To us normal people, cause and effect are linked together in a distinct order. The cause occurs first, and the effect follows after. But according to a new paper, that causal order breaks down if you apply quantum mechanics to gravity. Join me in my quest to wrap my head around this head-spinning (but also plausible) paper.

Physicists are stuck on trying to figure out why gravity and quantum mechanics don’t get along. For almost 100 years now, they have been looking for a theory of quantum gravity to solve the problem. But one of the most general expectations of a quantization of gravity is that space also has quantum fluctuations. And a team of researchers from Caltech now says they’ve got a tabletop experiment which could find those fluctuations. Could this solve the problem? Let’s take a look.



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Last year, Jonathan Oppenheim’s theory of post-quantum gravity was the only theory that made it into my Best of 2024 summary. Post-quantum gravity is one of the most interesting theories for merging quantum physics with gravity, which in turn is one of the most important problems in physics. Now, researchers say they’ve come up with a way to test the theory, though technology needs to advance before that test is possible. In this video I explain why I think it’s likely that post-quantum gravity will be falsified.

Heard anything of string theory lately? Well, there have been a few developments. Apparently it’s not dead, going by a recent review article. The article also lists all the things that string theorists have learned recently. And they indeed learned something. Let’s take a look.

Mathematician Stephen Wolfram has attempted to develop a theory of everything using hypergraphs, which are essentially sets of graphs that can describe space-time. Recently, another mathematician named Jonathan Gorard has used hypergraphs to describe what happens if a black hole accretes matter. He claims that evidence for hypergraphs should be observable in the energy that is emitted during the accretion. Big if true, as they say. Let’s take a look.

I was recently alerted to a video by my friend and colleague Brian Keating that claims Loop Quantum Gravity (LQG), string theory’s biggest competitor, has been disproven. I was somewhat surprised by this because I was pretty convinced it is for all practical purposes untestable -- much like string theory. I had a look at what he is talking about.


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I suspect that one of Einstein’s nightmares was that his theory of gravity would be turned into a quantum theory. I also suspect that we’re inching closer to that nightmare situation every day -- but not how Einstein might have expected. After countless attempts to develop a theory of quantum gravity, physicists are now trying their hand at measuring it through various experiments. Let’s have a look.

Physicists will soon begin an experiment at the South Pole to test if space has quantum fluctuations. Their new approach looks for decoherence in neutrinos oscillations that are sensitive to what has been dubbed "quantum foam" that could even contain tiny black holes. If successful, this experiment could uncover something that will combine Einstein’s theory of gravity and quantum physics? Let’s have a look.

For the first time in 4 decades, physicists have found a new approach to solving a problem which is almost a century old: How to combine quantum physics with gravity. I told you about this new approach, called “Postquantum Gravity” from Johnathan Oppenheim briefly before Christmas. He and his collaborators are now saying that their idea also explains dark matter and dark energy.



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Physicists at the University of Warwick in the UK are starting to build an experiment that could just save physics. They could be the first to measure the effects of quantum gravity and unlock progress in a field that has been stuck for more than 4 decades.

Every scientific discipline has its holy grail, and the holy grail of physics is definitely quantum gravity. Quantum gravity is Einstein’s unfinished revolution, the missing unification of General Relativity and Quantum Theory. String theory is the best-known contender, and this week have a strong newcomer.

[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. 

[This is a transcript of the video embedded below.]


Do we live in a hologram? String theorists think we do. But what does that mean? How do holograms work, and how are they related to string theory? That’s what we will talk about today.

In science fiction movies, holograms are 3-dimensional, moving images. But in reality, the technology for motion holograms hasn’t caught up with imagination. At least so far, holograms are still mostly stills.

The holograms you are most likely to have seen are not like those in the movies. They are not a projection of an object into thin air – however that’s supposed to work. Instead, you normally see a three-dimensional object above or behind a flat film. Small holograms are today frequently used as a security measure on credit cards, ID cards, or even banknotes, because they are easy to see, but difficult to copy.

If you hold such a hologram into light, you will see that it seems to have depth, even though it is printed on a flat surface. That’s because in photographs, we are limited to the one perspective from which the picture was taken, and that’s why they look flat. But you can tilt holograms and observe them from different angles, as if you were examining a three-dimensional object.

