceived promulgation of the wave-particle duality of light, and it had implications as profound as Einstein’s earlier theoretical breakthroughs. “Is it possible to combine energy quanta and the wave principles of radiation?” he merrily wrote to a physicist friend. “Appearances are against it, but the Almighty—it seems—managed the trick.”46
A vibrant discussion followed Einstein’s speech, led by Planck himself. Still unwilling to embrace the physical reality underlying the mathematical constant that he had devised nine years earlier, or to accept the revolutionary ramifications envisioned by Einstein, Planck now played protector of the old order. He admitted that radiation involved discrete “quanta, which are to be conceived as atoms of action.” But he insisted that these quanta existed only as part of the process of radiation being emitted or absorbed. “The question is where to look for these quanta,” he said. “According to Mr. Einstein, it would be necessary to conceive that free radiation in a vacuum, and thus the light waves themselves consist of atomistic quanta, and hence force us to give up Maxwell’s equations. This seems to me a step that is not yet necessary.”47
Within two decades, Einstein would assume a similar role as protector of the old order. Indeed, he was already looking for ways out of the eerie dilemmas raised by quantum theory. “I am very hopeful that I will solve the radiation problem, and that I will do so without light quanta,” he wrote a young physicist he was working with.48
It was all too mystifying, at least for the time being. So as he moved up the professorial ranks in the German-speaking universities of Europe, he turned his attention back to the topic that was uniquely his own, relativity, and for a while became a refugee from the wonderland of the quanta. As he lamented to a friend, “The more successes the quantum theory enjoys, the sillier it looks.”49
THE WANDERING PROFESSOR
As a self-assured 17-year-old, Einstein had enrolled at the Zurich Polytechnic and met Mileva Mari, the woman he would marry. Now, in October 1909, at age 30, he was returning to that city to take up his post as a junior professor at the nearby University of Zurich.
Their homecoming restored, at least temporarily, some of the romance to their relationship. Mari was thrilled to be back in their original nesting ground, and by the end of their first month there she became pregnant again.
The apartment they rented was in a building where, they happily discovered, Friedrich Adler and his wife lived, and the couples became even closer friends. “They run a bohemian household,” Adler wrote his father approvingly. “The more I talk to Einstein, the more I realize that my favorable opinion of him was justified.”
The two men discussed physics and philosophy most evenings, often retreating to the attic of the three-story building so they would not be disturbed by children or spouses. Adler introduced Einstein to the work of Pierre Duhem, whose 1906 book La Théorie Physique Adler had just published in German. Duhem offered a more holistic approach than Mach did to the relationship between theories and experimental evidence, one that seemed to influence Einstein as he staked out his own philosophy of science.1
Adler particularly respected Einstein’s “most independent” mind. There was, he told his father, a nonconformist streak in Einstein that reflected an inner security but not an arrogance. “We find ourselves in agreement on questions that the majority of physicists would not even understand,” Adler boasted.2
Einstein tried to persuade Adler to focus on science rather than be enticed into politics. “Be a little patient,” he said. “You will certainly be my successor in Zurich one day.” (Einstein was already assuming that he would move on to a more prestigious university.) But Adler ignored the advice and decided to become an editor at the Social Democratic Party newspaper. Loyalty to a party, Einstein felt, meant surrendering some independence of thought. Such conformity confounded him. “How an intelligent man can subscribe to a party I find a complete mystery,” Einstein later lamented about Adler.3
Einstein was also reunited with his former classmate and note-taker Marcel Grossmann, who had helped him get his job at the patent office and was now a professor of math at their old Polytechnic. Einstein would often visit Grossmann after lunch for help with the complex geometry and calculus he needed to extend relativity into a more general field theory.
Einstein was even able to forge a friendship with the other distinguished math professor at the Polytechnic, Adolf Hurwitz, whose classes he had often skipped and who had spurned his plea for a job. Einstein became a regular at the Sunday music recitals at Hurwitz’s home. When Hurwitz told him during a walk one day that his daughter had been given a math homework problem she did not understand, Einstein showed up that afternoon to help her solve it.4
As Kleiner predicted, Einstein’s teaching talents improved. He was not a polished lecturer, but instead used informality to his advantage. “When he took his chair in shabby attire with trousers too short for him, we were skeptical,” recalled Hans Tanner, who attended most of Einstein’s Zurich lectures. Instead of prepared notes, Einstein used a card-sized strip of paper with scribbles. So the students got to watch him develop his thoughts as he spoke. “We obtained some insight into his working technique,” said Tanner. “We certainly appreciated this more than any stylistically perfect lecture.”
At each step of the way, Einstein would pause and ask the students if they were following him, and he even permitted interruptions. “This comradely contact between teacher and student was, at that time, a rare occurrence,” according to Adolf Fisch, another who attended the lectures. Sometimes he would take a break and let the students gather around him for casual conversation. “With an impulsiveness and naturalness he would take students by the arm to discuss things,” recalled Tanner.
During one lecture, Einstein found himself momentarily stumped about the steps needed to complete a calculation. “There must be some silly mathematical transformation that I can’t find for a moment,” he said. “Can one of you gentlemen see it?” Not surprisingly, none of them could. So Einstein continued: “Then leave a quarter of a page. We won’t lose any time.”Ten minutes later, Einstein interrupted himself in the middle of another point and exclaimed, “I’ve got it.” As Tanner later marveled, “During the complicated development of his theme he had still found time to reflect upon the nature of that particular mathematical transformation.”
At the end of many of his evening lectures, Einstein would ask, “Who’s coming to the Café Terasse?” There, with an informal cadre on a terrace overlooking the Limmat River, they would talk until closing time.
On one occasion, Einstein asked if anyone wanted to come back to his apartment. “This morning I received some work from Planck in which there must be a mistake,” he said. “We could read it together.” Tanner and another student took him up on the offer and followed him home. There they all pored over Planck’s paper. “See if you can spot the fault while I make some coffee,” he said.
After a while, Tanner replied, “You must be mistaken, Herr Professor, there is no error in it.”
“Yes, there is,” Einstein said, pointing to some discrepancies in the data, “for otherwise that and that would become that and that.” It was a vivid example of Einstein’s great strength: he could look at a complex mathematical equation, which for others was merely an abstraction, and picture the physical reality that lay behind it.
Tanner was astounded. “Let’s write to Professor Planck,” he suggested, “and tell him of the mistake.”
Einstein had by then become slightly more tactful, especially with those he placed on a pedestal, such as Planck and Lorentz. “We won’t tell him he made a mistake,” he said. “The result is correct, but the proof is faulty. We’ll simply write and tell him how the real proof should run. The main thing is the content, not the mathematics.”5
Despite his work on his machine to measure electrical charges, Einstein had become a confirmed theorist rather than experimental physicist. When he was asked during his second year as a professor to supervise laboratory work, he was dismayed. He hardly dared, he told Tanner, “pick up a piece of apparatus for fear it might blow up.” To another eminent professor he confided, “My fears regarding the laboratory were rather well founded.”6
As he was finishing his first academic year at Zurich, in July 1910, Mari gave birth, again with difficulty, to their second son, named Eduard and called Tete. She was ill for weeks afterward. Her doctor, contending that she was overworked, suggested that Einstein find a way to make more money and pay for a maid. Mari was annoyed and protective. “Isn’t it clear to anyone that my husband works himself half dead?” she said. Instead, her mother came down from Novi Sad to help.7
Throughout his life, Einstein would sometimes appear aloof toward his two sons, especially Eduard, who suffered from increasingly severe mental illness as he grew older. But when they were young, he tended to be a good father. “When my mother was busy around the house, father would put aside his work and watch over us for hours, bouncing us on his knee,” Hans Albert later recalled. “I remember he would tell us stories—and he often played the violin in an effort to keep us quiet.”
One of his strengths as a thinker, if not as a parent, was that he had the ability, and the inclination, to tune out all distractions, a category that to him sometimes included his children and family. “Even the loudest baby-crying didn’t seem to disturb Father,” Hans Albert said. “He could go on with his work completely impervious to noise.”
One day his student Tanner came for a visit and found Einstein in his study poring over a pile of papers. He was writing with his right hand and holding Eduard with his left. Hans Albert was playing with toy bricks and trying to get his attention. “Wait a minute, I’ve nearly finished,” Einstein said, as he handed Eduard to Tanner and kept scribbling his equations. “It gave me,” said Tanner, “a glimpse into his immense powers of concentration.”8
Einstein had been in Zurich less than six months when he received, in March 1910, a solicitation to consider a more prestigious job: a full professorship at the German part of the University of Prague. Both the university and the academic position were a step up; however, moving from the familiar and friendly Zurich to the less congenial Prague would be disruptive for his family. For Einstein, the professional considerations outweighed the personal ones.
He was again going through difficult periods at home. “The bad mood that you noticed in me had nothing to do with you,” he wrote to his mother, who was now living in Berlin. “To dwell on the things that depress or anger us does not help in overcoming them. One must knock them down alone.”
His scientific work, on the other hand, was giving him great pleasure, and he expressed excitement about his possible new opportunity. “It is most probable that I will be offered the position of full professor at a large university with a significantly better salary than I now have.”9
When word of Einstein’s possible move spread in Zurich, fifteen of his students, led by Hans Tanner, signed a petition urging officials there “to do your utmost to keep this outstanding researcher and teacher at our university.” They stressed the importance of having a professor in “this newly created discipline” of theoretical physics, and they extolled him personally in effusive terms. “Professor Einstein has an amazing talent for presenting the most difficult problems of theoretical physics so clearly and so comprehensibly that it is a great delight for us to follow his lectures, and he is so good at establishing a perfect rapport with his audience.”10
The Zurich authorities were so eager to keep him that they raised his salary from its current 4,500 francs, which was the same as he made as a patent examiner, to 5,500 francs. Those attempting to lure him to Prague, on the other hand, were having a more difficult time.
The faculty department at Prague had settled on Einstein as its first choice and forwarded the recommendation to the education ministry in Vienna. (Prague was then part of the Austro-Hungarian Empire, and such an appointment had to be approved by Emperor Franz Joseph and his ministers.) The report was accompanied by the highest possible recommendation from the best possible authority, Max Planck. Einstein’s theory of relativity “probably exceeds in audacity everything that has been achieved so far in speculative science,” Planck proclaimed. “This principle has brought about a revolution in our physical picture of the world that can be compared only to that produced by Copernicus.” In a comment that might later have seemed prescient to Einstein, Planck added, “Non-Euclidean geometry is child’s play by comparison.”11
Planck’s imprimatur should have been enough. But it wasn’t. The ministry decided that it preferred the second-place candidate, Gustav Jaumann, who had two advantages: he was Austrian, and he was not Jewish. “I did not get the call to Prague,” Einstein lamented to a friend in August. “I was proposed by the faculty, but because of my Semitic origin the ministry did not approve.”
Jaumann, however, soon discovered that he was the faculty’s second choice, and he erupted. “If Einstein has been proposed as the first choice because of the belief that he has greater achievements to his credit,” he declared, “then I will have nothing to do with a university that chases after modernity and does not appreciate merit.” So by October 1910, Einstein could confidently declare that his own appointment was “almost certain.”
There was one final hurdle, also dealing with religion. Being a Jew was a disadvantage; being a nonbeliever who claimed no religion was a disqualifier. The empire required that all of its servants, including professors, be a member of some religion. On his official forms, Einstein had written that he had none. “Einstein is as unpractical as a child in cases like this,” Friedrich Adler’s wife noted.
As it turned out, Einstein’s desire for the job was greater than his ornery impracticality. He agreed to write “Mosaic” as his faith, and he also accepted Austro-Hungarian citizenship, with the proviso that he was allowed to remain a Swiss citizen as well. Along with the German citizenship that he had forsaken but that would soon be foisted back on him, that meant he had held, off and on, three citizenships by the age of 32. In January 1911, he was officially appointed to the post, with a pay twice what he had been making before his recent raise. He agreed to move to Prague that March.12
Einstein had two scientific heroes he had never met—Ernst Mach and Hendrik Lorentz—and he was able to visit them both before his move to Prague. When he went to Vienna for his formal presentation to the ministers there, he called on Mach, who lived in a suburb of that city. The aging physicist and preacher of empiricism, who so deeply influenced the Olympia Academy and instilled in Einstein a skepticism about unobservable concepts such as absolute time, had a gnarly beard and gnarlier personality. “Please speak loudly to me,” he barked when Einstein entered his room. “In addition to my other unpleasant characteristics I am also almost stone deaf.”
Einstein wanted to convince Mach of the reality of atoms, which the old man had long rejected as being imaginary constructs of the human mind. “Let us suppose that by assuming the existence of atoms in a gas we were able to predict an observable property of this gas that could not be predicted on the basis of non-atomistic theory,” Einstein asked. “Would you then accept such a hypothesis?”
“If with the help of the atomic hypothesis one could actually establish a connection between several observable properties which without it would remain isolated, then I should say that this hypothesis was an ‘economical’ one,” Mach grudgingly replied.
It was not a full acceptance, but it was enough for Einstein. “For the moment Einstein was satisfied,” his friend Philipp Frank noted. Nevertheless, Einstein began edging away from Mach’s skepticism about any theories of reality not built on directly observable data. He developed, said Frank, “a certain aversion to the Machist philosophy.”13 It was the beginning of an important conversion.
Just before moving to Prague, Einstein went to the Dutch town of Leiden to meet Lorentz. Mari accompanied him, and they accepted an invitation to stay with Lorentz and his wife. Einstein wrote that he was looking forward to having a conversation on “the radiation problem,” adding, “I wish to assure you in advance that I am not the orthodox light-quantizer for whom you take me.”14
Einstein had long idolized Lorentz from afar. Just before he went to visit, he wrote a friend: “I admire this man like no other; I might say, I love him.” The feeling was reinforced when they finally met. They stayed up late on Saturday night discussing such issues as the relationship between temperature and electrical conductivity.
Lorentz thought he had caught Einstein in a small mathematical mistake in one of his papers on light quanta, but in fact, as Einstein noted, it was simply “a one-time writing error” where he had left out a “½” that was included later in the paper.15 Both the hospitality and “scientific stimulus” made Einstein effusive in his next letter. “You radiate so much goodness and benevolence,” he wrote, “that the troubling conviction that I did not deserve the great kindness and honors could not even enter my mind during my stay at your house.”16
Lorentz became, in the words of Abraham Pais, “the one father figure in Einstein’s life.” After his pleasant visit to Lorentz’s study in Leiden, he would return whenever he could find an excuse. The atmosphere of such meetings was captured by their colleague Paul Ehrenfest:
The best easy chair was carefully pushed in place next to the large work table for his esteemed guest. A cigar was given to him, and then Lorentz quietly began to formulate questions concerning Einstein’s theory of the bending of light in a gravitational field . . . As Lorentz spoke on, Einstein began to puff less frequently on his cigar, and he sat more intently in his armchair. And when Lorentz had finished, Einstein bent over the slip of paper on which Lorentz had written mathematical formulas. The cigar was out, and Einstein pensively twisted his finger in a lock of hair over his right ear. Lorentz sat smiling at an Einstein completely lost in meditation, exactly the way that a father looks at a particularly beloved son—full of confidence that the youngster will crack the nut he has given him, but eager to see how. Suddenly, Einstein’s head sat up joyfully; he had it. Still a bit of give and take, interrupting one another, a partial disagreement, very quick clarification and a complete mutual understanding, and then both men with beaming eyes skimming over the shining riches of the new theory.
