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When formulating General Relatvity Einstein proposed that freely falling particles, that is those subject to no forces other than gravity, follows geodesics through spacetime. In other words, those particles follow the straightest path possible.

My question here is: what was Einstein's reasoning to conclude this? How did he conclude that the worldline of a freely falling particle is a geodesic? Was it with some thought experiment?

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  • $\begingroup$ Even with gravity, particles follow geodesics. In GR "gravity" is just mass distorting (geodesics in) spacetime. $\endgroup$ – Spencer Mar 14 '17 at 12:36
  • $\begingroup$ @Spencer, I know that. As I said "freely faling particles, that is those subject to no forces other than gravity". The point is: the equations of motion for a free particle (just gravity) are the geodesic equations. It could be something else. How did Einstein conclude that the correct equations were the geodesic equations? Historically how Einstein found out that particles follow geodesics? $\endgroup$ – user1620696 Mar 14 '17 at 14:08
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    $\begingroup$ My point is, you can't separate out gravity like that. You don't even need to use the term 'geodesic' unless space is curved. Someone else will have to write a fully fleshed answer but I'm going to guess he assumed conservation of momentum, and a path minimizing the momentum tensor, once you accept that space is curved, follows a geodesic. $\endgroup$ – Spencer Mar 14 '17 at 14:22
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    $\begingroup$ Einstein did not reason this way at all. He came to the form of his equations by trying to satisfy some relativity and invariance principles (equivalence, Mach's, general covariance), then he realized that the equations he was looking for might be analogous to the ones in the Gauss's theory of surfaces, and Grossman told him about Riemann, etc. See How was Einstein led to make a contact with Differential Geometry for his theory of General Relativity? $\endgroup$ – Conifold Mar 14 '17 at 21:09
  • $\begingroup$ To the best of my knowledge the starting point of the general relativity theory was the happiest thought of my life in 1907 when Einstein realized that the relativity principle could be extended to gravitational motions. $\endgroup$ – Jan Peter Schäfermeyer Mar 21 '17 at 18:19

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