Tag Archives: theoretical physics

At Geometries and Special Functions for Physics and Mathematics in Bonn

On Stubbornness and Breaking Down

In physics, we sometimes say that an idea “breaks down”. What do we mean by that?

When a theory “breaks down”, we mean that it stops being accurate. Newton’s theory of gravity is excellent most of the time, but for objects under strong enough gravity or high enough speed its predictions stop matching reality and a new theory (relativity) is needed. This is the sense in which we say that Newtonian gravity breaks down for the orbit of mercury, or breaks down much more severely in the area around a black hole.

When a symmetry is “broken”, we mean that it stops holding true. Most of physics looks the same when you flip it in a mirror, a property called parity symmetry. Take a pile of electric and magnetic fields, currents and wires, and you’ll find their mirror reflection is also a perfectly reasonable pile of electric and magnetic fields, currents and wires. This isn’t true for all of physics, though: the weak nuclear force isn’t the same when you flip it in a mirror. We say that the weak force breaks parity symmetry.

What about when a more general “idea” breaks down? What about space-time?

In order for space-time to break down, there needs to be a good reason to abandon the idea. And depending on how stubborn you are about it, that reason can come at different times.

You might think of space-time as just Einstein’s theory of general relativity. In that case, you could say that space-time breaks down as soon as the world deviates from that theory. In that view, any modification to general relativity, no matter how small, corresponds to space-time breaking down. You can think of this as the “least stubborn” option, the one with barely any stubbornness at all, that will let space-time break down with a tiny nudge.

But if general relativity breaks down, a slightly more stubborn person could insist that space-time is still fine. You can still describe things as located at specific places and times, moving across curved space-time. They just obey extra forces, on top of those built into the space-time.

Such a person would be happy as long as general relativity was a good approximation of what was going on, but they might admit space-time has broken down when general relativity becomes a bad approximation. If there are only small corrections on top of the usual space-time picture, then space-time would be fine, but if those corrections got so big that they overwhelmed the original predictions of general relativity then that’s quite a different situation. In that situation, space-time may have stopped being a useful description, and it may be much better to describe the world in another way.

But we could imagine an even more stubborn person who still insists that space-time is fine. Ultimately, our predictions about the world are mathematical formulas. No matter how complicated they are, we can always subtract a piece off of those formulas corresponding to the predictions of general relativity, and call the rest an extra effect. That may be a totally useless thing to do that doesn’t help you calculate anything, but someone could still do it, and thus insist that space-time still hasn’t broken down.

To convince such a person, space-time would need to break down in a way that made some important concept behind it invalid. There are various ways this could happen, corresponding to different concepts. For example, one unusual proposal is that space-time is non-commutative. If that were true then, in addition to the usual Heisenberg uncertainty principle between position and momentum, there would be an uncertainty principle between different directions in space-time. That would mean that you can’t define the position of something in all directions at once, which many people would agree is an important part of having a space-time!

Ultimately, physics is concerned with practicality. We want our concepts not just to be definable, but to do useful work in helping us understand the world. Our stubbornness should depend on whether a concept, like space-time, is still useful. If it is, we keep it. But if the situation changes, and another concept is more useful, then we can confidently say that space-time has broken down.

All About the Collab

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Sometimes, some scientists work alone. But mostly, scientists collaborate. We team up, getting more done together than we could alone.

Over the years, I’ve realized that theoretical physicists like me collaborate in a bit of a weird way, compared to other scientists. Most scientists do experiments, and those experiments require labs. Each lab typically has one principal investigator, or “PI”, who hires most of the other people in that lab. For any given project, scientists from the lab will be organized into particular roles. Some will be involved in the planning, some not. Some will do particular tests, gather data, manage lab animals, or do statistics. The whole experiment is at least roughly planned out from the beginning, and everyone has their own responsibility, to the extent that journals will sometimes ask scientists to list everyone’s roles when they publish papers. In this system, it’s rare for scientists from two different labs to collaborate. Usually it happens for a reason: a lab needs a statistician for a particularly subtle calculation, or one lab must process a sample so another lab can analyze it.

In contrast, theoretical physicists don’t have labs. Our collaborators sometimes come from the same university, but often they’re from a different one, frequently even in a different country. The way we collaborate is less like other scientists, and more like artists.

Sometimes, theoretical physicists have collaborations with dedicated roles and a detailed plan. This can happen when there is a specific calculation that needs to be done, that really needs to be done right. Some of the calculations that go into making predictions at the LHC are done in this way. I haven’t been in a collaboration like that (though in retrospect one collaborator may have had something like that in mind).

