# One hundred years of the general theory of relativity. Who helped Einstein

### One hundred years ago, in November 1915, Albert Einstein published General Theory of Relativity (GR)

Einstein published only four short articles in the Berlin journal Prussian Academy of Sciences: 1, 2 , 3 , 4 . The last of them was sent on November 25, 1915. The articles indicate one author, and the work is often taken as the work of one genius. But this is completely wrong.

*Marcel Grossmann (left) and Michelle Besso (right) were university friends of Albert Einstein (center)*

In fact, the physicist received invaluable help from friends and colleagues, most of whom never became famous and were undeservedly forgotten, writes Nature magazine with links to several literary sources whose authors studied the life of Einstein and the history of the creation of general relativity.

The most significant influence on the creation of general relativity was made by Einstein's two friends from his student years - Marcel Grossmann (Marcel Grossmann) and Michelle Besso (Michele Besso). Grossmann was a talented mathematician and diligent student, he helped the more dreamy and bizarre Albert at key moments when he was trying to formulate a theory. Besso is an engineer with imagination and in some ways disorganized. He maintained a friendship with Einstein for life. Others contributed.

All three studied at the Higher Technical School (Polytechnic), which is now called the Swiss Higher Technical School of Zurich (ETH), from 1896 to 1900. Albert himself hoped to learn to become a school teacher of physics and mathematics, here he met a classmate Mileva, whom he later married. According to legend, Einstein often missed classes (because of the future wife?), And then passed tests according to Grossmann's notes.

*Higher technical school in Zurich, where Albert Einstein met friends.*

Grossmann's father helped Einstein to get a job in the patent office in 1902, where Besso came a couple of years later. The debate between Besso and Einstein led to the most famous scientific works that Einstein published for his sole authorship in 1905. In them was formulatedspecial theory of relativity (STR).

In the same happy year of 1905, Albert Einstein completed his dissertation and received a doctorate in physics at the University of Zurich.

In 1907, Albert began to ponder a new idea that develops STR, which could universally connect gravity with the curvature of space-time. This theory was later called the general theory of relativity. The scientist began to work more closely on it after his dismissal from the patent office in 1909. He was promoted to professor at the University of Zurich, and two years later in Prague. In 1912, Einstein returned to Zurich and again contacted Grossman at ETH. The friends joined forces and together developed a full-fledged theory, which until then existed only in the form of an idea.

The collaboration of two physicists is described inZurich diary of Einstein. As a result, in 1913 they published a joint scientific work known as Entwurf (“The Plan”). The main difference between Entwurf of 1913 and the general theory of relativity of 1915 is the field equations, which describe how matter bends the fabric of space-time. In GR, the equations are of general covariants, that is, they retain their form in any reference frame, and in Entwurf theory the covariance is strictly limited.

In July 1913, two famous German physicists arrived in Zurich - Max Planck and Walter Nernst. They offered a 34-year-old Albert a high-paying and teaching-free post at the Prussian Academy of Sciences in Berlin. Einstein accepted the offer in March 1914. Gravity was not particularly interested in Planck and Nernst; they were interested in Einstein's ideas in the field of quantum physics.

But even before leaving for Berlin, a physicist worked on general relativity. To test the hypothesis, they, together with Besso, compiled formulas that would explain the anomalous precession of the perihelion of Mercury at 43˝ per century. Besso made a significant contribution to the work and asked interesting questions. For example, he once asked if there is a solution from the Entwurf equations that uniquely determines the gravitational field of the Sun. A modern analysis of Einstein's manuscripts showed that it was this question that gave Einstein an argument convincing him of the limited covariance of the equations of the Entwurf field.

Einstein's theory predicted that gravity bends light rays. In August 1914, he, together with the young German astronomer Erwin Finlay Freundlich (Erwin Finlay Freundlich) went to the Crimea to observe a solar eclipse to verify this, but were detained by the Russians (the First World War began). Evidence of the curvature of the light had to wait until the solar eclipse of 1919.

In May 1914, Einstein and Grossmann published a second collaboration with a refinement of Entwurf's theory. Then they could not work together, because Einstein went to work in Berlin.

A breakthrough came soon after. Albert's marriage broke up, and Milena returned back to Zurich with her two sons. Einstein resumed relations with his cousin Elsa, broken off two years ago. Einstein continued to work on theory, but by the summer of 1915 he began to get nervous because Entwurf equations did not converge in systems with rotational motion (Besso told him about this two years ago, but Einstein ignored the remark). Einstein turned to the astronomer Freindlich for help , since he himself cannot go beyond ("mind was in a deep rut"). It became clear that the problem is in the Entwurf field equations. At the same time, it was necessary to hurry, because the prominent German mathematician David Hilbert became interested in Einstein's ideas, and he certainly would be able to bring ideas to mind.

In a hurry, Einstein changed the field equations - and published a scientific paper in early November 1915. The following week, he changed them again - and again published a scientific paper. Then again. In the end, the field equations became covariant in the fourth paper, submitted for publication on November 25, 1915.

In his first work, Einstein wrote that theory is the “real triumph” of mathematicians Karl Gauss and Bernhard Riemann. He writes that if he and Grossmann two years ago were guided by pure mathematics, and not physics, then they would not allow field equations with limited covariance. But in reality, it was the collaboration with Grossmann, Besso, as well as the authors of a similar theory on GR - Gunnar Nordstrom and Adrian Fokker, among others - that helped him overcome the limitations of Entwurf theory, and not just Gauss and Riemann.

In a caricature from the journal Nature: the elite of Berlin physics (Fritz Haber, Walter Nernst, Heinrich Rubens, Max Planck) and members of his old and new family sadly watch Einstein test his new theory of gravity, supported by famous scientific figures (Isaac Newton, James Clerk Maxwell, Karl Gauss, Bernhard Riemann) and smaller scientists (Marcel Grossman, Gunnar Nordstrom, Erwin Finley Freindlich, Michelle Besso).