According to the equivalence principle, gravity and inertial forces are similar. And according to general Relativity, If there’s a large object in space-time, it warps the space time’s geometry and causes the light to bend ( or to be seen as if it was coming from a different source). Now, if there’s an observer in an accelerating frame of reference and there’s no mass, will the observer still see the light to be coming from a different source considering the frame’s acceleration to have the same effect as that of a mass according to the principle of equivalence?
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asked Nov 1, 2021 at 11:16
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1 Answer
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When you say "will the observer still see the light to be coming from a different source" I assume you mean that the light beam will bend therefore changing the apparent location of the source of light, so the position of the source appears to be in a different location.
According to the equivalence principle, a uniformly accelerated reference frame is equivalent to a uniform gravitational field and so the light ray will still bend as measured inside the accelerated reference frame even if there is no mass.
Let's assume the accelerated frame of reference is an elevator. Even if there was no mass, a light ray sent across the accelerating elevator will still bend as if the elevator were stationary in a uniform gravitational field. In fact, to test the principles of general relativity, during a solar eclipse, it was noted that light originating from behind the sun actually deflected toward sun since these rays showed that the apparent position of the stars to be in a different location to where they are actually were (what you mean by "observer still see the light to be coming from a different source").
Note that in the right diagram there is no gravitational field but there is a uniformly accelerated reference frame whereas in the left image there is only a uniform gravitational field. But in both cases, there is light bending. That is, both situations are equivalent.
