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The writings in this volume date from the beginning of 1912
to the spring of 1914, the two years before Einstein left Zurich for Berlin. While
his struggle with the problems of quanta, rather than those of relativity, had
dominated his work from 1909 through 1911 (see Volume 3), he was now
concentrating his efforts on attempting to construct a relativistic theory of
gravitation. Einstein's efforts would finally achieve their goal in the autumn
of 1915, when he completed his general theory of relativity.
Three scientific manuscripts, printed here for the first time, provide some
insight into Einstein's efforts to generalize his original relativity theory
into a relativistic theory of gravitation. The first is a review article on the
special theory of relativity (Doc. 1); the second consists of notes documenting
Einstein's research on gravitation as well as the support he received from his
friend and former fellow student at the Swiss Federal Institute of Technology
(ETH), the mathematician Marcel Grossmann (Doc. 10); and the third manuscript
contains calculations by Einstein in collaboration with Michele Besso, another
friend from his student days, on the problem of the motion of the perihelion of
Mercury (Doc. 14). The three unpublished manuscripts document the kinds of
trials and errors that cannot be reconstructed from Einstein's published
papers, and in this way add to our understanding of the creation of general
relativity.
During the period covered by this volume, Einstein's professional status
rose rapidly. As 1912 began, he was professor at the German University of
Prague, a relative backwater in scientific research. In the course of that
year, however, Einstein declined offers of professorships at the universities
of Utrecht and Leyden (where he would have succeeded H. A. Lorentz). He
accepted instead a professorship in Zurich, but this time at the ETH rather
than the university. A year after his return to Zurich in the summer of 1912,
negotiations began about a research appointment in Berlin. In the spring of
1914 Einstein was about to depart from Zurich to take up a handsomely-paid
position as a member of the Prussian Academy of Sciences, perhaps the crowning
achievement for a German scientist of his generation.
During this same period major changes in Einstein's personal life had also
begun. His marriage to Mileva Maric; was deteriorating; the couple would soon
separate and eventually divorce. Einstein had also become reacquainted with his
cousin Elsa when he visited Berlin in the spring of 1912, and they would marry
in 1919, a few months after his divorce from Mileva. These developments, both
professional and personal, are extensively documented in Einstein's
correspondence during the Swiss Years, published in Volume 5.
For those who think of Einstein primarily as the creator of
both the special and the general theories of relativity, it may come as a
surprise to learn that his increasing prominence in the years from 1905 through
1914 was due in large part to his contributions to the quantum theory.
Physicists generally were more interested in the unexpected experimental
connections that even the early quantum theories predicted than they were in
the abstractions of relativity, which were less capable of being tested
experimentally.
When, for example, Max Planck, Walther Nernst, Heinrich Rubens, and Emil
Warburg proposed Einstein for membership in the Prussian Academy of Sciences,
they began by discussing his early work on relativity, but went on to describe
his studies in the quantum theory, and particularly his work on the problem of
specific heats. Their language leaves no doubt about what they emphasized:
"His contributions to other questions on which contemporary interest is
focused have proved to be far more significant."
Einstein contributed very little to quantum theory in the years 1912-1914.
His major contribution was a derivation of the law of photochemical equivalence
from purely thermodynamic considerations, together with the law of mass action,
which led to the conclusion that photochemically active substances emit and
absorb radiation energy in discrete quantities. This work added much to the
understanding of the quantum hypothesis. His collaboration with Otto Stern on
the application of the quantum theory to rotating molecules, on the other hand,
at first seemed to provide an explanation of Arnold Eucken's measurements of
the specific heat of hydrogen. But soon afterwards the explanation lost its
foundation when Einstein lost confidence in the most important feature of the
paper, namely the introduction of a term representing zero-point energy.
Einstein's first attempt at generalizing his relativity
theory of 1905 to include accelerated frames of reference dates from 1907. His
hypothesis, formulated in a review paper that year, concerning the equality of
inertial and gravitational mass and the equivalence of a homogeneous
gravitational field with a uniformly accelerated frame of reference became a
corner stone for his subsequent attempts to generalize special relativity. Thus
the separate problem of a generalization of the relativity theory of 1905 to
accelerated frames of reference became linked to the development of a new
theory of gravitation.
As heuristically fruitful as this "principle of equivalence"
turned out to be for predicting such effects as the bending of light rays
passing through a gravitational field and the gravitational redshift of
spectral lines, Einstein initially hesitated to build a theory on it. He
continued to stress his efforts to deal with the quantum riddle. It was only
when his hope to solve this riddle waned that he began to concentrate on the
gravitation problem. Einstein also decided to make his results public even when
he had the feeling that they were not yet definitive. Cautiously proceeding
step by step, he attacked first the case of a static gravitational field. At
the end of March 1912 he was content with his preliminary results: "Lately,
I have worked furiously on the problem of gravitation. I am now finally
finished with the statics. I don't know anything yet about the dynamic field,
that is to follow next. . . . Every step is devilishly difficult, and what I
have derived so far is certainly only the easiest part."
Although difficulties with the principle that action equals reaction forced
him to limit the validity of the principle of equivalence, Einstein did not
give it up when he decided to move on to the dynamic case. Another guide Einstein
found useful was Mach's critique of Newton's mechanics. It suggested to
Einstein that a satisfactory generalization of the theory of relativity should
allow him to consider rotational motion as being equivalent to a state of rest.
