I have just come across a paper which involves a study about the speed of gravity. This has rocked me a bit, since I thought it was well known gravitational fields travel at the speed of light, in fact many entries on this website confirm it, e.g. How fast does gravity propagate? & "Speed" of Gravity and Speed of Light. Therefore, how come there are studies being published on the subject? To be fair, I've just finished my second year as an undergrad and therefore I don't yet have the level to understand most of the paper as I haven't studied neither Astro nor GR.
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11$\begingroup$ Studies are still being published on the mass of the photon. It's the same thing. Theoretical predictions should be constantly experimentally tested with better precision. $\endgroup$– PraharCommented Aug 14 at 11:00
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2$\begingroup$ Ultimately a physical theory is a conjecture about experimental results. "gravity propagates at the speed of light" really means "according to all the experiments we have performed so far, gravity propagates at the speed of light +- the experiments precision". $\endgroup$– RexcirusCommented Aug 15 at 12:08
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1$\begingroup$ A similar thing could be said about Kepler. It was a well established fact that heavenly bodies moved in epicycles about circular orbits, so why did he study Tycho Brahe's detailed measurements to see if it was actually true? $\endgroup$– Paul SinclairCommented Aug 16 at 16:42
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2 Answers
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It is well known that General Relativity predicts that gravitational waves exist [1] and that they travel at the speed of light. But, until the construction of LIGO, these were not experimental facts. Even in a well-tested theory like GR, every theoretical prediction should be subjected to experimental tests. There had been indirect evidence of such waves prior to this, namely the decay of the orbit of a binary pulsar.
Even after the binary neutron star collison observation, scientists will work to shrink the error bars on the measurement in order to see if the speed of gravity is actually $c$ or slightly different (although, according to equations 16 and 17 in the linked paper, the error bars are already very small). The latter case could point towards new physics beyond General Relativity (whether quantum gravity or something else entirely).
[1] This wasn't immediately apparent. Even Einstein was unsure whether gravitational waves were real or just a bit of coordinate system weirdness.
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The paper introduces a scalar parameter $\alpha_0$ that measures the difference between the speed of light and the speed of gravitational waves
$$\alpha_0 = 2\frac{v_{GW}-c}{c}, $$
and it states that $\alpha_0=0$ is the theoretical value in accordance to general relativity. However, general relativity is still a model of reality, and it may not be necessarily true that $\alpha_0=0$ and not some extremely small value. In page 4 they obtain some lower and upper bounds for $\alpha_0$ considering a case study and it's clear that, if it isn't zero, it's very close to zero. In fact, in page 8 the authors state
In our simulations, we successfully constrained the speed of gravity across all observation counts and prompt time delay models with an uncertainty $\Delta\alpha_0$ ranging from $∼ 2 · 10^{−16}$ down to $∼ 10^{−19}$.
I think Section IV is the most interesting as they show what the goal of the study really is. You can use the method they produce in two different ways, essentially: either you fix Hubble's constant (cosmological parameter) to measure the speed of gravity and prompt time delays, or you fix the speed of gravity according to GR ($\alpha_0=0$) and infer Hubble's constant and the prompt time delay distributions (there's a third approach where you try to infer all four parameters, but then you do not get a good result for $H_0$).
The quote above is from the first approach where they fix Hubble's constant and try to find the speed of gravity. However, the second approach is probably the more interesting one since the value of Hubble's constant is disputed and not as well known as the speed of gravitational waves. Check page 9 for more details on those results.