Instead, most of the collaborations I’ve been in have been more informal. They tend to start with a conversation. We chat by the coffee machine, or after a talk, anywhere there’s a blackboard nearby. It starts with “I’ve noticed something odd”, or “here’s something I don’t understand”. Then, we jam. We go back and forth, doing our thing and building on each other. Sometimes this happens in person, a barrage of questions and doubts until we hammer out something solid. Sometimes we go back to our offices, to calculate and look up references. Coming back the next day, we compare results: what did you manage to show? Did you get what I did? If not, why?

I make this sound spontaneous, but it isn’t completely. That starting conversation can be totally unplanned, but usually one of the scientists involved is trying to make it happen. There’s a different way you talk when you’re trying to start a collaboration, compared to when you just want to talk. If you’re looking for a collaboration, you go into more detail. If the other person is on the same wavelength, you start using “we” instead of “I”, or you start suggesting plans of action: “you could do X, while I do Y”. If you just want someone’s opinion, or just want to show off, then your conversation is less detailed, and less personal.

This is easiest to do with our co-workers, but we do it with people from other universities too. Sometimes this happens at conferences, more often during short visits for seminars. I’ve been on almost every end of this. As a visitor, I’ve arrived to find my hosts with a project in mind. As a host, I’ve invited a visitor with the goal of getting them involved in a collaboration, and I’ve received a visitor who came with their own collaboration idea.

After an initial flurry of work, we’ll have a rough idea of whether the project is viable. If it is, things get a bit more organized, and we sort out what needs to be done and a rough idea of who will do it. While the early stages really benefit from being done in person, this part is easier to do remotely. The calculations get longer but the concepts are clear, so each of us can work by ourselves, emailing when we make progress. If we get confused again, we can always schedule a Zoom to sort things out.

Once things are close (but often not quite done), it’s time to start writing the paper. In the past, I used Dropbox for this: my collaborators shared a folder with a draft, and we’d pass “control” back and forth as we wrote and edited. Now, I’m more likely to use something built for this purpose. Git is a tool used by programmers to collaborate on code. It lets you roll back edits you don’t like, and merge edits from two people to make sure they’re consistent. For other collaborations I use Overleaf, an online interface for the document-writing language LaTeX that lets multiple people edit in real-time. Either way, this part is also more or less organized, with a lot of “can you write this section?” that can shift around depending on how busy people end up being.

Finally, everything comes together. The edits stabilize, everyone agrees that the paper is good (or at least, that any dissatisfaction they have is too minor to be worth arguing over). We send it to a few trusted friends, then a few days later up on the arXiv it goes.

Then, the cycle begins again. If the ideas are still clear enough, the same collaboration might keep going, planning follow-up work and follow-up papers. We meet new people, or meet up with old ones, and establish new collaborations as we go. Our fortunes ebb and flow based on the conversations we have, the merits of our ideas and the strengths of our jams. Sometimes there’s more, sometimes less, but it keeps bubbling up if you let it.

Cabinet of Curiosities: The Train-Ladder

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I’ve got a new paper out this week, with Andrew McLeod, Roger Morales, Matthias Wilhelm, and Chi Zhang. It’s yet another entry in this year’s “cabinet of curiosities”, quirky Feynman diagrams with interesting traits.

A while back, I talked about a set of Feynman diagrams I could compute with any number of “loops”, bypassing the approximations we usually need to use in particle physics. That wasn’t the first time someone did that. Back in the 90’s, some folks figured out how to do this for so-called “ladder” diagrams. These diagrams have two legs on one end for two particles coming in, two legs on the other end for two particles going out, and a ladder in between, like so:

There are infinitely many of these diagrams, but they’re all beautifully simple, variations on a theme that can be written down in a precise mathematical way.

Change things a little bit, though, and the situation gets wildly more intractable. Let the rungs of the ladder peek through the sides, and you get something looking more like the tracks for a train:

These traintrack integrals are much more complicated. Describing them requires the mathematics of Calabi-Yau manifolds, involving higher and higher dimensions as the tracks get longer. I don’t think there’s any hope of understanding these things for all loops, at least not any time soon.

What if we aimed somewhere in between? A ladder that just started to turn traintrack?