Now, these holograms on your credit cards, or the ones that you find on postcards or book covers, are not “real” holograms. They are actually composed of several 2-dimensional images and depending on the angle, a different image is reflected back at you, which creates the illusion of a 3-dimensional image.

In a real hologram the image is indeed 3-dimensional. But the market for real holograms is small, so they are hard to come by, even though the technology to produce them is straightforward. A real hologram looks like this.

Real holograms actually encode a three-dimensional object on a flat surface. How is this possible? The answer is interference.

Light is electromagnetic waves, so it has crests and troughs. And a key property of waves is that they can be overlaid and then amplify or wash out each other. If two waves are overlaid so that two crests meet at the same point, that will amplify the wave. This is called constructive interference. But if a crest meets a trough, the waves will cancel. This is called destructive interference.

Now, we don’t normally see light cancelling out other light. That’s because to see interference one needs very regular light, where the crests and troughs are neatly aligned. Sunlight or LED light doesn’t have that property. But laser light has it, and so laser light can be interfered.

And this interference can be used to create holograms. For this, one first splits a laser beam in two with a semi-transparent glass or crystal, called a beam-splitter, and makes each beam broader with a diverging lens. Then, one aims one half of the beam at the object that one wants to take an image of. The light will not just bounce off the object in one single direction, but it will scatter in many different directions. And the scattered light contains information about the surface of the object. Then, one recombines the two beams and captures the intensity of the light with a light-sensitive screen.

Now, remember that laser light can interfere. This means, how large the intensity on the screen is, depends on whether the interference was destructive or constructive, which again depends on just where the object was located and how it was shaped. So, the screen has captured the full three-dimensional information. To view the hologram, one develops the film and shines light onto it at the same wavelength as the image was taken, which reproduces the 3-dimensional image.

To understand this in a little more detail, let us look at the image on the screen if one uses a very small point-like object. It looks like this. It’s called a zone plate. The intensity and width of the rings depends on the distance between the point-like object and the screen, and the wavelength of the light. But any object is basically a large number of point-like objects, so the interference image on the screen is generally an overlap of many different zone plates with these concentric rings.

The amazing thing about holograms is now this. Every part of the screen receives information from every part of the object. As a consequence, if you develop the image to get the hologram, you can take it apart into pieces, and each piece will still recreate the whole 3-dimensional object. To understand better how this works, look again at the zone plate, the one of a single point-like object. If you have only a small piece that contains part of the rings, you can infer the rest of the pattern, though it gets a little more difficult. If you have a general plate that overlaps many zone plates, this is still possible. So, at least mathematically, you can reconstruct the entire object from any part of the holographic plate. In reality, the quality of the image will go down.

So, now that you know how real holograms work, let us talk about the idea that the universe is a hologram.

When string theorists claim that our universe is a hologram, they mean the following. Our universe has a positive cosmological constant. But mathematically, universes with a negative cosmological constant are much easier to work with. So, this is what string theorists usually look at. These universes with a negative cosmological constant are called Anti-de Sitter spaces and into these Anti-de Sitter things they put supersymmetric matter. To best current knowledge, our universe is not Anti De Sitter and matter is not supersymmetric, but mathematically, you can certain do that.

For some specific examples, it has then been shown that the gravitational theory in such an Anti de Sitter universe is mathematically equivalent to a different theory on the conformal boundary of that universe. What the heck is the conformal boundary of the universe? Well, our actual universe doesn’t have one. But these Anti-De Sitter spaces do. Just exactly how they are defined isn’t all that important. You only need to know that this conformal boundary has one dimension of space less than the space it is a boundary of.

So, you have an equivalence between two theories in a different number of dimensions of space. A gravitational theory in this anti-De Sitter space with the weird matter. And a different theory on the boundary of that space, which also has weird matter. And just so you have heard the name: The theory on the boundary is what’s called a conformal field theory, and the whole thing is known as the Anti-de Sitter – Conformal Field Theory duality, or AdS/CFT for short.

This duality has been mathematically confirmed for some specific cases, but pretty much all string theorists seem to believe it is much more generally valid. In fact, a lot of them seem believe it is valid even in our universe, even though there is no evidence for that, neither observational nor mathematical. In this most general form, the duality is simply called the “holographic principle”.

If the holographic principle was correct, it would mean that the information about any volume in our universe is encoded on the boundary of that volume. That’s remarkable because naively, you’d think the amount of information you can store in a volume of space grows much faster than the information you can store on the surface. But according to the holographic principle, the information you can put into the volume somehow isn’t what we think it is. It must have more correlations than we realize. So it the holographic principle was true, that would be very interesting. I talked about this in more detail in an earlier video.

The holographic principle indeed sounds a little like optical holography. In both cases one encodes information about a volume on a surface with one dimension less. But if you look a little more closely, there are two important differences between the holographic principle and real holography:

First, an optical hologram is not actually captured in two dimensions; the holographic film has a thickness, and you need that thickness to store the information. The holographic principle, on the other hand, is a mathematical abstraction, and the encoding really occurs in one dimension less.

Second, as we saw earlier, in a real hologram, each part contains information about the whole object. But in the mathematics of the holographic universe, this is not the case. If you take only a piece of the boundary, that will not allow you to reproduce what goes on in the entire universe.

This is why I don’t think referring to this idea from string theory as holography is a good analogy. But now you know just exactly what the two types of holography do, and do not have in common.

Quanta Magazine has an article by Phillip Ball titled “Wormholes Reveal a Way to Manipulate Black Hole Information in the Lab”. It’s about using quantum simulations to study the behavior of black holes in Anti De-Sitter space, that is a space with a negative cosmological constant. A quantum simulation is a collection of particles with specifically designed interactions that can mimic the behavior of another system. To briefly remind you, we do not live in Anti De-Sitter space. For all we know, the cosmological constant in our universe is positive. And no, the two cases are not remotely similar.

It’s an interesting topic in principle, but unfortunately the article by Ball is full of statements that gloss over this not very subtle fact that we do not live in Anti De-Sitter space. We can read there for example:

“In principle, researchers could construct systems entirely equivalent to wormhole-connected black holes by entangling quantum circuits in the right way and teleporting qubits between them.”

The correct statement would be:

“Researchers could construct systems whose governing equations are in certain limits equivalent to those governing black holes in a universe we do not inhabit.”

Further, needless to say, a collection of ions in the laboratory is not “entirely equivalent” to a black hole. For starters that is because the ions are made of other particles which are yet again made of other particles, none of which has any correspondence in the black hole analogy. Also, in case you’ve forgotten, we do not live in Anti De-Sitter space.

Why do physicists even study black holes in Anti-De Sitter space? To make a long story short: Because they can. They can, both because they have an idea how the math works and because they can get paid for it.

Now, there is nothing wrong with using methods obtained by the AdS/CFT correspondence to calculate the behavior of many particle systems. Indeed, I think that’s a neat idea. However, it is patently false to raise the impression that this tells us anything about quantum gravity, where by “quantum gravity” I mean the theory that resolves the inconsistency between the Standard Model of particle physics and General Relativity in our universe. Ie, a theory that actually describes nature. We have no reason whatsoever to think that the AdS/CFT correspondence tells us something about quantum gravity in our universe.

As I explained in this earlier post, it is highly implausible that the results from AdS carry over to flat space or to space with a positive cosmological constant because the limit is not continuous. You can of course simply take the limit ignoring its convergence properties, but then the theory you get has no obvious relation to General Relativity.

Let us have a look at the paper behind the article. We can read there in the introduction:

“In the quest to understand the quantum nature of spacetime and gravity, a key difficulty is the lack of contact with experiment. Since gravity is so weak, directly probing quantum gravity means going to experimentally infeasible energy scales.”

This is wrong and it demonstrates that the authors are not familiar with the phenomenology of quantum gravity. Large deviations from the semi-classical limit can occur at small energy scales. The reason is, rather trivially, that large masses in quantum superpositions should have gravitational fields in quantum superpositions. No large energies necessary for that.

If you could, for example, put a billiard ball into a superposition of location you should be able to measure what happens to its gravitational field. This is unfeasible, but not because it involves high energies. It’s infeasible because decoherence kicks in too quickly to measure anything.

