In the far-reaching physics revolution that took place in the first 30 years of the 20th century, quantum mechanics was "easy to do." The special theory of relativity can be said to be "stone breaking the earth", although the two are very different, but it seems to be "away from whom the earth still turns". The proposal of quantum mechanics is to inherit Planck's "quantum hypothesis", and the proposal of special relativity is a historical necessity, and its purpose is to solve the contradictions that have been exposed in classical physics at that time, such as the aether crisis, and to stabilize the physical edifice.
Einstein and Bohr, The Theory of Relativity and Quantum Mechanics
Only general relativity is Einstein's one-man battle, and this epoch-breaking great theory can be said to have been proposed without Einstein, even in a few decades.
Einstein's late collaborator, the Polish physicist Infield, once recounted an interesting conversation in his book Einstein: His Work and Impact on Our World:
...... I said to Albert Einstein, "Whether you bring it up or not, I'm sure there's no delay in coming out of special relativity, because the time is ripe." Einstein replied, "Yes, that's true, but that's not the case with general relativity, and I suspect it hasn't been proposed until now."
Infield also commented that this answer is a good representation of Einstein's role in the history of the development of general relativity.
This is not only a footnote to the above-mentioned dialogue between Einstein himself and Infield, but also the common view of many other physicists. The famous American physicist Oppenheimer wrote an article titled "On Albert Einstein" in the collection of essays on the 100th anniversary of Einstein's death, which was later included in the collection of essays on the 100th anniversary of Einstein's birth, "On Albert Einstein":
Quantum discoveries are bound to come in one way or another... A deep understanding of the meaning that no signal can move faster than light is bound to emerge... The general theory of relativity, which has not been well confirmed by experiments to this day, will not be proposed for a long, long time without him.
Einstein's approach to general relativity seems uncontroversial, but it is not.
In the history of the birth of general relativity, there is still a very interesting episode, that is, the proposal of the core equation in general relativity, the field equation of general relativity.
The episode involves two people, one of course Einstein, and the other being Hilbert, the leader of the Göttingen School, the center of mathematics at the time, known as the "king of mathematics".
There was once a famous cartoonist who drew a cartoon for the invisible competition, with the title: Hilbert and Einstein, who arrived first? And this "arrival" refers to the field equation of general relativity.
After the birth of special relativity in 1905, Einstein began to explore general relativity, but encountered difficulties, Einstein studied general relativity with the purpose of finding mathematical equations that describe two intertwined processes - how the gravitational field acts on matter and makes it move in a certain way; how matter produces a gravitational field in space-time, causing it to bend in some form. Yet Einstein never found a mathematical expression that perfectly described his physical principles.
So Albert turned to Hilbert, a mathematician who was deeply involved in physics and had always made "the axiomatization of physics" his goal, in short, using a formula to represent all known states in nature.
In 1912, hilbert exchanged letters with Einstein while studying linear integral equations: he asked Einstein for papers on the theory of gas motion and radiation theory, and returned a newly published book on integral equations. He also invited Einstein to visit Göttingen during the Göttingen Week to give a report on the theory of gas motion, but Einstein declined.
In this series of letters, Einstein showed Hilbert the results of his research and revealed the difficulties he encountered, which also laid the groundwork for the invisible competition between the two.
In 1914, Einstein officially published a 56-page paper, Fundamentals of General Relativity, in which he proposed a theory of scalar gravity, and both Einstein and Hilbert were dissatisfied with the scalar gravitational theory in the paper, believing that it was not a mathematical expression that could perfectly describe its physical principles.
Manuscript of Einstein's Fundamentals of General Relativity
Although no such expression has been found, they all agree that a universal theory of covariant relativity is indeed necessary and achievable.
The difficulty of finding this equation is very high, because he has reached the "No Man's Land" and has no giant to rely on, Einstein once publicly stated:
I lost trust in the field equations I derived, and instead I looked for a way to limit the possibilities in a natural way. In this pursuit, I met the requirement of general covariance, which I left with a heavy heart three years ago when I was working with my friend Grossman. ”
Both of them made breakthroughs in their research work in 1915, and on November 7, 1915, Einstein and Hilbert exchanged letters, and through Hilbert's feedback, Einstein proposed a roughly coherent equation on November 11:
After several correspondence exchanges with Hilbert, Einstein proposed the final general relativity field equation on November 25:
Guv is the Einstein tensor; Ruv is a Richie tensor condensed from the Riemann tensor, representing the curvature term, indicating the degree of curvature of space; R is the curvature scalar condensed from the Ritchie tensor; guv is the degree gauge tensor; Tuv is the dynamic tensor, which indicates the distribution and motion of matter; G is the gravitational constant; c is the speed of light in a vacuum. The meaning of the whole equation is: the meaning of the whole equation is: the energy-momentum (T_uv) distribution of space matter = the curvature of space (R_uv). This equation is a second-order nonlinear tensor equation.
