Since the first paper on special relativity was published in 1905, Einstein has been working on his big theory from 19 15 to 1 1. However, it took him 10 years, from 1905 to1965,438+05 years, to popularize this theory and make it relate the curvature of space-time to the energy and momentum of any existing matter and radiation. Einstein's field equation (differential equation defining general relativity) describes this relationship, which is the last missing piece in his epic theory.
David hilbert is regarded as one of the greatest mathematicians of his time. 19 15 At the beginning of this year, when Einstein gave a speech on his new theory of gravity at the University of G? ttingen, Hilbert was also present. In fact, it was he who invited Einstein to give a speech. In his speech, Einstein introduced his progress and the difficulties he encountered in covariant the field equations (independent of their coordinate systems).
In autumn, Einstein made no obvious progress. However, Hilbert let people know through various channels that he is studying his own gravity theory and has made progress. By June 1 1, both of them were working frantically to provide correct equations for their theory.
19 19 Eddington's solar eclipse observation confirmed Einstein's general theory of relativity. Since then, the debate has continued. Who can find the basic equation of the most profound basic truth first? Who popularized relativity first? Was it created by Einstein or Hilbert, the master of mathematics?
The history of relativity can be traced back to Newton's gravity;
1897, when Einstein 18 years old, his friend Michelle Besso recommended Mach's book to him.
During the period of 1908- 1 1, Einstein temporarily stopped his research on relativity and focused on quantum theory, that is, the definitions of light quantum and blackbody radiation. 19 1 1 In June, Einstein returned to the study of gravity.
Therefore, by June191511,Einstein and Hilbert were convinced that a universal covariant theory of relativity was indeed necessary and achievable.
As Abraham Pais later reported, Einstein lacked the ability to define field equations in general covariant form, which is really understandable, because Einstein was far ahead of his time and explored what Pais aptly called "no man's land".
However, assuming that the determinant of the metric tensor is constant (-1), Einstein's new solution is still not generalized covariant. Although Hilbert's reply has been lost, it can be reasonably inferred from their later correspondence and Einstein's further revision of the theory that Hilbert actually doesn't "like" this solution.
A week later, Einstein contacted the Prussian Academy of Sciences with the same title as the previous week, denied his initial equation and proposed a new equation, probably based on Hilbert's feedback. Einstein suddenly put forward a general covariant equation:
However, only when the stress-energy tensor T is traceless, that is, the sum of the elements on the main diagonal of the matrix trace is zero, can this conform to his final (correct) equation and be correct for Maxwell electrodynamics. The very next day, Einstein sent a second letter to Hilbert, announcing that he had finally found the correct formula of the field equation satisfying the generalized covariance.
A few days later, Hilbert wrote back to Einstein and wrote a long letter. He pointed out that he was excited about his "axiomatic solution to a big problem" and noted that "as far as my understanding of your new paper is concerned, your solution is completely different from mine".
165438+1October15th, Einstein asked Hilbert for a sample of his speech. 165438+ 10/0/8, Hilbert gave Einstein a copy of his research results. As todorov pointed out, Einstein's paper has two points to explain. First of all, Einstein's assertion about his equation is incorrect:
Equation equivalent to Hilbert's paper165438+1October 20th:
The two are equal only when they are homogeneous, that is, the stress energy tensor is equal to zero. Secondly, Einstein did deduce the correct value of precession at the perihelion of Mercury. However, in his paper of June 1 65438+1October1day, he gave an incomplete equation.
165438+1On October 20th, Hilbert gave a speech in Gogentin, and he acknowledged Einstein's work for the first time:
Then, put forward an ambiguous statement:
Then Hilbert deduces the correct equation of variational principle and the second-order equation of metric tensor g_μν under the general covariant hypothesis.
165438+1October 25th, he denied the two basic equations he proposed earlier, and finally put forward the correct equation that we now know to describe his general relativity, although the stress-energy tensor was not correctly deduced:
This time, his equations are completely equivalent to Hilbert's, because both imply that R+κT = 0. Einstein didn't mention Hilbert's work in his paper.
Who came up with the correct equation first?
Einstein's paper published in1915165438+1October 25th describes the correct form of the field equation. Hilbert is165438+1October 20th. As we all know, Hilbert sent Einstein a copy of his research, which was probably received by Einstein before submitting the paper.
For a long time, it has been thought that Einstein and Hilbert discovered the gravitational field equation independently. This point has now caused quite extensive controversy. So for us, the priority problem still exists.
Hilbert priority
Those who advocate Hilbert priority think that Einstein got some hints from his letters, which helped him get the trace term of the field equation. If so, Einstein should admit it in his paper, but Einstein didn't.
In his book Black Hole and Time Distortion, Einstein's Amazing Legacy (1994), physicist Kip Thorne clearly stated his point of view: "Einstein was not the first person to discover the correct form of the equation of relativity [...], and it must be admitted that Hilbert discovered it first."
Einstein first
In Albert Einstein's biography, the author described Einstein as "complaining to Heinrich Sanger, who obviously thought Hilbert was trying to copy". However, at that time, most physicists and historians of science agreed that Einstein and Hilbert solved the field equation independently and in parallel, but Einstein was the first. Norton (1986) provided a very detailed argument (56 pages), which proved that Einstein first put forward the correct equation, including studying other materials in Einstein's notebook when he was working in June.
For Einstein, the most important evidence of priority may be a copy of Hilbert's certificate and his original correspondence of165438+1October 20th, which was found in Hilbert's file. This material is known by an article in Science magazine entitled "The latest decision of the Hilbert-Einstein priority dispute".
There is no doubt that Hilbert, like all his colleagues, admitted that Einstein was the sole founder of the theory of relativity. This has been confirmed in many places, even on the first page published by Hilbert. On February 4th, 65438, Hilbert even nominated Einstein as a correspondent member of Cogendian Mathematical Society. However, there was a tense period between them. 12 On February 20th, Einstein wrote to Hilbert, proposing reconciliation: