I saw the equation on general relativity and then I wondered: how did Einstein check if his equation was right or wrong?
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$\begingroup$ The fact that Hilbert took a different path to reach the same equations was a very solid indicator. $\endgroup$– DanielCCommented Jun 9, 2022 at 16:16
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1$\begingroup$ One more indicator is that they reproduced the Poission equation of gravity if you take the limit of almost flat space and non relativistic matter $\endgroup$– Thomas TappeinerCommented Jun 9, 2022 at 17:28
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Various experiments can be done to prove einsteins theory correct.
Einstein theory predicts the bending of light due to gravity.
He took photos of a constellation of stars at night , when the sun is behind the earth and thus doesn't greatly effect the trajectory of light.
He then waiting for a solar eclipse to happen, so that he could take a photo of those same stars when the sun is infront of the earth, which predicts great light bending. With the eclipse neccessary as you wouldn't be able to see the stars otherwise.
The 2 photos proved that gravity bends light, by the exact amount the math predicts.
answered Jun 9, 2022 at 16:11
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1$\begingroup$ Actually it was Eddington who took photographs from the island of Principe during the 1919 solar eclipse - see en.wikipedia.org/wiki/Eddington_experiment. And the deflection was less than 2 seconds of arc, so not "great" at all. $\endgroup$ Commented Jun 9, 2022 at 16:22
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1$\begingroup$ I'm going to say that Einstein was pretty sure he was right long before he saw these photographs. $\endgroup$– WillOCommented Jun 9, 2022 at 17:23