Hilbert proposed the field equation on November 20, 1915. Hilbert gave a report on the theory of gravity at the Royal Academy of Sciences in Göttingen, introducing the results of his research:
That is to say, Hilbert and Einstein, although in different forms, have found the correct gravitational field equation, and the scene of the calculus dispute between Newton and Leibniz 300 years ago has been staged again.
However, while later generations often debated who arrived first, physicist Kip Thorne made his point explicit in his book Black Holes and Time Warps: Einstein's Outrageous Legacy: "It is worth noting that Einstein was not the first to discover the correct form of the warpage law. Recognition of the first discovery must be attributed to Hilbert. “
Albert Fersin, the biographer of Einstein, argues that while seemingly convinced that Einstein and Hilbert independently came up with the correct form,:
In November, when Einstein was completely focused on his theory of gravity, he communicated essentially only with Hilbert, sending his publication to Hilbert and thanking him on November 18 for writing his draft article. Einstein must have received that article immediately before writing the letter. Could Einstein have set his sights on Hilbert's paper, who had discovered terms that were still lacking in his own equations and therefore "borrowed" from Hilbert?
Despite the controversy of later generations, Hilbert himself was very generous in giving up his merits and congratulating Einstein:
"Einstein has come up with profound ideas and unique concepts and invented ingenious ways to deal with them."
On 4 December 1915, Hilbert even nominated Einstein as a fellow of the Göttingen Mathematical Society. Albert's generosity touched Albert so much that Einstein wrote to Hilbert on December 20 to propose a settlement:
There was some resentment between us, and I don't want to analyze the causes further. I have struggled with the painful feelings and have succeeded. Once again, I think of you with meticulous kindness, and I ask you to do the same. Objectively, it would be a pity if two people liberated from this dilapidated world did not bring happiness to each other.
It's been 105 years since the field equations of general relativity were proposed, and history has given the two the fairest evaluations, as the American physicist Pais said in his famous Einstein biography, God is Subtle:
The discovery of the basic equation owes both Einstein and Hilbert.
This passage can be said to be the final conclusion for the achievements of Einstein and Hilbert in the discovery of the gravitational field equation. In any case, the academic controversy has promoted the progress of science, the proposal of the general relativity field equation is of great significance, is considered to be an endless treasure of the scientific community, and many scientists have come up with many important theories through the solution of the general relativity field equation.
Special objects such as black holes were discovered by solving field equations. In the field equations of general relativity, Einstein followed the traditional Cartesian coordinate system, so only an approximate solution can be given for the calculation of a symmetrical, unswitched, uncharged mass sphere. But the physicist Schwarzschild took a different approach, introducing a coordinate system similar to a polar coordinate system, which allowed for an accurate solution.
This precise solution is named the Schwarzschild gauge, which is the first precise solution of the field equation of general relativity.
On this basis, Schwarzschild issued a second paper, which gave the "Schwarzschild internal solution" and the formula for calculating the radius of the black hole's event horizon, so that the radius of the black hole's event horizon was called the "Schwarzschild radius", and the imaginary sphere at the Schwarzschild radius around the above celestial bodies was called the horizon.
In simple terms, Schwarzschild set such a celestial body with a charge of 0, that is, it is electrically neutral, its angular momentum is 0, that is, it does not rotate, and the cosmic constant is also 0. This could have been used to describe slow-spinning objects such as the Earth and the Sun, but if their mass had grown large enough, they would have escaped faster than the speed of light. This means that nothing escapes its clutches, so it cannot be seen in itself. The object was later named "black hole" by Wheeler.
In addition, the solutions to the field equations of general relativity include the Reisler-Nordsterom degree gauge, a black hole with such a scale form called a Reisler-Nordsterom black hole; and the Kerr degree gauge, in general relativity, the Kerr degree gauge or Kerr vacuum, describing the space-time geometry of the vacuum region around a rotating, spherically symmetrical mass massive object (e.g., a black hole).
As the central equation of general relativity, the field equation of general relativity has many unknown mysteries waiting for us to explore.