According to my understanding (I'm not a physicist just a fan), LIGO measures the changes in two path's lengths to detect gravitational waves by sending a particle down each path at the constant speed of light and measuring the time it takes. In networking, we use pings to measure how long a packet takes to reach a destination. Could the ping be used like LIGO to detect gravitational waves? Of course, this wouldn't be as accurate as LIGO, but the internet is a massive and (essentially) free infrastructure so you could use averages to compensate for errors.
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7$\begingroup$ The noise and random errors would be massively, extremely larger than the signal you're trying to measure. $\endgroup$– JavierJun 9, 2019 at 22:37
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$\begingroup$ @Javier heck, even if you replace the far router with a mirror and the near router with an atomic clock, the time resolution you can get on a computer - even with a custom firmware - isn't nearly enough for the task. $\endgroup$– John DvorakJun 10, 2019 at 13:21
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Gravitational waves are tidal effects so they cause a very small difference in forces acting on two freely-suspended masses separated by a few kilometers.
LIGO uses its intereferometer to detect the relative motion of the two masses due to to the different gravitational forces that they experience. It is not using the interferometer to measure redshifts or a difference in elapsed time.
The ends of an optical fibre are not freely suspended so you cannot measure the forces although you could ask about time delays due to redshifts.
Indeed you can use elapsed time measurements to detect gravitational effects. High-precision atomic clocks can detect the $(\Delta t)/t =gh/c^2$ elapsed time difference between two clocks with $h= 1$m of vertical separation after running for a day. However it is much easier to measure the same $gh$ potential difference by using a spring balance or a pendulum to find $g$ and a meter stick to find $h$. LIGO is like the pendulum and meterstick but still has a hard time to detect the waves. Imagine how much harder it would be using timing differences.
answered Jun 10, 2019 at 13:19