Here is the rest of the first paragraph of the paper. I have in bold face added corrections that any reviewer should have insisted on:

“However, a consequence of the holographic principle [3, 4] and its concrete realization in the AdS/CFT correspondence [5–7] (see also [8]) is that non-gravitational systems with sufficient entanglement may exhibit phenomena characteristic of quantum gravity in a space with a negative cosmological constant. This suggests that we may be able to use table-top physics experiments to indirectly probe quantum gravity in universes that we do not inhabit. Indeed, the technology for the control of complex quantum many-body systems is advancing rapidly, and we appear to be at the dawn of a new era in physics—the study of quantum gravity in the lab, except that, by the methods described in this paper, we cannot actually test quantum gravity in our universe. For this, other experiments are needed, which we will however not even mention.

The purpose of this paper is to discuss one way in which quantum gravity can make contact with experiment, if you, like us, insist on studying quantum gravity in fictional universes that for all we know do not exist.”

I pointed out that these black holes that string theorists deal with have nothing to do with real black holes in an article I wrote for Quanta Magazine last year. It was also the last article I wrote for them.

[Tim Palmer is a Royal Society Research Professor in Climate Physics at the University of Oxford, UK. He is only half as crazy as it seems.]

[Screenshot from Tim’s public lecture at Perimeter Institute]

Our three great theories of 20th Century physics – general relativity theory, quantum theory and chaos theory – seem incompatible with each other.

The difficulty combining general relativity and quantum theory to a common theory of “quantum gravity” is legendary; some of our greatest minds have despaired – and still despair – over it.

Superficially, the links between quantum theory and chaos appear to be a little stronger, since both are characterised by unpredictability (in measurement and prediction outcomes respectively). However, the Schrödinger equation is linear and the dynamical equations of chaos are nonlinear. Moreover, in the common interpretation of Bell’s inequality, a chaotic model of quantum physics, since it is deterministic, would be incompatible with Einstein’s notion of relativistic causality.

Finally, although the dynamics of general relativity and chaos theory are both nonlinear and deterministic, it is difficult to even make sense of chaos in the space-time of general relativity. This is because the usual definition of chaos is based on the notion that nearby initial states can diverge exponentially in time. However, speaking of an exponential divergence in time depends on a choice of time-coordinate. If we logarithmically rescale the time coordinate, the defining feature of chaos disappears. Trouble is, in general relativity, the underlying physics must not depend on the space-time coordinates.

So, do we simply have to accept that, “What God hath put asunder, let no man join together”? I don’t think so. A few weeks ago, the Foundational Questions Institute put out a call for essays on the topic of “Undecidability, Uncomputability and Unpredictability”. I have submitted an essay in which I argue that undecidability and uncomputability may provide a new framework for unifying these theories of 20th Century physics. I want to summarize my argument in this and a follow-on guest post.

To start, I need to say what undecidability and uncomputability are in the first place. The concepts go back to the work of Alan Turing who in 1936 showed that no algorithm exists that will take as input a computer program (and its input data), and output 0 if the program halts and 1 if the program does not halt. This “Halting Problem” is therefore undecidable by algorithm. So, a key way to know whether a problem is algorithmically undecidable – or equivalently uncomputable – is to see if the problem is equivalent to the Halting Problem.

Let’s return to thinking about chaotic systems. As mentioned, these are deterministic systems whose evolution is effectively unpredictable (because the evolution is sensitive to the starting conditions). However, what is relevant here is not so much this property of unpredictability, but the fact that no matter what initial condition you start from, there is a class of chaotic system where eventually (technically after an infinite time) the state evolves on a fractal subset of state space, sometimes known as a fractal attractor.

One defining characteristic of a fractal is that its dimension is not a simple integer (like that of a one-dimensional line or the two-dimensional surface of a sphere). Now, the key result I need is a theorem that there is no algorithm that will take as input some point x in state space, and halt if that point belongs to a set with fractional dimension. This implies that the fractal attractor A of a chaotic system is uncomputable and the proposition “x belongs to A” is algorithmically undecidable.

How does this help unify physics?

Firstly defining chaos in terms of the geometry of its fractal attractor (e.g. through the fractional dimension of the attractor) is a coordinate independent and hence more relativistic way to characterise chaos, than defining it in terms of exponential divergence of nearby trajectories. Hence the uncomputable fractal attractor provides a way to unify general relativity and chaos theory.

