The Road to Relativity: The History and Meaning of Einstein's "The Foundation of General Relativity", Featuring the Original Manuscript of Einstein's Masterpiece
264
The Road to Relativity: The History and Meaning of Einstein's "The Foundation of General Relativity", Featuring the Original Manuscript of Einstein's Masterpiece
264Paperback(Reprint)
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Overview
This richly annotated facsimile edition of "The Foundation of General Relativity" introduces a new generation of readers to Albert Einstein's theory of gravitation. Written in 1915, this remarkable document is a watershed in the history of physics and an enduring testament to the elegance and precision of Einstein's thought. Presented here is a beautiful facsimile of Einstein's original handwritten manuscript, along with its English translation and an insightful page-by-page commentary that places the work in historical and scientific context. Hanoch Gutfreund and Jürgen Renn's concise introduction traces Einstein's intellectual odyssey from special to general relativity, and their essay "The Charm of a Manuscript" provides a delightful meditation on the varied afterlife of Einstein's text. Featuring a foreword by John Stachel, this handsome edition also includes a biographical glossary of the figures discussed in the book, a comprehensive bibliography, suggestions for further reading, and numerous photos and illustrations throughout.
Product Details
| ISBN-13: | 9780691175812 |
|---|---|
| Publisher: | Princeton University Press |
| Publication date: | 05/09/2017 |
| Edition description: | Reprint |
| Pages: | 264 |
| Product dimensions: | 7.90(w) x 9.90(h) x 0.80(d) |
About the Author
Read an Excerpt
The Road to Relativity
By Hanoch Gutfreund, Jürgen Renn
PRINCETON UNIVERSITY PRESS
Copyright © 2015 Princeton University Press and The Hebrew University of JerusalemAll rights reserved.
ISBN: 978-0-691-16253-9
CHAPTER 1
EINSTEIN'S INTELLECTUAL ODYSSEY TO GENERAL RELATIVITY
Einstein's famous 1905 papers shook the foundations of classical physics. They challenged the idea of light as a wave, gave striking proof for the existence of atoms, led to a new understanding of space and time, and identified mass as a form of energy. The revolution of space and time that started in 1905 with Einstein's formulation of the special theory of relativity was soon seen to be incomplete. Attempts to fit Newton's well-established law of gravity into the framework of this theory did not succeed, at least not without giving up basic principles of mechanics. Although this problem did not lead to urgent empirical queries, it led Einstein in 1907 to question the special theory's concepts of space and time and caused him to continue the revolution with his 1915 theory of general relativity.
The following remarks introduce the reader to the development of Einstein's ideas and attitudes as he struggled for eight years to achieve a theory of general relativity that would meet the physical and mathematical requirements laid down at the outset. Many of the points discussed here will appear again in the annotations to the specific pages of the manuscript. However, before getting there, we present the whole story as it evolved, with all its dilemmas, wrong paths, misinterpretations, and misunderstandings, to which Einstein himself admitted as he progressed on the bumpy road to his final goal.
A TALE OF THREE CITIES: PRAGUE, ZURICH, BERLIN
The Einstein specialist John Stachel refers to the development of general relativity as "a drama in three acts." According to this scenario, the first act occurred in 1907 with the formulation of the basic idea to which Einstein referred as the "equivalence principle." The second act took place in 1912, when Einstein realized that the gravitational field is mathematically represented by 10 functions of spacetime coordinates, which form the metric tensor associated with the non-Euclidean geometry of spacetime. The third act, with its "happy end," occurred in November 1915, when Einstein formulated the gravitational field equations and explained the anomalous precession of the perihelion of the planet Mercury.
We propose another script for this dramatic development, which explores its geography. Einstein conceived the notion of the equivalence principle when he was still employed at the patent office in Bern, and he published it in a review article on special relativity in 1907. In that article Einstein also discussed some of its immediate implications, such as the bending of light rays in a gravitational field and the effect of gravitation on the pace of clocks. This can be viewed as a prelude to the real "drama," which began in 1911 when he went to Prague. Then, after a pause of four years, Einstein resumed his interest in gravitation and pursued it intensively—almost exclusively and sometimes obsessively—until his triumphal achievement. It is to this period that we refer as a "Tale of Three Cities" Each of these cities served as a stage for a specific chapter in this development. Each one provided a different social and political environment, and each was characterized by a different phase in his family life. How these circumstances related to his scientific work is discussed in several Einstein biographies.
Prague In 1909, Einstein was appointed extraordinary professor at the University of Zurich. For the first time he held a position that carried certain academic and public prestige. Less than six months later, he was offered the even more prestigious position of full professor at the German part of the Charles University of Prague when a vacancy in theoretical physics opened up there. Einstein's candidacy to this position was most strongly supported by Anton Lampa, a professor of experimental physics and ardent follower of Mach, who hoped that Einstein would further promote Mach's ideas.
