*[This is a transcript of the video embedded below. Some of the explanations may not make sense without the animations in the video.]*

Einstein’s theory of general relativity has made countless correct predictions. And yet physicists are constantly trying to prove it wrong. Why? What would it be good for to prove Einstein wrong? And how could it be done? That’s what we’ll talk about today. First of all, 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.

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.

Okay, so we have some reason to think general relativity is wrong, but how can we find out whether that’s indeed the case? The best way to do this is by testing the assumptions that Einstein based his theory on. The most important assumption is that the speed of light is the same in all directions and everywhere in the universe. To be precise, that refers to the speed of electromagnetic radiation at all frequencies, not just in the range of visible light, and it’s the speed in vacuum, usually denoted c. The speed of light in a medium depends on the rest frame of the medium.

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.

The currently best experiments for this come from analyzing electromagnetic radiation from gamma ray bursts. This is mostly because gamma ray bursts are bright, short, and can be far away, often several billion light years. Moreover, they emit electromagnetic radiation up to really high energies. Since one knows that the light must have been emitted in the burst at about the same time regardless of its energy, one can then test whether it also arrives at the same time. If it doesn’t, that would be evidence that the speed of light depends on the energy.

Since the gamma ray bursts are so far away, even tiny differences in the speed of light can add up to a noticeable delay. The most recent data on this were published just a few months ago by a group from Oxford and Stockholm. So far there is no indication that Einstein was wrong. You already knew this of course because otherwise you’d have seen the headlines! But that’s one way it could happen.

In general relativity it further turns out that gravitational waves also move with the speed of light. This is quite difficult to test because it requires one to measure both gravitational waves and light from the same source. Even if you manage to do that, it’s difficult to tell whether they were really emitted simultaneously. There is really only one measurement of this at the moment, which is a gravitational wave event from August 2017.

This is believed to have been a merger of two neutron stars, and it was accompanied by an electromagnetic signal. The electromagnetic signal was detected by the Fermi and INTEGRAL spacecraft beginning at about 1.7 seconds after the gravitational wave event began.

This is compatible with what Einstein predicts. However, it is pretty much impossible to prove Einstein wrong this way. Because if the two signals do not arrive together you don’t know whether that’s because one arrived 5 years earlier, or will arrive 100 years later, or maybe because you just didn’t measure it because it was too weak. Indeed, so far none of the other observed gravitational wave events came with an electromagnetic counterpart, and no one’s claimed that this means Einstein was wrong.

So that’s not a very promising way to prove Einstein wrong. But gravitational waves offer another opportunity to do that. In Einstein’s theory of general relativity, the black hole horizon is not a physical thing. It’s just the location of a surface that, once you’re inside, you can’t get out. It’s really just a name we give to this boundary much like city limits. But if Einstein’s theory is not fundamentally correct, then the black hole horizon could have physical properties, for example created by quantum effects in that yet-to-be-found theory of quantum gravity.

If that was so, then the gravitational waves emitted from black hole mergers would look different from what Einstein predicts. Because if the horizon is a physical thing, then it can ring and that creates echoes, not of sound waves, but of gravitational waves. In the gravitational wave data, this would look like a regular repetition of the original signal with decreasing amplitude.

There are a number of people who have looked for those. Niayesh Afshordi and his group at Perimeter Institute, some people from the LIGO collaboration, and a few others. They actually did find a signal that looked like an echo in the previously mentioned gravitational wave event from August 2017. Depending on whom you ask, the statistical significance is between 2 and 4.2 sigma.

However, after analyzing the data some more, astrophysicists seem to have mostly agreed that the alleged echo didn’t have anything to do with the black hole horizon itself. Remember this was a neutron star merger. People from Luciano Rezolla’s group have argued what happened is that the collapse to a black hole was somewhat delayed. This looks like an echo, but only once, and is also why the electromagnetic signal came 1.7 seconds after the gravitational wave signal had started.

