# LHC Black Holes for the Terminally Un-Reassured

Could the LHC have killed us all?

No, no it could not.

But…

I’ve had this conversation a few times over the years. Usually, the people I’m talking to are worried about black holes. They’ve heard that the Large Hadron Collider speeds up particles to amazingly high energies before colliding them together. They worry that these colliding particles could form a black hole, which would fall into the center of the Earth and busily gobble up the whole planet.

This pretty clearly hasn’t happened. But also, physicists were pretty confident that it couldn’t happen. That isn’t to say they thought it was impossible to make a black hole with the LHC. Some physicists actually hoped to make a black hole: it would have been evidence for extra dimensions, curled-up dimensions much larger than the tiny ones required by string theory. They figured out the kind of evidence they’d see if the LHC did indeed create a black hole, and we haven’t seen that evidence. But even before running the machine, they were confident that such a black hole wouldn’t gobble up the planet. Why?

The best argument is also the most unsatisfying. The LHC speeds up particles to high energies, but not unprecedentedly high energies. High-energy particles called cosmic rays enter the atmosphere every day, some of which are at energies comparable to the LHC. The LHC just puts the high-energy particles in front of a bunch of sophisticated equipment so we can measure everything about them. If the LHC could destroy the world, cosmic rays would have already done so.

That’s a very solid argument, but it doesn’t really explain why. Also, it may not be true for future colliders: we could build a collider with enough energy that cosmic rays don’t commonly meet it. So I should give another argument.

The next argument is Hawking radiation. In Stephen Hawking’s most famous accomplishment, he argued that because of quantum mechanics black holes are not truly black. Instead, they give off a constant radiation of every type of particle mixed together, shrinking as it does so. The radiation is faintest for large black holes, but gets more and more intense the smaller the black hole is, until the smallest black holes explode into a shower of particles and disappear. This argument means that a black hole small enough that the LHC could produce it would radiate away to nothing in almost an instant: not long enough to leave the machine, let alone fall to the center of the Earth.

This is a good argument, but maybe you aren’t as sure as I am about Hawking radiation. As it turns out, we’ve never measured Hawking radiation, it’s just a theoretical expectation. Remember that the radiation gets fainter the larger the black hole is: for a black hole in space with the mass of a star, the radiation is so tiny it would be almost impossible to detect even right next to the black hole. From here, in our telescopes, we have no chance of seeing it.

So suppose tiny black holes didn’t radiate, and suppose the LHC could indeed produce them. Wouldn’t that have been dangerous?

Here, we can do a calculation. I want you to appreciate how tiny these black holes would be.

From science fiction and cartoons, you might think of a black hole as a kind of vacuum cleaner, sucking up everything nearby. That’s not how black holes work, though. The “sucking” black holes do is due to gravity, no stronger than the gravity of any other object with the same mass at the same distance. The only difference comes when you get close to the event horizon, an invisible sphere close-in around the black hole. Pass that line, and the gravity is strong enough that you will never escape.

We know how to calculate the position of the event horizon of a black hole. It’s the Schwarzchild radius, and we can write it in terms of Newton’s constant G, the mass of the black hole M, and the speed of light c, as follows:

$\frac{2GM}{c^2}$

The Large Hadron Collider’s two beams each have an energy around seven tera-electron-volts, or TeV, so there are 14 TeV of energy in total in each collision. Imagine all of that energy being converted into mass, and that mass forming a black hole. That isn’t how it would actually happen: some of the energy would create other particles, and some would give the black hole a “kick”, some momentum in one direction or another. But we’re going to imagine a “worst-case” scenario, so let’s assume all the energy goes to form the black hole. Electron-volts are a weird physicist unit, but if we divide them by the speed of light squared (as we should if we’re using $E=mc^2$ to create a mass), then Wikipedia tells us that each electron-volt will give us $1.78\times 10^{-36}$ kilograms. “Tera” is the SI prefix for $10^{12}$. Thus our tiny black hole starts with a mass of

$14\times 10^{12}\times 1.78\times 10^{-36} = 2.49\times 10^{-23} \textrm{kg}$

Plugging in Newton’s constant ($6.67\times 10^{-11}$ meters cubed per kilogram per second squared), and the speed of light ($3\times 10^8$ meters per second), and we get a radius of,

$\frac{2\times 6.67\times 10^{-11}\times 14\times 10^{12}\times 1.78\times 10^{-36}}{\left(3\times 10^8\right)^2} = 3.7\times 10^{-50} \textrm{m}$

That, by the way, is amazingly tiny. The size of an atom is about $10^{-10}$ meters. If every atom was a tiny person, and each of that person’s atoms was itself a person, and so on for five levels down, then the atoms of the smallest person would be the same size as this event horizon.

Now, we let this little tiny black hole fall. Let’s imagine it falls directly towards the center of the Earth. The only force affecting it would be gravity (if it had an electrical charge, it would quickly attract a few electrons and become neutral). That means you can think of it as if it were falling through a tiny hole, with no friction, gobbling up anything unfortunate enough to fall within its event horizon.

For our first estimate, we’ll treat the black hole as if it stays the same size through its journey. Imagine the black hole travels through the entire earth, absorbing a cylinder of matter. Using the Earth’s average density of 5515 kilograms per cubic meter, and the Earth’s maximum radius of 6378 kilometers, our cylinder adds a mass of,

$\pi \times \left(3.7\times 10^{-50}\right)^2 \times 2 \times 6378\times 10^3\times 5515 = 3\times 10^{-88} \textrm{kg}$

That’s absurdly tiny. That’s much, much, much tinier than the mass we started out with. Absorbing an entire cylinder through the Earth makes barely any difference.

