Recent Experimental Tests Of General Relativity

Sabine Hossenfelder surveys a variety of recent tests of General Relativity and of recent idea about how to test it that have not been conducted or completed yet. She opens with an insightful point:

I have to clarify that when I say “proving Einstein wrong”, I mean proving Einstein’s theory of general relativity wrong. Einstein himself has actually been wrong about his own theory, and not only once.

For example, he originally thought the universe was static, that it remained at a constant size. He changed his mind after learning of Hubble’s discovery that the light of distant galaxies is systematically shifted to the red, which is evidence that the universe expands. Einstein also at some point came to think that gravitational waves don’t exist, and argued that black holes aren’t physically possible. We have meanwhile found evidence for both.

I’m not telling you this to belittle Einstein. I’m telling you this because it’s such an amazing example for how powerful mathematics is. Once you have formulated the mathematics correctly, it tells you how nature works, and that may not be how even its inventor thought it would work. It also tells us that it can take a long time to really understand a theory.

Deur's work on gravity, which attempts to explain dark matter and dark energy phenomena with the self-interaction of gravitational fields in the context of orthodox General Relativity (albeit not in the manner it is conventionally applied), if correct, would be an example of the idea that "it can take a long to to really understand a theory" even after it has been fully formulated mathematically and studied by extremely intelligent scientists like Einstein himself.

None of the scholarship that Hossenfelder reviews disprove General Relativity, despite well motivated theoretical arguments that ultimately classical General Relativity should be replaced by a quantum gravity theory, which she recaps as follows:

General Relativity is now more than a century old, and so far its predictions have all held up. Light deflection on the sun, red shift in the gravitational field, expansion of the universe, gravitational waves, black holes, they were right, right, right, and right again, to incredibly high levels of precision. But still, most physicists are pretty convinced Einstein’s theory is wrong and that’s why they constantly try to find evidence that it doesn’t work after all.

The most important reason physicists think that general relativity must be wrong is that it doesn’t work together with quantum mechanics. General relativity is not a quantum theory, it’s instead a “classical” theory as physicists say. It doesn’t know anything about the Heisenberg uncertainty principle or about particles that can be in two places at the same time and that kind of thing. And this means we simply don’t have a theory of gravity for quantum particles. Even though all matter is made of quantum particles.

Let that sink in for a moment. We don’t know how matter manages to gravitate even though the fact that matter does gravitate is the most basic observation about physics that we make in our daily life.

This is why most physicists currently believe that general relativity has a quantum version, often called “quantum gravity”, just that no one has yet managed to write down the equations for it. Another reason that physicists think Einstein’s theory can’t be entirely correct is that it predicts the existence of singularities, inside black holes and at the big bang. At those singularities, the theory breaks down, so general relativity basically predicts its own demise

Much of the literature is familiar but one comment in the discussion clarified a term that I had not previously understood very precisely:

According to Einstein, the speed of light in vacuum doesn’t depend on the energy of the light or its polarization. If the speed depends on the energy, that’s called dispersion, and if it depends on the polarization that’s called birefringence. We know that these effects both exist in medium. If we’d also see them in vacuum, that would mean Einstein was wrong indeed.

So far, this hasn't been seen. She doesn't cite to a March 21, 2022 preprint by Arefe Abghari's team on the topic, but it used cosmic microwave background measurements to severely constrain birefringence, although a March 9, 2022 release from the Planck experiment finds evidence of non-zero birefringence at a little less than the 3 sigma level contrary to an expected value one sigma. There are reasons, however, that the theoretical expectation could be wrong without deviating from general relativity, including, potentially, the some of the same sort of phenomena that can lead to the CMB peaks associated with dark matter phenomena.

A recent paper to which she links, ruling out, to the limits of experimental accuracy, Lorentz invariance violation in quantum gravity or photon mass is:

D. J. Bartlett, H. Desmond, P. G. Ferreira, and J. Jasche, "Constraints on quantum gravity and the photon mass from gamma ray bursts"104 Phys. Rev. D 103516 (17 November 2021).

The discrepancy between the speed of gravitational waves and the speed of light is limited by an August 2017 binary neutron star merger, but the 1.7 second discrepancy seen could come from the gravitational wave causing event and the light emitting event not occurring at precisely the same time.

She also cites a couple of recent papers on "black hole echoes" that argue that there is a single observed echo from that event, but again, this is limited by a weak understanding of the detailed sequencing the event itself, particularly given that a true "black hole echo" in which the event horizon of a black hole has physical reality, would repeat multiple times rather than just once in a gravitational wave single.

Quantum type interactions of gravity are hard to rule out or confirm since there is so much background quantum interaction from other sources.

Short distance gravity measurements also see nothing amiss, but only to not terribly short distances (0.057 mm) by quantum physics standards (often dealing with femtometer or smaller scales):

Another rather straight-forward test is to check whether the one-over-R-squared law holds at very short distances. Yes, that’s known as Newton’s law of gravity, but we also have it in general relativity. Whether this remains valid at short distances can be directly tested with high precision measurements. These are done for example by the group of Eric Adelberger in Washington DC. . . . Their most precise measurement yet was published in 2020 and confirms that one-over-R-squared law is correct all the way down to 57 micrometers.

Scientists have also confirmed that, to the limits of experimental precision, objects with different masses fall at the same rate in a gravitational field (one of several aspects of the similar but not identical equivalent principles). In particular, a recent paper looked for a difference in how two isotopes of Rubidium fall in the gravitational field of Earth.

Hossenfelder omits, however, the really interesting and observationally motivated area in which general relativity is being tested, which is in very weak gravitational fields of extremely massive sources at great distances from the source (where dark matter phenomena are observed). In this area, there is evidence consistent with deviations from the Newtonian approximation of general relativity conventionally applied at these scales, and of an "external field effect" which violates one of the equivalence principles, but not others.