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Golden binary strengthened relativity, aether crackpots don't care

Because it is the first combined electromagnetic-gravitational observation of an astrophysical event, the recent announcement of the LIGO-Virgo and electromagnetic discovery of the "golden binary" or "kilonova" has many consequences. One of them is about the process that may have created most of gold and platinum in the Universe, not to mention numerous less famous elements.

Another implication is the "standard siren". An article in Nature used the kilonova to measure the Hubble's constant in a new way. Instead of using "supernovae" as the "standard candles" whose distance may be determined from their luminosity, the "kilonova" is used as the "standard siren" whose distance is determined from their "sound" i.e. the gravitational wave. The terminology is supposed to be both witty (or creative) and self-explanatory so I hope you appreciate it.

But another consequence for "fundamental physics" is a new measurement of the speed difference between the gravitational and electromagnetic waves.

There was some moment when the neutron stars touched for the first time – and then some kind of an explosion began. So up to that moment of the collision, one could observe the periodic gravitational waves emitted by the two neutron stars that were orbiting each other, relatively peacefully.

After that moment, some violent changes of the matter around the neutron stars began. And that's observed by the regular electromagnetic telescopes. So most of the electromagnetic observations look at the events after the "touchdown". The earliest waves were the (very high-frequency) gamma-rays. The kilonova (merger of the neutron stars) manifested itself as a "short gamma-ray burst". In this way, gamma-ray burst experts have learned about an explanation for at least some of the short GRBs. Electromagnetic waves of lower frequencies were observed for longer periods – weeks etc. – after the "touchdown". The infrared observations were made even recently, a few months after the "touchdown"

Now, the gamma-ray burst occurred about two seconds after the "touchdown" extracted from the gravitational waves. The delay may be almost certainly attributed to some internal dynamics of the large chunk of matter that responded. Note that the diameter of the Sun is almost 2 light seconds, too. So some delays of this magnitude have to be expected.

Nevertheless, you should appreciate how tiny this delay relatively to the time that all the waves needed to get here. The distance of the kilonova was some 130 million light years. So it took 130 million years for the gravitational wave and the gamma-rays to get here. And they got here within at most two seconds after one another. Here is the ratio:

The speed ratio of the two waves differs from one at most by ten to the minus fifteenth power or so.

Let's try to consider some hypotheses that the speed of these waves isn't really equal to \(v=c\), to the maximum speed allowed by the special relativity. Write the difference between the (relatively low-frequency, LIGO-detectable, kHz or so, and that constant seems to be basically frequency-independent in the range, otherwise the LIGO signals would be totally screwed) gravitational waves' speed \(c\) and the speed \(v(E)\) of photons of energy \(E\) in terms of the ratio\[

f(E) = \frac{v(E)}{c}.

\] According to standard special relativity with massless gravitational and gravitational fields, we have \(f(E)=1\) for all \(E\). What are the empirically allowed deviations? Let's expand them in some power laws, use integer powers, the leading terms on both sides, and let's write the coefficients as multiples of the natural Planck mass \(M\):\[

f(E) = 1 + \frac{\alpha E}{M} + \frac{\beta M}{E}.

\] The coefficients \(\alpha,\beta\) stand in front of terms that are directly and indirectly proportional to the photon's energy \(E\), respectively. How big these dimensionless coefficients may be? The gamma-ray energy has reached up to some \(E=0.08\GeV\). So \(M/E\) is some \(1.5\times 10^{20}\).

The second, \(\beta\) term deviates primarily at low energies. We may see that \(\beta\lt 10^{-5}\) or so, to get 15 orders of magnitude from 20 orders of magnitude, from the gamma-rays themselves. And even smaller bounds on \(\beta\) may be obtained from the lower-frequency radiation (whose timing wasn't that precise but which have an even higher \(M/E\)). Clearly, no natural values of \(\beta\) – of order one – are allowed empirically.

On the other hand \(E/M\sim 10^{-20}\) so values up to \(\alpha\sim 10^{5}\) could still be allowed in the first term, the term that makes the very high, especially Planckian, energy electromagnetic radiation deviate from the actual maximum speed in the Universe. It's extremely unlikely that the experiments will be improved so that you would be able to prove \(\alpha\lt 1\) just from the delays: the distances in the Universe can be increased at most by two orders of magnitude but the "delay indistinguishable from zero" is linked to the radius of the binaries and those can't really be much smaller than what LIGO and EM friends saw in August – there aren't substellars neutron stars etc.

In this sense, the \(\alpha\) term in the dispersion relations will always be allowed by experiments that measure the delay and nothing else. This is the term that would indicate a very different speed of light for Planckian energies – which we can't achieve at colliders. For example, if you wrote some dispersion relations for a lattice whose spacing is one Planck length, you could get predictions that will always be compatible with these basic tests.

But some of the constraints on the violations of the Lorentz invariance have surely been improved by several orders of magnitude. See this LIGO-Fermi paper about the golden binary for some more details about it.

However, Backreaction has completely ignored the golden binary and the newest text over there is titled Space may not be as immaterial as we thought. It promotes some kind of an aether. While it's true that the golden binary hasn't disproved all conceivable aether-like or Lorentz-violating theories, I still find the insensitivity to experiments amazing. Ms Hossenfelder either doesn't understand the relevance of experiments and observations such as the "golden binary" for the theories at all; and she just doesn't care about this relevance at all. Both options are just plain terrible.

Even if you were imagining some theory that violates the Lorentz symmetry near the Planck scale, its low energy limit at much lower energies would have to be Lorentz-preserving. So the well-motivated part of the effective theory could still be made Lorentz-covariant. Even in quantum gravity, there is no known advantage that one could gain by abandoning the assumption of the (local etc.) Lorentz invariance.

It's been some 9 years since Leslie Winkle disagreed with Sheldon Cooper about the dependence of the speed of light on the frequency. It was the first episode of TBBT that I actually watched but I have re-watched the previous ones many times afterwards, both in English and in Czech. One still can't "totally rigorously prove" that Sheldon was right but there's been an impressive increase of evidence that Cooper (and Motl whom he really represented there) was right while Winkle (and Smolin etc.) was not.

One could say that these improvements are "analogous" to the negative results about supersymmetry. But this analogy is inadequate quantitatively. While the lower bounds on some superpartner masses have only improved by less than an order of magnitude, the upper bounds on numerous Lorentz-violating effects have improved by many orders of magnitude. There are still lots of natural reasons to think that supersymmetry could or should exist at relatively low, heavily sub-Planckian energies; but the well-motivated reasons for a violation of the Lorentz symmetry have faded away much more dramatically.

Positive articles about the aether mean that for some people, the empirical evidence just doesn't matter at all. There are lots of parasitic people – like Ms Hossenfelder – who pretend to be scientists but their whole lives are based on constant, permanent lies.

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