You might object, though, that the black hole is gaining mass as it goes. So really we ought to use a differential equation. If the black hole travels a distance r, absorbing mass as it goes at average Earth density $\rho$, then we find,

$\frac{dM}{dr}=\pi\rho\left(\frac{2GM(r)}{c^2}\right)^2$

Solving this, we get

$M(r)=\frac{M_0}{1- M_0 \pi\rho\left(\frac{2G}{c^2}\right)^2 r }$

Where $M_0$ is the mass we start out with.

Plug in the distance through the Earth for r, and we find…still about $3\times 10^{-88} \textrm{kg}$! It didn’t change very much, which makes sense, it’s a very very small difference!

But you might still object. A black hole falling through the Earth wouldn’t just go straight through. It would pass through, then fall back in. In fact, it would oscillate, from one side to the other, like a pendulum. This is actually a common problem to give physics students: drop an object through a hole in the Earth, neglect air resistance, and what does it do? It turns out that the time the object takes to travel through the Earth is independent of its mass, and equal to roughly 84.5 minutes.

So let’s ask a question: how long would it take for a black hole, oscillating like this, to double its mass?

We want to solve,

$2=\frac{1}{1- M_0 \pi\rho\left(\frac{2G}{c^2}\right)^2 r }$

so we need the black hole to travel a total distance of

$r=\frac{1}{2M_0 \pi\rho\left(\frac{2G}{c^2}\right)^2} = 5.3\times 10^{71} \textrm{m}$

That’s a huge distance! The Earth’s radius, remember, is 6378 kilometers. So traveling that far would take

$5.3\times 10^{71} \times 84.5/60/24/365 = 8\times 10^{67} \textrm{y}$

Ten to the sixty-seven years. Our universe is only about ten to the ten years old. In another five times ten to the nine years, the Sun will enter its red giant phase, and swallow the Earth. There simply isn’t enough time for this tiny tiny black hole to gobble up the world, before everything is already gobbled up by something else. Even in the most pessimistic way to walk through the calculation, it’s just not dangerous.

I hope that, if you were worried about black holes at the LHC, you’re not worried any more. But more than that, I hope you’ve learned three lessons. First, that even the highest-energy particle physics involves tiny energies compared to day-to-day experience. Second, that gravitational effects are tiny in the context of particle physics. And third, that with Wikipedia access, you too can answer questions like this. If you’re worried, you can make an estimate, and check!

# The Problem of Quantum Gravity Is the Problem of High-Energy (Density) Quantum Gravity

I’ve said something like this before, but here’s another way to say it.

The problem of quantum gravity is one of the most famous problems in physics. You’ve probably heard someone say that quantum mechanics and general relativity are fundamentally incompatible. Most likely, this was narrated over pictures of a foaming, fluctuating grid of space-time. Based on that, you might think that all we have to do to solve this problem is to measure some quantum property of gravity. Maybe we could make a superposition of two different gravitational fields, see what happens, and solve the problem that way.

I mean, we could do that, some people are trying to. But it won’t solve the problem. That’s because the problem of quantum gravity isn’t just the problem of quantum gravity. It’s the problem of high-energy quantum gravity.

Merging quantum mechanics and general relativity is actually pretty easy. General relativity is a big conceptual leap, certainly, a theory in which gravity is really just the shape of space-time. At the same time, though, it’s also a field theory, the same general type of theory as electromagnetism. It’s a weirder field theory than electromagnetism, to be sure, one with deeper implications. But if we want to describe low energies, and weak gravitational fields, then we can treat it just like any other field theory. We know how to write down some pretty reasonable-looking equations, we know how to do some basic calculations with them. This part is just not that scary.

The scary part happens later. The theory we get from these reasonable-looking equations continues to look reasonable for a while. It gives formulas for the probability of things happening: things like gravitational waves bouncing off each other, as they travel through space. The problem comes when those waves have very high energy, and the nice reasonable probability formula now says that the probability is greater than one.

For those of you who haven’t taken a math class in a while, probabilities greater than one don’t make sense. A probability of one is a certainty, something guaranteed to happen. A probability greater than one isn’t more certain than certain, it’s just nonsense.

So we know something needs to change, we know we need a new theory. But we only know we need that theory when the energy is very high: when it’s the Planck energy. Before then, we might still have a different theory, but we might not: it’s not a “problem” yet.

Now, a few of you understand this part, but still have a misunderstanding. The Planck energy seems high for particle physics, but it isn’t high in an absolute sense: it’s about the energy in a tank of gasoline. Does that mean that all we have to do to measure quantum gravity is to make a quantum state out of your car?

Again, no. That’s because the problem of quantum gravity isn’t just the problem of high-energy quantum gravity either.

Energy seems objective, but it’s not. It’s subjective, or more specifically, relative. Due to special relativity, observers moving at different speeds observe different energies. Because of that, high energy alone can’t be the requirement: it isn’t something either general relativity or quantum field theory can “care about” by itself.

Instead, the real thing that matters is something that’s invariant under special relativity. This is hard to define in general terms, but it’s best to think of it as a requirement for not energy, but energy density.

(For the experts: I’m justifying this phrasing in part because of how you can interpret the quantity appearing in energy conditions as the energy density measured by an observer. This still isn’t the correct way to put it, but I can’t think of a better way that would be understandable to a non-technical reader. If you have one, let me know!)

