David Bodanis
A Biography
of the World's Most
Famous Equation
Copyright © 2000 by David Bodanis
All rights reserved. No part of this book may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or by any information storage and retrieval system, without permission in writing from the Publisher.
First published in the United States of America in 2000 by
Walker Publishing Company, Inc. This edition published in 2005.
Distributed to the trade by Holtzbrinck Publishers
Photograph of Einstein on title page from the Leo Baeck Institute/ Archive Photos
Library of Congress Cataloging-in-Publication Data
Bodanis, David.
E=mc2: a biography of the world's most famous equation /
David Bodanis.
p. cm.
Includes index.
eISBN: 978-0-802-71821-1
1. Force and energy. 2. Mass (Physics) 3. Mathematical
physics. 4. Einstein, Albert, 1879-1955 I. Title.
OC73.8.C6 B63 2000
530.11—dc21 00-040857
BOOK DESIGN BY RALPH L. FOWLER
Printed in the United States of America
10 9 8 7 6 5 4 3 2 1
Contents
Foreword Simon Singh
Preface
PART I
Birth
1 Bern Patent Office, 1905
PART 2
Ancestors of E=mc2
2 E Is for Energy
3 =
4 m Is for mass
5 c Is for celeritas
6 2
PART 3
The Early Years
7 Einstein and the Equation
8 Into the Atom
9 Quiet in the Midday Snow
PART 4
Adulthood
10 Germany's Turn
11 Norway
12 America's Turn
13 8:16 A.M.—Over Japan
PART 5
Till the End of Time
14 The Fires of the Sun
15 Creating the Earth
16 A Brahmin Lifts His Eyes Unto the Sky
Epilogue:
What Else Einstein Did
Appendix:
Follow-Up of Other Key Participants
Notes
Guide to Further Reading
Acknowledgments
Foreword
Einstein's Miracle Year
Not every physicist has an annus mirabilis. Indeed, there have only been two such wonder years in the history of science, and Albert Einstein experienced one of them in 1905. But what defines a wonder year? What exactly did Einstein do that was so wondrous? And why is E=mc2 Einstein's most famous legacy of 1905?
The term annus mirabilis was originally the title of a John Dryden poem about the sensational events that took place in 1666, namely London's endurance through the great fire, Britain's recovery after the great plague, and the victory of the British fleet over the Dutch. Scientists, however, soon adopted the term to describe the same year for quite different reasons.
Scientists judged the discoveries of Sir Isaac Newton to be the true wonders of 1666. His annus mirabilis included major breakthroughs in calculus, the nature of light, and, most famously, gravity. These were discoveries that transformed science, allowing physicists to explore the universe with renewed confidence. Newton had combined mathematics, theory, and experiment to give scientists a deeper understanding of the laws of nature.
Scientists assumed that nobody would ever match Newton's annus mirabilis, yet 1905 witnessed a series of groundbreaking papers from Albert Einstein that took physics from the classical post-Newtonian era into the age of modern physics. Einstein's research shook the foundations of physics.
In one paper, Einstein analyzed a phenomenon known as Brownian motion and presented a brilliant argument to support the theory that matter is composed of atoms and molecules. Physicists already suspected that atoms were at the heart of matter, but it was Einstein who proved that this was indeed the case. In another paper, he showed that a well-established phenomenon called the photoelectric effect could be fully explained using the newly developed theory of quantum physics. Not surprisingly, this paper went on to win Einstein a Nobel Prize.
The third paper was even more brilliant. It summarized Einstein's thoughts over the previous decade on the speed of light and its implications for the nature of space and time. Einstein's special theory of relativity created an entirely new framework for physics. The repercussions were so mind boggling that even Einstein himself had been shaken to the core as he conducted the research that underpinned special relativity. He was still a very young man, barely 26 years old, and he had experienced periods of enormous self-doubt as he developed his theory: "I must confess that at the very beginning when the special theory of relativity began to germinate in me, I was visited by all sorts of nervous conflicts. When young I used to go away for weeks in a state of confusion, as one who at the time had yet to overcome the state of stupefaction in his first encounter with such questions."
Einstein's special theory of relativity is astonishing because it makes extraordinary claims about the speed of light, the elasticity of space, and the plasticity of time. However, one aspect of the theory above all others has achieved iconic status, namely the equation E=mc2. Why has this particular equation become so spectacularly famous?
The rest of this book will explain the physics of the equation, so I will attempt to explain its fame by concentrating on its aesthetics. In short, I would argue that E=mc2 is so famous because it is so unbearably beautiful, which is obvious to anybody who has any appreciation of its meaning and significance. Beauty is something that scientists often talk about in relation to their work, and they all recognize beauty when they see it, but it is rather hard to define. Nevertheless, when I tried to work out what lay behind the beauty of E=mc2, I was struck by two facets.