After some delay and despite the reluctance of his wife Mileva to leave Zurich, where she felt more comfortable, and despite appeals of students to the authorities of the university to make every effort to keep him in Zurich, Einstein accepted the offer and went to Prague in April, 1911.
In Prague, Einstein wrote 11 scientific papers, 6 of which were devoted to relativity. In the first of these papers, published in 1911, he discussed the bending of light and the gravitational redshift, which he had already discovered in 1907, but now Einstein explored them as observable effects. In the Prague papers, he focused on developing a consistent theory of the static gravitational field based on the equivalence principle. Just like Newton's theory of gravity, it involved a gravitational potential represented by a single scalar function, now given by a variable speed of light. Nevertheless, some basic features of the final theory of general relativity had already been conceived by then. Among them was the understanding that the source of the gravitational potential is not only the mass of concrete bodies but also the equivalent mass of the energy of the gravitational field itself. However, until the end of this period Einstein still assumed that the gravitational potential was represented by a single function—the space-dependent speed of light—and the theory he developed was restricted to a static gravitational field.
It is interesting to note that Einstein's work on gravitation in Prague was done to a large extent within the context of a controversy with the physicist Max Abraham, famous for his contributions to electrodynamics and electron theory. Abraham was the first to publish, in January 1912, a complete theory of the gravitational field formulated within the framework of Minkowski's four-dimensional spacetime. At first, Einstein was impressed but then reacted skeptically. To his friend Besso he wrote: "At first (for 14 days) I too was completely bluffed by the beauty and simplicity of his formulas." Yet, in the ensuing controversy both Abraham and Einstein developed important insights.
In a foreword to the Czech edition of 1923 of his famous little popular book "About the Special and General Theory of Relativity in Plain Terms," Einstein refers to his work in Prague:
I am pleased that this small book ... should now appear in the native language of the country in which I found the necessary concentration for developing the basic idea of the general theory of relativity which I had already conceived in 1908 [he must have meant 1907]. In the quiet rooms of the Institute of Theoretical Physics of Prague's German University in Vinicna Street, I discovered that the principle of equivalence implies the deflection of light rays near the Sun by an observable amount.... In Prague I also discovered the shift of spectral lines towards the red ... However, the decisive idea of the analogy between the mathematical formulation of the theory and the Gaussian theory of surfaces came to me only in 1912 after my return to Zurich, without being aware at that time of the work of Riemann, Ricci, and Levi-Civita. This was first brought to my attention by my friend Grossmann.
Zurich In 1911, Marcel Grossmann was appointed dean of the mathematics-physics department of the Swiss Federal Institute of Technology (ETH). One of his first initiatives as dean was to write to Einstein asking if he would be interested in returning to Zurich to join the ETH. Einstein agreed, declining an earlier offer from Utrecht as well as an opportunity to go to Leiden, both of which would have been enticing given the proximity of colleagues such as H. A. Lorentz. Whatever the reasons Einstein had for preferring Zurich over Utrecht or Leiden, at that time it was the right decision. A short time after returning to Zurich in August 1912, he began an intensive and fruitful collaboration with Grossmann that became a landmark in the development of general relativity.
During the Zurich period, Einstein produced three documents that played a significant role in the search for a theory of general relativity: the Zurich Notebook, the Einstein-Grossmann Entwurf paper, and the Einstein-Besso manuscript. We shall discuss the contents and significance of these documents in the relevant sections of this account of Einstein's roadmap to general relativity, so we only briefly describe them now.
The Zurich Notebook contains Einstein's notes from the intermediate phase of his search for a relativistic theory of gravitation, when he was exploring, with the help of Grossmann, the concepts and methods of tensor calculus and Riemannian geometry. The notebook consists of 96 pages, not all of them devoted to relativity. Einstein nevertheless gave it the title "Relativität" The notes were written between mid-1912 and the beginning of 1913. Einstein used the notebook from both the front and the back, and his entries meet upside down about a quarter way through. This notebook constitutes a very important document in the history of science and is of pivotal importance for our understanding of the origins of the general theory of relativity.
The Zurich Notebook essentially contains the blueprint for the generally covariant theory, but owing to a yet immature physical understanding to be described shortly, Einstein abandoned this theory. Instead, he and Grossmann published the "Outline of a Generalized Theory of Relativity and of a Theory of Gravitation," which has since been termed the Entwurf theory from its German title, which means outline. Although this theory did not meet Einstein's initial requirement of general covariance, he convinced himself that this was the best that could be done, and despite this and other shortcomings of the theory, he expressed satisfaction with it until the summer of 1915.