A crucial insight, which occurred to Einstein probably in the summer of 1912,
was the recognition of an analogy between the mathematical problems of a
generalized relativity theory and Gauss's geometry of curved surfaces. From
this analogy he concluded that the gravitational field had to be represented
not by a scalar potential but by a ten-component metrical tensor, a crucial
step towards general relativity. When Einstein returned from Prague to Zurich
in August 1912, his friend Marcel Grossmann, professor of mathematics at the
ETH, played an important role in extending his horizon to include the works of
Riemann, Christoffel, Ricci, and Levi-Civita, and also in assisting him in his
search for gravitational field equations based on tensor calculus.
In May 1913, more than a year after the completion of the static theory,
Einstein and Grossmann published a preliminary but comprehensive version of a
generalized theory of relativity and gravitation (Doc. 13). Although they had
made important progress, their results remained unsatisfactory, not only to
their critics but also to the authors themselves. The reason was that they had
searched for a generally covariant theory but had not reached their goal. In
fact, they were not even sure whether transformations to rotating coordinates were
permitted by their equations so that it was not clear whether a rotating frame
of reference could be considered as being equivalent to a rest frame. After the
publication of the paper, Einstein wrote to H. A. Lorentz: "Thus, if not
all systems of equations of the theory . . . admit transformations other than
linear ones, then the theory violates its own point of departure; it is then
left up in the air."
With hindsight it is easy to see how close Einstein and Grossmann came to
the final general theory of relativity. In a retrospective account Einstein
recalled how he had initially considered the Riemann curvature tensor as a
possible basis upon which to construct generally covariant field equations, but
had failed to understand that it was indeed applicable. Only after two years of
hard work on conceptual as well as mathematical problems had he come back to it
and based his final theory on it. What made Einstein reject the Riemann tensor
is a question that has been widely discussed in the literature. Material
presented in this volume provides important clues toward an answer. Einstein's
research notes on gravitation, covering the period of his collaboration with
Grossmann from the summer of 1912 to the publication of their joint paper and
published here as Doc. 10, are an especially important source.
Attempts to understand the covariance properties of the new theory, attempts
to relate it to empirical data, and efforts to convince his colleagues
dominated Einstein's activities before his departure for Berlin in the spring
of 1914. At the time, no empirical results on the gravitational bending of
light or the gravitational redshift were available, and Einstein's attempt,
undertaken with the help of Besso, to explain the perihelion advance of Mercury
on the basis of the new theory of gravitation failed.
The lack of empirical support for Einstein and Grossmann's generalized
theory of relativity became even more noticeable when, in 1913, Gunnar
Nordstrom published a special relativistic scalar theory of gravitation. This
theory avoided earlier objections by Einstein against such theories and thus
was a serious competitor. Einstein discussed Nordstrom's theory as well as the
Einstein-Grossmann theory in the masterful lecture he gave at the 1913 meeting
of the Gesellschaft Deutscher Naturforscher und Arzte in Vienna and came to the
conclusion that only experience could decide between the two (Doc. 17).
Nordstrom's theory turned out to be more than a competitor for the
Einstein-Grossmann theory. In a joint paper with Adriaan Fokker (Doc. 28),
Einstein showed that it could be formulated within the same mathematical
framework of tensor calculus and that Nordstrom's simpler theory served to
illuminate the essential conceptual features of the application of this framework
to a theory of gravitation.
The unfamiliar approach that Einstein took in his search for
a theory of gravitation made his work controversial at first. Einstein expected
little else: Even before the publication of his joint work with Grossmann he
had written to Paul Ehrenfest that he expected "a murmur of indignation to
go through the ranks of colleagues when the paper appears." Even his
future colleagues in Berlin, Max Planck and Max von Laue, who had themselves
made important contributions to the development of relativity, remained
skeptical in their responses to Einstein's recent work. Einstein, on his part,
used every occasion to expound the conceptual problems and epistemological
considerations that had motivated him. As several papers in this volume clearly
demonstrate, Einstein did not address his writings exclusively to specialists;
he also hoped that his ideas would be understood by a wider public. One of his
papers, for example, includes an imaginary dialogue between a specialist and a
layman on the concept of absolute space: "Our fearless observer will
interject: `You may be incomparably learned, but just as I could never be
persuaded to believe in ghosts, can I believe in that giant object, of which
you speak and that you call space. I can neither see such a thing, nor can I
imagine it.'"
Einstein did not encounter skepticism from all sides, however. There were
some who stimulated and encouraged him. Evidence is provided by lively
correspondence with, among others, Michele Besso, Paul Ehrenfest, and H. A.
Lorentz. He also used the opportunity of a lecture course on electricity and
magnetism to present his ideas to students, although the amount of stimulation
he received from them must have been limited. When Einstein moved to Berlin in
April 1914, the early history of general relativity was not yet complete, but
the foundations of the later development had been laid. Only a few weeks
earlier Einstein had written: "Nature only shows us the tail of the lion.
I am convinced, however, that the lion is attached to it, even though he cannot
reveal himself directly because of his enormous size. We see him only as would
a louse that sits on him."
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