When Lorentz died in 1928, Einstein would say in his eulogy, “I stand at the grave of the greatest and noblest man of our times.” And in 1953, for the celebration of the hundredth anniversary of Lorentz’s birth, Einstein wrote an essay on his importance. “Whatever came from this supreme mind was as lucid and beautiful as a good work of art,” he wrote. “He meant more to me personally than anybody else I have met in my lifetime.”18
Mari was unhappy about moving to Prague. “I am not going there gladly and I expect very little pleasure,” she wrote a friend. But initially, until the city’s dirtiness and snobbishness became oppressive, their life there was nice enough. They had electric lighting in their home for the first time, and both the space and money for a live-in maid. “The people are haughty, shabby-genteel, or subservient, depending on their lot in life,” Einstein said. “Many of them possess a certain grace.”19
From Einstein’s office at the university he could look down on a beautiful park with shady trees and manicured gardens. In the morning, it would be filled just with women, and in the afternoon just with men. Some walked alone as if deep in thought, Einstein noticed, while others clustered in groups holding animated arguments. Eventually, Einstein asked what the park was. It belonged, he was told, to an insane asylum. When he showed his friend Philipp Frank the view, Einstein commented ruefully, “Those are the madmen who do not occupy themselves with the quantum theory.”20
The Einsteins became acquainted with Bertha Fanta, a delightfully cultured woman who hosted at her home a literary and musical salon for Prague’s Jewish intelligentsia. Einstein was the ideal catch: a rising scholar who was willing, with equal gusto, to play the violin or discuss Hume and Kant, depending on the spirit of the occasion. Other habitués included the young writer Franz Kafka and his friend Max Brod.
In his book The Redemption of Tycho Brahe, Brod seemed to use (though he sometimes denied it) Einstein as the model for the character of Johannes Kepler, the brilliant astronomer who had been Brahe’s assistant in Prague in 1600. The character is devoted to his scientific work and is always willing to throw away conventional thinking. But in the realm of the personal, he is protected from “the aberrations of feeling” by his aloof and abstracted air. “He had no heart and therefore nothing to fear from the world,” Brod wrote. “He was not capable of emotion or love.” When the novel came out, a fellow scientist, Walther Nernst, said to Einstein, “You are this man Kepler.”21
Not really. Despite the image he sometimes cast as a loner, Einstein continued to establish, as he had back in Zurich and Bern, intimate friendships and emotional bonds, particularly with fellow thinkers and scientists. One such friend was Paul Ehrenfest, a young Jewish physicist from Vienna who was teaching at the University of St. Petersburg but feeling professionally stymied there because of his background. In early 1912, he embarked on a trip through Europe looking for a new job, and on his way toward Prague contacted Einstein, with whom he had been corresponding about gravity and radiation. “Do stay at my house so that we can make good use of the time,” Einstein responded.22
When Ehrenfest arrived one rainy Friday afternoon in February, a cigar-puffing Einstein and his wife were at the train station to meet him. They all walked to a café, where they compared the great cities of Europe. When Mari left, the discussion turned to science, most notably statistical mechanics, and they continued talking as they walked to Einstein’s office. “On the way to the institute, first argument about everything,” Ehrenfest recorded in his diary of the seven days he spent in Prague.
Ehrenfest was a mousy and insecure man, but his eagerness for friendship and his love of physics made it easy for him to forge a bond with Einstein.23 They both seemed to crave arguing about science, and Einstein later said that “within a few hours we were friends as if Nature created us for each other.”Their intense discussions continued the next day, as Einstein explained his efforts to generalize his theory of relativity. On Sunday evening, they relaxed a bit by performing Brahms, with Ehrenfest on piano, Einstein on violin, and 7-year-old Hans Albert singing. “Yes we will be friends,” Ehrenfest wrote in his diary that night. “Was awfully happy.”24
Einstein was already thinking of leaving Prague, and he suggested Ehrenfest as a possible successor. But he “adamantly refuses to profess any religious affiliation,” Einstein lamented. Unlike Einstein, who was willing to relent and write “Mosaic” on his official forms, Ehrenfest had abandoned Judaism and would not profess otherwise. “Your stubborn refusal to acknowledge any religious affiliation really bugs me,” Einstein wrote him in April. “Drop it for your children’s sake. After all, after becoming a professor here you could revert to this strange hobby horse of yours.”25
Matters eventually came to a happy resolution when Ehrenfest accepted an offer, which Einstein had earlier received but declined, to replace the revered Lorentz, who was cutting back from full-time teaching at the University of Leiden. Einstein was thrilled, for it meant he would now have two friends there to visit regularly. It became, for Einstein, almost a second academic home and a way to escape the oppressive atmosphere he later found in Berlin. Almost every year for the next two decades, until 1933 when Ehrenfest committed suicide and Einstein moved to America, Einstein would make regular pilgrimages to see him and Lorentz in Leiden or at the seaside resorts nearby.26
The 1911 Solvay Conference
Ernest Solvay was a Belgian chemist and industrialist who reaped a fortune by inventing a method for making soda. Because he wanted to do something unusual yet useful with his money, and also because he had some odd theories of gravity that he wanted scientists to listen to, he decided to fund an elite gathering of Europe’s top physicists. Scheduled for the end of October 1911, it eventually spawned a series of influential meetings, known as Solvay Conferences, that were held sporadically over the ensuing years.
Twenty of Europe’s most famous scientists showed up at the Grand Hotel Metropole in Brussels. At 32, Einstein was the youngest. There was Max Planck, Henri Poincaré, Marie Curie, Ernest Rutherford, and Wilhelm Wien. The chemist Walther Nernst organized the event and acted as chaperone for the quirky Ernest Solvay. The kindly Hendrik Lorentz served as the chairman, as his fan Einstein put it, “with incomparable tact and unbelievable virtuosity.”27
The focus of the conference was “the quantum problem,” and Einstein was asked to present a paper on that topic, making him one of only eight “particularly competent members” thus honored. He expressed some annoyance, perhaps a bit more feigned than real, about the prestigious assignment. He dubbed the upcoming meeting “the witch’s Sabbath” and complained to Besso, “My twaddle for the Brussels conference weighs down on me.”28
Einstein’s talk was titled “The Present State of the Problem of Specific Heats.” Specific heat—the quantity of energy required to increase the temperature of a specific amount of substance by a certain amount—had been a specialty of Einstein’s former professor and antagonist at the Zurich Polytechnic, Heinrich Weber. Weber had discovered some anomalies, especially at low temperatures, in the laws that were supposed to govern specific heat. Beginning in late 1906, Einstein had come up with what he called a “quantized” approach to the problem by surmising that the atoms in each substance could absorb energy only in discrete packets.
In his 1911 Solvay lecture, Einstein put these issues into the larger context of the so-called quantum problem. Was it possible, he asked, to avoid accepting the physical reality of these atomistic particles of light, which were like bullets aimed at the heart of Maxwell’s equations and, indeed, all of classical physics?
Planck, who had pioneered the concept of the quanta, continued to insist that they came into play only when light was being emitted or absorbed. They were not a real-world feature of light itself, he argued. Einstein, in his talk to the conference, sorrowfully demurred: “These discontinuities, which we find so distasteful in Planck’s theory, seem really to exist in nature.”29
Really to exist in nature. It was, for Einstein, an odd phrase. To a pure proponent of Mach, or for that matter of Hume, the whole phrase “really to exist in nature” lacked clear meaning. In his special relativity theory, Einstein had avoided assuming the existence of such things as absolute time and absolute distance, because it seemed meaningless to say that they “really” existed in nature when they couldn’t be observed. But henceforth, during the more than four decades in which he would express his discomfort with quantum theory, he increasingly sounded like a scientific realist, someone who believed that an underlying reality existed in nature that was independent of our ability to observe or measure it.
When he was finished, Einstein faced a barrage of challenges from Lorentz, Planck, Poincaré, and others. Some of what Einstein said, Lorentz rose to point out,“seems in fact to be totally incompatible with Maxwell’s equations.”
Einstein agreed, perhaps too readily, that “the quantum hypothesis is provisional” and that it “does not seem compatible with the experimentally verified conclusions of the wave theory.” Somehow it was necessary, he told his questioners, to accommodate both wave and particle approaches to the understanding of light. “In addition to Maxwell’s electrodynamics, which is essential to us, we must also admit a hypothesis such as that of quanta.”30
It was unclear, even to Einstein, whether Planck was persuaded of the reality of quanta. “I largely succeeded in convincing Planck that my conception is correct, after he has struggled against it for so many years,” Einstein wrote his friend Heinrich Zangger. But a week later, Einstein gave Zangger another report: “Planck stuck stubbornly to some undoubtedly wrong preconceptions.”
As for Lorentz, Einstein remained as admiring as ever: “A living work of art! He was in my opinion the most intelligent of the theoreticians present.” He dismissed Poincaré, who paid little attention to him, with a brusque stroke: “Poincaré was simply negative in general, and, all his acumen notwithstanding, he showed little grasp of the situation.”31
Overall he gave low marks to the conference, where most of the time was spent bewailing rather than resolving quantum theory’s threat to classical mechanics. “The congress in Brussels resembled the lamentations on the ruins of Jerusalem,” he wrote Besso. “Nothing positive has come out of it.”32
There was one interesting sideshow for Einstein: the romance between the widowed Marie Curie and the married Paul Langevin. Dignified and dedicated, Madame Curie was the first woman to win a Nobel Prize; she shared the 1903 physics prize with her husband and one other scientist for their work on radiation. Three years later, her husband was killed by a horse-drawn wagon. She was bereft, and so was her late husband’s protégé, Langevin, who taught physics at the Sorbonne with the Curies. Langevin was trapped in a marriage with a wife who physically abused him, and soon he and Marie Curie were having an affair in a Paris apartment. His wife had someone break into it and steal their love letters.
Just as the Solvay Conference was getting under way, with both Curie and Langevin in attendance, the purloined letters began appearing in a Paris tabloid as a prelude to a sensational divorce case. In addition, at that very moment, it was announced that Curie had won the Nobel Prize in chemistry, for discovering radium and polonium.* A member of the Swedish Academy wrote her to suggest that she not appear to receive it, given the furor raised by her relationship with Langevin, but she coolly responded, “I believe there is no connection between my scientific work and the facts of private life.” She headed to Stockholm and accepted the prize.33
The whole furor seemed silly to Einstein. “She is an unpretentious, honest person,” he said, with “a sparkling intelligence.” He also rather bluntly came to the conclusion, not justified, that she was not pretty enough to wreck anyone’s marriage. “Despite her passionate nature,” he said, “she is not attractive enough to represent a danger to anyone.”34
More gracious was the sturdy letter of support he sent her later that month:
Do not laugh at me for writing you without having anything sensible to say. But I am so enraged by the base manner in which the public is presently daring to concern itself with you that I absolutely must give vent to this feeling. I am impelled to tell you how much I have come to admire your intellect, your drive, and your honesty, and that I consider myself lucky to have made your personal acquaintance in Brussels. Anyone who does not number among these reptiles is certainly happy, now as before, that we have such personages among us as you, and Langevin too, real people with whom one feels privileged to be in contact. If the rabble continues to occupy itself with you, then simply don’t read that hogwash, but rather leave it to the reptile for whom it has been fabricated.
As Einstein wandered around Europe giving speeches and basking in his rising renown, his wife stayed behind in Prague, a city she hated, and brooded about not being part of the scientific circles that she once struggled to join. “I would like to have been there and listened a little, and seen all these fine people,” she wrote him after one of his talks in October 1911. “It is so long since we saw each other that I wonder if you will recognize me.” She signed herself, “Deine alte D,” your old D, as if she were still his Dollie, albeit a bit older.36
Her circumstances, perhaps combined with an innate disposition, caused her to become gloomy, even depressed. When Philipp Frank met her in Prague for the first time, he thought that she might be schizophrenic. Einstein concurred, and he later told a colleague that her gloominess “is doubtless traceable to a schizophrenic genetic disposition coming from her mother’s family.”37
Thus it was that Einstein’s marriage was once again in an unstable state when he traveled alone to Berlin during the Easter holidays in 1912. There he became reacquainted with a cousin, three years older, whom he had known as a child.
Elsa Einstein* was the daughter of Rudolf (“the rich”) Einstein and Fanny Koch Einstein. She was Einstein’s cousin on both sides. Her father was the first cousin of Einstein’s father, Hermann, and had helped fund his business. Her mother was the sister of Einstein’s mother, Pauline (making Elsa and Albert first cousins). After Hermann’s death, Pauline had moved in with Rudolf and Fanny Einstein for a few years, helping them keep house.
As children, Albert and Elsa had played together at the home of Albert’s parents in Munich and on one occasion had shared a first artistic experience at the opera.38 Since then, Elsa had been married, divorced, and now, at age 36, was living with her two daughters, Margot and Ilse, in the same apartment building as her parents.
The contrast with Einstein’s wife was stark. Mileva Mari was exotic, intellectual, and complex. Elsa wasn’t. Instead, she was conventionally handsome and domestically nurturing. She loved heavy German comfort foods and chocolate, which tended to give her a rather ample, matronly look. Her face was similar to her cousin’s, and it would become strikingly more so as they aged.39
Einstein was looking for new companionship, and he first flirted with Elsa’s sister. But by the end of his Easter visit, he had settled on Elsa as offering the comfort and nurturing that he now craved. The love he was seeking, it seems, was not wild romance but uncomplicated support and affection.
And Elsa, who revered her cousin, was eager to give it. When he returned to Prague, she wrote him right away—sending the letter to his office, not his home, and proposing a way they could correspond in secret. “How dear of you not to be too proud to communicate with me in such a way!” he responded. “I can’t even begin to tell you how fond I have become of you during these few days.” She asked him to destroy her letters, which he did. She, on the other hand, kept his responses for the rest of her life in a folder that she tied and later labeled “Especially beautiful letters from better days.”40
Einstein apologized for his flirtation with her sister Paula.“It is hard for me to understand how I could have taken a fancy to her,” he declared. “But it is in fact simple. She was young, a girl, and complaisant.”
A decade earlier, when he was writing his love letters to Mari that celebrated their own rarefied and bohemian approach to life, Einstein would likely have lumped relatives such as Elsa into the category of “bourgeois philistines.” But now, in letters that were almost as effusive as the ones he had written to Mari, he professed his new passion for Elsa. “I have to have someone to love, otherwise life is miserable,” he wrote. “And this someone is you.”
She knew how to make him defensive: she teased him for being under Mari’s thumb and asserted that he was “henpecked.” As she may have hoped, Einstein responded by protesting that he would show her otherwise. “Do not think about me in such a way!” he said. “I categorically assure you that I consider myself a full-fledged male. Perhaps I will sometime have the opportunity to prove it to you.”
Spurred by this new affection and by the prospect of working in the world’s capital of theoretical physics, Einstein developed a desire to move to Berlin. “The chances of getting a call to Berlin are, unfortunately, slight,” he admitted to Elsa. But on his visit, he did what he could to increase his chances of someday getting a position there. In his notebook he listed appointments he had been able to get with important academic leaders, including the scientists Fritz Haber, Walther Nernst, and Emil Warburg.41
Einstein’s son Hans Albert later recalled that it was just after his eighth birthday, in the spring of 1912, when he noticed that his parents’ marriage was falling apart. But after returning to Prague from Berlin, Einstein seemed to develop qualms about his affair with his cousin. He tried, in two letters, to put an end to it. “There would only be confusion and misfortune if we were to give into our mutual attraction,” he wrote Elsa.
Later that month, he tried to be even more definitive. “It will not be good for the two of us, as well as for the others, if we form a closer attachment. So, I am writing to you today for the last time and am submitting again to the inevitable, and you must do the same. You know that it is not hardness of heart or lack of feeling that makes me talk like this, because you know that, like you, I bear my cross without hope.”42
Einstein and Mari shared one thing: a feeling that living among the middle-class German community in Prague had become wearisome. “These are not people with natural sentiments,” he told Besso. They displayed “a peculiar mixture of snobbery and servility, without any kind of goodwill toward their fellow men.” The water was un-drinkable, the air was full of soot, and an ostentatious luxury was juxtaposed with misery on the streets. But what offended Einstein most were the artificial class structures. “When I come to the institute,” he complained, “a servile man who smells of alcohol bows and says, ‘your most humble servant.’ ”43
Mari worried that the bad water, milk, and air were hurting the health of their younger son, Eduard. He had lost his appetite and was not sleeping well. It was also now clear that her husband cared more about his science than his family. “He is tirelessly working on his problems; one can say that he lives only for them,” she told her friend Helene Savi. “I must confess with a bit of shame that we are unimportant to him and take second place.”44
So Einstein and his wife decided to return to the one place they thought could restore their relationship.