Why do we need quantum gravity to fully understand black holes? Not just because they have a lot of mass, but because they have a lot of mass concentrated in a small area, a high energy density. Ditto for the Big Bang, when the whole universe had a very large energy density. Particle colliders are useful not just because they give particles high energy, but because they give particles high energy and put them close together, creating a situation with very high energy density.

Once you understand this, you can use it to think about whether some experiment or observation will help with the problem of quantum gravity. Does the experiment involve very high energy density, much higher than anything we can do in a particle collider right now? Is that telescope looking at something created in conditions of very high energy density, or just something nearby?

It’s not impossible for an experiment that doesn’t meet these conditions to find something. Whatever the correct quantum gravity theory is, it might be different from our current theories in a more dramatic way, one that’s easier to measure. But the only guarantee, the only situation where we know we need a new theory, is for very high energy density.

# Simulated Wormhole Analogies

Last week, I talked about how Google’s recent quantum simulation of a toy model wormhole was covered in the press. What I didn’t say much about, was my own opinion of the result. Was the experiment important? Was it worth doing? Did it deserve the hype?

Here on this blog, I don’t like to get into those kinds of arguments. When I talk about public understanding of science, I share the same concerns as the journalists: we all want to prevent misunderstandings, and to spread a clearer picture. I can argue that some choices hurt the public understanding and some help it, and be reasonably confident that I’m saying something meaningful, something that would resonate with their stated values.

For the bigger questions, what goals science should have and what we should praise, I have much less of a foundation. We don’t all have a clear shared standard for which science is most important. There isn’t some premise I can posit, a fundamental principle I can use to ground a logical argument.

That doesn’t mean I don’t have an opinion, though. It doesn’t even mean I can’t persuade others of it. But it means the persuasion has to be a bit more loose. For example, I can use analogies.

So let’s say I’m looking at a result like this simulated wormhole. Researchers took advanced technology (Google’s quantum computer), and used it to model a simple system. They didn’t learn anything especially new about that system (since in this case, a normal computer can simulate it better). I get the impression they didn’t learn all that much about the advanced technology: the methods used, at this point, are pretty well-known, at least to Google. I also get the impression that it wasn’t absurdly expensive: I’ve seen other people do things of a similar scale with Google’s machine, and didn’t get the impression they had to pay through the nose for the privilege. Finally, the simple system simulated happens to be “cool”: it’s a toy model studied by quantum gravity researchers, a simple version of that sci-fi standard, the traversible wormhole.

What results are like that?

Occasionally, scientists build tiny things. If the tiny things are cute enough, or cool enough, they tend to get media attention. The most recent example I can remember was a tiny snowman, three microns tall. These tiny things tend to use very advanced technology, and it’s hard to imagine the scientists learn much from making them, but it’s also hard to imagine they cost all that much to make. They’re amusing, and they absolutely get press coverage, spreading wildly over the web. I don’t think they tend to get published in Nature unless they are a bit more advanced, but I wouldn’t be too surprised if I heard of a case that did, scientific journals can be suckers for cute stories too. They don’t tend to get discussed in glowing terms linking them to historical breakthroughs.

That seems like a pretty close analogy. Taken seriously, it would suggest the wormhole simulation was probably worth doing, probably worth a press release and some media coverage, likely not worth publication in Nature, and definitely not worth being heralded as a major breakthrough.

Ok, but proponents of the experiment might argue I’m leaving something out here. This experiment isn’t just a cute simulation. It’s supposed to be a proof of principle, an early version of an experiment that will be an actually useful simulation.

As an analogy for that…did you know LIGO started taking data in 2002?

Most people first heard of the Laser Interferometer Gravitational-Wave Observatory in 2016, when they reported their first detection of gravitational waves. But that was actually “advanced LIGO”. The original LIGO ran from 2002 to 2010, and didn’t detect anything. It just wasn’t sensitive enough. Instead, it was a prototype, an early version designed to test the basic concept.

Similarly, while this wormhole situation didn’t teach anything new, future ones might. If the quantum simulation was made larger, it might be possible to simulate more complicated toy models, ones that are too complicated to simulate on a normal computer. These aren’t feasible now, but may be feasible with somewhat bigger quantum computers: still much smaller than the computers that would be needed to break encryption, or even to do simulations that are useful for chemists and materials scientists. Proponents argue that some of these quantum toy models might teach them something interesting about the mathematics of quantum gravity.

Here, though, a number of things weaken the analogy.

LIGO’s first run taught them important things about the noise they would have to deal with, things that they used to build the advanced version. The wormhole simulation didn’t show anything novel about how to use a quantum computer: the type of thing they were doing was well-understood, even if it hadn’t been used to do that yet.

Detecting gravitational waves opened up a new type of astronomy, letting us observe things we could never have observed before. For these toy models, it isn’t obvious to me that the benefit is so unique. Future versions may be difficult to classically simulate, but it wouldn’t surprise me if theorists figured out how to understand them in other ways, or gained the same insight from other toy models and moved on to new questions. They’ll have a while to figure it out, because quantum computers aren’t getting bigger all that fast. I’m very much not an expert in this type of research, so maybe I’m wrong about this…but just comparing to similar research programs, I would be surprised if the quantum simulations end up crucial here.