That was easy! The rest is not so easy which is why I need two guest posts and not one!

When it comes to combining chaos theory with quantum mechanics, the first step is to realize that the linearity of the Schrödinger equation is not at all incompatible with the nonlinearity of chaos.

To understand this, consider an ensemble of integrations of a particular chaotic model based on the Lorenz equations – see Fig 1. These Lorenz equations describe fluid dynamical motion, but the details need not concern us here. The fractal Lorenz attractor is shown in the background in Fig 1. These ensembles can be thought of as describing the evolution of probability – something of practical value when we don’t know the initial conditions precisely (as is the case in weather forecasting).

Fig 1: Evolution of a contour of probability, based on ensembles of integrations of the Lorenz equations, is shown evolving in state space for different initial conditions, with the Lorenz attractor as background.

In the first panel in Fig 1, small uncertainties do not grow much and we can therefore be confident in the predicted evolution. In the third panel, small uncertainties grow explosively, meaning we can have little confidence in any specific prediction. The second panel is somewhere in between.

Now it turns out that the equation which describes the evolution of probability in such chaotic systems, known as the Liouville equation, is itself a linear equation. The linearity of the Liouville equation ensures that probabilities are conserved in time. Hence, for example, if there is an 80% chance that the actual state of the fluid (as described by the Lorenz equation state) lies within a certain contour of probability at initial time, then there is an 80% chance that the actual state of the fluid lies within the evolved contour of probability at the forecast time.

The remarkable thing is that the Liouville equation is formally very similar to the so-called von-Neumann form of the Schrödinger equation – too much, in my view, for this to be a coincidence. So, just as the linearity of the Liouville equation says nothing about the nonlinearity of the underlying deterministic dynamics which generate such probability, so too the linearity of the Schrödinger equation need say nothing about the nonlinearity of some underlying dynamics which generates quantum probabilities.

However, as I wrote above, in order to satisfy Bell’s theorem, it would appear that, being deterministic, a chaotic model will have to violate relativistic causality, seemingly thwarting the aim of trying to unify our theories of physics. At least, that’s the usual conclusion. However, the undecidable uncomputable properties of fractal attractors provide a novel route to allow us to reassess this conclusion. I will explain how this works in the second part of this post.

Molecules are made of atoms. Atomic nuclei are made of neutrons and protons. And the neutrons and protons are made of quarks and gluons. Many physicists think that this is not the end of the story, but that quarks and gluons are made of even smaller things, for example the tiny vibrating strings that string theory is all about. But then what? Are strings made of smaller things again? Or is there a smallest scale beyond which nature just does not have any further structure? Does nature have a minimal length?

This is what we will talk about today.



When physicists talk about a minimal length, they usually mean the Planck length, which is about 10^-35 meters. The Planck length is named after Max Planck, who introduced it in 1899. 10^-35 meters sounds tiny and indeed it is damned tiny.

To give you an idea, think of the tunnel of the Large Hadron Collider. It’s a ring with a diameter of about 10 kilometers. The Planck length compares to the diameter of a proton as the radius of a proton to the diameter of the Large Hadron Collider.

Currently, the smallest structures that we can study are about ten to the minus nineteen meters. That’s what we can do with the energies produced at the Large Hadron Collider and that is still sixteen orders of magnitude larger than the Planck length.

What’s so special about the Planck length? The Planck length seems to be setting a limit to how small a structure can be so that we can still measure it. That’s because to measure small structures, we need to compress more energy into small volumes of space. That’s basically what we do with particle accelerators. Higher energy allows us to find out what happens on shorter distances. But if you stuff too much energy into a small volume, you will make a black hole.

More concretely, if you have an energy E, that will in the best case allow you to resolve a distance of about ℏc/E. I will call that distance Δx. Here, c is the speed of light and ℏ is a constant of nature, called Planck’s constant. Yes, that’s the same Planck! This relation comes from the uncertainty principle of quantum mechanics. So, higher energies let you resolve smaller structures.

Now you can ask, if I turn up the energy and the size I can resolve gets smaller, when do I get a black hole? Well that happens, if the Schwarzschild radius associated with the energy is similar to the distance you are trying to measure. That’s not difficult to calculate. So let’s do it.