The Zurich Polytechnic, where Einstein and Mari had blissfully shared their books and their souls, had been upgraded in June 1911 to a full university, now named the Eidgenössische Technische Hochschule (ETH), or the Swiss Federal Institute of Technology, with the right to grant graduate degrees. At 32 and by now quite famous in the world of theoretical physics, Einstein should have been an easy and obvious choice for one of the new professorships available there.
That possibility had been discussed a year earlier. Before he left for Prague, Einstein had made a deal with officials in Zurich. “I promised in private that I would advise them before accepting another offer from somewhere else, so that the administration of the Polytechnic could also make me an offer if they find it fit to do so,” he told a Dutch professor who was trying to recruit him to Utrecht.45
By November 1911, Einstein had received such an offer from Zurich, or at least so he thought, and as a result he declined the offer to go to Utrecht. But the matter was not completely settled, because some of Zurich’s education officials objected. They argued that a professor in theoretical physics was a “luxury,” that there was not enough lab space to accommodate one, and that Einstein personally was not a good teacher.
Heinrich Zangger, a longtime friend who was a medical researcher in Zurich, intervened on Einstein’s behalf. “A proper theoretical physicist is a necessity these days,” he wrote in a letter to one of the top Swiss councilors. He also pointed out that in such a role Einstein “needs no laboratory.” As for Einstein’s teaching talents, Zangger provided a wonderfully nuanced and revealing description:
He is not a good teacher for mentally lazy gentlemen who merely want to fill a notebook and then learn it by heart for an exam; he is not a
smooth talker, but anyone wishing to learn honestly how to develop his ideas in physics in an honest way, from deep within, and how to examine all premises carefully and see the pitfalls and the problems in his reflections, will find Einstein a first-class teacher, because all of this is expressed in his lectures, which force the audience to think along.
Zangger wrote Einstein to express his outrage at the dithering in Zurich, and Einstein replied, “The dear Zurich folks can kiss my . . . [und die lieben Züricher können mich auch . . . (ellipses are in original letter)].” He told Zangger not to push the matter further. “Leave the Polytechnic* to God’s inscrutable ways.”47
Einstein, however, decided not to drop the matter but instead to push the Polytechnic through a light ruse. Officials at the university in Utrecht were just about to offer their open post to someone else, Peter Debye, when Einstein asked them to hold off. “I am turning to you with a strange request,” he wrote. The Zurich Polytechnic had initially seemed very eager to recruit him, he said, and it had been proceeding with haste out of fear that he would go to Utrecht. “But if they were to learn in the near future that Debye is going to Utrecht, they would lose their fervor at once and keep me forever in suspense. I ask you therefore to wait a little longer with the official offer to Debye.”48
Rather oddly, Einstein found himself needing letters of recommendation to secure a post at his own alma mater. Marie Curie wrote one. “In Brussels, where I attended a scientific conference in which Mr. Einstein also participated, I was able to admire the clarity of his intellect, the breadth of his information, and the profundity of his knowledge,” she noted.49
Adding to the irony was that his other main letter of recommendation came from Henri Poincaré, the man who had almost come up with the special theory of relativity but still had not embraced it. Einstein was “one of the most original minds I have ever come across,” he said. Particularly poignant was his description of Einstein’s willingness, which Poincaré himself lacked, to make radical conceptual leaps: “What I admire in him in particular is the facility with which he adapts himself to new concepts. He does not remain attached to classical principles, and, when presented with a problem in physics, is prompt to envision all the possibilities.” Poincaré, however, could not resist asserting, perhaps with relativity in mind, that Einstein might not be right in all his theories: “Since he seeks in all directions one must expect the majority of the paths on which he embarks to be blind alleys.”50
Soon it all worked out. Einstein would move back to Zurich in July 1912. He thanked Zangger for helping him to prevail “against all odds,” and exulted, “I am enormously happy that we will be together again.” Mari was thrilled as well. She thought that the return could help save both her sanity and their marriage. Even the children seemed happy to be out of Prague and back to the city of their birth. As Einstein put it in a postcard to another friend,“Great joy about it among us old folks and the two bear cubs.”51
His departure caused a minor controversy in Prague. Newspaper articles noted that anti-Semitism at the university may have played a role. Einstein felt compelled to issue a public statement. “Despite all presumptions,” he said,“I did not feel and did not notice any religious prejudice.” The appointment of Philipp Frank, a Jew, as his successor, he added, confirmed that “such considerations”were not a major problem.52
Life in Zurich should have been glorious. The Einsteins were able to afford a modern six-room apartment with grand views. They were reunited with friends such as Zangger and Grossmann, and there was even one fewer adversary. “The fierce Weber has died, so it will be very pleasant from a personal point of view,” Einstein wrote of their undergraduate physics professor and nemesis, Heinrich Weber.53
Once again there were musical gatherings at the home of math professor Adolf Hurwitz. The programs included not only Mozart, Einstein’s favorite, but also Schumann, who was Mari’s. On Sunday afternoons, Einstein would arrive with his wife and two little boys at the doorstep and announce, “Here comes the whole Einstein hen house.”
Despite being back with such friends and diversions, Mari’s depression continued to deepen, and her health to decline. She developed rheumatism, which made it hard for her to go out, especially when the streets became icy in winter. She attended the Hurwitz recitals less frequently, and when she did show up her gloom was increasingly evident. In February 1913, to entice her out, the Hurwitz family planned an all-Schumann recital. She came, but seemed paralyzed by pain, both mental and physical.54
Thus the atmosphere was ripe for a catalyst that would disrupt this unstable family situation. It came in the form of a letter. After almost a year of silence, Elsa Einstein wrote to her cousin.
The previous May, when he had declared that he was writing her “for the last time,” Einstein had nonetheless given her the address of what would be his new office in Zurich. Now Elsa decided to send him a greeting for his thirty-fourth birthday, and she added a request for a picture of him and a recommendation of a good book she could read on relativity. She knew how to flatter.55
“There is no book on relativity that is comprehensible to the layman,” he replied. “But what do you have a relativity cousin for? If you ever happen to be in Zurich, then we (without my wife, who is unfortunately very jealous) will take a nice walk, and I will tell you about all of those curious things that I discovered.” Then he went a bit further. Instead of sending a picture, wouldn’t it be better to see each other in person? “If you wish to make me truly happy, then arrange to spend a few days here sometime.”56
A few days later, he wrote again, with word that he had instructed a photographer to send her a picture. He had been working on generalizing his theory of relativity, he reported, and it was exhausting. As he had a year earlier, he complained about being married to Mari: “What I wouldn’t give to be able to spend a few days with you, but without my cross!” He asked Elsa if she would be in Berlin later that summer. “I would like to come for a short visit.”57
It was therefore not surprising that Einstein was very receptive, a few months later, when the two towers of Berlin’s scientific establishment—Max Planck and Walther Nernst—came to Zurich with an enticing proposal. Having been impressed by Einstein at the Solvay Conference of 1911, they had already been sounding out colleagues about getting him to Berlin.
The offer they brought with them, when they arrived with their wives on the night train from Berlin on July 11, 1913, had three impressive components: Einstein would be elected to a coveted vacancy in the Prussian Academy of Sciences, which would come with a hefty stipend; he would become the director of a new physics institute; and he would be made a professor at the University of Berlin. The package included a lot of money, and it was not nearly as much work as it may have seemed on the surface. Planck and Nernst made it clear that Einstein would have no required teaching duties at the university and no real administrative tasks at the institute. And though he would be required to accept German citizenship once again, he could keep his Swiss citizenship as well.
The visitors made their case during a long visit to Einstein’s sunny office at the Polytechnic. He said he needed a few hours to think it over, though it is likely he knew he would accept. So Planck and Nernst took their wives on an excursion by funicular railway up one of the nearby mountains. With puckish amusement, Einstein told them he would be awaiting their return to the station with a signal. If he had decided to decline, he would be carrying a white rose, and if he was going to accept, a red rose (some accounts have the signal being a white handkerchief). When they stepped off the train, they happily discovered that he had accepted.58
That meant that Einstein would become, at 34, the youngest member of the Prussian Academy. But first Planck had to get him elected. The letter he wrote, which was also signed by Nernst and others, had the memorable but incorrect concession, quoted earlier, that “he might sometimes have overshot the target in his speculations, as for example in his light quantum hypothesis.” But the rest of the letter was suffused with extravagant praise for each of his many scientific contributions. “Among the great problems abundant in modern physics, there is hardly one to which Einstein has not made a remarkable contribution.”59
The Berliners were taking a risk, Einstein realized. He was being recruited not for his teaching skills (as he would not be teaching), nor for his administrative ones. And even though he had been publishing outlines and papers describing his ongoing efforts to generalize relativity, it was unclear whether he would succeed in that quest. “The Germans are gambling on me as they would on a prize-winning hen,” he told a friend as they were leaving a party, “but I don’t know if I can still lay eggs.”60
Einstein, likewise, was taking a risk. He had a secure and lucrative post in a city and society that he, his wife, and his family loved. The Swiss personality agreed with him. His wife had a Slav’s revulsion for all things Teutonic, and he had a similar distaste that had been in-grained in childhood. As a boy he had run away from Prussian-accented parades and Germanic rigidity. Only the opportunity to be gloriously coddled in the world capital of science could have compelled him to make such a move.
Einstein found the prospect thrilling and a bit amusing. “I am going to Berlin as an Academy-man without any obligations, rather like a living mummy,” he wrote fellow physicist Jakob Laub. “I’m already looking forward to this difficult career!”61 To Ehrenfest he admitted, “I accepted this odd sinecure because giving lectures gets on my nerves.”62 However, to the venerable Hendrik Lorentz in Holland Einstein displayed more gravitas: “I could not resist the temptation to accept a position in which I am relieved of all responsibilities so that I can give myself over completely to rumination.”63
There was, of course, another factor that made the new job enticing: the chance to be with his cousin and new love, Elsa. As he would later admit to his friend Zangger, “She was the main reason for my going to Berlin, you know.”64
The same evening that Planck and Nernst left Zurich, Einstein wrote Elsa an excited letter describing the “colossal honor” they had offered. “Next spring at the latest, I’ll come to Berlin for good,” he exulted. “I already rejoice at the wonderful times we will spend together!”
During the ensuing week, he sent two more such notes. “I rejoice at the thought that I will soon be coming to you,” he wrote in the first. And a few days later: “Now we will be together and rejoice in each other!” It is impossible to know for sure what relative weight to assign to each of the factors enticing him to Berlin: the unsurpassed scientific community there, the glories and perks of the post he was offered, or the chance to be with Elsa. But at least to her he claimed it was primarily the latter. “I look forward keenly to Berlin, mainly because I look forward to you.”65
Elsa had actually tried to help him get the offer. Earlier in the year, on her own initiative, she had dropped in on Fritz Haber, who ran the Kaiser Wilhelm Institute of Chemistry in Berlin, and let him know that her cousin might be open to a position that would bring him to Berlin. When he learned of Elsa’s intervention, Einstein was amused. “Haber knows who he is dealing with. He knows how to appreciate the influence of a friendly female cousin . . . The nonchalance with which you dropped in on Haber is pure Elsa. Did you tell anyone about it, or did you consult only with your wicked heart? If only I could have looked on!”66
Even before Einstein moved to Berlin, he and Elsa began to correspond as if they were a couple. She worried about his exhaustion and sent him a long letter prescribing more exercise, rest, and a healthier diet. He responded by saying that he planned to “smoke like a chimney, work like a horse, eat without thinking, go for a walk only in really pleasant company.”
He made clear, however, that she should not expect him to abandon his wife: “You and I can very well be happy with each other without her having to be hurt.”67
Indeed, even amid his flurry of love letters with Elsa, Einstein was still trying to be a suitable family man. For his August 1913 vacation, he decided to take his wife and two sons hiking with Marie Curie and her two daughters. The plan was to go through the mountains of southeastern Switzerland down to Lake Como, where he and Mari had spent their most passionate and romantic moments twelve years earlier.
As it turned out, the sickly Eduard was unable to make the trip, and Mari stayed behind for a few days to get him settled with friends. Then she joined them as they neared Lake Como. During the hikes, Curie challenged Einstein to name all the peaks. They also talked science, especially when the children ran ahead. At one point Einstein stopped suddenly and grabbed Curie’s arm. “You understand, what I need to know is exactly what happens to the passengers in an elevator when it falls into emptiness,” he said, referring to his ideas about the equivalence of gravity and acceleration. As Curie’s daughter noted later, “Such a touching preoccupation made the younger generation roar with laughter.”68
Einstein then accompanied Mari and their children to visit her family in Novi Sad and at their summer house in Ka. On their final Sunday in Serbia, Mari took the children, without her husband, to be baptized. Hans Albert remembered later the beautiful singing; his brother, Eduard, only 3, was disruptive. As for their father, he seemed sanguine and bemused afterward. “Do you know what the result is?” he told Hurwitz.“They’ve turned Catholic. Well, it’s all the same to me.”69
The façade of familial harmony, however, masked the deterioration of the marriage. After his visit to Serbia and a stop in Vienna for his annual appearance at the conference of German-speaking physicists, Einstein continued on to Berlin, alone. There he was reunited with Elsa. “I now have someone I can think about with pure delight and I can live for,” he told her.70
Elsa’s home cooking, a hearty pleasure she lavished on him like a mother, became a theme in their letters. Their correspondence, like their relationship, was a stark contrast to that between Einstein and Mari a dozen years earlier. He and Elsa tended to write to each other about domestic comforts—food, tranquillity, hygiene, fondness—rather than about romantic bliss and planted kisses, or intimacies of the soul and insights of the intellect.
Despite such conventional concerns, Einstein still fancied their relationship could avoid sinking into a mundane pattern. “How nice it would be if one of these days we could share in managing a small bohemian household,” he wrote. “You have no idea how charming such a life with very small needs and without grandeur can be!”71 When Elsa gave him a hairbrush, he initially prided himself on his progress in personal grooming, but then he reverted to more slovenly ways and told her, only half jokingly, that it was to guard against the philistines and the bourgeoisie. Those were words he had used with Mari as well, but more earnestly.
Elsa wanted not only to domesticate Einstein but to marry him. Even before he moved to Berlin, she wrote to urge him to divorce Mari. It would become a running battle for years, until she finally won her way. But for the moment, Einstein was resistant. “Do you think,” he asked her, “it is so easy to get a divorce if one does not have any proof of the other party’s guilt?” She should accept that he had virtually separated from Mari even if he was not going to divorce her. “I treat my wife as an employee whom I cannot fire. I have my own bedroom and avoid being alone with her.” Elsa was upset that Einstein did not want to marry her, and she was fearful of how an illicit relationship would affect her daughters, but Einstein insisted it was for the best.72
Mari was understandably depressed by the prospect of moving to Berlin. There she would have to deal with Einstein’s mother, who had never liked her, and his cousin, whom she rightly suspected of being a rival. In addition, Berlin had sometimes been less tolerant to Slavs than it was even to Jews. “My wife whines to me incessantly about Berlin and her fear of the relatives,” Einstein wrote Elsa. “Well, there is some truth in this.” In another letter, when he noted that Mari was afraid of her, he added, “Rightly so I hope!”73
Indeed, by this point all of the women in his life—his mother, sister, wife, and kissing cousin—were at war with one another. As Christmas 1913 neared, Einstein’s struggle to generalize relativity had the added benefit of being a way to avoid family emotions. The effort produced yet another eloquent restatement of how science could rescue him from the merely personal. “The love of science thrives under these circumstances,” he told Elsa, “for it lifts me impersonally from the vale of tears into peaceful spheres.”74
With the approach of the spring of 1914 and their move to Berlin, Eduard came down with an ear infection that made it necessary for Mari to take him to an Alpine resort to recover. “This has a good side,” Einstein told Elsa. He would initially be traveling to Berlin alone, and “in order to savor that,” he decided to skip a conference in Paris so that he could arrive earlier.
