Do Black Holes Echo?

What happens with the event horizon of two black holes if they merge? Might gravitational waves emitted from such a merger tell us if Einstein’s theory of general relativity is wrong? Yes, they might. But it’s unlikely. In this video, I will explain why. In more detail, I will tell you about the possibility that a gravitational wave signal from a black hole merger has echoes.


But first, some context. We know that Einstein’s theory of general relativity is incomplete. We know that because it cannot handle quantum properties. To complete General Relativity, we need a theory of quantum gravity. But progress in theory development has been slow and experimental evidence for quantum gravity is hard to come by because quantum fluctuations of space-time are so damn tiny. In my previous video I told you about the most promising ways of testing quantum gravity. Today I want to tell you about testing quantum gravity with black hole horizons in particular.

The effects of quantum gravity become large when space and time are strongly curved. This is the case towards the center of a black hole, but it is not the case at the horizon of a black hole. Most people get this wrong, so let me repeat this. The curvature of space is not strong at the horizon of a black hole. It can, in fact, be arbitrarily weak. That’s because the curvature at the horizon is inversely proportional to the square of the black hole’s mass. This means the larger the black hole, the weaker the curvature at the horizon. It also means we have no reason to think that there are any quantum gravitational effects near the horizon of a black hole. It’s an almost flat and empty space.

Black holes do emit radiation by quantum effects. This is the Hawking radiation named after Stephen Hawking. But Hawking radiation comes from the quantum properties of matter. It is an effect of ordinary quantum mechanics and *not an effect of quantum gravity.

However, one can certainly speculate that maybe General Relativity does not correctly describe black hole horizons. So how would you do that? In General Relativity, the horizon is the boundary of a region that you can only get in but never get out. The horizon itself has no substance and indeed you would not notice crossing it. But quantum effects could change the situation. And that might be observable.

Just what you would observe has been studied by Niayesh Afshordi and his group at Perimeter Institute. They try to understand what happens if quantum effects turn the horizon into a physical obstacle that partly reflects gravitational waves. If that was so, the gravitational waves produced in a black hole merger would bounce back and forth between the horizon and the black hole’s photon sphere.

The photon sphere is a potential barrier at about one and a half times the radius of the horizon. The gravitational waves would slowly leak during each iteration rather than escape in one bang. And if that is what is really going on, then gravitational wave interferometers like LIGO should detect echoes of the original merger signal.

And here is the thing! Niayesh and his group did find an echo signal in the gravitational wave data. This signal is in the first event ever detected by LIGO in September 2015. The statistical significance of this echo was originally at 2.5 σ. This means roughly one-in-a-hundred times random fluctuations conspire to look like the observed echo. So, it’s not a great level of significance, at least not by physics standards. But it’s still 2.5σ better than nothing.

Some members of the LIGO collaboration then went and did their own analysis of the data. And they also found the echo, but at a somewhat smaller significance. There has since been some effort by several groups to extract a signal from the data with different techniques of analysis using different models for the exact type of echo signal. The signal could for example be dampened over time, or it’s frequency distribution could change. The reported false alarm rate of these findings ranges from 5% to 0.002%, the latter is a near discovery.

However, if you know anything about statistical analysis, then you know that trying out different methods of analysis and different models until you find something is not a good idea. Because if you try long enough, you will eventually find something. And in the case of black hole echoes, I suspect that most of the models that gave negative results never appeared in the literature. So the statistical significance may be misleading.

I also have to admit that as a theorist, I am not enthusiastic about black hole echoes because there are no compelling theoretical reasons to expect them. We know that quantum gravitational effects become important towards the center of the black hole. But that’s hidden deep inside the horizon and the gravitational waves we detect are not sensitive to what is going on there. That quantum gravitational effects are also relevant at the horizon is speculative and pure conjecture, and yet that’s what it takes to have black hole echoes.

But theoretical misgivings aside, we have never tested the properties of black hole horizons before, and on unexplored territory all stones should be turned. You find a summary of the current status of the search for black hole echoes in Afshordi’s most recent paper.

Travel and Book Update

My book “Lost in Math” has meanwhile also been translated to Hungarian and Polish. Previous translations have appeared in German, Spanish, Italian, and French, I believe. I have somewhat lost overview. There should have been a Chinese and Romanian translation too, I think, but I’m not sure what happened to these. In case someone spots them, please let me know. The paperback version of the US-Edition is scheduled to appear in June.