Finally, even if the analogy held, I don’t think it proves very much. In particular, as far as I can tell, the original LIGO didn’t get much press. At the time, I remember meeting some members of the collaboration, and they clearly didn’t have the fame the project has now. Looking through google news and the archives of the New York times, I can’t find all that much about the experiment: a few articles discussing its progress and prospects, but no grand unveiling, no big press releases.

So ultimately, I think viewing the simulation as a proof of principle makes it, if anything, less worth the hype. A prototype like that is only really valuable when it’s testing new methods, and only in so far as the thing it’s a prototype for will be revolutionary. Recently, a prototype fusion device got a lot of press for getting more energy out of a plasma than they put into it (though still much less than it takes to run the machine). People already complained about that being overhyped, and the simulated wormhole is nowhere near that level of importance.

If anything, I think the wormhole-simulators would be on a firmer footing if they thought of their work like the tiny snowmen. It’s cute, a fun side benefit of advanced technology, and as such something worth chatting about and celebrating a bit. But it’s not the start of a new era.

# The Undefinable

If I can teach one lesson to all of you, it’s this: be precise. In physics, we try to state what we mean as precisely as we can. If we can’t state something precisely, that’s a clue: maybe what we’re trying to state doesn’t actually make sense.

Someone recently reached out to me with a question about black holes. He was confused about how they were described, about what would happen when you fall in to one versus what we could see from outside. Part of his confusion boiled down to a question: “is the center really an infinitely small point?”

I remembered a commenter a while back who had something interesting to say about this. Trying to remind myself of the details, I dug up this question on Physics Stack Exchange. user4552 has a detailed, well-referenced answer, with subtleties of General Relativity that go significantly beyond what I learned in grad school.

According to user4552, the reason this question is confusing is that the usual setup of general relativity cannot answer it. In general relativity, singularities like the singularity in the middle of a black hole aren’t treated as points, or collections of points: they’re not part of space-time at all. So you can’t count their dimensions, you can’t see whether they’re “really” infinitely small points, or surfaces, or lines…

This might surprise people (like me) who have experience with simpler equations for these things, like the Schwarzchild metric. The Schwarzchild metric describes space-time around a black hole, and in the usual coordinates it sure looks like the singularity is at a single point where r=0, just like the point where r=0 is a single point in polar coordinates in flat space. The thing is, though, that’s just one sort of coordinates. You can re-write a metric in many different sorts of coordinates, and the singularity in the center of a black hole might look very different in those coordinates. In general relativity, you need to stick to things you can say independent of coordinates.

Ok, you might say, so the usual mathematics can’t answer the question. Can we use more unusual mathematics? If our definition of dimensions doesn’t tell us whether the singularity is a point, maybe we just need a new definition!

According to user4552, people have tried this…and it only sort of works. There are several different ways you could define the dimension of a singularity. They all seem reasonable in one way or another. But they give different answers! Some say they’re points, some say they’re three-dimensional. And crucially, there’s no obvious reason why one definition is “right”. The question we started with, “is the center really an infinitely small point?”, looked like a perfectly reasonable question, but it actually wasn’t: the question wasn’t precise enough.

This is the real problem. The problem isn’t that our question was undefined, after all, we can always add new definitions. The problem was that our question didn’t specify well enough the definitions we needed. That is why the question doesn’t have an answer.

Once you understand the difference, you see these kinds of questions everywhere. If you’re baffled by how mass could have come out of the Big Bang, or how black holes could radiate particles in Hawking radiation, maybe you’ve heard a physicist say that energy isn’t always conserved. Energy conservation is a consequence of symmetry, specifically, symmetry in time. If your space-time itself isn’t symmetric (the expanding universe making the past different from the future, a collapsing star making a black hole), then you shouldn’t expect energy to be conserved.

I sometimes hear people object to this. They ask, is it really true that energy isn’t conserved when space-time isn’t symmetric? Shouldn’t we just say that space-time itself contains energy?

And well yes, you can say that, if you want. It isn’t part of the usual definition, but you can make a new definition, one that gives energy to space-time. In fact, you can make more than one new definition…and like the situation with the singularity, these definitions don’t always agree! Once again, you asked a question you thought was sensible, but it wasn’t precise enough to have a definite answer.

Keep your eye out for these kinds of questions. If scientists seem to avoid answering the question you want, and keep answering a different question instead…it might be their question is the only one with a precise answer. You can define a method to answer your question, sure…but it won’t be the only way. You need to ask precise enough questions to get good answers.

# Duality and Emergence: When Is Spacetime Not Spacetime?

Spacetime is doomed! At least, so say some physicists. They don’t mean this as a warning, like some comic-book universe-destroying disaster, but rather as a research plan. These physicists believe that what we think of as space and time aren’t the full story, but that they emerge from something more fundamental, so that an ultimate theory of nature might not use space or time at all. Other, grumpier physicists are skeptical. Joined by a few philosophers, they think the “spacetime is doomed” crowd are over-excited and exaggerating the implications of their discoveries. At the heart of the argument is the distinction between two related concepts: duality and emergence.

In physics, sometimes we find that two theories are actually dual: despite seeming different, the patterns of observations they predict are the same. Some of the more popular examples are what we call holographic theories. In these situations, a theory of quantum gravity in some space-time is dual to a theory without gravity describing the edges of that space-time, sort of like how a hologram is a 2D image that looks 3D when you move it. For any question you can ask about the gravitational “bulk” space, there is a matching question on the “boundary”. No matter what you observe, neither description will fail.

