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A red shift would result in the peaks and troughs being more distant than before, both in time and in space. This should show up as a phase shift and so should be observable IMHO.
The basic question seems to be, “is the laser beam affected by the gravitational wave?”My apologies for being so pedantic.
Thinking of it again, how is this 'gravity wave' thought to act?If it is just a 'ripple' in spacetimes fabric will it have a depth?Will it act as a 'vertical plane' passing the interferometer by if you see how I mean?Or will it have a 'horizontal' saturation with a peak?Can gravity have that? If I think of it as a vibration propagating in tightly woven 'strings' there seems to be that possibility, but then I think we should noticed it macroscopically already?
So are you saying that there is a saturation with a 'peak' somewhere in it?