What did Einstein create?

In 1912, Einstein returned to work at his alma mater in Zurich. With the help of Grossmann, his classmate and professor of mathematics at his alma mater, he found the mathematical tools to establish the general theory of relativity in Riemannian geometry and tensor analysis. After a year of hard cooperation, they published the important paper "Outline of General Relativity and Theory of Gravity" in 1913, proposing the metric field theory of gravity. This is the first time that gravity and metrics have been combined to give Riemannian geometry real physical meaning.

However, the gravitational field equation they obtained at that time was only covariant for linear transformations, and did not yet have covariance under any coordinate transformation required by the principle of general relativity. This is because Einstein was not familiar with tensor operations at the time and mistakenly believed that as long as he adhered to the law of conservation, he had to limit the choice of coordinate systems. In order to maintain causality, he had to give up the requirement of universal covariance.

The second peak of scientific achievements

The three years from 1915 to 1917 were the second peak of Einstein’s scientific achievements. Similar to 1905, he It has also achieved historic achievements in three different fields. In addition to the final completion of the general theory of relativity in 1915, which is recognized as one of the greatest achievements in the history of human thought, the theory of gravitational waves in terms of radiation quantum was proposed in 1916, and modern cosmology was created in 1917.

After July 1915, after more than two years of detours, Einstein returned to the requirement of universal covariance. From October to November 1915, he concentrated on exploring new gravitational field equations and submitted four papers to the Prussian Academy of Sciences on November 4, 11, 18 and 25.

In the first paper, he obtained the universal covariant gravitational field equation that satisfies the conservation law, but added an unnecessary restriction. In the third paper, based on the new gravitational field equation, it was calculated that the deflection of light passing through the surface of the sun is 1.7 arc seconds. It was also calculated that the precession of Mercury's perihelion every 100 years was 43 seconds, which completely solved the problem that has been solved for more than 60 years. One of the great problems of astronomy.

In his paper "Field Equations of Gravity" on November 25, 1915, he gave up unnecessary restrictions on the transformation group, established a truly universal covariant gravitational field equation, and declared the general theory of relativity as a This logical structure is finally completed. In the spring of 1916, Einstein wrote a concluding paper "The Foundations of General Relativity"; at the end of the same year, he wrote a popular pamphlet "A Brief Introduction to Special and General Relativity".

In June 1916, while studying the approximate integral of the gravitational field equation, Einstein discovered that when a mechanical system changes, it will inevitably emit gravitational waves propagating at the speed of light, thus proposing the gravitational wave theory. In 1979, 24 years after Einstein's death, the existence of gravitational waves was indirectly proven.

In 1917, Einstein used the results of general relativity to study the space-time structure of the universe and published his groundbreaking paper "An Investigation of the Universe According to the General Theory of Relativity." The paper analyzes the traditional concept that "the universe is infinite in space" and points out that it is incompatible with Newton's gravity theory and general relativity. He believes that the possible way out is to regard the universe as a self-closed continuous area with a limited space volume, and use scientific arguments to deduce that the universe is finite and boundless in space. This is a bold initiative in human history, making the universe Science got rid of the speculation of pure conjecture and entered the field of modern science.

A long and difficult exploration

After the completion of the general theory of relativity, Einstein still felt dissatisfied and wanted to extend the general theory of relativity to include not only the gravitational field, but also the electromagnetic field. He believed that this was the third stage in the development of relativity, that is, unified field theory.

After 1925, Einstein went all out to explore a unified field theory. In the first few years, he was very optimistic and thought that victory was in sight; later he found many difficulties and he believed that the existing mathematical tools were not enough; after 1928, he turned to the exploration of pure mathematics. He tried various methods, but failed to achieve results of real physical significance.

In the 30 years from 1925 to 1955, apart from the completeness of quantum mechanics, gravitational waves and the motion problems of general relativity, Einstein devoted almost all of his scientific and creative energy to The search for unified field theory.

In 1937, with the cooperation of two assistants, he derived the equations of motion from the gravitational field equations of general relativity, further revealing the unity between space, time, matter, and motion. This is the generalized theory of The major development of the theory of relativity was also the last major achievement achieved by Einstein in his scientific creation activities.

In terms of the same theory, he never succeeded. He never got discouraged and started from the beginning with full confidence every time. Because he stayed away from the mainstream of physics research at that time and attacked problems on his own that were unsolvable at the time, he was very isolated in the physics community in his later years, contrary to his situation in the 1920s. However, he remained fearless and unswervingly followed the path he had identified. Until the day before his death, he was still preparing to continue his mathematical calculations on the unified field theory in his hospital bed.