If theories with gravity can be described by theories without gravity, does that mean gravity doesn’t really exist? If you’re asking that question, you’re asking whether gravity is emergent. An emergent theory is one that isn’t really fundamental, but instead a result of the interaction of more fundamental parts. For example, hydrodynamics, the theory of fluids like water, emerges from more fundamental theories that describe the motion of atoms and molecules.

(For the experts: I, like most physicists, am talking about “weak emergence” here, not “strong emergence”.)

The “spacetime is doomed” crowd think that not just gravity, but space-time itself is emergent. They expect that distances and times aren’t really fundamental, but a result of relationships that will turn out to be more fundamental, like entanglement between different parts of quantum fields. As evidence, they like to bring up dualities where the dual theories have different concepts of gravity, number of dimensions, or space-time. Using those theories, they argue that space and time might “break down”, and not be really fundamental.

The skeptics, though, bring up an important point. If two theories are really dual, then no observation can distinguish them: they make exactly the same predictions. In that case, say the skeptics, what right do you have to call one theory more fundamental than the other? You can say that gravity emerges from a boundary theory without gravity, but you could just as easily say that the boundary theory emerges from the gravity theory. The whole point of duality is that no theory is “more true” than the other: one might be more or less convenient, but both describe the same world. If you want to really argue for emergence, then your “more fundamental” theory needs to do something extra: to predict something that your emergent theory doesn’t predict.

Sometimes this is a fair objection. There are members of the “spacetime is doomed” crowd who are genuinely reckless about this, who’ll tell a journalist about emergence when they really mean duality. But many of these people are more careful, and have thought more deeply about the question. They tend to have some mix of these two perspectives:

First, if two descriptions give the same results, then do the descriptions matter? As physicists, we have a history of treating theories as the same if they make the same predictions. Space-time itself is a result of this policy: in the theory of relativity, two people might disagree on which one of two events happened first or second, but they will agree on the overall distance in space-time between the two. From this perspective, a duality between a bulk theory and a boundary theory isn’t evidence that the bulk theory emerges from the boundary, but it is evidence that both the bulk and boundary theories should be replaced by an “overall theory”, one that treats bulk and boundary as irrelevant descriptions of the same physical reality. This perspective is similar to an old philosophical theory called positivism: that statements are meaningless if they cannot be derived from something measurable. That theory wasn’t very useful for philosophers, which is probably part of why some philosophers are skeptics of “space-time is doomed”. The perspective has been quite useful to physicists, though, so we’re likely to stick with it.

Second, some will say that it’s true that a dual theory is not an emergent theory…but it can be the first step to discover one. In this perspective, dualities are suggestive evidence that a deeper theory is waiting in the wings. The idea would be that one would first discover a duality, then discover situations that break that duality: examples on one side that don’t correspond to anything sensible on the other. Maybe some patterns of quantum entanglement are dual to a picture of space-time, but some are not. (Closer to my sub-field, maybe there’s an object like the amplituhedron that doesn’t respect locality or unitarity.) If you’re lucky, maybe there are situations, or even experiments, that go from one to the other: where the space-time description works until a certain point, then stops working, and only the dual description survives. Some of the models of emergent space-time people study are genuinely of this type, where a dimension emerges in a theory that previously didn’t have one. (For those of you having a hard time imagining this, read my old post about “bubbles of nothing”, then think of one happening in reverse.)

It’s premature to say space-time is doomed, at least as a definite statement. But it is looking like, one way or another, space-time won’t be the right picture for fundamental physics. Maybe that’s because it’s equivalent to another description, redundant embellishment on an essential theoretical core. Maybe instead it breaks down, and a more fundamental theory could describe more situations. We don’t know yet. But physicists are trying to figure it out.

# A Non-Amplitudish Solution to an Amplitudish Problem

There was an interesting paper last week, claiming to solve a long-standing problem in my subfield.

I calculate what are called scattering amplitudes, formulas that tell us the chance that two particles scatter off each other. Formulas like these exist for theories like the strong nuclear force, called Yang-Mills theories, they also exist for the hypothetical graviton particles of gravity. One of the biggest insights in scattering amplitude research in the last few decades is that these two types of formulas are tied together: as we like to say, gravity is Yang-Mills squared.

A huge chunk of my subfield grew out of that insight. For one, it’s why some of us think we have something useful to say about colliding black holes. But while it’s been used in a dozen different ways, an important element was missing: the principle was never actually proven (at least, not in the way it’s been used).

Now, a group in the UK and the Czech Republic claims to have proven it.

I say “claims” not because I’m skeptical, but because without a fair bit more reading I don’t think I can judge this one. That’s because the group, and the approach they use, isn’t “amplitudish”. They aren’t doing what amplitudes researchers would do.

In the amplitudes subfield, we like to write things as much as possible in terms of measurable, “on-shell” particles. This is in contrast to the older approach that writes things instead in terms of more general quantum fields, with formulas called Lagrangians to describe theories. In part, we avoid the older Lagrangian framing to avoid redundancy: there are many different ways to write a Lagrangian for the exact same physics. We have another reason though, which might seem contradictory: we avoid Lagrangians to stay flexible. There are many ways to rewrite scattering amplitudes that make different properties manifest, and some of the strangest ones don’t seem to correspond to any Lagrangian at all.

If you’d asked me before last week, I’d say that “gravity is Yang-Mills squared” was in that category: something you couldn’t make manifest fully with just a Lagrangian, that you’d need some stranger magic to prove. If this paper is right, then that’s wrong: if you’re careful enough you can prove “gravity is Yang-Mills squared” in the old-school, Lagrangian way.