On one of their last evenings in Zurich, he and Mari went to the Hurwitz house for a farewell musical evening. Once again, the program featured Schumann, in an attempt to cheer her up. It didn’t. She instead sat by herself in a corner and did not speak to anyone.75
By April 1914, Einstein had settled into a spacious apartment just west of Berlin’s city center. Mari had picked it out when she visited Berlin over Christmas vacation, and she arrived in late April, after Eduard’s ear infection had subsided.76
The tensions in Einstein’s domestic life were exacerbated by overwork and mental strain. He was settling into a new job—actually three new jobs—and still struggling with his fitful attempts to generalize his theory of relativity and tie it into a theory of gravity. That first April in Berlin, for example, he engaged in an intense correspondence with Paul Ehrenfest over ways to calculate the forces affecting rotating electrons in a magnetic field. He started writing a theory for such situations, then realized it was wrong. “The angel had unveiled itself halfway in its magnificence,” he told Ehrenfest, “then on further unveiling a cloven hoof appeared and I ran away.”
Even more revealing, perhaps more than he meant it to be, was his comment to Ehrenfest about his personal life in Berlin.“I really delight in my local relatives,” he reported, “especially in a cousin of my age.”77
When Ehrenfest came for a visit at the end of April, Mari had just arrived, and he found her gloomy and yearning for Zurich. Einstein, on the other hand, had thrown himself into his work. “He had the impression that the family was taking a bit too much of his time, and that he had the duty to concentrate completely on his work,” his son Hans Albert later recollected about that fateful spring of 1914.78
Personal relationships involve nature’s most mysterious forces. Outside judgments are easy to make and hard to verify. Einstein repeatedly and plaintively stressed to all of their mutual friends—especially the Bessos, Habers, and Zanggers—that they should try to see the breakup of his marriage from his perspective, despite his own apparent culpability.
It is probably true that he was not solely to blame. The decline of the marriage was a downward spiral. He had become emotionally withdrawn, Mari had become more depressed and dark, and each action reinforced the other. Einstein tended to avoid painful personal emotions by immersing himself in his work. Mari, for her part, was bitter about the collapse of her own dreams and increasingly resentful of her husband’s success. Her jealousy made her hostile toward anyone else who was close to Einstein, including his mother (the feeling was reciprocal) and his friends. Her mistrustful nature was, understandably, to some extent an effect of Einstein’s detachment, but it was also a cause.
By the time they moved to Berlin, Mari had developed at least one personal involvement of her own, with a mathematics professor in Zagreb named Vladimir Variak, who had challenged Einstein’s interpretations of how special relativity applied to a rotating disk. Einstein was aware of the situation. “He had a kind of relationship with my wife, which can’t be held against either of them,” he wrote to Zangger in June. “It only made me feel my sense of isolation doubly painfully.”79
The end came in July. Amid the turmoil, Mari moved with her two boys into the house of Fritz Haber, the chemist who’d recruited Einstein and who ran the institute where his office was located. Haber had his own experience with domestic discord. His wife, Clara, would end up committing suicide the following year after a fight over Haber’s participation in the war. But for the time being, she was Mileva Mari’s only friend in Berlin, and Fritz Haber became the intermediary as the Einsteins’ battles broke into the open.
Through the Habers, Einstein delivered to Mari in mid-July a brutal cease-fire ultimatum. It was in the form of a proposed contract, one in which Einstein’s cold scientific approach combined with his personal hostility and emotional alienation to produce an astonishing document. It read in full:
A. You will make sure
1. that my clothes and laundry are kept in good order;
2. that I will receive my three meals regularly
in my room
3. that my bedroom and study are kept neat, and especially that my desk is left for
my use only.
B. You will renounce all personal relations with me insofar as they are not completely necessary for social reasons. Specifically, you will forego
1. my sitting at home with you;
2. my going out or traveling with you.
C. You will obey the following points in your relations with me:
1. you will not expect any intimacy from me, nor will you reproach me in any way;
2. you will stop talking to me if I request it;
3. you will leave my bedroom or study immediately without protest if I request it.
D. You will undertake not to belittle me in front of our children, either through words or behavior.
Mari accepted the terms. When Haber delivered her response, Einstein insisted on writing to her again “so that you are completely clear about the situation.” He was prepared to live together again “because I don’t want to lose the children and I don’t want them to lose me.” It was out of the question that he would have a “friendly” relationship with her, but he would aim for a “businesslike” one. “The personal aspects must be reduced to a tiny remnant,” he said. “In return, I assure you of proper comportment on my part, such as I would exercise to any woman as a stranger.”81
Only then did Mari realize that the relationship was not salvageable. They all met at Haber’s house on a Friday to work out a separation agreement. It took three hours. Einstein agreed to provide Mari and his children 5,600 marks a year, just under half of his primary salary. Haber and Mari went to a lawyer to have the contract drawn up; Einstein did not accompany them, but instead sent his friend Michele Besso, who had come from Trieste to represent him.82
Einstein left the meeting at Haber’s house and went directly to the home of Elsa’s parents, who were also his aunt and uncle. They arrived home late from dinner to find him there, and they received the news about the situation with “a mild distaste.” Nevertheless, he ended up staying at their house. Elsa was on summer vacation in the Bavarian Alps with her two daughters, and Einstein wrote to inform her that he was now sleeping in her bed in the apartment upstairs. “It’s peculiar how confusingly sentimental one gets,” he told her. “It is just a bed like any other, as though you had never slept in it. And yet I find it comforting.” She had invited him to visit her in the Bavarian Alps, but he said he could not, “for fear of damaging your reputation again.”83
The way to a divorce had now been paved, he assured Elsa, and he called it “a sacrifice” he had made on her behalf. Mari would move back to Zurich and take custody of the two boys, and when they came to visit their father they could meet only on “neutral ground,” not in any house he shared with Elsa. “This is justified,” Einstein conceded to Elsa, “because it is not right to have the children see their father with a woman other than their own mother.”
The prospect of parting with his children was devastating for Einstein. He pretended to be detached from personal sentiments, and sometimes he was. But he became deeply emotional as he imagined life apart from his sons. “I would be a real monster if I felt any other way,” he wrote Elsa. “I have carried these children around innumerable times day and night, taken them out in their pram, played with them, romped around and joked with them. They used to shout with joy when I came; the little one cheered even now, because he was still too small to grasp the situation. Now they will be gone forever, and their image of their father is being spoiled.”84
Mari and the two boys left Berlin, accompanied by Michele Besso, aboard the morning train to Zurich on Wednesday, July 29, 1914. Haber went to the station with Einstein, who “bawled like a little boy” all afternoon and evening. It was the most wrenching personal moment for a man who took perverse pride in avoiding personal moments. For all of his reputation of being inured to deep human attachments, he had been madly in love with Mileva Mari and bonded to his children. For one of the few times in his adult life, he found himself crying.
The next day he went to visit his mother, who cheered him up. She had never liked Mari and was delighted that she was gone. “Oh, if your poor Papa had only lived to see it!” she said about the separation. She even professed herself pleased for Elsa, although they had occasionally clashed. And Elsa’s mother and father also seemed happy enough with the resolution, though they did express resentment that Einstein had been too financially generous to Mari, which meant the income left for him and Elsa might be “a bit meager.”85
The whole ordeal left Einstein so drained that, despite what he had said to Elsa just a week earlier, he decided that he was not prepared to get married again. Thus he would not have to force the issue of a legal divorce, which Mari fiercely resisted. Elsa, still on vacation, was “bitterly disappointed” by the news. Einstein sought to reassure her. “For me there is no other female creature besides you,” he wrote. “It is not a lack of true affection which scares me away again and again from marriage! Is it a fear of the comfortable life, of nice furniture, of the odium that I burden myself with or even of becoming some sort of contented bourgeois? I myself don’t know; but you will see that my attachment to you will endure.”
He insisted that she should not feel ashamed or let people pity her for consorting with a man who would not marry her. They would take walks together and be there for each other. Should she choose to offer even more, he would be grateful. But by not marrying, they would be protecting themselves from lapsing into a “contented bourgeois” existence and preventing their relationship “from becoming banal and from growing pale.” To him, marriage was confining, which was a state he instinctively resisted. “I’m glad our delicate relationship does not have to founder on a provincial narrow-minded lifestyle.”86
In the old days, Mari had been the type of soul mate who responded to such bohemian sentiments. Elsa was not such a person. A comfortable life with comfortable furniture appealed to her. So did marriage. She would accept his decision not to get married for a while, but not forever.
In the meantime, Einstein became embroiled in a long-distance battle with Mari over money, furniture, and the way she was allegedly “poisoning” their children against him.87 And all around them, a chain reaction was taking Europe into the most incomprehensibly bloody war in its history.
Not surprisingly, Einstein reacted to all of this turmoil by throwing himself into his science.
Light and Gravity
After Einstein formulated his special theory of relativity in 1905, he realized that it was incomplete in at least two ways. First, it held that no physical interaction can propagate faster than the speed of light; that conflicted with Newton’s theory of gravity, which conceived of gravity as a force that acted instantly between distant objects. Second, it applied only to constant-velocity motion. So for the next ten years, Einstein engaged in an interwoven effort to come up with a new field theory of gravity and to generalize his relativity theory so that it applied to accelerated motion.1
His first major conceptual advance had come at the end of 1907, while he was writing about relativity for a science yearbook. As noted earlier, a thought experiment about what a free-falling observer would feel led him to embrace the principle that the local effects of being accelerated and of being in a gravitational field are indistinguishable.* A person in a closed windowless chamber who feels his feet pressed to the floor will not be able to tell whether it’s because the chamber is in outer space being accelerated upward or because it is at rest in a gravitational field. If he pulls a penny from his pocket and lets it go, it will fall to the floor at an accelerating speed in either case. Likewise, a person who feels she is floating in the closed chamber will not know whether it’s because the chamber is in free fall or hovering in a gravity-free region of outer space.2
This led Einstein to the formulation of an “equivalence principle” that would guide his quest for a theory of gravity and his attempt to generalize relativity. “I realized that I would be able to extend or generalize the principle of relativity to apply to accelerated systems in addition to those moving at a uniform velocity,” he later explained. “And in so doing, I expected that I would be able to resolve the problem of gravitation at the same time.”
Just as inertial mass and gravitational mass are equivalent, so too there is an equivalence, he realized, between all inertial effects, such as resistance to acceleration, and gravitational effects, such as weight. His insight was that they are both manifestations of the same structure, which we now sometimes call the inertio-gravitational field.3
One consequence of this equivalence is that gravity, as Einstein had noted, should bend a light beam. That is easy to show using the chamber thought experiment. Imagine that the chamber is being accelerated upward. A laser beam comes in through a pinhole on one wall. By the time it reaches the opposite wall, it’s a little closer to the floor, because the chamber has shot upward. And if you could plot its trajectory across the chamber, it would be curved because of the upward acceleration. The equivalence principle says that this effect should be the same whether the chamber is accelerating upward or is instead resting still in a gravitational field. Thus, light should appear to bend when going through a gravitational field.
For almost four years after positing this principle, Einstein did little with it. Instead, he focused on light quanta. But in 1911, he confessed to Michele Besso that he was weary of worrying about quanta, and he turned his attention back to coming up with a field theory of gravity that would help him generalize relativity. It was a task that would take him almost four more years, culminating in an eruption of genius in November 1915.
In a paper he sent to the Annalen der Physik in June 1911, “On the Influence of Gravity on the Propagation of Light,” he picked up his insight from 1907 and gave it rigorous expression. “In a memoir published four years ago I tried to answer the question whether the propagation of light is influenced by gravitation,” he began. “I now see that one of the most important consequences of my former treatment is capable of being tested experimentally.” After a series of calculations, Einstein came up with a prediction for light passing through the gravitational field next to the sun: “A ray of light going past the sun would undergo a deflection of 0.83 second of arc.”*
Once again, he was deducing a theory from grand principles and postulates, then deriving some predictions that experimenters could proceed to test. As before, he ended his paper by calling for just such a test. “As the stars in the parts of the sky near the sun are visible during total eclipses of the sun, this consequence of the theory may be observed. It would be a most desirable thing if astronomers would take up the question.”4
Erwin Finlay Freundlich, a young astronomer at the Berlin University observatory, read the paper and became excited by the prospect of doing this test. But it could not be performed until an eclipse, when starlight passing near the sun would be visible, and there would be no suitable one for another three years.
So Freundlich proposed that he try to measure the deflection of starlight caused by the gravitational field of Jupiter. Alas, Jupiter did not prove big enough for the task. “If only we had a truly larger planet than Jupiter!” Einstein joked to Freundlich at the end of that summer. “But nature did not deem it her business to make the discovery of her laws easy for us.”5
The theory that light beams could be bent led to some interesting questions. Everyday experience shows that light travels in straight lines. Carpenters now use laser levels to mark off straight lines and construct level houses. If a light beam curves as it passes through regions of changing gravitational fields, how can a straight line be determined?
One solution might be to liken the path of the light beam through a changing gravitational field to that of a line drawn on a sphere or on a surface that is warped. In such cases, the shortest line between two points is curved, a geodesic like a great arc or a great circle route on our globe. Perhaps the bending of light meant that the fabric of space, through which the light beam traveled, was curved by gravity. The shortest path through a region of space that is curved by gravity might seem quite different from the straight lines of Euclidean geometry.
There was another clue that a new form of geometry might be needed. It became apparent to Einstein when he considered the case of a rotating disk. As a disk whirled around, its circumference would be contracted in the direction of its motion when observed from the reference frame of a person not rotating with it. The diameter of the circle, however, would not undergo any contraction. Thus, the ratio of the disk’s circumference to its diameter would no longer be given by pi. Euclidean geometry wouldn’t apply to such cases.
Rotating motion is a form of acceleration, because at every moment a point on the rim is undergoing a change in direction, which means that its velocity (a combination of speed and direction) is undergoing a change. Because non-Euclidean geometry would be necessary to describe this type of acceleration, according to the equivalence principle, it would be needed for gravitation as well.6
Unfortunately, as he had proved at the Zurich Polytechnic, non-Euclidean geometry was not a strong suit for Einstein. Fortunately, he had an old friend and classmate in Zurich for whom it was.
When Einstein moved back to Zurich from Prague in July 1912, one of the first things he did was call on his friend Marcel Grossmann, who had taken the notes Einstein used when he skipped math classes at the Zurich Polytechnic. Einstein had gotten a 4.25 out of 6 in his two geometry courses at the Polytechnic. Grossmann, on the other hand, had scored a perfect 6 in both of his geometry courses, had written his dissertation on non-Euclidean geometry, published seven papers on that topic, and was now the chairman of the math department.7
“Grossmann, you’ve got to help me or I will go crazy,” Einstein said. He explained that he needed a mathematical system that would express—and perhaps even help him discover—the laws that governed the gravitational field. “Instantly, he was all afire,” Einstein recalled of Grossmann’s response.8
Until then, Einstein’s scientific success had been based on his special talent for sniffing out the underlying physical principles of nature. He had left to others the task, which to him seemed less exalted, of finding the best mathematical expressions of those principles, as his Zurich colleague Minkowski had done for special relativity.
