Exploring the Roller Coaster Ride of LIGO Photons

[Leo.Ki]

I am trying to understand how the photons in the LIGO beams behave when going along the "slopes" of the gravitational waves, in particular how the Shapiro delay gets factored into the resulting interference.

To simplify the situation, suppose that a LIGO photon starts orthogonally to a wave "crest." Both traveling in the same direction at the same velocity, the photon will get Shapiro-delayed at a constant rate until it reflects upon the mirror. Then on the way back it goes "down the slope" and the calculation becomes more complicated. Depending on the gravitational wave's wave length and the beam's length, it might reach the "trough" and maybe pass another "crest."

Since the gravitational waves are analysed only through the interferences, how can we be sure of what the Shapiro delay was really and what the actual "orientation" of the wave was? It looks like a puzzle to solve, possibly with several solutions. I know that multiple measures get correlated to solve this, but still, I am wondering how we can be sure.

 

[Orodruin]

The time taken for an EM wave to pass the LIGO arms is about 27 microseconds. This is much smaller than the GW period.

 

[Leo.Ki]

Thank you Orodruin. The 250 Hz peak frequency is very small indeed - even if, for the way back in the case study I described, it is double that - or the arm is very short. But on theoretical grounds, how important is the Shapiro effect compared to the other effects causing the interference detection? Or is the Shapiro effect ultimately exactly the same thing as what is described as arm length change in the papers?