When Einstein published the general relativity theory in 1911, why was the light deviation not predicted correctly? What was the incompleteness of the theory when he published it in 1911? When and how did he realize he was wrong?

I don't know much about general relativity theory. I can understand special relativity to a reasonable extent.


1 Answer 1


The 1911 paper can be found here in German and there is an English translation here.

The GR prediction is roughly $\displaystyle \frac{2GM}{R}\left(\frac{1}{v^2}+\frac{1}{c^2}\right)$ radians, and he calculated the first term correctly but missed the second.

His arguments were based on the equivalence principle. If you have a rocket ship accelerating at $g$ and something flies across it in a total time $Δt$ according to onboard clocks, then the ship's velocity changes by $gΔt$ in that time regardless of the object's speed. Therefore, the acceleration of light in a gravitational field, relative to stationary clocks, must be the same $g$ as the acceleration of slower-moving objects. That gives the first term, which is also the prediction of a Newtonian corpuscular model. (Actually, he made a more complicated argument, deriving gravitational time dilation from the equivalence principle and then considering wave propagation in a vacuum with "variable refractive index" due to the time dilation, but he also noted that you could get the same result from the equivalence principle more directly.)

The second term is due to an "angular defect" in the spacetime geometry, which can't be seen in the equivalence-principle argument because it's inherently nonlocal. See this answer for an illustration of it.


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