I’m curious how this is going to develop: what amplitudes people will think about it, what will happen as the experts chime in. For now, as mentioned, I’m reserving judgement, except to say “interesting if true”.

# Breakthrough Prize for Supergravity

This week, \$3 Million was awarded by the Breakthrough Prize to Sergio Ferrara, Daniel Z. Freedman and Peter van Nieuwenhuizen, the discoverers of the theory of supergravity, part of a special award separate from their yearly Fundamental Physics Prize. There’s a nice interview with Peter van Nieuwenhuizen on the Stony Brook University website, about his reaction to the award.

The Breakthrough Prize was designed to complement the Nobel Prize, rewarding deserving researchers who wouldn’t otherwise get the Nobel. The Nobel Prize is only awarded to theoretical physicists when they predict something that is later observed in an experiment. Many theorists are instead renowned for their mathematical inventions, concepts that other theorists build on and use but that do not by themselves make testable predictions. The Breakthrough Prize celebrates these theorists, and while it has also been awarded to others who the Nobel committee could not or did not recognize (various large experimental collaborations, Jocelyn Bell Burnell), this has always been the physics prize’s primary focus.

The Breakthrough Prize website describes supergravity as a theory that combines gravity with particle physics. That’s a bit misleading: while the theory does treat gravity in a “particle physics” way, unlike string theory it doesn’t solve the famous problems with combining quantum mechanics and gravity. (At least, as far as we know.)

It’s better to say that supergravity is a theory that links gravity to other parts of particle physics, via supersymmetry. Supersymmetry is a relationship between two types of particles: bosons, like photons, gravitons, or the Higgs, and fermions, like electrons or quarks. In supersymmetry, each type of boson has a fermion “partner”, and vice versa. In supergravity, gravity itself gets a partner, called the gravitino. Supersymmetry links the properties of particles and their partners together: both must have the same mass and the same charge. In a sense, it can unify different types of particles, explaining both under the same set of rules.

In the real world, we don’t see bosons and fermions with the same mass and charge. If gravitinos exist, then supersymmetry would have to be “broken”, giving them a high mass that makes them hard to find. Some hoped that the Large Hadron Collider could find these particles, but now it looks like it won’t, so there is no evidence for supergravity at the moment.

Instead, supergravity’s success has been as a tool to understand other theories of gravity. When the theory was proposed in the 1970’s, it was thought of as a rival to string theory. Instead, over the years it consistently managed to point out aspects of string theory that the string theorists themselves had missed, for example noticing that the theory needed not just strings but higher-dimensional objects called “branes”. Now, supergravity is understood as one part of a broader string theory picture.

In my corner of physics, we try to find shortcuts for complicated calculations. We benefit a lot from toy models: simpler, unrealistic theories that let us test our ideas before applying them to the real world. Supergravity is one of the best toy models we’ve got, a theory that makes gravity simple enough that we can start to make progress. Right now, colleagues of mine are developing new techniques for calculations at LIGO, the gravitational wave telescope. If they hadn’t worked with supergravity first, they would never have discovered these techniques.

The discovery of supergravity by Ferrara, Freedman, and van Nieuwenhuizen is exactly the kind of work the Breakthrough Prize was created to reward. Supergravity is a theory with deep mathematics, rich structure, and wide applicability. There is of course no guarantee that such a theory describes the real world. What is guaranteed, though, is that someone will find it useful.

# What’s in a Conjecture? An ER=EPR Example

A few weeks back, Caltech’s Institute of Quantum Information and Matter released a short film titled Quantum is Calling. It’s the second in what looks like will become a series of pieces featuring Hollywood actors popularizing ideas in physics. The first used the game of Quantum Chess to talk about superposition and entanglement. This one, featuring Zoe Saldana, is about a conjecture by Juan Maldacena and Leonard Susskind called ER=EPR. The conjecture speculates that pairs of entangled particles (as investigated by Einstein, Podolsky, and Rosen) are in some sense secretly connected by wormholes (or Einstein-Rosen bridges).

The film is fun, but I’m not sure ER=EPR is established well enough to deserve this kind of treatment.

At this point, some of you are nodding your heads for the wrong reason. You’re thinking I’m saying this because ER=EPR is a conjecture.

I’m not saying that.

The fact of the matter is, conjectures play a very important role in theoretical physics, and “conjecture” covers a wide range. Some conjectures are supported by incredibly strong evidence, just short of mathematical proof. Others are wild speculations, “wouldn’t it be convenient if…” ER=EPR is, well…somewhere in the middle.

Most popularizers don’t spend much effort distinguishing things in this middle ground. I’d like to talk a bit about the different sorts of evidence conjectures can have, using ER=EPR as an example.

Our friendly neighborhood space octopus

The first level of evidence is motivation.

At its weakest, motivation is the “wouldn’t it be convenient if…” line of reasoning. Some conjectures never get past this point. Hawking’s chronology protection conjecture, for instance, points out that physics (and to some extent logic) has a hard time dealing with time travel, and wouldn’t it be convenient if time travel was impossible?

For ER=EPR, this kind of motivation comes from the black hole firewall paradox. Without going into it in detail, arguments suggested that the event horizons of older black holes would resemble walls of fire, incinerating anything that fell in, in contrast with Einstein’s picture in which passing the horizon has no obvious effect at the time. ER=EPR provides one way to avoid this argument, making event horizons subtle and smooth once more.

