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Comment by ry454 | Hacker News Reader

T is indeed independent from R, but how do we know that F and R are also independent? Would theory fall apart if we try to model F as microscopic modulations of R?

I'm trying to look at R and F from the signal processing point of view: if we apply Fourier transform to both, we'd see that R is described by low frequency band (planetary scale distortions), while F would be ideally described by a high frequency band.

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I wonder about something different - if R and F are independent, and R also tells you the shape of space, what would happen if EM and gravity waves crossed through each other? My guess is the EM wave would be modulated somehow, within the intersection volume, as if crossing into a different matter medium, while gravity wave would be unaffected.

Both effects can occur; GW <-> EMW. You can search for Gertsenshtein Effect, there is also this old paper by Zel'dovich: http://jetp.ac.ru/cgi-bin/dn/e_038_04_0652.pdf

That's correct. The "shape of space" can act as a lens for light. Even in static situations this can be quite interesting:

https://en.wikipedia.org/wiki/Einstein_ring#:~:text=An%20Ein....

It's possible that you could observe a kind of "shimmer" in the position of background stars as a gravitational wave passes between you and them. In fact there is an attempt to detect gravitational waves this way through pulsar timing:

https://en.wikipedia.org/wiki/Pulsar_timing_array

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