But by 1912, Einstein had come to appreciate that math could be a tool for discovering—and not merely describing—nature’s laws. Math was nature’s playbook. “The central idea of general relativity is that gravity arises from the curvature of spacetime,” says physicist James Hartle. “Gravity is geometry.”9
“I am now working exclusively on the gravitation problem and I believe that, with the help of a mathematician friend here, I will overcome all difficulties,” Einstein wrote to the physicist Arnold Sommerfeld. “I have gained enormous respect for mathematics, whose more subtle parts I considered until now, in my ignorance, as pure luxury!”10
Grossmann went home to think about the question. After consulting the literature, he came back to Einstein and recommended the non-Euclidean geometry that had been devised by Bernhard Riemann.11
Riemann (1826–1866) was a child prodigy who invented a perpetual calendar at age 14 as a gift for his parents and went on to study in the great math center of Göttingen, Germany, under Carl Friedrich Gauss, who had been pioneering the geometry of curved surfaces. This was the topic Gauss assigned to Riemann for a thesis, and the result would transform not only geometry but physics.
Euclidean geometry describes flat surfaces. But it does not hold true on curved surfaces. For example, the sum of the angles of a triangle on a flat page is 180°. But look at the globe and picture a triangle formed by the equator as the base, the line of longitude running from the equator to the North Pole through London (longitude 0°) as one side, and the line of longitude running from the equator to the North Pole through New Orleans (longitude 90°) as the third side. If you look at this on a globe, you will see that all three angles of this triangle are right angles, which of course is impossible in the flat world of Euclid.
Gauss and others had developed different types of geometry that could describe the surface of spheres and other curved surfaces. Riemann took things even further: he developed a way to describe a surface no matter how its geometry changed, even if it varied from spherical to flat to hyperbolic from one point to the next. He also went beyond dealing with the curvature of just two-dimensional surfaces and, building on the work of Gauss, explored the various ways that math could describe the curvature of three-dimensional and even four-dimensional space.
That is a challenging concept. We can visualize a curved line or surface, but it is hard to imagine what curved three-dimensional space would be like, much less a curved four dimensions. But for mathematicians, extending the concept of curvature into different dimensions is easy, or at least doable. This involves using the concept of the metric, which specifies how to calculate the distance between two points in space.
On a flat surface with just the normal x and y coordinates, any high school algebra student, with the help of old Pythagoras, can calculate the distance between points. But imagine a flat map (of the world, for example) that represents locations on what is actually a curved globe. Things get stretched out near the poles, and measurement gets more complex. Calculating the actual distance between two points on the map in Greenland is different from doing so for points near the equator. Riemann worked out ways to determine mathematically the distance between points in space no matter how arbitrarily it curved and contorted.12
To do so he used something called a tensor. In Euclidean geometry, a vector is a quantity (such as of velocity or force) that has both a magnitude and a direction and thus needs more than a single simple number to describe it. In non-Euclidean geometry, where space is curved, we need something more generalized—sort of a vector on steroids—in order to incorporate, in a mathematically orderly way, more components. These are called tensors.
A metric tensor is a mathematical tool that tells us how to calculate the distance between points in a given space. For two-dimensional maps, a metric tensor has three components. For three-dimensional space, it has six independent components. And once you get to that glorious four-dimensional entity known as spacetime, the metric tensor needs ten independent components.*
Riemann helped to develop this concept of the metric tensor, which was denoted as gmn and pronounced gee-mu-nu. It had sixteen components, ten of them independent of one another, that could be used to define and describe a distance in curved four-dimensional spacetime.13
The useful thing about Riemann’s tensor, as well as other tensors that Einstein and Grossmann adopted from the Italian mathematicians Gregorio Ricci-Curbastro and Tullio Levi-Civita, is that they are generally covariant. This was an important concept for Einstein as he tried to generalize a theory of relativity. It meant that the relationships between their components remained the same even when there were arbitrary changes or rotations in the space and time coordinate system. In other words, the information encoded in these tensors could go through a variety of transformations based on a changing frame of reference, but the basic laws governing the relationship of the components to each other remained the same.14
Einstein’s goal as he pursued his general theory of relativity was to find the mathematical equations describing two complementary processes:
1. How a gravitational field acts on matter, telling it how to move.
2. And in turn, how matter generates gravitational fields in space-time, telling it how to curve.
His head-snapping insight was that gravity could be defined as the curvature of spacetime, and thus it could be represented by a metric tensor. For more than three years he would fitfully search for the right equations to accomplish his mission.15
Years later, when his younger son, Eduard, asked why he was so famous, Einstein replied by using a simple image to describe his great insight that gravity was the curving of the fabric of spacetime. “When a blind beetle crawls over the surface of a curved branch, it doesn’t notice that the track it has covered is indeed curved,” he said. “I was lucky enough to notice what the beetle didn’t notice.”16
The Zurich Notebook, 1912
Beginning in that summer of 1912, Einstein struggled to develop gravitational field equations using tensors along the lines developed by Riemann, Ricci, and others. His first round of fitful efforts are preserved in a scratchpad notebook. Over the years, this revealing “Zurich Notebook” has been dissected and analyzed by a team of scholars including Jürgen Renn, John D. Norton, Tilman Sauer, Michel Janssen, and John Stachel.17
In it Einstein pursued a two-fisted approach. On the one hand, he engaged in what was called a “physical strategy,” in which he tried to build the correct equations from a set of requirements dictated by his feel for the physics. At the same time, he pursued a “mathematical strategy,” in which he tried to deduce the correct equations from the more formal math requirements using the tensor analysis that Gross-mann and others recommended.
Einstein’s “physical strategy” began with his mission to generalize the principle of relativity so that it applied to observers who were accelerating or moving in an arbitrary manner. Any gravitational field equation he devised would have to meet the following physical requirements:
• It must revert to Newtonian theory in the special case of weak and static gravitational fields. In other words, under certain normal conditions, his theory would describe Newton’s familiar laws of gravitation and motion.
• It should preserve the laws of classical physics, most notably the conservation of energy and momentum.
• It should satisfy the principle of equivalence, which holds that observations made by an observer who is uniformly accelerating would be equivalent to those made by an observer standing in a comparable gravitational field.
Einstein’s “mathematical strategy,” on the other hand, focused on using generic mathematical knowledge about the metric tensor to find a gravitational field equation that was generally (or at least broadly) covariant.
The process worked both ways: Einstein would examine equations that were abstracted from his physical requirements to check their covariance properties, and he would examine equations that sprang from elegant mathematical formulations to see if they met the requirements of his physics. “On page after page of the notebook, he approached the problem from either side, here writing expressions suggested by the physical requirements of the Newtonian limit and energy-momentum conservation, there writing expressions naturally suggested by the generally covariant quantities supplied by the mathematics of Ricci and Levi-Civita,” says John Norton.18
But something disappointing happened. The two groups of requirements did not mesh. Or at least Einstein thought not. He could not get the results produced by one strategy to meet the requirements of the other strategy.
Using his mathematical strategy, he derived some very elegant equations. At Grossmann’s suggestion, he had begun using a tensor developed by Riemann and then a more suitable one developed by Ricci. Finally, by the end of 1912, he had devised a field equation using a tensor that was, it turned out, pretty close to the one that he would eventually use in his triumphant formulation of late November 1915. In other words, in his Zurich Notebook he had come up with what was quite close to the right solution.19
But then he rejected it, and it would stagnate in his discard pile for more than two years. Why? Among other considerations, he thought (somewhat mistakenly) that this solution did not reduce, in a weak and static field, to Newton’s laws. When he tried it a different way, it did not meet the requirement of the conservation of energy and momentum. And if he introduced a coordinate condition that allowed the equations to satisfy one of these requirements, it proved incompatible with the conditions needed to satisfy the other requirement.20
As a result, Einstein reduced his reliance on the mathematical strategy. It was a decision that he would later regret. Indeed, after he finally returned to the mathematical strategy and it proved spectacularly successful, he would from then on proclaim the virtues—both scientific and philosophical—of mathematical formalism.21
The Entwurf and Newton’s Bucket, 1913
In May 1913, having discarded the equations derived from the mathematical strategy, Einstein and Grossmann produced a sketchy alternative theory based more on the physical strategy. Its equations were constructed to conform to the requirements of energy-momentum conservation and of being compatible with Newton’s laws in a weak static field.
Even though it did not seem that these equations satisfied the goal of being suitably covariant, Einstein and Grossmann felt it was the best they could do for the time being. Their title reflected their tentativeness: “Outline of a Generalized Theory of Relativity and of a Theory of Gravitation.” The paper thus became known as the Entwurf, which was the German word they had used for “outline.”22
For a few months after producing the Entwurf, Einstein was both pleased and depleted. “I finally solved the problem a few weeks ago,” he wrote Elsa. “It is a bold extension of the theory of relativity, together with a theory of gravitation. Now I must give myself some rest, otherwise I will go kaput.”23
However, he was soon questioning what he had wrought. And the more he reflected on the Entwurf, the more he realized that its equations did not satisfy the goal of being generally or even broadly covariant. In other words, the way the equations applied to people in arbitrary accelerated motion might not always be the same.
His confidence in the theory was not strengthened when he sat down with his old friend Michele Besso, who had come to visit him in June 1913, to study the implications of the Entwurf theory. They produced more than fifty pages of notes on their deliberations, each writing about half, which analyzed how the Entwurf accorded with some curious facts that were known about the orbit of Mercury.24
Since the 1840s, scientists had been worrying about a small but unexplained shift in the orbit of Mercury. The perihelion is the spot in a planet’s elliptical orbit when it is closest to the sun, and over the years this spot in Mercury’s orbit had slipped a tiny amount more—about 43 seconds of an arc each century—than what was explained by Newton’s laws. At first it was assumed that some undiscovered planet was tugging at it, similar to the reasoning that had earlier led to the discovery of Neptune. The Frenchman who discovered Mercury’s anomaly even calculated where such a planet would be and named it Vulcan. But it was not there.
Einstein hoped that his new theory of relativity, when its gravitational field equations were applied to the sun, would explain Mercury’s orbit. Unfortunately, after a lot of calculations and corrected mistakes, he and Besso came up with a value of 18 seconds of an arc per century for how far Mercury’s perihelion should stray, which was not even halfway correct. The poor result convinced Einstein not to publish the Mercury calculations. But it did not convince him to discard his Entwurf theory, at least not yet.
Einstein and Besso also looked at whether rotation could be considered a form of relative motion under the equations of the Entwurf theory. In other words, imagine that an observer is rotating and thus experiencing inertia. Is it possible that this is yet another case of relative motion and is indistinguishable from a case where the observer is at rest and the rest of the universe is rotating around him?
The most famous thought experiment along these lines was that described by Newton in the third book of his Principia. Imagine a bucket that begins to rotate as it hangs from a rope. At first the water in the bucket stays rather still and flat. But soon the friction from the bucket causes the water to spin around with it, and it assumes a concave shape. Why? Because inertia causes the spinning water to push outward, and therefore it pushes up the side of the bucket.
Yes, but if we suspect that all motion is relative, we ask: What is the water spinning relative to? Not the bucket, because the water is concave when it is spinning along with the bucket, and also when the bucket stops and the water keeps spinning inside for a while. Perhaps the water is spinning relative to nearby bodies such as the earth that exert gravitational force.
But imagine the bucket spinning in deep space with no gravity and no reference points. Or imagine it spinning alone in an otherwise empty universe. Would there still be inertia? Newton believed so, and said it was because the bucket was spinning relative to absolute space.
When Einstein’s early hero Ernst Mach came along in the mid-nineteenth century, he debunked this notion of absolute space and argued that the inertia existed because the water was spinning relative to the rest of the matter in the universe. Indeed, the same effects would be observed if the bucket was still and the rest of the universe was rotating around it, he said.25
The general theory of relativity, Einstein hoped, would have what he dubbed “Mach’s Principle” as one of its touchstones. Happily, when he analyzed the equations in his Entwurf theory, he concluded that they did seem to predict that the effects would be the same whether a bucket was spinning or was motionless while the rest of the universe spun around it.
Or so Einstein thought. He and Besso made a series of very clever calculations designed to see if indeed this was the case. In their notebook, Einstein wrote a joyous little exclamation at what appeared to be the successful conclusion of these calculations: “Is correct.”
Unfortunately, he and Besso had made some mistakes in this work. Einstein would eventually discover those errors two years later and realize, unhappily, that the Entwurf did not in fact satisfy Mach’s principle. In all likelihood, Besso had already warned him that this might be the case. In a memo that he apparently wrote in August 1913, Besso suggested that a “rotation metric” was not in fact a solution permitted by the field equations in the Entwurf.
But Einstein dismissed these doubts, in letters to Besso as well as to Mach and others, at least for the time being.26 If experiments upheld the theory, “your brilliant investigations on the foundations of mechanics will have received a splendid confirmation,” Einstein wrote to Mach days after the Entwurf was published. “For it shows that inertia has its origin in some kind of interaction of the bodies, exactly in accordance with your argument about Newton’s bucket experiment.”27
What worried Einstein most about the Entwurf, justifiably, was that its mathematical equations did not prove to be generally covariant, thus deflating his goal of assuring that the laws of nature were the same for an observer in accelerated or arbitrary motion as they were for an observer moving at a constant velocity. “Regrettably, the whole business is still so very tricky that my confidence in the theory is still rather hesitant,” he wrote in reply to a warm letter of congratulations from Lorentz.“The gravitational equations themselves unfortunately do not have the property of general covariance.”28
He was soon able to convince himself, at least for a while, that this was inevitable. In part he did so through a thought experiment, which became known as the “hole argument,”29 that seemed to suggest that the holy grail of making the gravitational field equations generally covariant was impossible to reach, or at least physically uninteresting. “The fact that the gravitational equations are not generally covariant, something that quite disturbed me for a while, is unavoidable,” he wrote a friend. “It can easily be shown that a theory with generally covariant equations cannot exist if the demand is made that the field is mathematically completely determined by matter.”30
For the time being, very few physicists embraced Einstein’s new theory, and many came forth to denounce it.31 Einstein professed pleasure that the issue of relativity “has at least been taken up with the requisite vigor,” as he put it to his friend Zangger. “I enjoy controversies. In the manner of Figaro: ‘Would my noble Lord venture a little dance? He should tell me! I will strike up the tune for him.’ ”32
Through it all, Einstein continued to try to salvage his Entwurf approach. He was able to find ways, or so he thought, to achieve enough covariance to satisfy most aspects of his principle about the equivalence of gravity and acceleration. “I succeeded in proving that the gravitational equations hold for arbitrarily moving reference systems, and thus that the hypothesis of the equivalence of acceleration and gravitational field is absolutely correct,” he wrote Zangger in early 1914. “Nature shows us only the tail of the lion. But I have no doubt that the lion belongs with it even if he cannot reveal himself all at once. We see him only the way a louse that sits upon him would.”33
Freundlich and the 1914 Eclipse
There was, Einstein knew, one way to quell doubts. He often concluded his papers with suggestions for how future experiments could confirm whatever he had just propounded. In the case of general relativity, this process had begun in 1911, when he specified with some precision how much he thought light from a star would be deflected by the gravity of the sun.
This was something that could, he hoped, be measured by photographing stars whose light passed close to the sun and determining whether there appeared to be a tiny shift in their position compared to when their light did not have to pass right by the sun. But this was an experiment that had to be done during an eclipse, when the starlight would be visible.
So it was not surprising that, with his theory arousing noisy attacks from colleagues and quiet doubts in his own mind, Einstein became keenly interested in what could be discovered during the next suitable total eclipse of the sun, which was due to occur on August 21, 1914. That would require an expedition to the Crimea, in Russia, where the path of the eclipse would fall.
