Liveblogging History: November 25, 1915: Einstein
Section V of Einstein’s 1907 review article... begins the long road from the special theory to the general theory of relativity. Let us follow him on that road, marked by trials, by errors, and by long pauses, until finally, on November 25, 1915, the structure of the general theory as we now know it lay before him.... His first important paper on relativity theory after 1905 is the 1907 review... written at the request of Stark, the editor of the Jahrbuch....
It seems most probable that Einstein’s ‘happiest thought’ came to him sometime in November 1907.... In his Kyoto lecture he told the story:
I was sitting in a chair in the patent office at Bern when all of a sudden a thought occurred to me: ‘If a person falls freely he will not feel his own weight.’ I was startled. This simple thought made a deep impression on me. It impelled me toward a theory of gravitation.
Was Einstein first drawn to gravitation because he wanted to include it in special relativity or because he saw that he could extend special relativity with its help? The way I read the quoted lines from the Morgan manuscript, the answer would seem to be that, by asking for the inclusion, he at once or almost at once came upon the extension. That is also Einstein’s own recollection, again found in the Kyoto lecture:
In 1907, while I was writing a review of the consequences of special relativity… I realized that all the natural phenomena could be discussed in terms of special relativity except for the law of gravitation. I felt a deep desire to understand the reason behind this.… It was most unsatisfactory to me that, although the relation between inertia and energy is so beautifully derived [in special relativity], there is no relation between inertia and weight. I suspected that this relationship was inexplicable by means of special relativity....
Three main issues are raised in Section V of the Jahrbuch article. 1. The Equivalence Principle.... We shall therefore assume the complete physical equivalence of a gravitational field and the corresponding acceleration of the reference frame.... 2. The Gravitational Red Shift... calculating the red shift by means of the Doppler effect of light falling from the top to the bottom of an upwardly accelerating elevator. That is indeed the derivation he gave in 1911 (Chapter 11). However, he was already aware of the red shift in 1907. The derivation he gave at that time is less general, more tortured, and yet, oddly, more sophisticated... the existence of local Lorentz frames and the constancy of the velocity of light for infinitesimally small paths.... 3. Maxwell’s Equations; Bending of Light; Gravitational Energy = mc2....
On December 24, Einstein wrote to Conrad Habicht:
At this time I am [again] busy with considerations on relativity theory in connection with the law of gravitation…. I hope to clear up the so-far unexplained secular changes of the perihelion length of Mercury… [but] so far it does not seem to work....
On November 25, 1915, Einstein presented to the physics-mathematics section of the Prussian Academy of Sciences a paper in which ‘finally the general theory of relativity is closed as a logical structure’.... On the first of January 1916, when it was all over, Einstein wrote to Lorentz, ‘During the past autumn, the gradually dawning realization of the incorrectness of the old gravitational equations caused me hard times (böse Zeiten)’. It appears that this crisis occurred between late July and early October 1915....
On June 20, 1933, Einstein, exiled from Germany, gave a lecture at the University of Glasgow on the origins of the general theory of relativity. In concluding this address, he said: The years of searching in the dark for a truth that one feels but cannot express, the intense desire and the alternations of confidence and misgiving until one breaks through to clarity and understanding are known only to him who has himself experienced them....
On November 25 Einstein presented his final version of the gravitational equations to the Prussian Academy. Five days earlier, David Hilbert had submitted a paper to the Gesellschaft der Wissenschaften in Goettingen which contained the identical equation but with one qualification.... Suffice it to say that it was Hilbert’s aim to give not just a theory of gravitation but an axiomatic theory of the world. This lends an exalted quality to his paper, from the title, ‘Die Grundlagen der Physik,’ The Foundations of Physics, to the concluding paragraph, in which he expressed his conviction that his fundamental equations would eventually solve the riddles of atomic structure....
Let us come back to Einstein’s paper of November 18. It was written at a time in which (by his own admission) he was beside himself about his perihelion discovery (formally announced that same day), very tired, unwell, and still at work on the November 25 paper. It seems most implausible to me that he would have been in a frame of mind to absorb the content of the technically difficult paper Hilbert had sent him on November 18....
I rather subscribe to Klein’s opinion that the two men ‘talked past each other, which is not rare among simultaneously productive mathematicians’.... I do believe that Einstein was the sole creator of the physical theory of general relativity and that both he and Hilbert should be credited for the discovery of the fundamental equation. I am not sure that the two protagonists would have agreed.
Something happened between these two men between November 20 and December 20, when Einstein wrote to Hilbert:
There has been a certain pique between us, the causes of which I do not wish to analyze. I have struggled with complete success against a feeling of bitterness connected with that. I think of you once again with untroubled friendliness and ask you to try to do the same regarding me. It is really a shame if two real fellows who have freed themselves to some extent from this shabby world should not enjoy each other.
The full story may never be known. However, in a reply to a query, E. G. Straus wrote to me, ‘Einstein felt that Hilbert had, perhaps unwittingly, plagiarized Einstein’s [largely wrong!] ideas given in a colloquium talk at Goettingen.'
The way Einstein told it, Hilbert sent a written apology in which he said that ‘[this talk] had completely slipped his mind…’. Whatever happened, Einstein and Hilbert survived. The tone of their subsequent correspondence is friendly...