The Schwarzschild radius is approximately M times G/c² where G is Newton’s constant and M is the mass. We are asking, when is that radius similar to the distance Δx. As you almost certainly know, the mass associated with the energy is E=Mc². And, as we previously saw, that energy is just ℏc/Δx. You can then solve this equation for Δx. And this is what we call the Planck length. It is associated with an energy called the Planck energy. If you go to higher energies than that, you will just make larger black holes. So the Planck length is the shortest distance you can measure.

Now, this is a neat estimate and it’s not entirely wrong, but it’s not a rigorous derivation. If you start thinking about it, it’s a little handwavy, so let me assure you there are much more rigorous ways to do this calculation, and the conclusion remains basically the same. If you combine quantum mechanics with gravity, then the Planck length seems to set a limit to the resolution of structures. That’s why physicists think nature may have a fundamentally minimal length.

Max Planck by the way did not come up with the Planck length because he thought it was a minimal length. He came up with that simply because it’s the only unit of dimension length you can create from the fundamental constants, c, the speed of light, G, Newton’s constant, and ℏ. He thought that was interesting because, as he wrote in his 1899 paper, these would be natural units that also aliens would use.

The idea that the Planck length is a minimal length only came up after the development of general relativity when physicists started thinking about how to quantize gravity. Today, this idea is supported by attempts to develop a theory of quantum gravity, which I told you about in an earlier video.

In string theory, for example, if you squeeze too much energy into a string it will start spreading out. In Loop Quantum Gravity, the loops themselves have a finite size, given by the Planck length. In Asymptotically Safe Gravity, the gravitational force becomes weaker at high energies, so beyond a certain point you can no longer improve your resolution.

When I speak about a minimal length, a lot of people seem to have a particular image in mind, which is that the minimal length works like a kind of discretization, a pixilation of an photo or something like that. But that is most definitely the wrong image. The minimal length that we are talking about here is more like an unavoidable blur on an image, some kind of fundamental fuzziness that nature has. It may, but does not necessarily come with a discretization.

What does this all mean? Well, it means that we might be close to finding a final theory, one that describes nature at its most fundamental level and there is nothing more beyond that. That is possible, but. Remember that the arguments for the existence of a minimal length rest on extrapolating 16 orders magnitude below the distances what we have tested so far. That’s a lot. That extrapolation might just be wrong. Even though we do not currently have any reason to think that there should be something new on distances even shorter than the Planck length, that situation might change in the future.

Still, I find it intriguing that for all we currently know, it is not necessary to think about distances shorter than the Planck length.

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.

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.

For more than 2000 years, ever since Democritus’ first musings about atoms, reductionism has driven scientific inquiry. The idea is simple enough: Things are made of smaller things, and if you know what the small things do, you learn what the large things do. Simple – and stunningly successful.

After 2000 years of taking things apart into smaller things, we have learned that all matter is made of molecules, and that molecules are made of atoms. Democritus originally coined the word “atom” to refer to indivisible, elementary units of matter. But what we have come to call “atoms”, we now know, is made of even smaller particles. And those smaller particles are yet again made of even smaller particles.

© Sabine Hossenfelder

The smallest constituents of matter, for all we currently know, are the 25 particles which physicists collect in the standard model of particle physics. Are these particles made up of yet another set of smaller particles, strings, or other things?

It is certainly possible that the particles of the standard model are not the ultimate constituents of matter. But we presently have no particular reason to think they have a substructure. And this raises the question whether attempting to look even closer into the structure of matter is a promising research direction – right here, right now.

It is a question that every researcher in the foundations of physics will be asking themselves, now that the Large Hadron Collider has confirmed the standard model, but found nothing beyond that.

20 years ago, it seemed clear to me that probing physical processes at ever shorter distances is the most reliable way to better understand how the universe works. And since it takes high energies to resolve short distances, this means that slamming particles together at high energies is the route forward. In other words, if you want to know more, you build bigger particle colliders.

This is also, unsurprisingly, what most particle physicists are convinced of. Going to higher energies, so their story goes, is the most reliable way to search for something fundamentally new. This is, in a nutshell, particle physicists’ major argument in favor of building a new particle collider, one even larger than the presently operating Large Hadron Collider.