On the one hand, the equation is incredibly shocking. At school we are told that mass can neither be created nor destroyed, and the same goes for energy. Also, we can see for ourselves that mass and energy appear to be totally different entities. Yet E=mc2 tells us that energy (E) and mass (m) are effectively equivalent and can be transformed into each other, such that energy could be destroyed and matter could be created, or vice versa.
Coupled with the equation's shock value is its incredible simplicity. E=mc2 is not an equation full of integral signs, fractions, a dozen Greek symbols, and a random array of numbers quoted to several decimal places. Instead, it simply has energy on one side and mass on the other, with a conversion factor (c2) thrown in to explain the rate at which energy and mass can be converted into each other. E=mc2 is beautiful because it is shockingly simple.
A similar opinion on beauty comes from Graham Farmelo, who edited a book entitled It Must Be Beautiful, which sought to explore the meaning of beauty in scientific equations. In his introduction he made a point that is particularly relevant to the beauty of E=mc2: "Great equations also share with the finest poetry an extraordinary power—poetry is the most concise and highly charged form of language, just as the great equations of science are the most succinct form of understanding of the aspect of physical reality they describe."
Surely there can be no other example of five characters revealing such a dramatic and astonishing insight into the nature of the universe. E=mc2 does indeed have a poetic power and beauty. And if the physicist Paul Dirac is correct, then E=mc2 is even better than the best poetry: "In science one tries to tell people, in such a way as to be understood by everyone, something that no one ever knew before. But in poetry, it's the exact opposite."
—SIMON SINGH
&nbs
p; Preface
A while ago I was reading an interview with the actress Cameron Diaz in a movie magazine. At the end the interviewer asked her if there was anything she wanted to know, and she said she'd like to know what E=mc2 really means. They both laughed, then Diaz mumbled that she'd meant it, and then the interview ended.
"You think she did mean it?" one of my friends asked, after I read it aloud. I shrugged, but everyone else in the room—architects, two programmers, and even one historian (my wife!)—was adamant. They knew exactly what she intended: They wouldn't mind understanding what the famous equation meant too.
It got me thinking. Everyone knows that E=mc2 is really important, but they usually don't know what it means, and that's frustrating, because the equation is so short that you'd think it would be understandable.
There are plenty of books that try to explain it, but who can honestly say they understand them? To most readers they contain just a mass of odd diagrams—those little trains or rocketships or flashlights that are utterly mystifying. Even firsthand instruction doesn't always help, as Chaim Weizmann found when he took a long Atlantic crossing with Einstein in 1921: "Einstein explained his theory to me every day," Weizmann said, "and soon I was fully convinced that he understood it."
I realized there could be a different approach. The overall surveys of relativity fail not because they're poorly written, but because they take on too much. Instead of writing yet another account of all of relativity, let alone another biography of Einstein—those are interesting topics, but have been done to death—I could simply write about E=mc2. That's possible, for it's just one part of Einstein's wider work. To a large extent, it stands on its own.
The moment I started thinking this way, it became clear how to go ahead. Instead of using the rocketship-and-flashlight approach, I could write the biography of E=mc2. Everyone knows that a biography entails stories of the ancestors, childhood, adolescence, and adulthood of your subject. It's the same with the equation.
The book begins, accordingly, with the history of each part of the equation—the symbols E, m, c, =, and 2. For each of these—the equation's "ancestors"—I focus on a single person or research group whose work was especially important in creating our modern understanding of the terms.
Once the nature of those symbols is clear, it's time to turn to the equation's "birth." This is where Einstein enters the book: his life as a patent clerk in 1905; what he'd been reading, and what he'd been thinking about, which led to all those symbols he wove together in the equation hurtling into place in his mind.
If the equation and its operations had stayed solely in Einstein's hands, our book would simply have continued with Einstein's life after 1905. But pretty quickly after this great discovery his interests shifted to other topics; his personal story fades from the book, and instead we pick up with other physicists: more empirical ones now, such as the booming, rugby-playing Ernest Rutherford, and the quiet, ex-POW James Chadwick, who together helped reveal the detailed structures within the atom that could—in principle—be manipulated to allow the great power the equation spoke of to come out.
In any other century those theoretical discoveries might have taken a long time to be turned into practical reality, but the details of how Einstein's equation might be used became clear early in 1939, just as the twentieth century's greatest war was beginning. A long, central section of the book homes in on the equation's coming of age here, in the furious race between scientists based in the United States and those in Nazi Germany to see who could build a deathly, planet-controlling bomb first. The history is often presented as if America's victory were inevitable, due to the country's industrial superiority, but it turns out that Germany came dangerously closer to success than is often realized. Even as late as D Day in June 1944, Army Chief of Staff George Marshall saw to it that several of the U.S. units landing in France were supplied with Geiger counters as a precaution against a possible Nazi attack with radioactive weapons.
