There we can read his papers about general relativity, both in German and in an English translation.
Einstein writes very well and explains clearly the motivation for his claims. The language is somewhat convoluted. It probably was customary to write long sentences in the German language during that time.
It turns out that Albert Einstein after 1915 immediately suggested that gravitational waves exist, presented a plane wave solution, and calculated the power output of a binary star.
He also described the familiar cosmological model where the spatial slice is the 3D surface of a 4D sphere, and matter is uniformly spread over space. In 1917, Einstein introduced the cosmological constant Λ to make the model static.
The cosmological model shows that Einstein believed in the geometric interpretation of general relativity. In the Minkowski space, a spatial slice cannot have that topology.
That is, Einstein believed that spacetime truly is curved. He did not think that gravity only simulates a modified geometry of spacetime.
What about a cosmological model where we have an island of matter in an asymptotically Minkowski space? Einstein writes that then the average density of matter in the infinite space has to be zero. He did not like the idea that there is an infinite almost empty extent of space, and a small island of matter. He writes that light would escape from that island, and would never come back.
Motivation of general relativity
Albert Einstein several times writes that he wants Mach's principle to be true.
However, the principle is not true in general relativity.
A rotating massive body creates a "magnetic" field which deflects masses moving close to it, just like a magnetic field deflects electric charges. But that is really not a realization of Mach's principle, which requires that masses even very far away would determine which frame is inertial and which is rotating.
Einstein refers to the Galilei symmetry of inertial frames in newtonian physics.
He also writes about the equivalence principle of gravity and acceleration. If a scientist in a laboratory feels acceleration, there is no way for him to detect inside the laboratory if it really is gravity or genuine acceleration in space.
In 1917 Einstein published a popular science book, in which he gives a very detailed account of the motivation behind special and general relativity. The book is an excellent piece of science.
The rotating disk
One of the examples in Einstein's popular science book is the rotating disk. People living on the disk would measure that the circumference of the disk is more than 2 π times the radius of the disk. This is because a measuring rod on the circumference is length-contracted. A measuring rod on the radius is not length-contracted because its velocity is normal to the rod.
People living on the disk might think that their spacetime is curved.
The rotating disk is actually a good example of the illusion of curved space. People who are inertial, and not on the rotating disk, see that the spacetime around the disk is not curved. It is the ordinary Minkowski space. The illusion of curved space is due to the acceleration of the observers on the disk.
Observers on the rotating disk have centrifugal acceleration and measure the circumference to be greater than 2 π r.
If the observers would form a ring around the Schwarzschild metric, they would have centripetal acceleration, and measure the circumference to be less than 2 π r.
We in our blog claim that in both cases, the curved metric of spacetime is just an illusion.
The problem of complex interactions
Albert Einstein apparently did not write anything about gravity interacting with complex matter fields, though he did spend a lot of time later in his life trying to find a "geometric" interpretation for electromagnetism.
On October 10, 2021 in our blog post we wrote about the complex system S, where the stress energy tensor and the Einstein field equations say that the electric charge q of the particle affects the metric of spacetime through changing the pressure around it.
In the system S there is no meaningful way to divide the potential energy between gravity and electromagnetism. Why would one of the fields deform the metric of spacetime, and the other not?
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