But this simple story is too simple.

The idea that reductionism means things are made of smaller things is what philosophers more specifically call “methodological reductionism”. It’s a statement about the properties of stuff. But there is another type of reductionism, “theory reductionism”, which instead refers to the relation between theories. One theory can be “reduced” to another one, if the former can be derived from the latter.

Now, the examples of reductionism that particle physicists like to put forward are the cases where both types of reductionism coincide: Atomic physics explains chemistry. Statistical mechanics explains the laws of thermodynamics. The quark model explains regularities in proton collisions. And so on.

But not all cases of successful theory reduction have also been cases of methodological reduction. Take Maxwell’s unification of the electric and magnetic force. From Maxwell’s theory you can derive a whole bunch of equations, such as the Coulomb law and Faraday’s law, that people used before Maxwell explained where they come from. Electromagnetism, is therefore clearly a case of theory reduction, but it did not come with a methodological reduction.

Another well-known exception is Einstein’s theory of General Relativity. General Relativity can be used in more situations than Newton’s theory of gravity. But it is not the physics on short distances that reveals the differences between the two theories. Instead, it is the behavior of bodies at high relative speed and strong gravitational fields that Newtonian gravity cannot cope with.

Another example that belongs on this list is quantum mechanics. Quantum mechanics reproduces classical mechanics in suitable approximations. It is not, however, a theory about small constituents of larger things. Yes, quantum mechanics is often portrayed as a theory for microscopic scales, but, no, this is not correct. Quantum mechanics is really a theory for all scales, large to small. We have observed quantum effects over distances exceeding 100km and for objects weighting as “much” as a nanogram, composed of more than 10¹³ atoms. It’s just that quantum effects on large scales are difficult to create and observe.

Finally, I would like to mention Noether’s theorem, according to which symmetries give rise to conservation laws. This example is different from the previous ones in that Noether’s theorem was not applied to any theory in particular. But it has resulted in a more fundamental understanding of natural law, and therefore I think it deserve a place on the list.

In summary, history does not support particle physicists’ belief that a deeper understanding of natural law will most likely come from studying shorter distances. On the very contrary, I have begun to worry that physicists’ confidence in methodological reductionism stands in the way of progress. That’s because it suggests we ask certain questions instead of others. And those may just be the wrong questions to ask.

If you believe in methodological reductionism, for example, you may ask what dark energy is made of. But maybe dark energy is not made of anything. Instead, dark energy may be an artifact of our difficulty averaging non-linear equations.

It’s similar with dark matter. The methodological reductionist will ask for a microscopic theory and look for a particle that dark matter is made of. Yet, maybe dark matter is really a phenomenon associated with our misunderstanding of space-time on long distances.

The maybe biggest problem that methodological reductionism causes lies in the area of quantum gravity, that is our attempt to resolve the inconsistency between quantum theory and general relativity. Pretty much all existing approaches – string theory, loop quantum gravity, causal dynamical triangulation (check out my video for more) – assume that methodological reductionism is the answer. Therefore, they rely on new hypotheses for short-distance physics. But maybe that’s the wrong way to tackle the problem. The root of our problem may instead be that quantum theory itself must be replaced by a more fundamental theory, one that explains how quantization works in the first place.

Approaches based on methodological reductionism – like grand unified forces, supersymmetry, string theory, preon models, or technicolor – have failed for the past 30 years. This does not mean that there is nothing more to find at short distances. But it does strongly suggest that the next step forward will be a case of theory reduction that does not rely on taking things apart into smaller things.

Today, I want to tell you what ideas physicists have come up with to quantize gravity. But before I get to that, I want to tell you why it matters.



That we do not have a theory of quantum gravity is currently one of the biggest unsolved problems in the foundations of physics. A lot of people, including many of my colleagues, seem to think that a theory of quantum gravity will remain an academic curiosity without practical relevance.

I think they are wrong. That’s because whatever solves this problem will tell us something about quantum theory, and that’s the theory on which all modern electronic devices run, like the ones on which you are watching this video. Maybe it will take 100 years for quantum gravity to find a practical application, or maybe it will even take a 1000 years. But I am sure that understanding nature better will not forever remain a merely academic speculation.