My upcoming trips are to Cambridge, UK, for a public debate on the question “How is the scientific method doing?” (on Jan 28th) and a seminar about Superdeterminism (on Jan 29). On Feb 13, I am in Oxford (again) giving a talk about Superfluid Dark Matter (again), but this time at the physics department. On Feb 24th, I am in London for the Researcher to Reader Conference 2020.

On March 9th I am giving a colloq at Brown University. On March 19th I am in Zurich for some kind of panel discussion, details of which I have either forgotten or never knew. On April 8, I am in Gelsenkirchen for a public lecture.

Our Superdeterminism workshop is scheduled for the first week of May (details to come soon). Mid of May I am in Copenhagen for a public lecture. In June I’ll be on Long Island for a conference on peer review organized by the APS.

The easiest way to keep track of my whatabouts and whereabouts is to follow me on Twitter or on Facebook.

How to test quantum gravity

Today I want to talk about a topic that most physicists get wrong: How to test quantum gravity. Most physicists believe it is just is not possible. But it is possible.


Einstein’s theory of general relativity tells us that gravity is due to the curvature of space and time. But this theory is strictly speaking wrong. It is wrong because according to general relativity, gravity does not have quantum properties. I told you all about this in my earlier videos. This lacking quantum behavior of gravity gives rise to mathematical inconsistencies that make no physical sense. To really make sense of gravity, we need a theory of quantum gravity. But we do not have such a theory yet. In this video, we will look at the experimental possibilities that we have to find the missing theory.

But before I do that, I want to tell you why so many physicists think that it is not possible to test quantum gravity.

The reason is that gravity is a very weak force and its quantum effects are even weaker. Gravity does not seem weak in everyday life. But that is because gravity, unlike all the other fundamental forces, does not neutralize. So, on long distances, it is the only remaining force and that’s why we notice it so prominently. But if you look at, for example, the gravitational force between an electron and a proton and the electromagnetic force between them, then the electromagnetic force is a factor 10^40 stronger.

One way to see what this means is to look at a fridge magnet. The magnetic force of that tiny thing is stronger than the gravitational pull of the whole planet.

Now, in most approaches to quantum gravity, the gravitational force is mediated by a particle. This particle is called the graviton, and it belongs to the gravitational force the same way that the photon belongs to the electromagnetic force. But since gravity is so much weaker than the electromagnetic force, you need ridiculously high energies to produce a measureable amount of gravitons. With the currently available technology, it would take a particle accelerator about the size of the Milky Way to reach sufficiently high energies.

And this is why most physicists think that one cannot test quantum gravity. It is testable in principle, all right, but not in practice, because one needs these ridiculously large accelerators or detectors.

However, this argument is wrong. It is wrong because one does not need to produce a quantum of a field to demonstrate that the field must be quantized. Take electromagnetism as an example. We have evidence that it must be quantized right here. Because if it was not quantized, then atoms would not be stable. Somewhat more quantitatively, the discrete energy levels of atomic spectral lines demonstrate that electromagnetism is quantized. And you do not need to detect individual photons for that.

With the quantization of gravity, it’s somewhat more difficult, but not impossible. A big advantage of gravity is that the gravitational force becomes stronger for larger systems because, recall, gravity, unlike the other forces, does not neutralize and therefore adds up. So, we can make quantum gravitational effects stronger by just taking larger masses and bringing them into quantum states, for example into a state in which the masses are in two places at once. One should then be able to tell whether the gravitational field is also in two places at once. And if one can do that, one can demonstrate that gravity has quantum behavior.

But the trouble is that quantum effects for large objects quickly fade away, or “decohere” as the physicists say. So the challenge to measuring quantum gravity comes down to producing and maintaining quantum states of heavy objects. “Heavy” here means something like a milli-gram. That doesn’t sound heavy, but it is very heavy compared to the masses of elementary particles.

The objects you need for such an experiment have to be heavy enough so that one can actually measure the gravitational field. There are a few experiments attempting to measure this. But presently the masses that one can bring into quantum states are not quite high enough. However, it is something that will reasonably become possible in the coming decades.

Another good chance to observe quantum gravitational effects is to use the universe as laboratory. Quantum gravitational effects should be strong right after the big bang and inside of black holes. Evidence from what happened in the early universe could still be around today, for example in the cosmic microwave background. Indeed, several groups are trying to find out whether the cosmic microwave background can be analyzed to show that gravity must have been quantized. But at least for now the signal is well below measurement precision.