Einstein was so eager to have his theory tested during the eclipse that, when it seemed there might be no money for such an expedition, he offered to pay part of the costs himself. Erwin Freundlich, the young Berlin astronomer who had read the light-bending predictions in Einstein’s 1911 paper and become eager to prove him correct, was ready to take the lead. “I am extremely pleased that you have taken up the question of the bending of light with so much zeal,” Einstein wrote him in early 1912. In August 1913, he was still bombarding the astronomer with encouragement.“Nothing more can be done by the theorists,” he wrote. “In this matter it is only you, the astronomers, who can next year perform a simply invaluable service to theoretical physics.”34
Freundlich got married in August 1913 and decided to take his honeymoon in the mountains near Zurich, in the hope that he could meet Einstein. It worked. When Freundlich described his honeymoon schedule in a letter, Einstein invited him over for a visit. “This is wonderful because it fits in with our plans,” Freundlich wrote his fiancée, whose reaction to the prospect of spending part of her honeymoon with a theoretical physicist she had never met is lost to history.
When the newlyweds pulled into the Zurich train station, there was a disheveled Einstein wearing, as Freundlich’s wife recalled, a large straw hat, with the plump chemist Fritz Haber at his side. Einstein brought the group to a nearby town where he was giving a lecture, after which he took them to lunch. Not surprisingly, he had forgotten to bring any money, and an assistant who had come along slipped him a 100 franc note under the table. For most of the day, Freundlich discussed gravity and the bending of light with Einstein, even when the group went on a nature hike, leaving his new wife to admire the scenery in peace.35
At his speech that day, which was on general relativity, Einstein pointed out Freundlich to the audience and called him “the man who will be testing the theory next year.”The problem, however, was raising the money. At the time, Planck and others were trying to lure Einstein from Zurich to Berlin to become a member of the Prussian Academy, and Einstein used the courtship to write Planck and urge him to provide Freundlich the money to undertake the task.
In fact, on the very day that Einstein formally accepted the Berlin post and election to the Academy—December 7, 1913—he wrote Freundlich with the offer to reach into his own pocket. “If the Academy shies away from it, then we will get that little bit of mammon from private individuals,” said Einstein. “Should everything fail, then I will pay for the thing myself out of the little bit that I have saved, at least the first 2,000 marks.” The main thing, Einstein stressed, was that Freundlich should proceed with his preparations. “Just go ahead and order the photographic plates, and do not let the time be squandered because of the money problem.”36
As it turned out, there were enough private donations, mainly from the Krupp Foundation, to make the expedition possible. “You can imagine how happy I am that the external difficulties of your undertaking have now more or less been overcome,” Einstein wrote. He added a note of confidence about what would be found: “I have considered the theory from every angle, and I have every confidence in the thing.”37
Freundlich and two colleagues left Berlin on July 19 for the Crimea, where they were joined by a group from the Córdoba observatory in Argentina. If all went well, they would have two minutes to make photographs that could be used to analyze whether the starlight was deflected by the sun’s gravity.
All did not go well. Twenty days before the eclipse, Europe tumbled into World War I and Germany declared war on Russia. Freundlich and his German colleagues were captured by the Russian army, and their equipment was confiscated. Not surprisingly, they were unable to convince the Russian soldiers that, with all of their powerful cameras and location devices, they were mere astronomers planning to gaze at the stars in order to better understand the secrets of the universe.
Even if they had been granted safe passage, it is likely that the observations would have failed. The skies were cloudy during the minutes of the eclipse, and an American group that was also in the region was unable to get any usable photographs.38
Yet the termination of the eclipse mission had a silver lining. Einstein’s Entwurf equations were not correct. The degree to which gravity would deflect light, according to Einstein’s theory at the time, was the same as that predicted by Newton’s emission theory of light. But, as Einstein would discover a year later, the correct prediction would end up being twice that. If Freundlich had succeeded in 1914, Einstein might have been publicly proven wrong.
“My good old astronomer Freundlich, instead of experiencing a solar eclipse in Russia, will now be experiencing captivity there,” Einstein wrote to his friend Ehrenfest. “I am concerned about him.”39There was no need to worry. The young astronomer was released in a prisoner exchange within weeks.
Einstein, however, had other reasons to worry in August 1914. His marriage had just exploded. His masterpiece theory still needed work. And now his native country’s nationalism and militarism, traits that he had abhorred since childhood, had plunged it into a war that would cast him as a stranger in a strange land. In Germany, it would turn out, that was a dangerous position to be in.
World War I
The chain reaction that pushed Europe into war in August 1914 inflamed the patriotic pride of the Prussians and, in an equal and opposite reaction, the visceral pacifism of Einstein, a man so gentle and averse to conflict that he even disliked playing chess. “Europe in its madness has now embarked on something incredibly preposterous,” he wrote Ehrenfest that month. “At such times one sees to what deplorable breed of brutes we belong.”40
Ever since he ran away from Germany as a schoolboy and was exposed to the gauzy internationalism of Jost Winteler in Aarau, Einstein had harbored sentiments that disposed him toward pacifism, one-world federalism, and socialism. But he had generally shunned public activism.
World War I changed that. Einstein would never forsake physics, but he would henceforth be unabashedly public, for most of his life, in pushing his political and social ideals.
The irrationality of the war made Einstein believe that scientists in fact had a special duty to engage in public affairs. “We scientists in particular must foster internationalism,” he said. “Unfortunately, we have had to suffer serious disappointments even among scientists in this regard.”41 He was especially appalled by the lockstep pro-war mentality of his three closest colleagues, the scientists who had lured him to Berlin: Fritz Haber, Walther Nernst, and Max Planck.42
Haber was a short, bald, and dapper chemist who was born Jewish but tried mightily to assimilate by converting, getting baptized, and adopting the dress, manner, and even pince-nez glasses of a proper Prussian. The director of the chemistry institute where Einstein had his office, he had been mediating the war between Einstein and Mari just as the larger war in Europe was breaking out. Although he hoped for a commission as an officer in the army, because he was an academic of Jewish heritage he had to settle for being made a sergeant.43
Haber reorganized his institute to develop chemical weapons for Germany. He had already found a way to synthesize ammonia from nitrogen, which permitted the Germans to mass-produce explosives. He then turned his attention to making deadly chlorine gas, which, heavier than air, would flow down into the trenches and painfully asphyxiate soldiers by burning through their throats and lungs. In April 1915, modern chemical warfare was inaugurated when some five thousand French and Belgians met that deadly fate at Ypres, with Haber personally supervising the attack. (In an irony that may have been lost on the inventor of dynamite, who endowed the prize, Haber won the 1918 Nobel in chemistry for his process of synthesizing ammonia.)
His colleague and occasional academic rival Nernst, bespectacled and 50, had his wife inspect his style as he practiced marching and saluting in front of their house. Then he took his private car and showed up at the western front to be a volunteer driver. Upon his return to Berlin, he experimented with tear gas and other irritants that could be used as a humane way to flush the enemy out of the trenches, but the generals decided they preferred the lethal approach that Haber was taking, so Nernst became part of that effort.
Even the revered Planck supported what he called Germany’s “just war.” As he told his students when they went off to battle, “Germany has drawn its sword against the breeding ground of insidious perfidy.”44
Einstein was able to avoid letting the war cause a personal rift between him and his three colleagues, and he spent the spring of 1915 tutoring Haber’s son in math.45 But when they signed a petition defending Germany’s militarism, he felt compelled to break with them politically.
The petition, published in October 1914, was titled “Appeal to the Cultured World” and became known as the “Manifesto of the 93,” after the number of intellectuals who endorsed it. With scant regard for the truth, it denied that the German army had committed any attacks on civilians in Belgium and went on to proclaim that the war was necessary. “Were it not for German militarism, German culture would have been wiped off the face of the earth,” it asserted. “We shall wage this fight to the very end as a cultured nation, a nation that holds the legacy of Goethe, Beethoven, and Kant no less sacred than hearth and home.”46
It was no surprise that among the scientists who signed was the conservative Philipp Lenard, of photoelectric effect fame, who would later become a rabid anti-Semite and Einstein hater. What was distressing was that Haber, Nernst, and Planck also signed. As both citizens and scientists, they had a natural instinct to go along with the sentiments of others. Einstein, on the other hand, often displayed a natural inclination not to go along, which sometimes was an advantage both as a scientist and as a citizen.
A charismatic adventurer and occasional physician named Georg Friedrich Nicolai, who had been born Jewish (his original name was Lewinstein) and was a friend of both Elsa and her daughter Ilse, worked with Einstein to write a pacifist response. Their “Manifesto to Europeans” appealed for a culture that transcended nationalism and attacked the authors of the original manifesto. “They have spoken in a hostile spirit,” Einstein and Nicolai wrote. “Nationalist passions cannot excuse this attitude, which is unworthy of what the world has heretofore called culture.”
Einstein suggested to Nicolai that Max Planck, even though he had been one of the signers of the original manifesto, might also want to participate in their countermanifesto because of his “broad-mindedness and good will.” He also gave Zangger’s name as a possibility. But neither man, apparently, was willing to get involved. In an indication of the temper of the times, Einstein and Nicolai were able to garner only two other supporters. So they dropped their effort, and it was not published at the time.47
Einstein also became an early member of the liberal and cautiously pacifist New Fatherland League, a club that pushed for an early peace and the establishment of a federal structure in Europe to avoid future conflicts. It published a pamphlet titled “The Creation of the United States of Europe,” and it helped get pacifist literature into prisons and other places. Elsa went with Einstein to some of the Monday evening meetings until the group was banned in early 1916.48
One of the most prominent pacifists during the war was the French writer Romain Rolland, who had tried to promote friendship between his country and Germany. Einstein visited him in September 1915 near Lake Geneva. Rolland noted in his diary that Einstein, speaking French laboriously, gave “an amusing twist to the most serious of subjects.”
As they sat on a hotel terrace amid swarms of bees plundering the flowering vines, Einstein joked about the faculty meetings in Berlin where each of the professors would anguish over the topic “why are we Germans hated in the world” and then would “carefully steer clear of the truth.” Daringly, maybe even recklessly, Einstein openly said that he thought Germany could not be reformed and therefore hoped the allies would win, “which would smash the power of Prussia and the dynasty.”49
The following month, Einstein got into a bitter exchange with Paul Hertz, a noted mathematician in Göttingen who was, or had been, a friend. Hertz was an associate member of the New Fatherland League with Einstein, but he had shied away from becoming a full member when it became controversial. “This type of cautiousness, not standing up for one’s rights, is the cause of the entire wretched political situation,” Einstein berated. “You have that type of valiant mentality the ruling powers love so much in Germans.”
“Had you devoted as much care to understanding people as to understanding science, you would not have written me an insulting letter,” Hertz replied. It was a telling point, and true. Einstein was better at fathoming physical equations than personal ones, as his family knew, and he admitted so in his apology. “You must forgive me, particularly since—as you yourself rightly say—I have not bestowed the same care to understanding people as to understanding science,” he wrote.50
In November, Einstein published a three-page essay titled “My Opinion of the War” that skirted the border of what was permissible, even for a great scientist, to say in Germany. He speculated that there existed “a biologically determined feature of the male character” that was one of the causes of wars. When the article was published by the Goethe League that month, a few passages were deleted for safety’s sake, including an attack on patriotism as potentially containing “the moral requisites of bestial hatred and mass murder.”51
The idea that war had a biological basis in male aggression was a topic Einstein also explored in a letter to his friend in Zurich, Heinrich Zangger. “What drives people to kill and maim each other so savagely?” Einstein asked. “I think it is the sexual character of the male that leads to such wild explosions.”
The only method of containing such aggression, he argued, was a world organization that had the power to police member nations.52 It was a theme he would pick up again eighteen years later, in the final throes of his pure pacifism, when he engaged in a public exchange of letters with Sigmund Freud on both male psychology and the need for world government.
The Home Front, 1915
The early months of the war in 1915 made Einstein’s separation from Hans Albert and Eduard more difficult, both emotionally and logistically. They wanted him to come visit them in Zurich for Easter that year, and Hans Albert, who was just turning 11, wrote him two letters designed to pull at his heart: “I just think: At Easter you’re going to be here and we’ll have a Papa again.”
In his next postcard, he said that his younger brother told him about having a dream “that Papa was here.” He also described how well he was doing in math. “Mama assigns me problems; we have a little booklet; I could do the same with you as well.”53
The war made it impossible for him to come at Easter, but he responded to the postcards by promising Hans Albert that he would come in July for a hiking vacation in the Swiss Alps. “In the summer I will take a trip with just you alone for a fortnight or three weeks,” he wrote. “This will happen every year, and Tete [Eduard] may also come along when he is old enough for it.”
Einstein also expressed his delight that his son had taken a liking to geometry. It had been his “favorite pastime” when he was about the same age, he said, “but I had no one to demonstrate anything to me, so I had to learn it from books.” He wanted to be with his son to help teach him math and “tell you many fine and interesting things about science and much else.” But that would not always be possible. Perhaps they could do it by mail? “If you write me each time what you already know, I’ll give you a nice little problem to solve.” He sent along a toy for each of his sons, along with an admonition to brush their teeth well. “I do the same and am very happy now to have kept enough healthy teeth.”54
But the tension in the family worsened. Einstein and Mari exchanged letters arguing about both money and vacation timing, and at the end of June a curt postcard came from Hans Albert. “If you’re so unfriendly to her,” he said of his mother, “I don’t want to go with you.” So Einstein canceled his planned trip to Zurich and instead went with Elsa and her two daughters to the Baltic sea resort of Sellin.
Einstein was convinced that Mari was turning the children against him. He suspected, probably correctly, that her hand was behind the postcards Hans Albert was sending, both the plaintive ones making him feel guilty for not being in Zurich and the sharper ones rejecting vacation hikes. “My fine boy had been alienated from me for a few years already by my wife, who has a vengeful disposition,” he complained to Zangger. “The postcard I received from little Albert had been inspired, if not downright dictated, by her.”
He asked Zangger, who was a professor of medicine, to check on young Eduard, who had been suffering ear infections and other ailments. “Please write me what is wrong with my little boy,” he pleaded. “I’m particularly fondly attached to him; he was still so sweet to me and innocent.”55
It was not until the beginning of September that he finally made it to Switzerland. Mari felt it would be proper for him to stay with her and the boys, despite the strain. They were, after all, still married. She had hopes of reconciling. But Einstein showed no interest in being with her. Instead, he stayed in a hotel and spent a lot of time with his friends Michele Besso and Heinrich Zangger.
As it turned out, he got a chance to see his sons only twice during the entire three weeks he was in Switzerland. In a letter to Elsa, he blamed his estranged wife: “The cause was mother’s fear of the little ones becoming too dependent on me.” Hans Albert let his father know that the whole visit made him feel uncomfortable.56
After Einstein returned to Berlin, Hans Albert paid a call on Zangger. The kindly medical professor, friends of all sides in the dispute, tried to work out an accord so that Einstein could visit his sons. Besso also played intermediary. Einstein could see his sons, Besso advised in a formal letter he wrote after consulting with Mari, but not in Berlin nor in the presence of Elsa’s family. It would be best to do it at “a good Swiss inn,” initially just with Hans Albert, where they could spend some time on their own free of all distractions. Over Christmas, Hans Albert was planning to visit Besso’s family, and he suggested that perhaps Einstein could come then.57
The Race to General Relativity, 1915
What made the flurry of political and personal turmoil in the fall of 1915 so remarkable was that it highlighted Einstein’s ability to concentrate on, and compartmentalize, his scientific endeavors despite all distractions. During that period, with great effort and anxiety, he was engaged in a competitive rush to what he later called the greatest accomplishment of his life.58
Back when Einstein had moved to Berlin in the spring of 1914, his colleagues had assumed that he would set up an institute and attract acolytes to work on the most pressing problem in physics: the implications of quantum theory. But Einstein was more of a lone wolf. Unlike Planck, he did not want a coterie of collaborators or protégés, and he preferred to focus on what again had become his personal passion: the generalization of his theory of relativity.59
So after his wife and sons left him for Zurich, Einstein moved out of their old apartment and rented one that was nearer to Elsa and the center of Berlin. It was a sparsely furnished bachelor’s refuge, but still rather spacious: it had seven rooms on the third floor of a new five-story building.60
Einstein’s study at home featured a large wooden writing table that was cluttered with piles of papers and journals. Padding around this hermitage, eating and working at whatever hours suited him, sleeping when he had to, he waged his solitary struggle.
