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Please note that this is not an inquiry into the mechanisms of technology that LIGO uses to detect gravitational waves. Also, I am not a flat-earther.

I was watching physicists vs. flat-earthers debate (who knew reality could be up for debate) and a point was brought up by a flat-earther:

"A core aspect of Einstein's relativity is that time and space are woven into a 4D spacetime. So gravitational waves warp space (the distance of LIGO arms that light must travel) and time (ticking of clocks slows for light). If the speed of light is constant, and time and space warp accordingly to keep it constant, therefore you won't be able to detect an interference pattern --> Einstein was wrong (if they detect something that means the speed of light wasn't constant, and if they don't then general relativity is wrong)."

tl;dr the warping of space is cancelled out by dilation of time (to keep light's speed constant) so the photon will always be in phase and no interference pattern will be seen.

I know that there is something VERY wrong with this argument, but sadly I am not well-studied enough in special and general relativity to figure it out. My hunch is that the warping of the time component of spacetime is irrelevant for photon as they do not experience time...they move purely through space. I find unsatisfactory because the measurements are made in our reference frame, not that of the photons.

I'm not even sure if that's what the man is getting out so I included the link: https://www.youtube.com/watch?v=_ZnAvjzjTBY (The argument beings at 20:35)

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    $\begingroup$ Essentially a dupe of physics.stackexchange.com/q/153657/25301 and the linked Qs therein. $\endgroup$
    – Kyle Kanos
    Commented May 12, 2018 at 16:18
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    $\begingroup$ Ironically, Einstein was for many years convinced of exactly this, that gravitational waves were unphysical coordinate changes only. So- and I hope this doesn't shock anyone- it may be the case that those flat Earthers are indulging in a bit of revisionism. (Although to be fair, I believe he did eventually come around to the correct result) $\endgroup$
    – Rococo
    Commented May 12, 2018 at 19:26
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    $\begingroup$ "I find unsatisfactory because the measurements are made in our reference frame, not that of the photons." - to be sure and as stated here so many, many times, there is no inertial reference frame in which photons are rest - no inertial clocks and rulers at rest with respect to a photon. $\endgroup$
    – Alfred Centauri
    Commented May 13, 2018 at 1:08
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    $\begingroup$ en.wikipedia.org/wiki/Shapiro_time_delay $\endgroup$
    – timm
    Commented May 13, 2018 at 15:43
  • $\begingroup$ Aniekan "My hunch is that the warping of the time component of spacetime is irrelevant for photon as they do not experience time", true they don't, but that isn't related to gravitational time delay. This refers to the elapsed proper time an observer measures for light which travels through curved space-time close to a mass. For more see Shapiro time delay. This effect is absolutely negligible regarding the tiny "warping of space" due to a gravitational wave. $\endgroup$
    – timm
    Commented May 13, 2018 at 16:09

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The detection of a gravitational wave passing by the interferometer is essentially a lenght measurement by means of laser technics. Due to the bending of space-time the stretching of one arm coincides with the shrinking of the other arm due to a tiny displacement (swinging) of the mirrors. So the measurement is based on the comparison of two simultaneously different lengths. The phase of the photon doesn't play a role because the frequency of the laser light is much much higher than that of the gravitational wave. Therefore the wave period of the gravitational wave is much longer than that of the light.

Another aspect, the light travel time along the arms and back is very short compared to the change of the phase of the gravitational wave. Thus as the speed of light doesn't change a net difference of light travel time is measured.

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  • $\begingroup$ As such,timm, my current layman understanding of ligo as a big interferometer in which somehow an arm change due to a "suspended" mirror is quite correct. Right? $\endgroup$
    – Alchimista
    Commented Dec 28, 2018 at 14:37
  • $\begingroup$ And second doubt: i was tempted to stretch the wavelength instead but this should shouldn't have effect as for the different periods of light and GW. Is it so? Thanks in advance $\endgroup$
    – Alchimista
    Commented Dec 28, 2018 at 14:39
  • $\begingroup$ Hi, Alchimista, yes the suspended mirror being in free fall horizontally keeps track of the change of the distance due to the gravitational wave passing by. And this change is measured by means of the light travel time of the laser pulse along the respective arm and back, so that a corresponding change of the light period isn't relevant. Notice also that this period is many orders shorter than that of the GW. $\endgroup$
    – timm
    Commented Dec 30, 2018 at 14:54

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