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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The fact that Hilbert took a different path to reach the same equations was a very solid indicator. – DanielC Jun 09 '22 at 16:16
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1One more indicator is that they reproduced the Poission equation of gravity if you take the limit of almost flat space and non relativistic matter – Thomas Tappeiner Jun 09 '22 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.

jensen paull
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1Actually it was Eddington who took photographs from the island of Principe during the 1919 solar eclipse - see https://en.wikipedia.org/wiki/Eddington_experiment. And the deflection was less than 2 seconds of arc, so not "great" at all. – gandalf61 Jun 09 '22 at 16:22
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1I'm going to say that Einstein was pretty sure he was right long before he saw these photographs. – WillO Jun 09 '22 at 17:23