In a new paper which just appeared a few weeks ago, Niayesh’s group claims again they’ve found a signal of a black hole echo. They just can’t give up trying to prove Einstein wrong. This time they say they found it in a different gravitational wave event and at 2.6 sigma, so that’s about a 1 in 200 chance to be coincidence. Personally I think it’s very implausible that we will find evidence that Einstein was wrong in black hole signals, but it’s worth looking for.

Another way physicists try to find ways to prove general relativity wrong is by showing that it doesn’t correctly work together with quantum mechanics. The major challenge for doing this is that in the experiments that we have been able to do so far, we either measure quantum effects, but then the masses of the objects are so small that we can’t measure the gravitational field. Or we can measure the gravitational field, but then the objects are so massive we can’t measure their quantum effects.

So one of the ways to prove Einstein wrong is to bring more massive objects into quantum superpositions and then measure their gravitational field. If the gravitational field is also in a quantum superposition, then that means general relativity is out and Einstein wrong. This avenue is pursued for example by the group of Markus Aspelmeyer in Vienna.

A related idea is to show that gravity can cause entanglement. Entanglement is a quantum effect and if it can be caused by gravity, then this means gravity must have quantum properties too, which it can’t in Einstein’s theory. So that too would prove Einstein wrong. This is a good idea in principle, but I suspect that in practice it will be very, very difficult to show that the entanglement didn’t come about in other ways.

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.

This image shows the key component of their measuring device. These two parts are rotated against each other while the gravitational attraction between them is being measured. This creates a periodically changing force which is a really clever way to filter out noise. 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. So again, they didn’t find anything out of the order so far, but this is another way Einstein could turn out to be wrong.

Finally, one can test a key assumption underlying general relativity, which is the equivalence principle. The equivalence principle says loosely speaking that all objects should fall the same and, most importantly, that how fast they fall doesn’t depend on their mass. This is much easier to measure than the gravitational field of particles because when you test the equivalence principle you are looking for a difference.

You can make your life even easier by looking for a difference between two objects that are very similar except for their mass, like two different isotopes of the same atom. This has been done most recently by a group in Stanford, California who looked for a difference in how two isotopes of Rubidium fall in the gravitational field of Earth. Again you already know they didn’t find any violation of the equivalence principle because otherwise you’d have heard of it. But this too is a way that Einstein could turn out to be wrong.

What would it be good for to prove Einstein wrong? Well, first of all it would give us experimental guidance to develop a theory of quantum gravity, and that could help us understand the quantum properties of space and time, as well as what’s inside black holes or what happened at the big bang.

Many physicists also hope that it will shed light on other puzzles, such as dark matter and dark energy, or explain some nagging anomalous observations in cosmology, like the presence of too many large structures in the universe, which we talked about in an earlier video, or that different measurement of the Hubble rate don’t give the same results.

Personally I think the most promising way to prove Einstein wrong is the approach pursued by the group of Aspelmeyer. And if they succeed they’ll almost certainly win a Nobel Prize. But it’s quite possible that in the end the breakthrough will happen in a way that no one saw coming.

You can make your life even easier by looking for a difference between two objects that are very similar except for their mass, like two different isotopes of the same atom. This has been done most recently by a group in Stanford, California who looked for a difference in how two isotopes of Rubidium fall in the gravitational field of Earth. Again you already know they didn’t find any violation of the equivalence principle because otherwise you’d have heard of it. But this too is a way that Einstein could turn out to be wrong.

What would it be good for to prove Einstein wrong? Well, first of all it would give us experimental guidance to develop a theory of quantum gravity, and that could help us understand the quantum properties of space and time, as well as what’s inside black holes or what happened at the big bang.

Many physicists also hope that it will shed light on other puzzles, such as dark matter and dark energy, or explain some nagging anomalous observations in cosmology, like the presence of too many large structures in the universe, which we talked about in an earlier video, or that different measurement of the Hubble rate don’t give the same results.

Personally I think the most promising way to prove Einstein wrong is the approach pursued by the group of Aspelmeyer. And if they succeed they’ll almost certainly win a Nobel Prize. But it’s quite possible that in the end the breakthrough will happen in a way that no one saw coming.

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