Through the spring and summer of 1915, Einstein wrestled with his Entwurf theory, refining it and defending it against a variety of challenges. He began calling it “the general theory” rather than merely “a generalized theory” of relativity, but that did not mask its problems, which he kept trying to deflect.
He claimed that his equations had the greatest amount of covariance that was permissible given his hole argument and other strictures of physics, but he began to suspect that this was not correct. He also got into an exhausting debate with the Italian mathematician Tullio Levi-Civita, who pointed out problems with his handling of the tensor calculus. And there was still the puzzle of the incorrect result the theory gave for the shift in Mercury’s orbit.
At least his Entwurf theory still successfully explained—or so he thought through the summer of 1915—rotation as being a form of relative motion, that is, a motion that could be defined only relative to the positions and motions of other objects. His field equations, he thought, were invariant under the transformation to rotating coordinates.61
Einstein was confident enough in his theory to show it off at a weeklong series of two-hour lectures, starting at the end of June 1915, at the University of Göttingen, which had become the preeminent center for the mathematical side of theoretical physics. Foremost among the geniuses there was David Hilbert, and Einstein was particularly eager—too eager, it would turn out—to explain all the intricacies of relativity to him.
The visit to Göttingen was a triumph. Einstein exulted to Zangger that he had “the pleasurable experience of convincing the mathematicians there thoroughly.” Of Hilbert, a fellow pacifist, he added, “I met him and became quite fond of him.” A few weeks later, after again reporting, “I was able to convince Hilbert of the general theory of relativity,” Einstein called him “a man of astonishing energy and independence.” In a letter to another physicist, Einstein was even more effusive: “In Göttingen I had the great pleasure of seeing that everything was understood down to the details. I am quite enchanted with Hilbert!”62
Hilbert was likewise enchanted with Einstein and his theory. So much so that he soon set out to see if he could beat Einstein to the goal of getting the field equations right. Within three months of his Göttingen lectures, Einstein was confronted with two distressing discoveries: that his Entwurf theory was indeed flawed, and that Hilbert was racing feverishly to come up with the correct formulations on his own.
Einstein’s realization that his Entwurf theory was unraveling came from an accumulation of problems. But it culminated with two major blows in early October 1915.
The first was that, upon rechecking, Einstein found that the Entwurf equations did not actually account for rotation as he had thought.63 He hoped to prove that rotation could be conceived of as just another form of relative motion, but it turned out that the Entwurf didn’t actually prove this. The Entwurf equations were not, as he had believed, covariant under a transformation that uniformly rotated the coordinate axes.
Besso had warned him in a memo in 1913 that this seemed to be a problem. But Einstein had ignored him. Now, upon redoing his calculations, he was dismayed to see this pillar knocked away. “This is a blatant contradiction,” he lamented to the astronomer Freundlich.
He assumed that the same mistake also accounted for his theory’s inability to account fully for the shift in Mercury’s orbit. And he despaired that he would not be able to find the problem. “I do not believe I am able to find the mistake myself, for in this matter my mind is too set in a deep rut.”64
In addition, he realized that he had made a mistake in what was called his “uniqueness” argument: that the sets of conditions required by energy-momentum conservation and other physical restrictions uniquely led to the field equations in the Entwurf. He wrote Lorentz explaining in detail his previous “erroneous assertions.”65
Added to these problems were ones he already knew about: the Entwurf equations were not generally covariant, meaning that they did not really make all forms of accelerated and nonuniform motion relative, and they did not fully explain Mercury’s anomalous orbit. And now, as this edifice was crumbling, he could hear what seemed to be Hilbert’s footsteps gaining on him from Göttingen.
Part of Einstein’s genius was his tenacity. He could cling to a set of ideas, even in the face of “apparent contradiction” (as he put it in his 1905 relativity paper). He also had a deep faith in his intuitive feel for the physical world. Working in a more solitary manner than most other scientists, he held true to his own instincts, despite the qualms of others.
But although he was tenacious, he was not mindlessly stubborn. When he finally decided his Entwurf approach was untenable, he was willing to abandon it abruptly. That is what he did in October 1915.
To replace his doomed Entwurf theory, Einstein shifted his focus from the physical strategy, which emphasized his feel for basic principles of physics, and returned to a greater reliance on a mathematical strategy, which made use of the Riemann and Ricci tensors. It was an approach he had used in his Zurich notebooks and then abandoned, but on returning to it he found that it could provide a way to generate generally covariant gravitational field equations. “Einstein’s reversal,” writes John Norton, “parted the waters and led him from bondage into the promised land of general relativity.”66
Of course, as always, his approach remained a mix of both strategies. To pursue a revitalized mathematical strategy, he had to revise the physical postulates that were the foundation for his Entwurf theory. “This was exactly the sort of convergence of physical and mathematical considerations that eluded Einstein in the Zurich notebook and in his work on the Entwurf theory,” write Michel Janssen and Jürgen Renn.67
Thus he returned to the tensor analysis that he had used in Zurich, with its greater emphasis on the mathematical goal of finding equations that were generally covariant. “Once every last bit of confidence in the earlier theories had given way,” he told a friend, “I saw clearly that it was only through general covariance theory, i.e., with Riemann’s covariant, that a satisfactory solution could be found.”68
The result was an exhausting, four-week frenzy during which Einstein wrestled with a succession of tensors, equations, corrections, and updates that he rushed to the Prussian Academy in a flurry of four Thursday lectures. It climaxed, with the triumphant revision of Newton’s universe, at the end of November 1915.
Every week, the fifty or so members of the Prussian Academy gathered in the grand hall of the Prussian State Library in the heart of Berlin to address each other as “Your Excellency” and listen to fellow members pour forth their wisdom. Einstein’s series of four lectures had been scheduled weeks earlier, but until they began—and even after they had begun—he was still working furiously on his revised theory.
The first was delivered on November 4. “For the last four years,” he began, “I have tried to establish a general theory of relativity on the assumption of the relativity even of non-uniform motion.” Referring to his discarded Entwurf theory, he said he “actually believed I had discovered the only law of gravitation” that conformed to physical realities.
But then, with great candor, he detailed all of the problems that theory had encountered. “For that reason, I completely lost trust in the field equations” that he had been defending for more than two years. Instead, he said, he had now returned to the approach that he and his mathematical caddy, Marcel Grossmann, had been using in 1912. “Thus I went back to the requirement of a more general covariance of the field equations, which I had left only with a heavy heart when I worked together with my friend Grossmann. In fact, we had then already come quite close to the solution.”
Einstein reached back to the Riemann and Ricci tensors that Grossmann had introduced him to in 1912. “Hardly anyone who truly understands it can resist the charm of this theory,” he lectured. “It signifies a real triumph of the method of the calculus founded by Gauss, Riemann, Christoffel, Ricci, and Levi-Civita.”69
This method got him much closer to the correct solution, but his equations on November 4 were still not generally covariant. That would take another three weeks.
Einstein was in the throes of one of the most concentrated frenzies of scientific creativity in history. He was working, he said, “horrendously intensely.”70 In the midst of this ordeal, he was also still dealing with the personal crisis within his family. Letters arrived from both his wife and Michele Besso, who was acting on her behalf, that pressed the issue of his financial obligations and discussed the guidelines for his contact with his sons.
On the very day he turned in his first paper, November 4, he wrote an anguished—and painfully poignant—letter to Hans Albert, who was in Switzerland:
I will try to be with you for a month every year so that you will have a father who is close to you and can love you. You can learn a lot of good things from me that no one else can offer you. The things I have gained from so much strenuous work should be of value not only to strangers but especially to my own boys. In the last few days I completed one of the finest papers of my life. When you are older, I will tell you about it.
He ended with a small apology for seeming so distracted: “I am often so engrossed in my work that I forget to eat lunch.”71
Einstein also took time off from furiously revising his equations to engage in an awkward fandango with his erstwhile friend and competitor David Hilbert, who was racing him to find the equations of general relativity. Einstein had been informed that the Göttingen mathematician had figured out the flaws in the Entwurf equations. Worried about being scooped, he wrote Hilbert a letter saying that he himself had discovered the flaws four weeks earlier, and he sent along a copy of his November 4 lecture. “I am curious whether you will take kindly to this new solution,” Einstein asked with a touch of defensiveness.72
Hilbert was not only a better pure mathematician than Einstein, he also had the advantage of not being as good a physicist. He did not get all wrapped up, the way Einstein did, in making sure that any new theory conformed to Newton’s old one in a weak static field or that it obeyed the laws of causality. Instead of a dual math-and-physics strategy, Hilbert pursued mainly a math strategy, focusing on finding the equations that were covariant. “Hilbert liked to joke that physics was too complicated to be left to the physicists,” notes Dennis Overbye.73
Einstein presented his second paper the following Thursday, November 11. In it, he used the Ricci tensor and imposed new coordinate conditions that allowed the equations thus to be generally covariant. As it turned out, that did not greatly improve matters. Einstein was still close to the final answer, but making little headway.74
Once again, he sent the paper off to Hilbert. “If my present modification (which does not change the equations) is legitimate, then gravitation must play a fundamental role in the composition of matter,” Einstein said. “My own curiosity is interfering with my work!”75
The reply that Hilbert sent the next day must have unnerved Einstein. He said he was about ready to oblige with “an axiomatic solution to your great problem.” He had planned to hold off discussing it until he explored the physical ramifications further. “But since you are so interested, I would like to lay out my theory in very complete detail this coming Tuesday,” which was November 16.
He invited Einstein to come to Göttingen and have the dubious pleasure of personally hearing him lay out the answer. The meeting would begin at 6 p.m., and Hilbert helpfully provided Einstein with the arrival times of the two afternoon trains from Berlin. “My wife and I would be very pleased if you stayed with us.”
Then, after signing his name, Hilbert felt compelled to add what must surely have been a tantalizing and disconcerting postscript. “As far as I understand your new paper, the solution given by you is entirely different from mine.”
Einstein wrote four letters on November 15, a Monday, that give a glimpse into why he was suffering stomach pains. To his son Hans Albert, he suggested that he would like to travel to Switzerland around Christmas and New Year’s to visit him. “Maybe it would be better if we were alone somewhere,” such as at a secluded inn, he suggested to his son. “What do you think?”
He also wrote his estranged wife a conciliatory letter that thanked her for her willingness not “to undermine my relations with the boys.” And he reported to their mutual friend Zangger, “I have modified the theory of gravity, having realized that my earlier proofs had a gap ...I shall be glad to come to Switzerland at the turn of the year in order to see my dear boy.”76
Finally, he replied to Hilbert and declined his invitation to visit Göttingen the next day. His letter did not hide his anxiety: “Your analysis interests me tremendously . . . The hints you gave in your messages awaken the greatest of expectations. Nevertheless, I must refrain from traveling to Göttingen for the moment ...I am tired out and plagued by stomach pains . . . If possible, please send me a correction proof of your study to mitigate my impatience.”77
Fortunately for Einstein, his anxiety was partly alleviated that week by a joyous discovery. Even though he knew his equations were not in final form, he decided to see whether the new approach he was taking would yield the correct results for what was known about the shift in Mercury’s orbit. Because he and Besso had done the calculations once before (and gotten a disappointing result), it did not take him long to redo the calculations using his revised theory.
The answer, which he triumphantly announced in the third of his four November lectures, came out right: 43 arc-seconds per century.78 “This discovery was, I believe, by far the strongest emotional experience in Einstein’s scientific life, perhaps in all his life,” Abraham Pais later said. He was so thrilled he had heart palpitations, as if “something had snapped” inside. “I was beside myself with joyous excitement,” he told Ehrenfest. To another physicist he exulted: “The results of Mercury’s perihelion movement fills me with great satisfaction. How helpful to us is astronomy’s pedantic accuracy, which I used to secretly ridicule!”79
In the same lecture, he also reported on another calculation he had made. When he first began formulating general relativity eight years earlier, he had said that one implication was that gravity would bend light. He had previously figured that the bending of light by the gravitational field next to the sun would be approximately 0.83 arc-second, which corresponded to what would be predicted by Newton’s theory when light was treated as if a particle. But now, using his newly revised theory, Einstein calculated that the bending of light by gravity would be twice as great, because of the effect produced by the curvature of spacetime. Therefore, the sun’s gravity would bend a beam by about 1.7 arc-seconds, he now predicted. It was a prediction that would have to wait for the next suitable eclipse, more than three years away, to be tested.
That very morning, November 18, Einstein received Hilbert’s new paper, the one that he had been invited to Göttingen to hear presented. Einstein was surprised, and somewhat dismayed, to see how similar it was to his own work. His response to Hilbert was terse, a bit cold, and clearly designed to assert the priority of his own work:
The system you furnish agrees—as far as I can see—exactly with what I found in the last few weeks and have presented to the Academy. The difficulty was not in finding generally covariant equations ...for this is easily achieved with Riemann’s tensor . . . Three years ago with my friend Grossmann I had already taken into consideration the only covariant equations, which have now been shown to be the correct ones. We had distanced ourselves from it, reluctantly, because it seemed to me that the physical discussion yielded an incongruity with Newton’s law. Today I am presenting to the Academy a paper in which I derive quantitatively out of general relativity, without any guiding hypothesis, the perihelion motion of Mercury. No gravitational theory has achieved this until now.
Hilbert responded kindly and quite generously the following day, claiming no priority for himself. “Cordial congratulations on conquering perihelion motion,” he wrote. “If I could calculate as rapidly as you, in my equations the electron would have to capitulate and the hydrogen atom would have to produce its note of apology about why it does not radiate.”81
Yet the day after, on November 20, Hilbert sent in a paper to a Göttingen science journal proclaiming his own version of the equations for general relativity. The title he picked for his piece was not a modest one. “The Foundations of Physics,” he called it.
It is not clear how carefully Einstein read the paper that Hilbert sent him or what in it, if anything, affected his thinking as he busily prepared his climactic fourth lecture at the Prussian Academy. Whatever the case, the calculations he had done the week earlier, on Mercury and on light deflection, helped him realize that he could avoid the constraints and coordinate conditions he had been imposing on his gravitational field equations. And thus he produced in time for his final lecture—“The Field Equations of Gravitation,” on November 25, 1915—a set of covariant equations that capped his general theory of relativity.
The result was not nearly as vivid to the layman as, say, E=mc2. Yet using the condensed notations of tensors, in which sprawling complexities can be compressed into little subscripts, the crux of the final Einstein field equations is compact enough to be emblazoned, as it indeed often has been, on T-shirts designed for proud physics students. In one of its many variations,82 it can be written as:
The left side of the equation starts with the term Rmn, which is the Ricci tensor he had embraced earlier. The term gmn is the all-important metric tensor, and the term R is the trace of the Ricci tensor called the Ricci scalar. Together, this left side of the equation—which is now known as the Einstein tensor and can be written simply as Gmn—compresses together all of the information about how the geometry of spacetime is warped and curved by objects.
The right side describes the movement of matter in the gravitational field. The interplay between the two sides shows how objects curve spacetime and how, in turn, this curvature affects the motion of objects. As the physicist John Wheeler has put it, “Matter tells space-time how to curve, and curved space tells matter how to move.”83
Thus is staged a cosmic tango, as captured by another physicist, Brian Greene:
Space and time become players in the evolving cosmos. They come alive. Matter here causes space to warp there, which causes matter over here to move, which causes space way over there to warp even more, and so on. General relativity provides the choreography for an entwined cosmic dance of space, time, matter, and energy.