Motivation isn’t just “wouldn’t it be convenient if…” though. It can also include stronger arguments: suggestive comparisons that, while they could be coincidental, when put together draw a stronger picture.

In ER=EPR, this comes from certain similarities between the type of wormhole Maldacena and Susskind were considering, and pairs of entangled particles. Both connect two different places, but both do so in an unusually limited way. The wormholes of ER=EPR are non-traversable: you cannot travel through them. Entangled particles can’t be traveled through (as you would expect), but more generally can’t be communicated through: there are theorems to prove it. This is the kind of suggestive similarity that can begin to motivate a conjecture.

(Amusingly, the plot of the film breaks this in both directions. Keanu Reeves can neither steal your cat through a wormhole, nor send you coded messages with entangled particles.)

Nor live forever as the portrait in his attic withers away

Motivation is a good reason to investigate something, but a bad reason to believe it. Luckily, conjectures can have stronger forms of evidence. Many of the strongest conjectures are correspondences, supported by a wealth of non-trivial examples.

In science, the gold standard has always been experimental evidence. There’s a reason for that: when you do an experiment, you’re taking a risk. Doing an experiment gives reality a chance to prove you wrong. In a good experiment (a non-trivial one) the result isn’t obvious from the beginning, so that success or failure tells you something new about the universe.

In theoretical physics, there are things we can’t test with experiments, either because they’re far beyond our capabilities or because the claims are mathematical. Despite this, the overall philosophy of experiments is still relevant, especially when we’re studying a correspondence.

“Correspondence” is a word we use to refer to situations where two different theories are unexpectedly computing the same thing. Often, these are very different theories, living in different dimensions with different sorts of particles. With the right “dictionary”, though, you can translate between them, doing a calculation in one theory that matches a calculation in the other one.

Even when we can’t do non-trivial experiments, then, we can still have non-trivial examples. When the result of a calculation isn’t obvious from the beginning, showing that it matches on both sides of a correspondence takes the same sort of risk as doing an experiment, and gives the same sort of evidence.

Some of the best-supported conjectures in theoretical physics have this form. AdS/CFT is technically a conjecture: a correspondence between string theory in a hyperbola-shaped space and my favorite theory, N=4 super Yang-Mills. Despite being a conjecture, the wealth of nontrivial examples is so strong that it would be extremely surprising if it turned out to be false.

ER=EPR is also a correspondence, between entangled particles on the one hand and wormholes on the other. Does it have nontrivial examples?

Some, but not enough. Originally, it was based on one core example, an entangled state that could be cleanly matched to the simplest wormhole. Now, new examples have been added, covering wormholes with electric fields and higher spins. The full “dictionary” is still unclear, with some pairs of entangled particles being harder to describe in terms of wormholes. So while this kind of evidence is being built, it isn’t as solid as our best conjectures yet.

I’m fine with people popularizing this kind of conjecture. It deserves blog posts and press articles, and it’s a fine idea to have fun with. I wouldn’t be uncomfortable with the Bohemian Gravity guy doing a piece on it, for example. But for the second installment of a star-studded series like the one Caltech is doing…it’s not really there yet, and putting it there gives people the wrong idea.

I hope I’ve given you a better idea of the different types of conjectures, from the most fuzzy to those just shy of certain. I’d like to do this kind of piece more often, though in future I’ll probably stick with topics in my sub-field (where I actually know what I’m talking about 😉 ). If there’s a particular conjecture you’re curious about, ask in the comments!

# You Go, LIGO!

Well folks, they did it. LIGO has detected gravitational waves!

FAQ:

What’s a gravitational wave?

Gravitational waves are ripples in space and time. As Einstein figured out a century ago, masses bend space and time, which causes gravity. Wiggle masses in the right way and you get a gravity wave, like a ripple on a pond.

Ok, but what is actually rippling? It’s some stuff, right? Dust or something?

In a word, no. Not everything has to be “stuff”. Energy isn’t “stuff”, and space-time isn’t either, but space-time is really what vibrates when a gravitational wave passes by. Distances themselves are changing, in a way that is described by the same math and physics as a ripple in a pond.

What’s LIGO?

LIGO is the Laser Interferometer Gravitational-Wave Observatory. In simple terms, it’s an observatory (or rather, a pair of observatories in Washington and Louisiana) that can detect gravitational waves. It does this using beams of laser light four kilometers long. Gravitational waves change the length of these beams when they pass through, causing small but measurable changes in the laser light observed.

Are there other gravitational wave observatories?

Not currently in operation. LIGO originally ran from 2002 to 2010, and during that time there were other gravitational wave observatories also in operation (VIRGO in Italy and GEO600 in Germany). All of them (including LIGO) failed to detect anything, and so LIGO and VIRGO were shut down in order for them to be upgraded to more sensitive, advanced versions. Advanced LIGO went into operation first, and made the detection. VIRGO is still under construction, as is KAGRA, a detector in Japan. There are also plans for a detector in India.

Other sorts of experiments can detect gravitational waves on different scales. eLISA is a planned space-based gravitational wave observatory, while Pulsar Timing Arrays could use distant neutron stars as an impromptu detector.

What did they detect? What could they detect?

The gravitational waves that LIGO detected came from a pair of black holes merging. In general, gravitational waves come from a pair of masses, or one mass with an uneven and rapidly changing shape. As such, LIGO and future detectors might be able to observe binary stars, supernovas, weird-shaped neutron stars, colliding galaxies…pretty much any astrophysical event involving large things moving comparatively fast.

