What if the relativity theory failed?
100 Years of Relativity: How Einstein Reinvented Reality
On the morning of his third lecture on November 18, Einstein received Hilbert's new draft and was dismayed at how it resembled his own work. His feedback to Hilbert was short and clearly formulated his priority claim. "The system you have given is - as far as I can see - exactly the same as what I have found over the past few weeks and presented to the Academy," he wrote. "Today I am handing over to the academy a paper in which I derive the perihelion of Mercury discovered by Leverrier quantitatively from general relativity without an auxiliary hypothesis.
Hilbert reacted accommodatingly and benevolently the following day, claiming no priority for himself. "My warmest congratulations on overpowering the perihelion movement. If I could calculate as quickly as you can, the electron would have to capitulate in my equations and the hydrogen atom would have to show its excuse as to why it does not shine." The next day, however, Hilbert submitted a paper to a Göttingen science journal in which he presented the equations he had found for general relativity. The title of the article was not exactly chosen modestly: "The basics of physics".
How carefully Einstein read Hilbert's work and how much it influenced his considerations when he was preparing his fourth lecture at the Prussian Academy is unclear. In any case, he presented a covariant system of equations for general relativity in time for his last lecture on November 25th - entitled "The field equations of gravitation".
The result was by far not as comprehensible for the layperson as the formula E = mc, for example2. But with the compact spelling of tensors, in which complex mathematical formulas are compressed into small indices, the final Einstein field equations even fit easily on a T-shirt for physics enthusiasts. In one of the many forms, the field equations can be defined as follows:
R.μν - 1/2 gμν R = -8 Π G Tμν
The left side of the equation - called the Einstein tensor and called Gμν abbreviated - describes how the geometry of space-time is curved by mass objects. The right side describes the movement of matter in the gravitational field. The interplay between the two sides shows how objects bend space-time and how this curvature in turn influences the movement of objects.
Then as now there is a controversial discussion about which elements in the mathematical equations of general relativity were first discovered by Hilbert and not by Einstein. Either way, it was Einstein's theory that was formalized by these equations - and this theory he had presented to Hilbert during their time together in the summer of 1915 in Göttingen. Hilbert noted this benevolently in the final version of his treatise: "The resulting differential equations of gravitation are, it seems to me, in accordance with the generous theory of general relativity put forward by Einstein in his later treatises." He later summed up: "And yet it was Einstein who actually did the work, and not the mathematicians."
Within a few weeks, the relationship between Einstein and Hilbert improved again. Hilbert suggested Einstein for membership in the Royal Society of Sciences in Göttingen and Einstein then wrote a well-meaning letter. Accordingly, two men who deal with transcendent theories should not dwell on earthly emotions. "There was a certain resentment between us, the cause of which I do not want to analyze," wrote Einstein. "I have fought against the associated feeling of bitterness, and with complete success. I remember you again with unclouded joy, and ask you to try the same with me have worked something out of this shabby world are not mutually pleasing. "
"My wildest dreams"
Einstein's arrogance was all too understandable. By the age of 36, he had drastically changed our perception of the universe. His general theory of relativity was not just about the interpretation of experimental data or the more precise formulation of laws. It was a whole new look at reality. With his special theory of relativity, Einstein had shown that space and time are not independent quantities, but rather together form a spacetime structure. With the general theory of relativity, spacetime became more than just a container for objects and events. Instead, it has its own dynamic, determined by the movement of objects in it, which in turn also influence space-time - analogous to a bowling and some billiard balls that roll over a trampoline and bend the jumping mat. At the same time, the curvature of the trampoline fabric determines the path of the rolling balls and allows the billiard balls to move in the direction of the bowling ball.
The curved spacetime explains gravity, its equivalence to acceleration and the general relativity of all forms of motion. According to Nobel Prize winner Paul Dirac, a pioneer in quantum mechanics, it was "probably the greatest scientific discovery of all time". And Max Born, another great figure among the physicists of the 20th century, called it "the greatest achievement of human reflection on nature, the most beautiful combination of philosophical penetration, physical intuition and mathematical ability".All that had happened had drained Einstein. His marriage was broken and the war ravaged Europe. Still, he couldn't be happier. "The wildest dreams have now come true," he wrote to his best friend, engineer Michele Besso. "General covariance. Mercury's perihelion movement wonderfully accurate." He said goodbye with the words "Your satisfied, but rather broken Albert".
Years later his younger son asked Eduard why he was so famous. To explain his fundamental knowledge that gravity can be interpreted as the curvature of space-time, Einstein used a simple picture: "When a blind beetle crawls over the surface of a sphere, it does not notice that the path it has traveled is curved. I, however was lucky enough to notice it. "
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