At last Einstein had equations that were truly covariant and thus a theory that incorporated, at least to his satisfaction, all forms of motion, whether it be inertial, accelerated, rotational, or arbitrary. As he proclaimed in the formal presentation of his theory that he published the following March in the Annalen der Physik, “The general laws of nature are to be expressed by equations that hold true for all systems of coordinates, that is they are covariant with respect to any substitutions whatever.”85
Einstein was thrilled by his success, but at the same time he was worried that Hilbert, who had presented his own version five days earlier in Göttingen, would be accorded some of the credit for the theory. “Only one colleague has really understood it,” he wrote to his friend Heinrich Zangger, “and he is seeking to nostrify it (Abraham’s expression) in a clever way.” The expression “to nostrify” (nostrifizieren), which had been used by the Göttingen-trained mathematical physicist Max Abraham, referred to the practice of nostrification by which German universities converted degrees granted by other universities into degrees of their own. “In my personal experience I have hardly come to know the wretchedness of mankind better.” In a letter to Besso a few days later, he added, “My colleagues are acting hideously in this affair. You will have a good laugh when I tell you about it.”86
So who actually deserves the primary credit for the final mathematical equations? The Einstein-Hilbert priority issue has generated a small but intense historical debate, some of which seems at times to be driven by passions that go beyond mere scientific curiosity. Hilbert presented a version of his equations in his talk on November 16 and a paper that he dated November 20, before Einstein presented his final equations on November 25. However, a team of Einstein scholars in 1997 found a set of proof pages of Hilbert’s article, on which Hilbert had made revisions that he then sent back to the publisher on December 16. In the original version, Hilbert’s equations differed in a small but important way from Einstein’s final version of the November 25 lecture. They were not actually generally covariant, and he did not include a step that involved contracting the Ricci tensor and putting the resulting trace term, the Ricci scalar, into the equation. Einstein did this in his November 25 lecture. Apparently, Hilbert made a correction in the revised version of his article to match Einstein’s version. His revisions, quite generously, also added the phrase “first introduced by Einstein” when he referred to the gravitational potentials.
Hilbert’s advocates (and Einstein’s detractors) respond with a variety of arguments, including that the page proofs are missing one part and that the trace term at issue was either unnecessary or obvious.
It is fair to say that both men—to some extent independently but each also with knowledge of what the other was doing—derived by November 1915 mathematical equations that gave formal expression to the general theory. Judging from Hilbert’s revisions to his own page proofs, Einstein seems to have published the final version of these equations first. And in the end, even Hilbert gave Einstein credit and priority.
Either way, it was, without question, Einstein’s theory that was being formalized by these equations, one that he had explained to Hilbert during their time together in Göttingen that summer. Even the physicist Kip Thorne, one of those who give Hilbert credit for producing the correct field equations, nonetheless says that Einstein deserves credit for the theory underlying the equations. “Hilbert carried out the last few mathematical steps to its discovery independently and almost simultaneously with Einstein, but Einstein was responsible for essentially everything that preceded these steps,” Thorne notes. “Without Einstein, the general relativistic laws of gravity might not have been discovered until several decades later.”87
Hilbert, graciously, felt the same way. As he stated clearly in the final published version of his paper, “The differential equations of gravitation that result are, as it seems to me, in agreement with the magnificent theory of general relativity established by Einstein.” Henceforth he would always acknowledge (thus undermining those who would use him to diminish Einstein) that Einstein was the sole author of the theory of relativity.88 “Every boy in the streets of Göttingen understands more about four-dimensional geometry than Einstein,” he reportedly said. “Yet, in spite of that, Einstein did the work and not the mathematicians.”89
Indeed, Einstein and Hilbert were soon friendly again. Hilbert wrote in December, just weeks after their dash for the field equations was finished, to say that with his support Einstein had been elected to the Göttingen Academy. After expressing his thanks, Einstein added, “I feel compelled to say something else to you.” He explained:
There has been a certain ill-feeling between us, the cause of which I do not want to analyze. I have struggled against the feeling of bitterness attached to it, with complete success. I think of you again with unmixed geniality and ask you to try to do the same with me. It is a shame when two real fellows who have extricated themselves somewhat from this shabby world do not afford each other mutual pleasure.
They resumed their regular correspondence, shared ideas, and plotted to get a job for the astronomer Freundlich. By February Einstein was even visiting Göttingen again and staying at Hilbert’s home.
Einstein’s pride of authorship was understandable. As soon as he got printed copies of his four lectures, he mailed them out to friends. “Be sure you take a good look at them,” he told one. “They are the most valuable discovery of my life.” To another he noted, “The theory is of incomparable beauty.”91
Einstein, at age 36, had produced one of history’s most imaginative and dramatic revisions of our concepts about the universe. The general theory of relativity was not merely the interpretation of some experimental data or the discovery of a more accurate set of laws. It was a whole new way of regarding reality.
Newton had bequeathed to Einstein a universe in which time had an absolute existence that tick-tocked along independent of objects and observers, and in which space likewise had an absolute existence. Gravity was thought to be a force that masses exerted on one another rather mysteriously across empty space. Within this framework, objects obeyed mechanical laws that had proved remarkably accurate—almost perfect—in explaining everything from the orbits of the planets, to the diffusion of gases, to the jiggling of molecules, to the propagation of sound (though not light) waves.
With his special theory of relativity, Einstein had shown that space and time did not have independent existences, but instead formed a fabric of spacetime. Now, with his general version of the theory, this fabric of spacetime became not merely a container for objects and events. Instead, it had its own dynamics that were determined by, and in turn helped to determine, the motion of objects within it—just as the fabric of a trampoline will curve and ripple as a bowling ball and some billiard balls roll across it, and in turn the dynamic curving and rippling of the trampoline fabric will determine the path of the rolling balls and cause the billiard balls to move toward the bowling ball.
The curving and rippling fabric of spacetime explained gravity, its equivalence to acceleration, and, Einstein asserted, the general relativity of all forms of motion.92 In the opinion of Paul Dirac, the Nobel laureate pioneer of quantum mechanics, it was “probably the greatest scientific discovery ever made.” Another of the great giants of twentieth-century physics, Max Born, called it “the greatest feat of human thinking about nature, the most amazing combination of philosophical penetration, physical intuition and mathematical skill.”93
The entire process had exhausted Einstein but left him elated. His marriage had collapsed and war was ravaging Europe, but Einstein was as happy as he would ever be. “My boldest dreams have now come true,” he exulted to Besso. “General covariance. Mercury’s perihelion motion wonderfully precise.” He signed himself “contented but kaput.”94
With Elsa, June 1922
“The Narrow Whirlpool of Personal Experience”
As a young man, Einstein had predicted, in a letter to the mother of his first girlfriend, that the joys of science would be a refuge from painful personal emotions. And thus it was. His conquest of general relativity proved easier than finding the formulas for the forces swirling within his family.
Those forces were complex. At the very moment he was finalizing his field equations—the last week of November 1915—his son Hans Albert was telling Michele Besso that he wanted to spend time alone with his father over Christmas, preferably on Zugerberg mountain or someplace similarly isolated. But simultaneously, the boy was writing his father a nasty letter saying he did not want him to come to Switzerland at all.1
How to explain the contradiction? Hans Albert’s mind seemed at times to display a duality—he was, after all, only 11—and he had powerfully conflicted attitudes toward his father. That was no surprise. Einstein was intense and compelling and at times charismatic. He was also aloof and distracted and had distanced himself, physically and emotionally, from the boy, who was guarded by a doting mother who felt humiliated.
The stubborn patience that Einstein displayed when dealing with scientific problems was equaled by his impatience when dealing with personal entanglements. So he informed the boy he was canceling the trip. “The unkind tone of your letter dismays me very much,” Einstein wrote just days after finishing his last lecture on general relativity. “I see that my visit would bring you little joy, therefore I think it’s wrong to sit in a train for two hours and 20 minutes.”
There was also the question of a Christmas present. Hans Albert had become an avid little skier, and Mari gave him a set of equipment that cost 70 francs. “Mama bought them for me on condition that you also contribute,” he wrote. “I consider them a Christmas present.” This did not please Einstein. He replied that he would send him a gift in cash, “but I do think that a luxury gift costing 70 francs does not match our modest circumstances,” Einstein wrote, underlining the phrase.2
Besso put on what he called his “pastoral manner” to mediate. “You should not take serious offense at the boy,” he said. The source of the friction was Mari, Besso believed, but he asked Einstein to remember that she was composed “not only of meanness but of goodness.” He should try to understand, Besso urged, how difficult it was for Mari to deal with him. “The role as the wife of a genius is never easy.”3 In the case of Einstein, that was certainly true.
The anxiety surrounding Einstein’s proposed visit was partly due to a misunderstanding. Einstein had assumed that the plan to have him and his son meet at the Bessos’ had been arranged because Mari and Hans Albert wanted it that way. Instead, the boy had no desire to be a bystander while his father and Besso discussed physics. Just the opposite: he wanted his father to himself.
Mari ended up writing to clear up the matter, which Einstein appreciated. “I was likewise a bit disappointed that I would not get Albert to myself but only under Besso’s protection,” he said.
So Einstein reinstated his plan to visit Zurich, and he promised it would be one of many such trips to see his son. “[Hans] Albert* is now entering the age at which I can mean very much to him,” he said. “I want mainly to teach him to think, judge and appreciate things objectively.” A week later, in another letter to Mari, he reaffirmed that he was happy to make the trip, “for there is a faint chance that I’ll please Albert by coming.” He did, however, add rather pointedly, “See to it that he receives me fairly cheerfully. I am quite tired and overworked, and not capable of enduring new agitations and disappointments.”4
It was not to be. Einstein’s exhaustion lingered, and the war made the border crossing from Germany difficult. Two days before Christmas of 1915, when he was supposed to be departing for Switzerland, Einstein instead wrote his son a letter. “I have been working so hard in the last few months that I urgently need a rest during the Christmas holidays,” he said. “Aside from this, coming across the border is very uncertain at present, since it has been almost constantly closed recently. That is why I must unfortunately deprive myself of visiting you now.”
Einstein spent Christmas at home. That day, he took out of his satchel some of the drawings that Hans Albert had sent him and wrote the boy a postcard saying how much they pleased him. He would come for Easter, he promised, and he expressed delight that his son enjoyed playing piano. “Maybe you can practice something to accompany a violin, and then we can play at Easter when we are together.”5
After he and Mari separated, Einstein had initially decided not to seek a divorce. One reason was that he had no desire to marry Elsa. Companionship without commitment suited him just fine. “The attempts to force me into marriage come from my cousin’s parents and is mainly attributable to vanity, though moral prejudice, which is still very much alive in the old generation, plays a part,” Einstein wrote Zangger the day after presenting his climactic November 1915 lecture. “If I let myself become trapped, my life would become complicated, and above all it would probably be a heavy blow for my boys. Therefore, I must allow myself not to be moved either by my inclination or by tears, but must remain as I am.” It was a resolution he repeated to Besso as well.6
Besso and Zangger agreed that he should not seek a divorce. “It is important that Einstein knows that his truest friends,” Besso wrote Zangger, “would regard a divorce and subsequent remarriage as a great evil.”7
But Elsa and her family kept pushing. So in February 1916, Einstein wrote Mari to propose—indeed, beg—that she agree to a divorce, “so that we can arrange the rest of our lives independently.” The separation agreement they had worked out with the help of Fritz Haber, he suggested, could serve as the basis for a divorce. “It will surely be possible to have the details settled to your satisfaction,” he promised. His letter also included instructions on how to keep their boys from suffering from calcium deficiency.8
When Mari resisted, Einstein became more insistent. “For you it involves a mere formality,” he said. “For me, however, it is an imperative duty.” He informed Mari that Elsa had two daughters whose reputations and chances of marriage were being compromised by “the rumors” that were circulating about the illicit relationship their mother was having with Einstein. “This weighs on me and ought to be redressed by a formal marriage,” he told Mari. “Try to imagine yourself in my position for once.”
As an enticement, he offered more money. “You would gain from this change,” he told Mari. “I wish to do more than I had obligated myself to before.” He would transfer 6,000 marks into a fund for the children and increase her payments to 5,600 marks annually. “By making myself such a frugal bed of straw, I am proving to you that my boys’ well-being is closest to my heart, above all else in the world.”
In return, he wanted the right to have his sons visit him in Berlin. They would not come into contact with Elsa, he pledged. He even added a somewhat surprising promise: he would not be living with Elsa even if they got married. Instead, he would keep his own apartment. “For I shall never give up the state of living alone, which has manifested itself as an indescribable blessing.”
Mari did not consent to give him the right to have the boys visit him in Berlin. But she did tentatively agree—or at least so Einstein thought—to allow the start of divorce discussions.9
As he had promised Hans Albert, Einstein arrived in Switzerland in early April 1916 for a three-week Easter vacation, moving into a hotel near the Zurich train station. Initially, things went very well. The boys came to see him and greeted him joyously. From his hotel, he sent Mari a note of thanks:
My compliments on the good condition of our boys. They are in such excellent physical and mental shape that I could not have wished for more. And I know that this is for the most part due to the proper up-bringing you provide them. I am likewise thankful that you have not alienated me from the children. They came to meet me spontaneously and sweetly.
Mari sent word that she wanted to see Einstein herself. Her goal was to be assured that he truly wanted a divorce and was not merely being pressured by Elsa. Both Besso and Zangger tried to arrange such a meeting, but Einstein declined. “There would be no point in a conversation between us and it could serve only to reopen old wounds,”s he wrote in a note to Mari.10
Einstein took Hans Albert off alone, as the boy wished, for what was planned as a ten-day hiking excursion in a mountain resort overlooking Lake Lucerne. There they were caught in a late-season snowstorm that kept them confined to the inn, which initially pleased them both. “We are snowed in at Seelisberg but are enjoying ourselves immensely,” Einstein wrote Elsa. “The boy delights me, especially with his clever questions and his undemanding way. No discord exists between us.” Unfortunately, soon the weather, and perhaps also their enforced togetherness, became oppressive, and they returned to Zurich a few days early.11
Back in Zurich, the tensions revived. One morning, Hans Albert came to visit his father at the physics institute to watch an experiment. It was a pleasant enough activity, but as the boy was leaving for lunch, he urged his father to come by the house and at least pay a courtesy call on Mari.
Einstein refused. Hans Albert, who was just about to turn 12, became angry and said he would not come back for the completion of the experiment that afternoon unless his father relented. Einstein would not. “That’s how it remained,” he reported to Elsa a week later, on the day he left Zurich. “And I have seen neither of the children since.”12
Mari subsequently went into an emotional and physical melt-down. She had a series of minor heart incidents in July 1916, accompanied by extreme anxiety, and her doctors told her to remain in bed. The children moved in with the Bessos, and then to Lausanne, where they stayed with Mari’s friend Helene Savi, who was riding out the war there.
Besso and Zangger tried to get Einstein to come down from Berlin to be with his sons. But Einstein demurred. “If I go to Zurich, my wife will demand to see me,” he wrote Besso. “This I would have to refuse, partly on an inalterable resolve partly also to spare her the agitation. Besides, you know that the personal relations between the children and me deteriorated so much during my stay at Easter (after a very promising start) that I doubt very much whether my presence would be reassuring for them.”
Einstein assumed that his wife’s illness was largely psychological and even, perhaps, partly faked. “Isn’t it possible that nerves are behind it all?” he asked Zangger. To Besso, he was more blunt: “I have the suspicion that the woman is leading both of you kind-hearted men down the garden path. She is not afraid to use all means when she wants to achieve something. You have no idea of the natural craftiness of such a woman.”13 Einstein’s mother agreed. “Mileva was never as sick as you seem to think,” she told Elsa.14
Einstein asked Besso to keep him informed of the situation and made a stab at scientific humor by saying that his reports did not need to have logical “continuity” because “this is permissible in the age of quantum theory.” Besso was not sympathetic; he wrote Einstein a sharp letter saying Mari’s condition was not “a deception” but was instead caused by emotional stress. Besso’s wife, Anna, was even harsher, adding a postscript to the letter that addressed Einstein with the formal Sie.15