The so-called Einstein-Besso manuscript is a collection of about fifty pages of calculations, about half of them in Einstein's handwriting and the other half in Besso's. These pages contain a calculation of the precession of the perihelion of Mercury based on the field equation of the Entwurf theory and a calculation of the metric tensor in a rotating frame of reference.
The Swiss Department of the Interior approved the request of ETH for a full professorship for Einstein. However, it lasted only three semesters. Einstein was in great demand, and the next offer he could not refuse came from Berlin.
Berlin In 1913, Max Planck was elected secretary of the Royal Prussian Academy of Sciences. Shortly after his election, Planck launched a campaign to elect Einstein to the academy. In July 1913, Planck went to Zurich with Walther Nernst to present to Einstein a tempting three-part proposal: election to the academy with generous financial support, directorship of the Kaiser Wilhelm Institute of Physics without a real administrative burden, and a professorship at the University of Berlin without teaching obligations.
Einstein accepted the offer, giving different reasons to different people in justifying his decision. To Lorentz he wrote: "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." But to his good friend Heinrich Zangger he admitted that the main reason for accepting this offer was that this would bring him close to his cousin Elsa, whom he was passionately courting at that time and who would later become his second wife: "Despite being in Berlin, I am living in tolerable solitude. But here I have something that makes for a warmer life, namely, a woman whom I feel closely attached to.... She was the main reason for my coming to Berlin, you know."
In November 1913, His Imperial and Royal Majesty Wilhelm II confirmed Einstein's election as a regular member of the physics-mathematics section of the academy. Thus, at the age of 34, he became the youngest-ever member of the academy.
Shortly after Einstein's arrival in Berlin, World War I broke out. Confronted with the realities of war, he eventually left the ivory tower of science to become a political opponent of Germany's involvement in the war. In Berlin, Einstein encountered the phenomenon of anti-Semitism and became aware, more than ever before, of his Jewish identity. In Berlin, his relations with Mileva deteriorated to the point of separation—Mileva and the children returned to Zurich. In the midst of all this, Einstein ardently pursued his scientific work and, according to his own testimony, worked harder than ever.
Einstein continued to work on his and Grossmann's Entwurf theory of gravitation and suggested new arguments to support its validity. His satisfaction with the Entwurf theory solidified to the point that he was ready in October 1914 to summarize it in a review article, "The Formal Foundation of the General Theory of Relativity," which he published in the meeting reports of the Royal Prussian Academy of Sciences. It took him less than a year to regret it.
Einstein's doubts concerning the Entwurf theory began to build in the summer of 1915. He finally abandoned the theory and, in an outburst of creativity and hard work, completed in November of that year his general theory of relativity.
Einstein had joined Max Planck, Walther Nernst, and many others in Berlin, which at the time was the world capital of physics. Even during the hardships of the war years, the city maintained an inspiring atmosphere and work routine in the physics community. Gerald Holton, a pioneer of Einstein scholarship in its historical and philosophical context, addressed the question, "How much did these facts contribute to Einstein's unique ability to develop, between 1915 and late 1917, his general relativity theory in Berlin? Could he have done so if he had accepted a grand offer from a city in another country?" Holton's clear answer is, "No other man than Einstein could have produced General Relativity, and in no other city than in Berlin," albeit not without help from his friends in Zurich!
THE CHALLENGE OF GRAVITATION
The 1905 theory of relativity had established a new understanding of space and time, and all physical interactions needed henceforth to fit within its framework. In addition, the theory had combined the laws of conservation of energy and momentum into a single law and it had demonstrated that mass is a form of energy. The consequences of this theory could be conveniently described in the framework of a new mathematical formalism developed by Herman Minkowski, Einstein's former teacher at the ETH in Zurich. This formalism combines space and time into one entity—spacetime—and assigns a geometric distance between any two physical events that occur at different positions and different times. One usually refers to points in spacetime as events because they are characterized by location and time of occurrence. The square of this distance is simply the square of the time separation between the two events minus the square of their spatial separation. Observers moving at constant velocity with respect to each other may compute this value using their respective positions and time measurements, and they will get the same result. In other words, Minkowski's four-dimensional spacetime is equipped with a "metric" instruction that is employed to measure the distance between events. This may be compared with the familiar metric instruction to measure the distance between two points in three-dimensional space: sum the squares of the Cartesian coordinate separations.
It was not difficult to adapt the domain of electromagnetism to the new spacetime framework of the theory of special relativity, which had actually been inspired by Maxwell's electrodynamics. But gravitation, that is, the force of gravity between two masses, presented problems in this respect. Because Newton's law of gravity assumes an instantaneous action at a distance, this law in its classical form was not directly compatible with the special theory of relativity. One of the consequences of this theory is that no physical effect can propagate with a speed exceeding that of light in a vacuum. Thus, a new gravitational theory was needed, but it was not clear how such a theory should look, what heuristic assumptions could be made, and even what specific criteria it should satisfy.
