It stands to reason if gravity changes the color of light then the color will be affected by gravitational waves. My question is, when the waves pass, will the color change be permanent or will the light always return to its original color? It seems to me that if gravitational waves have energy and momentum and can impart this upon objects it could do so also to photons – changing their frequency.
My question is, when the waves pass, will the color change be permanent or will the light always return to it's original color?
One has to keep clear in discussing light , its particle nature, and its classical electrodynamics wave nature. The classical electrodynamic wave can be mathematically shown to emerge from the underlying quantum mechanical. In simpler words the light we see is a confluence of an enormous number of photons. In analogy, it is usually assumed that gravitational waves are a confluence of an enormous number of gravitons.
Photons and gravitons are quantum mechanical particles. Once they scatter there can be energy transferred and this means that the photon frequency will change . This change collectively will show effects only in the $dt$ time and dV volume where there is the crossing of the two classical waves, when the particles interact. The waves before and after are unaffected.
There cannot be a permanent change in the color of the classical light , because new photons of the original frequency are continually traveling in the direction of classical light. Only at the crossing point there will be changes in the frequency of the photons if the scattering is inelastic. Considering the coupling constants involved in the interaction between photons and gravitons this would be hardly detectable, as most would not interact.
Why would the photons change their state forever? As the gravitational waves approaches, the space-time in their vicinity is distorted. As the waves pass, the space-time will revert to its original state. If you were able to observe the photons as the waves come in and pass, then you will momentarily observe a change in the paths of the photons. After the waves pass there is no reason for this effect to last forever. So the photons will not change their frequency forever (this would also violate the law of conservation of energy, wouldn't it? Assuming there is nothing more complex happening like "graviton-photon scattering").