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To be exact Einstein made a claim that it is gravity that curves space-time. You can follow his reasoning in his "Relativity: The Special and General Theory." Einstein started off with comparing acceleration caused by gravity to acceleration in a lift (assuming it moves with accelerated motion) going up. He claimed that these two accelerations are ...


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According to the excellent and very well researched scientific biography "Subtle is the Lord" by A. Pais, as late as 1912 Einstein was still assuming a flat Euclidean space (at that point he had been working on the general theory for 5 years). Then (in 1912) Some time between August 10 and August 16, it became clear to Einstein that Riemannian geometry ...


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About.. locally measured your time never differ, aka, 'c' relative your wristwatch for example, although some might want to argue that a acceleration is different there, which I don't agree too. But we can keep it to uniform motions and then also conclude that this fact is what makes 'repeatable experiments' work, as well as constants. Assume this wrong, ...



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