Before I go on, I want to be clear that quantizing gravity by itself is not the problem. We can, and have, quantized gravity the same way that we quantize the other interactions. The problem is that the theory which one gets this way breaks down at high energies, and therefore it cannot be how nature works, fundamentally.

This naïve quantization is called “perturbatively quantized gravity” and it was worked out in the 1960s by Feynman and DeWitt and some others. Perturbatively quantized gravity is today widely believed to be an approximation to whatever is the correct theory.

So really the problem is not just to quantize gravity per se, you want to quantize it and get a theory that does not break down at high energies. Because energies are proportional to frequencies, physicists like to refer to high energies as “the ultraviolet” or just “the UV”. Therefore, the theory of quantum gravity that we look for is said to be “UV complete”.

Now, let me go through the five most popular approaches to quantum gravity.

1. String Theory

The most widely known and still the most popular attempt to get a UV-complete theory of quantum gravity is string theory. The idea of string theory is that instead of talking about particles and quantizing them, you take strings and quantize those. Amazingly enough, this automatically has the consequence that the strings exchange a force which has the same properties as the gravitational force.

This was discovered in the 1970s and at the time, it got physicists very excited. However, in the past decades several problems have appeared in string theory that were patched, which has made the theory increasingly contrived. You can hear all about this in my earlier video. It has never been proved that string theory is indeed UV-complete.

2. Loop Quantum Gravity

Loop Quantum Gravity is often named as the biggest competitor of string theory, but this comparison is somewhat misleading. String theory is not just a theory for quantum gravity, it is also supposed to unify the other interactions. Loop Quantum Gravity on the other hand, is only about quantizing gravity.

It works by discretizing space in terms of a network, and then using integrals around small loops to describe the space, hence the name. In this network, the nodes represent volumes and the links between nodes the areas of the surfaces where the volumes meet.

Loop Quantum Gravity is about as old as string theory. It solves the problem of combining general relativity and quantum mechanics to one consistent theory but it has remained unclear just exactly how one recovers general relativity in this approach.

3. Asymptotically Safe Gravity

Asymptotic Safety is an idea that goes back to a 1976 paper by Steven Weinberg. It says that a theory which seems to have problems at high energies when quantized naively, may not have a problem after all, it’s just that it’s more complicated to find out what happens at high energies than it seems. Asymptotically Safe Gravity applies the idea of asymptotic safety to gravity in particular.

This approach also solves the problem of quantum gravity. Its major problem is currently that it has not been proved that the theory which one gets this way at high energies still makes sense as a quantum theory.

4. Causal Dynamical Triangulation

The problem with quantizing gravity comes from infinities that appear when particles interact at very short distances. This is why most approaches to quantum gravity rely on removing the short distances by using objects of finite extensions. Loop Quantum Gravity works this way, and so does String Theory.

Causal Dynamical Triangulation also relies on removing short distances. It does so by approximating a curved space with triangles, or their higher-dimensional counterparts respectively. In contrast to the other approaches though, where the finite extension is a postulated, new property of the underlying true nature of space, in Causal Dynamical Triangulation, the finite size of the triangles is a mathematical aid, and one eventually takes the limit where this size goes to zero.

The major reason why many people have remained unconvinced of Causal Dynamical Triangulation is that it treats space and time differently, which Einstein taught us not to do.

5. Emergent Gravity

Emergent gravity is not one specific theory, but a class of approaches. These approaches have in common that gravity derives from the collective behavior of a large number of constituents, much like the laws of thermodynamics do. And much like for thermodynamics, in emergent gravity, one does not actually need to know all that much about the exact properties of these constituents to get the dynamical law.

If you think that gravity is really emergent, then quantizing gravity does not make sense. Because, if you think of the analogy to thermodynamics, you also do not obtain a theory for the structure of atom by quantizing the equations for gases. Therefore, in emergent gravity one does not quantize gravity. One instead removes the inconsistency between gravity and quantum mechanics by saying that quantizing gravity is not the right thing to do.

Which one of these theories is the right one? No one knows. The problem is that it’s really, really hard to find experimental evidence for quantum gravity. But that it’s hard doesn’t mean impossible. I will tell you some other time how we might be able to experimentally test quantum gravity after all. So, stay tuned.