However, the gravitational field equation they got at that time was covariant only for linear transformation, and it was not covariant under any coordinate transformation required by the principle of general relativity. This is because Einstein was not familiar with tensor operation at that time, and mistakenly thought that as long as the conservation law was observed, the choice of coordinate system would be limited, and in order to maintain causality, the requirement of universal covariation would be abandoned.
The second peak of scientific achievements
The three years from 19 15 to 19 17 were the second peak of Einstein's scientific achievements, similar to 1905, and he also made historic achievements in three different fields. Except for the general theory of relativity, which is recognized as one of the greatest achievements in the history of human thought, it was finally established in 19 15. 19 16 put forward gravitational wave theory in radiation quantum, and 19 17 started modern cosmology.
19 15 After July, Einstein returned to the requirement of covariation after more than two years of detours. From June 19 15 to June 1 10, he concentrated on exploring new gravitational field equations. On June 165438+ 10/0/4,1kloc.
In the first paper, he obtained the universal covariant gravitational field equation satisfying the conservation law, but added an unnecessary restriction. In the third paper, according to the new gravitational field equation, the deflection of light passing through the surface of the sun is calculated to be 1.7 arc seconds, and the precession of Mercury's perihelion is calculated to be 43 seconds every 100 years, which completely solves a major problem in astronomy for more than 60 years.
In his paper Gravitational Field Equation on 19 1 15125 October, he gave up unnecessary restrictions on transformation groups, established a truly universal covariant gravitational field equation, and declared that general relativity was finally completed as a logical structure. 19 16 In the spring, Einstein wrote a summary paper "The Basis of General Relativity"; At the end of the same year, a popular booklet "On Special and General Relativity" came out.
19 16 In June, when Einstein was studying the approximate integral of the gravitational field equation, he found that a mechanical system would inevitably emit gravitational waves propagating at the speed of light when it changed, and thus put forward the gravitational wave theory. 1979, 24 years after Einstein's death, the existence of gravitational waves was indirectly proved.
19 17 years, Einstein used the achievements of general relativity to study the space-time structure of the universe and published a groundbreaking paper, "A Survey of the Universe Based on General Relativity". This paper analyzes the traditional concept of "the universe is infinite in space" and points out that it is incompatible with Newton's theory of gravity and general relativity. In his view, the possible way out is to regard the universe as a closed continuous area with limited space volume and infer that the universe is infinite in space with scientific arguments. This is a bold pioneering work in human history, which makes cosmology get rid of pure speculation and enter the field of modern science.
A long and difficult exploration
After the completion of the general theory of relativity, Einstein still felt dissatisfied, so he wanted to extend the general theory of relativity to include not only the gravitational field, but also the electromagnetic field. He believes that this is the third stage of the development of relativity, namely the unified field theory.
After 1925, Einstein went all out to explore the unified field theory In the first few years, he was optimistic that victory was in sight; It turned out to be a lot more difficult. He thinks that the existing mathematical tools are not enough. Exploration of 1928 to pure mathematics. He tried various methods, but he didn't get any results with real physical significance.
During the 30 years from 1925 to 1955, except for the completeness of quantum mechanics, gravitational waves and general relativity, Einstein devoted almost all his scientific creative energy to the exploration of unified field theory.
1937, with the cooperation of two assistants, he deduced the equation of motion from the gravitational field equation of general relativity, further revealing the unity of time and space, matter and motion, which was a major development of general relativity and the last major achievement Einstein made in scientific creation activities.
He never succeeded in the same theory. He never gets discouraged and always starts from scratch with confidence. Because he was far away from the mainstream of physics research at that time, he went alone to overcome the problems that could not be solved at that time. So contrary to the situation in the 1920s, he was very isolated in physics in his later years. However, he is still fearless and unswervingly follows his own path. Until the day before his death, he was still in his hospital bed preparing to continue his mathematical calculation of the unified field theory.