What does this say about string theory?

Basically nothing. There are gravity waves in string theory, sure (and they play a fairly important role), but there were gravity waves in Einstein’s general relativity. As far as I’m aware, no-one at this point seriously thought that gravitational waves didn’t exist. Nothing that LIGO observed has any bearing on the quantum properties of gravity.

But what about cosmic strings? They mentioned those in the announcement!

Cosmic strings, despite the name, aren’t a unique prediction of string theory. They’re big, string-shaped wrinkles in space and time, possible results of the rapid expansion of space during cosmic inflation. You can think of them a bit like the cracks that form in an over-inflated balloon right before it bursts.

Cosmic strings, if they exist, should produce gravitational waves. This means that in the future we may have concrete evidence of whether or not they exist. This wouldn’t say all that much about string theory: while string theory does have its own explanations for cosmic strings, it’s unclear whether it actually has unique predictions about them. It would say a lot about cosmic inflation, though, and would presumably help distinguish it from proposed alternatives. So keep your eyes open: in the next few years, gravitational wave observatories may well have something important to say about the overall history of the universe.

Why is this discovery important, though? If we already knew that gravitational waves existed, why does discovering them matter?

LIGO didn’t discover that gravitational waves exist. LIGO discovered that we can detect them.

The existence of gravitational waves is no discovery. But the fact that we now have observatories sensitive enough to detect them is huge. It opens up a whole new type of astronomy: we can now observe the universe not just by the light it sheds (and neutrinos), but through a whole new lens. And every time we get another observational tool like this, we notice new things, things we couldn’t have seen without it. It’s the dawn of a new era in astronomy, and LIGO was right to announce it with all the pomp and circumstance they could muster.

My impressions from the announcement:

Speaking of pomp and circumstance, I was impressed by just how well put-together LIGO’s announcement was.

As the US presidential election heats up, I’ve seen a few articles about the various candidates’ (well, usually Trump’s) use of the language of political propaganda. The idea is that there are certain visual symbols at political events for which people have strong associations, whether with historical events or specific ideas or the like, and that using these symbols makes propaganda more powerful.

What I haven’t seen is much discussion of a language of scientific propaganda. Still, the overwhelming impression I got from LIGO’s announcement is that it was shaped by a master in the use of such a language. They tapped in to a wide variety of powerful images: from the documentary-style interviews at the beginning, to Weiss’s tweed jacket and handmade demos, to the American flag in the background, that tied LIGO’s result to the history of scientific accomplishment.

Perimeter’s presentations tend to have a slicker look, my friends at Stony Brook are probably better at avoiding jargon. But neither is quite as good at propaganda, at saying “we are part of history” and doing so without a hitch, as the folks at LIGO have shown themselves to be with this announcement.

I was also fairly impressed that they kept this under wraps for so long. While there were leaks, I don’t think many people had a complete grasp of what was going to be announced until the week before. Somehow, LIGO made sure a collaboration of thousands was able to (mostly) keep their mouths shut!

Beyond the organizational and stylistic notes, my main thought was “What’s next?” They’ve announced the detection of one event. I’ve heard others rattle off estimates, that they should be detecting anywhere from one black hole merger per year to a few hundred. Are we going to see more events soon, or should we settle into a long wait? Could they already have detected more, with the evidence buried in their data, to be revealed by careful analysis? (The waves from this black hole merger were clear enough for them to detect them in real-time, but more subtle events might not make things so easy!) Should we be seeing more events already, and does not seeing them tell us something important about the universe?

Most of the reason I delayed my post till this week was to see if anyone had an answer to these questions. So far, I haven’t seen one, besides the “one to a few hundred” estimate mentioned. As more people weigh in and more of LIGO’s run is analyzed, it will be interesting to see where that side of the story goes.

# Gravitational Waves, and Valentine’s Day Physics Poem 2016

By the time this post goes up, you’ll probably have seen Advanced LIGO’s announcement of the first direct detection of a gravitational wave. We got the news a bit early here at Perimeter, which is why we were able to host a panel discussion right after the announcement.

From what I’ve heard, this is the real deal. They’ve got a beautifully clear signal, and unlike BICEP, they kept this under wraps until they could get it looked at by non-LIGO physicists. While I think peer review gets harped on a little too much in these sorts of contexts, in this case their paper getting through peer review is a good sign that they’re really seeing something.

Pictured: a very clear, very specific something

I’ll have more to say next week: explanations of gravitational waves and LIGO for my non-expert audience, and impressions from the press release and PI’s panel discussion for those who are interested. For now, though, I’ll wait until the dust (metaphorical this time) settles. If you’re hungry for immediate coverage, I’m sure that half the blogs on my blogroll have posts up, or will in the next few days.

In the meantime, since Valentine’s Day is in two days, I’ll continue this blog’s tradition and post one of my old physics poems.

When a sophisticated string theorist seeks an interaction

He does not go round and round in loops

As a young man would.

Mature, the string theorist knows

That what happens on

(And between)

The (world) sheets,

Is universal.

That the process is the same

No matter which points

Which interactions

One chooses.

Only the shapes of things matter.

Only the topology.

For such a man there is no need.

To obsess

To devote

To choose

One point or another.

The interaction is the same.

The world, though

Is not an exercise in theory.

Is not a mere possibility.

And if a theorist would compute

An experiment

A probability

He must pick and choose

Obsess and devote

Label his interactions with zeroes and infinities

Because there is more to life

Than just the shapes of things

Than just topology.