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Einstein made intensive use of non-Eucliden geometry already developed by mathematicians. The difference being that the real manifolds (well, one of them) as imagined by the mathematicians were supposed by Einstein to correspond to real spacetime.

Was Einstein influenced in forming his ideas by the ideas of people like Riemann? Was he the first to consider the spaces or manifolds as corresponding to real spacetime?

Deschele Schilder
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  • According to a New Scientist article - Einstein was not even the second person to think about the possibility of space in our Universe being curved, and he had to be pushed along the path by others, including Grossman. – nwr Jul 12 '21 at 15:55
  • @Nick Then GR should not be assigned to him, I think. Einstein would have been the last to admit, I guess. Or did he? – Deschele Schilder Jul 12 '21 at 16:02
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    Many of the ideas used in GR were floating around at the time. It was Einstein who brought them all together into a coherent whole. – nwr Jul 12 '21 at 16:09
  • @Nick But shouldnt he believe in curved spacetime then too? Well, maybe initially he didnt believe in it. Later he made it the foundation of gravity. – Deschele Schilder Jul 12 '21 at 16:13
  • @Nick: Nice article! At one point: "Since light has no mass, how can it be affected by gravity? The answer, as Einstein found with a little help from Grossman .... Doesn't light have mass via $E=mc^2$? I recall reading somewhere (Max Born's semi-popular relativity book?) that regarding the famous 1919 eclipse measurements, there were essentially three possible outcomes predicted: no bending of sunlight, bending consistent with $E=mc^2$ from special relativity, and bending consistent with general relativity, with the general relativity bending being about twice that of special relativity. – Dave L Renfro Jul 12 '21 at 18:23
  • @DaveLRenfro Is there bending in SR? Do you mean accelerated frames? – Deschele Schilder Jul 12 '21 at 19:15
  • I'm simply talking about what one would predict using Newtonian mechanics and gravity considerations, along with the assumption that light would bend in the same way a passing meteor would. See the 2nd paragraph of the Wikipedia subsection Criticism and legacy. I just located my copy of Born's book, and the discussion is on pp. 358-359 of the 1962 revised Dover edition and on pp. 285-286 of the original 1922 edition. – Dave L Renfro Jul 12 '21 at 19:34
  • @DaveLRenfo Yes. The famous factor two. EM radiation excerts twice as much pressure as mass (the factor half in Einstein famous formula). I imagine you in the middle of a gigantic library somehow... in the middle of a giant heap of books... – Deschele Schilder Jul 12 '21 at 19:56
  • @DaveLRenfro I know next to nothing about physics but my guess would be that gravity bends space so that when light travels in a straight line through curved space it appears to be following a curved path from a third-person point of view. As for energy-mass equivalence, would the energy of light be "potential mass" rather than "actual mass"? I think this may be what is termed "relativistic mass". – nwr Jul 12 '21 at 19:56
  • @Nick Imagine an accelerated frame in outer space. It looks as if gravity is present (equilalence principle). Light curves in this frame. – Deschele Schilder Jul 12 '21 at 20:03
  • @DescheleSchilder Does light curve "in this frame". Or does it just appear to curve from a third-person view outside of the frame? – nwr Jul 12 '21 at 20:10
  • @Nick For a person inside the frame (at rest wrt this frame) there is gravity present. Thats the priciple of equivalence (or relativity as relative to one observer gravity is present and relative to another not). On earth you are constantly accelerated upward. So gravity is present. Contrary to an accelerated frame in space you dont move in space though. – Deschele Schilder Jul 12 '21 at 20:15
  • @DescheleSchilder Thanks. That kind of makes sense, but I'm working with a rather patchy foundation here, never having read physics beyond grade school other than a few popular science books. – nwr Jul 12 '21 at 20:20
  • @Nick Nevermind! You seem to know a lot of the history and be very interested. – Deschele Schilder Jul 12 '21 at 20:36
  • (just returned, briefly, after various errands the last 3 hours) @Nick: I think you and Deschele are misunderstanding what I was saying. From special relativity we know that light has mass, and thus is affected by the sun's gravitational attraction. In the same way that an object passing close to the sun will have its trajectory bent due to the sun's gravity pulling the object in a little as it passes by, so too will light we see that passes close to the sun. However, the general relativity calculations for light bending includes effects above and beyond the simple fact that light has mass. – Dave L Renfro Jul 12 '21 at 23:03
  • @DaveLRenfro Yes, re-reading your original comment I see now that the question was rhetorical and you were in fact offering an explanation. Thanks. – nwr Jul 13 '21 at 02:18
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    Does this answer your question? How was Einstein led to make a contact with Differential Geometry for his theory of General Relativity? – Conifold Jul 13 '21 at 02:45

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