einstein

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. 90
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