With black holes, it’s more complicated, because the region where quantum gravity is strong is hidden behind the event horizon. But some computer simulations seem to show that stars can collapse without forming a horizon. In this case we could look right at the quantum gravitational effects. The challenge with this idea is to find out just how the observations would differ between a “normal” black hole and a singularity without horizon but with quantum gravitational effects. Again, that’s subject of current research.

And there are other options. For example, the theory of quantum gravity may violate symmetries that are respected by general relativity. Symmetry violations can show up in high-precision measurements at low energies, even if they are very small. This is something that one can look for with particle decays or particle interactions and indeed something that various experimental groups are looking for.

There are several other ways to test quantum gravity, but these are more speculative in that they look for properties that a theory of quantum gravity may not have.

For example, the way in which gravitational waves are emitted in a black hole merger is different if the black hole horizon has quantum effects. However, this may just not be the case. The same goes for ideas that space itself may have the properties of a medium give rise to dispersion, which means that light of different colors travels at different speed, or may have viscosity. Again, this is something that one can look for, and that physicists are looking for. It’s not our best shot though, because quantum gravity may not give rise to these effects.

In any case, as you can see, clearly it is possible to test quantum gravity. Indeed I think it is possible that we will see experimental evidence for quantum gravity in the next 20 years, most likely by the type of test that I talked about first, with the massive quantum objects.

Update January 2020

A quick update on some topics that I previously told you about.


Remember I explained the issue with the missing electromagnetic counterparts to gravitational wave detections? In a recent paper a group of physicists from Russia claimed they had evidence for the detection of a gamma ray event coincident with the gravitational wave detection from a binary neutron star merger. They say they found it in the data from the INTEGRAL satellite mission.

Their analysis was swiftly criticized informally by other experts in the field, but so far there is no formal correspondence about this. So the current status is that we are still missing confirmation that the LIGO and Virgo gravitational wave interferometers indeed detect signals from outer space.

So much about gravitational waves. There is also news about dark energy. Last month I told you that a new analysis of the supernova data showed they can be explained without dark energy. The supernova data, to remind you, are the major evidence that physicists have for dark energy. And if that evidence does not hold up, that’s a big deal because the discovery of dark energy was awarded a nobel prize in 2011.

However, that new analysis of the supernova data was swiftly criticized by another group. This criticism, to be honest, did not make much sense to me because they picked on the use of the coordinate system, which was basically the whole point of the original analysis. In any case, the authors of the original paper then debunked the criticism. And that is still the status today.

Quanta Magazine was happy to quote a couple of astrophysicists saying that the evidence for dark energy from supernovae is sound without giving further reasons.

Unfortunately, this is a very common thing to happen. Someone, or a group, goes and challenges a widely accepted result. Then someone else criticizes the new work. So far, so good. But after this, what frequently happens is that everybody else, scientists as well as the popular science press, will just quote the criticism as having sorted out the situation just so that they do not have to think about the problem themselves. I do not know, but I am afraid that this is what’s going on.

I was about to tell you more about this, but something better came to my mind. The lead author of the supernova paper, Subir Sakar is located in Oxford and I will be visiting Oxford next month. So, I asked if he would be in for an interview and he kindly agreed on that. So you will have him explain his work himself.

Speaking of supernovae. There was another paper just a few days ago that claimed that actually supernovae are not very good standards for standard candles, and that indeed their luminosity might just depend on the average age of the star that goes supernova.

Now, if you look at more distant supernovae, the light has had to travel for a long time to reach us, which means they are on the average younger. So, if younger stars that go bang have a different luminosity than older ones, that introduces a bias in the analysis that can mimic the effect of dark energy. Indeed, the authors of that new paper also claim that one does not need dark energy to explain the observations.

This gives me somewhat of a headache because these are two different reasons for why dark energy might not exist. Which raises the question what happens if you combine them. Maybe that makes the expansion too slow? Also, I said this before, but let me emphasize again that the supernova data are not the only evidence for dark energy. Someone’s got to do a global fit of all the available data before we can draw conclusions.

One final point for today, the well-known particle physicist Mikhail Shifman has an article on the arXiv that could best be called an opinion piece. It is titled “Musings on the current status of high energy physics”. In this article he writes “Low energy-supersymmetry is ruled out, and gone with it is the concept of naturalness, a basic principle which theorists cherished and followed for decades.” And in a footnote he adds “By the way, this principle has never been substantiated by arguments other than aesthetical.”

This is entirely correct and one of the main topics in my book “Lost in Math”. Naturalness, to remind you, was the main reason so many physicists thought that the Large Hadron Collider should see new particles besides the Higgs boson. Which has not happened. The principle of naturalness is now pretty much dead because it’s just in conflict with observation.