But, there was an obvious way to make classical gravitational theory formally compatible with the principles of the special theory of relativity, and Einstein initially pursued this line of thinking. However, the problem with this obvious generalization was that the resulting theory of gravitation seemed to violate Galileo's principle that all bodies fall with equal acceleration. This is one of the basic principles of classical physics, mythically established by Galileo dropping material objects from the top of the tower of Pisa.
Galileo's principle stipulates that the acceleration of free fall is the same for all bodies. Newton accounted for this principle by setting inertial mass equal to gravitational mass. The inertial mass determines the acceleration of a body caused by a given force, while the gravitational mass determines the force exerted on a body by a given gravitational field. The dependence of inertial mass on energy in special relativity must imply that in a relativistic theory of gravitation, the gravitational mass of a physical system should also depend on the energy in a precisely known way so as to maintain Galileo's principle. Einstein concluded that if the theory did not achieve this in a natural way, it was to be abandoned. Contemporary scientists such as Max Abraham and Gustav Mie were quite ready to abandon Galileo's principle in order to obtain a relativistic theory of gravitation in the sense of special relativity.
(Continues...)
Excerpted from The Road to Relativity by Hanoch Gutfreund, Jürgen Renn. Copyright © 2015 Princeton University Press and The Hebrew University of Jerusalem. Excerpted by permission of PRINCETON UNIVERSITY PRESS.
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Table of Contents
- Frontmatter, pg. i
- CONTENTS, pg. vii
- A Brief Note on the Publication of this Work, pg. xi
- Foreword, pg. xiii
- Preface, pg. xvii
- The Charm of a Manuscript, pg. 1
- Einstein’s Intellectual Odyssey to General Relativity, pg. 7
- The Annotated Manuscript, pg. 37
- Notes on the Annotation Pages, pg. 141
- Postscript: The Drama Continues . . ., pg. 149
- A Chronology of the Genesis of General Relativity and its Formative Years, pg. 159
- Physicists, Mathematicians, and Philosophers Relevant to Einstein’s Thinking, pg. 165
- Further Reading, pg. 179
- English Translation of “The Foundation of the General Theory of Relativity”, pg. 183
- English Translation of “Hamilton’s Principle and the General Theory of Relativity”, pg. 227
- Index, pg. 233
What People are Saying About This
"The feeling a physicist has in reading Einstein's handwritten manuscript on general relativity must be like what a pianist would feel upon seeing a draft of Bach's Goldberg Variations. What kind of human creativity can produce something like this? Gutfreund and Renn provide the context for the paper, and the English translation enables readers not fluent in German to see it as a whole. This book is a little treasure."—Jeremy Bernstein, Aspen Center for Physics"We have in The Road to Relativity an approachable, precise, and riveting account of one of the great intellectual voyages of the last hundred and fifty years. I commend this book to anyone fascinated by gravity and the shape of the universe, to be sure, but also to anyone passionate about one of the great odysseys of modern science."—Peter Galison, Harvard University"Gutfreund and Renn have compiled a wonderful book, a real primer to Einstein's long and complex journey to the general theory of relativity. In this well written distillation of several decades of historical-scientific scholarship, we find not only Einstein's own papers, concisely and clearly explained, but also a rich tapestry of the contextual background to the revolutionary transformations in theoretical physics initiated by an entire generation of scientists in the early twentieth century."—Diana Kormos Buchwald, Einstein Papers Project, Caltech"This book takes you on a wonderful journey of discovery. Its centerpiece is Einstein's handwritten exposition of the general theory of relativity, written shortly after the decisive breakthrough of November 1915. In their splendid introduction and insightful commentary, Gutfreund and Renn tell the story of how Einstein found his new theory of space-time and gravity, making both the theory itself and Einstein's arduous path to it come alive for general readers."—Michel Janssen, University of Minnesota"This is a lovely book and an excellent way to mark the centennial of Einstein's general relativity. The facsimile reproduction of Einstein's manuscript is wonderful to behold, and Gutfreund and Renn have done a superb job of guiding nonspecialists through Einstein's argument and placing the work in a broader intellectual and historical context."—David Kaiser, author of How the Hippies Saved Physics: Science, Counterculture, and the Quantum Revival"The centenary of Einstein's theory of gravitation is a fitting moment to recommend one of the greatest landmarks in the history of physics. The historical introduction and page-by-page annotations provide a careful narrative of Einstein's path from special to general relativity."—Michael D. Gordin, author of Five Days in August: How World War II Became a Nuclear War