In the final sections of the book we switch away from war; the equation's "adulthood" has begun. We'll see how E=mc2 is at the heart of many medical devices, such as the PET scanners used for finding tumors; its effects are also widespread in our ordinary household devices, including televisions and smoke alarms. But even more significant is how its power stretches far out into the universe, helping to explain how stars ignite, and our planet keeps warm; how black holes are created, and how our world will end. At the very end of the book, there are detailed notes, for readers interested in more mathematical or historical depth; further background explanations are available at the Web site davidbodanis.com.
The stories along the way are as much about passion, love, and revenge as they are about cool scientific discovery. There will be Michael Faraday, a boy from a poor London family desperate for a mentor to lift him to a better life, and Emilie du Châtelet, a woman trapped in the wrong century, trying to carve out a space where she wouldn't be mocked for using her mind. There are accounts of Knut Haukelid and a team of fellow young Norwegians, forced to attack their own countrymen to avert a greater Nazi evil; Cecilia Payne, an Englishwoman who finds her career destroyed after daring to glimpse the sun's fate in the year A.D. 6 billion; and a nineteen-year-old Brahmin, Subrahmanyan Chandrasekhar, who discovers something even more fearful, out in the beating heat of the Arabian Sea in midsummer. Through all their stories—as well as highlights from those of Isaac Newton, Werner Heisenberg, and other researchers—the meaning of each part of the equation becomes clear.
PART I
Birth
Bern Patent Office, 1905 1
From THE COLLECTED PAPERS OF ALBERT EINSTEIN, VOLUME I:
13 April 1901
Professor Wilhelm Ostwald
University of Leipzig
Leipzig, Germany
Esteemed Herr Professor!
Please forgive a father who is so bold as to turn to you, esteemed Herr Professor, in the interest of his son.
I shall start by telling you that my son Albert is 22 years old, that . . . he feels profoundly unhappy with his present lack of position, and his idea that he has gone off the tracks with his career & is now out of touch gets more and more entrenched each day. In addition, he is oppressed by the thought that he is a burden on us, people of modest means. . . .
I have taken the liberty of turning [to you] with the humble request to . . . write 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 for now or the next autumn, my gratitude would know no bounds. . . .
I am also taking the liberty of mentioning that my son does not know anything about my unusual step.
I remain, highly esteemed Herr Professor,
your devoted
Hermann Einstein
No answer from Professor Ostwald was ever received.
The world of 1905 seems distant to us now, but there were many similarities to life today. European newspapers complained that there were too many American tourists, while Americans were complaining that there were too many immigrants. The older generation everywhere complained that the young were disrespectful, while politicians in Europe and America worried about the disturbing turbulence in Russia. There were newfangled "aerobics" classes; there was a trend-setting vegetarian society, and calls for sexual freedom (which were rebuffed by traditionalists standing for family values), and much else.
The year 1905 was also when Einstein wrote a series of papers that changed our view of the universe forever. On the surface, he seemed to have been leading a pleasant, quiet life until then. He had often been interested in physics puzzles as a child, and was now a recent university graduate, easygoing enough to have many friends. He had married a bright fellow student, Mileva, and was earning enough money from a civil service job in the patent office to spend his evenings and Sundays in pub visits, or long walks—above all, he had a great deal of time to think.
Although
his father's letter hadn't succeeded, a friend of Einstein's from the university, Marcel Grossman, had pulled the right strings to get Einstein the patent job in 1902. Grossman's help was necessary not so much because Einstein's final university grades were unusually low—through cramming with the ever-useful Grossman's notes, Einstein had just managed to reach a 4.91 average out of a possible 6, which was almost average— but because one professor, furious at Einstein for telling jokes and cutting classes, had spitefully written unacceptable references. Teachers over the years had been irritated by his lack of obedience, most notably Einstein's high school Greek grammar teacher, Joseph Degenhart, the one who has achieved immortality in the history books through insisting that "nothing would ever become of you." Later, when told it would be best if he left the school, Degenhart had explained, "Your presence in the class destroys the respect of the students."
Outwardly Einstein appeared confident, and would joke with his friends about the way everyone in authority seemed to enjoy putting him down. The year before, in 1904, he had applied for a promotion from patent clerk third class to patent clerk second class. His supervisor, Dr. Haller, had rejected him, writing in an assessment that although Einstein had "displayed some quite good achievements," he would still have to wait "until he has become fully familiar with mechanical engineering."
In reality, though, the lack of success was becoming serious. Einstein and his wife had given away their first child, a daughter born before they were married, and were now trying to raise the second on a patent clerk's salary. Einstein was twenty-six. He couldn't even afford the money for part-time help to let his wife go back to her studies. Was he really as wise as his adoring younger sister, Maja, had told him?
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