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My impression is that the equivalence of the force experienced in an accelerating elevator to the force experienced as a result of gravity is what inspired Einstein to quantify gravity in terms of the curvature of space. However I don’t see the connection. If I were being strict, I would quantify gravity as the acceleration of motion and this would lead me to derive equations like this:

https://math.ucr.edu/home/baez/physics/Relativity/SR/Rocket/rocket.html

Where does the idea of space curvature come from? What were the other models which never saw the light of day? Why didn't he, for example, posit a gradient in the size of the occupiable quanta of space- as smaller cells are more numerous in a given volume and so allow many more degrees of freedom of occupancy --- the random motion of atoms would tend to move them in that direction. This would least be in line with the accepted conceptions of statistical mechanics.

The idea of space curvature seems idiosyncratic as it has nothing to do with motion. There are some clues in this thread

https://physics.stackexchange.com/questions/38379/how-did-einstein-derive-general-relativity

There is this statement

"eventually he realized that the spacetime had to be curved, by arguments based on the equivalence principle, and it must be described by the Riemannian geometry. "

The equivalence principle relates the sensation of acceleration to different reference frames. Curvature of any kind is not mentioned.

Is there a coherent description of the steps/jumps in thought that led to the idea of curvature of space?

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The account in Subtle is the Lord, by Abraham Pais, is excellent.

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    $\begingroup$ thank you. This account has the detail I was looking for. $\endgroup$ Jul 29, 2022 at 21:21

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