However, the particle physics community has still not analyzed how it could possibly be that such a large group of people for such a long time based their research on an argument that was so obviously non-scientific. Something has seriously gone wrong here and if we do not understand what, it can happen again.

The Real Butterfly Effect

If a butterfly flaps its wings in China today, it may cause a tornado in America next week. Most of you will be familiar with this “Butterfly Effect” that is frequently used to illustrate a typical behavior of chaotic systems: Even smallest disturbances can grow and have big consequences.


The name “Butterfly Effect” was popularized by James Gleick in his 1987 book “Chaos” and is usually attributed to the meteorologist Edward Lorenz. But I recently learned that this is not what Lorenz actually meant by Butterfly Effect.

I learned this from a paper by Tim Palmer, Andreas Döring, and Gregory Seregin called “The Real Butterfly Effect” and that led me to dig up Lorenz’ original paper from 1969.

Lorenz, in this paper, does not write about butterfly wings. He instead refers to a sea gull’s wings, but then attributes that to a meteorologist whose name he can’t recall. The reference to a butterfly seems to have come from a talk that Lorenz gave in 1972, which was titled “Does the Flap of a Butterfly’s Wings in Brazil set off a Tornado in Texas?”

The title of this talk was actually suggested by the session chair, a meteorologist by name Phil Merilees. In any case, it was the butterfly that stuck instead of the sea gull. And what was the butterfly talk about? It was a summary of Lorentz 1969 paper. So what’s in that paper?

In that paper, Lorenz made a much stronger claim than that a chaotic system is sensitive to the initial conditions. The usual butterfly effect says that any small inaccuracy in the knowledge that you have about the initial state of the system will eventually blow up and make a large difference. But if you did precisely know the initial state, then you could precisely predict the outcome, and if only you had good enough data you could make predictions as far ahead as you like. It’s chaos, alright, but it’s still deterministic.

Now, in the 1969 paper, Lorenz looks at a system that has an even worse behavior. He talks about weather, so the system he considers is the Earth, but that doesn’t really matter, it could be anything. He says, let us divide up the system into pieces of equal size. In each piece we put a detector that makes a measurement of some quantity. That quantity is what you need as input to make a prediction. Say, air pressure and temperature. He further assumes that these measurements are arbitrarily accurate. Clearly unrealistic, but that’s just to make a point.

How well can you make predictions using the data from your measurements? You have data on that finite grid. But that does not mean you can generally make a good prediction on the scale of that grid, because errors will creep into your prediction from scales smaller than the grid. You expect that to happen of course because that’s chaos; the non-linearity couples all the different scales together and the error on the small scales doesn’t stay on the small scales.

But you can try to combat this error by making the grid smaller and putting in more measurement devices. For example, Lorenz says, if you have a typical grid of some thousand kilometers, you can make a prediction that’s good for, say, 5 days. After these 5 days, the errors from smaller distances screw you up. So then you go and decrease your grid length by a factor of two.

Now you have many more measurements and much more data. But, and here comes the important point: Lorenz says this may only increase the time for which you can make a good prediction by half of the original time. So now you have 5 days plus 2 and a half days. Then you can go and make your grid finer again. And again you will gain half of the time. So now you have 5 days plus 2 and half plus 1 and a quarter. And so on.

Most of you will know that if you sum up this series all the way to infinity it will converge to a finite value, in this case that’s 10 days. This means that even if you have an arbitrarily fine grid and you know the initial condition precisely, you will only be able to make predictions for a finite amount of time.

And this is the real butterfly effect. That a chaotic system may be deterministic and yet still be non-predictable beyond a finite amount of time .

This of course raises the question whether there actually is any system that has such properties. There are differential equations which have such a behavior. But whether the real butterfly effect occurs for any equation that describes nature is unclear. The Navier-Stokes equation, which Lorenz was talking about may or may not suffer from the “real” butterfly effect. No one knows. This is presently one of the big unsolved problems in mathematics.

However, the Navier-Stokes equation, and really any other equation for macroscopic systems, is strictly speaking only an approximation. On the most fundamental level it’s all particle physics and, ultimately, quantum mechanics. And the equations of quantum mechanics do not have butterfly effects because they are linear. Then again, no one would use quantum mechanics to predict the weather, so that’s a rather theoretical answer.

The brief summary is that even in a deterministic system predictions may only be possible for a finite amount of time and that is what Lorenz really meant by “Butterfly Effect.”