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I did General Relatively years ago at Uni. I have revised a lot of the maths demo Dirac''s book. It is incredible the leap in thought to noting from the Bianchi identities that the curvature term's on the left might equal the stress tensor energy tensor on the right. But what I don't get is a feel for what initially prompted Einstein to think that mass might.curve space in the first place.

So my question is: what was the initial clue that made Einstein thing that space might be curved?

I do see how it might occur to him to think of the Lorentz invariant "proper distance" or "proper time" as a pseudo distance metric? The implication being that space and time might form a pseudo Riemann manifold. In general a manifold is of course curved. Is that all that prompted him? Or is it something to do with the Equivalence Principle, or was them some other physical clue that prompted him?

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    $\begingroup$ This might be better suited for the History of Science and Mathematics StackExchange. $\endgroup$
    – probably_someone
    Oct 26, 2019 at 13:27
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    $\begingroup$ I'm voting to close this question as off-topic because it is about the history of science. It would be an ideal question for the History of Science SE. $\endgroup$
    – John Rennie
    Oct 26, 2019 at 14:34
  • $\begingroup$ See the history-questions FAQ on meta for guidance on what questions are better suited on History of Science and Mathematics. $\endgroup$
    – Emilio Pisanty
    Oct 27, 2019 at 14:59
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    $\begingroup$ Personally, I'm not sure which side of the fence this falls into - it's in the gray area in between. Are you asking about Einstein the historical person? Or about Einstein the projected unconscious of how we structure our understanding of GR? If the former, it's probably best migrated. $\endgroup$
    – Emilio Pisanty
    Oct 27, 2019 at 14:59
  • $\begingroup$ To whatever extent PSE might be useful in increasing whatever basic knowledge of physics (or changes in that knowledge) may be obtained by ordinary language (i.e., philosophy), diagrams, or other visualizations (which last have sometimes been described as less accessible to people with an exceptionally easy grasp of math), questions like this can be useful in keeping our species in touch with reality, especially in regions (that shall remain unnamed here) where non- or anti-scientific philosophical positions are maintained thru the educational systems. $\endgroup$
    – Edouard
    Oct 28, 2019 at 2:58

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I believe the initial clue was the (accelerating) elevator. This gave the idea for gravitational lensing.

enter image description here

Light follows a geodesic, and as the elevator accelerates, photons entering perpendicularly to the elevator sidewalls, those photons' path will be curved. Only acceleration can do that, and due to the equivalence principle, it is the same as the effect of a gravitational field.

https://en.wikipedia.org/wiki/General_relativity

Thus, the gravitational field of a massive body must curve spacetime itself, creating a bent path around the body for light.

https://medium.com/starts-with-a-bang/this-is-why-einstein-knew-that-gravity-must-bend-light-2fafcc8b5532

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  • $\begingroup$ A similar description (using a rocket instead of an elevator) of the Equivalence Principle was given by George Gamow in a pop.-sci. book he wrote years ago, around 1950. $\endgroup$
    – Edouard
    Oct 28, 2019 at 3:04
  • $\begingroup$ Vis-a-vis the motion to close the question, I hope the equivalence between a passenger elevator and a passenger rocket shows its timelessness. $\endgroup$
    – Edouard
    Oct 29, 2019 at 20:53
  • $\begingroup$ Hi Arpad! Thanks for this. Yes I was aware of this. This suggests gravity bends light. If it was know that light must follow a geodesic, then that would indeed mean that space must be bent. But how did Einstein know that light must follow a geodesic? Is this because of Snells Law? $\endgroup$
    – Rory Cornish
    Nov 1, 2019 at 17:53
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The field form of the Newton gravitational law: $\nabla^2\Phi = 4\pi G\rho$, where $\Phi$ is a scalar field and $\rho$ is the density of matter might have been a starting point.

But a relativistic equation should be a tensor equation.

If we replace the scalar field with a tensor field, the Ricci tensor can be thought as a good candidate to play the role of the Laplacian as a sum of second derivatives.

And the density of mass is of course replaced by the Energy-moment tensor, due to the energy - mass equivalence.

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