Is Time-Reversal Symmetry Valid in Curved Spacetime?

[birulami]

Hi,

in high school I think we all learned that "the path of light is invertible (reversible?)". My interpretation would be that if a ray of light hits a flat mirror at 90^{o}, it will trace its path exactly back.

Question: does this still hold in the general theory of relativity when space is bent by masses?

Harald.

 

[HallsofIvy]

That's a rather restricted "interpretation". More generally, if a light beam from a given source, at position A, strikes a wall, at position B, then a light source at position B
will produce a beam that passes through position A. That light beam may strike any number of mirrors at any angles between A and B and a light source at position B will still produce a light beam that will pass through position A.

Yes, that is still true in general relativity- as far as light is concerned, the universe is isotropic.

 

[Passionflower]

Yes, that is still true in general relativity.

Why would that be true?

If the curvature changes in time, e.g. if we have a non stationary spacetime, the return path of the light signal after it bounces of the mirror may no longer be the same. No?

 

[bcrowell]

I think the OP's question was about time-reversal symmetry, not isotropy. The answer to the question actually depends on whether the spacetime is static and the observer is static. If the experiment is done on Earth, then the spacetime is static to quite a good approximation, but the lab frame is not static because it's rotating with the Earth, and we can tell this because the Sagnac effect doesn't vanish. The biggest relativistic non-reversibility effect you will see is precisely the Sagnac effect.