Add just a single pair of rungs, and it turns out that things remain relatively simple. If we do this, it turns out we don’t need any complicated Calabi-Yau manifolds. We just need the simplest Calabi-Yau manifold, called an elliptic curve. It’s actually the same curve for every version of the diagram. And the situation is simple enough that, with some extra cleverness, it looks like we’ve found a trick to calculate these diagrams to any number of loops we’d like.

(Another group figured out the curve, but not the calculation trick. They’ve solved different problems, though, studying all sorts of different traintrack diagrams. They sorted out some confusion I used to have about one of those diagrams, showing it actually behaves precisely the way we expected it to. All in all, it’s been a fun example of the way different scientists sometimes hone in on the same discovery.)

These developments are exciting, because Feynman diagrams with elliptic curves are still tough to deal with. We still have whole conferences about them. These new elliptic diagrams can be a long list of test cases, things we can experiment with with any number of loops. With time, we might truly understand them as well as the ladder diagrams!

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

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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.

What Might Lie Beyond, and Why

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As the new year approaches, people think about the future. Me, I’m thinking about the future of fundamental physics, about what might lie beyond the Standard Model. Physicists search for many different things, with many different motivations. Some are clear missing pieces, places where the Standard Model fails and we know we’ll need to modify it. Others are based on experience, with no guarantees but an expectation that, whatever we find, it will be surprising. Finally, some are cool possibilities, ideas that would explain something or fill in a missing piece but aren’t strictly necessary.

The Almost-Sure Things

Science isn’t math, so nothing here is really a sure thing. We might yet discover a flaw in important principles like quantum mechanics and special relativity, and it might be that an experimental result we trust turns out to be flawed. But if we chose to trust those principles, and our best experiments, then these are places we know the Standard Model is incomplete:

Neutrino Masses: The original Standard Model’s neutrinos were massless. Eventually, physicists discovered this was wrong: neutrinos oscillate, switching between different types in a way they only could if they had different masses. This result is familiar enough that some think of it as already part of the Standard Model, not really beyond. But the masses of neutrinos involve unsolved mysteries: we don’t know what those masses are, but more, there are different ways neutrinos could have mass, and we don’t yet know which is present in nature. Neutrino masses also imply the existence of an undiscovered “sterile” neutrino, a particle that doesn’t interact with the strong, weak, or electromagnetic forces.
Dark Matter Phenomena (and possibly Dark Energy Phenomena): Astronomers first suggested dark matter when they observed galaxies moving at speeds inconsistent with the mass of their stars. Now, they have observed evidence for it in a wide variety of situations, evidence which seems decisively incompatible with ordinary gravity and ordinary matter. Some solve this by introducing dark matter, others by modifying gravity, but this is more of a technical difference than it sounds: in order to modify gravity, one must introduce new quantum fields, much the same way one does when introducing dark matter. The only debate is how “matter-like” those fields need to be, but either approach goes beyond the Standard Model.
Quantum Gravity: It isn’t as hard to unite quantum mechanics and gravity as you might think. Physicists have known for decades how to write down a naive theory of quantum gravity, one that follows the same steps one might use to derive the quantum theory of electricity and magnetism. The problem is, this theory is incomplete. It works at low energies, but as the energy increases it loses the ability to make predictions, eventually giving nonsensical answers like probabilities greater than one. We have candidate solutions to this problem, like string theory, but we might not know for a long time which solution is right.
Landau Poles: Here’s a more obscure one. In particle physics we can zoom in and out in our theories, using similar theories at different scales. What changes are the coupling constants, numbers that determine the strength of the different forces. You can think of this in a loosely reductionist way, with the theories at smaller scales determining the constants for theories at larger scales. This gives workable theories most of the time, but it fails for at least one part of the Standard Model. In electricity and magnetism, the coupling constant increases as you zoom in. Eventually, it becomes infinite, and what’s more, does so at a finite energy scale. It’s still not clear how we should think about this, but luckily we won’t have to very soon: this energy scale is vastly vastly higher than even the scale of quantum gravity.
Some Surprises Guarantee Others: The Standard Model is special in a way that gravity isn’t. Even if you dial up the energy, a Standard Model calculation will always “make sense”: you never get probabilities greater than one. This isn’t true for potential deviations from the Standard Model. If the Higgs boson turns out to interact differently than we expect, it wouldn’t just be a violation of the Standard Model on its own: it would guarantee mathematically that, at some higher energy, we’d have to find something new. That was precisely the kind of argument the LHC used to find the Higgs boson: without the Higgs, something new was guaranteed to happen within the energy range of the LHC to prevent impossible probability numbers.

The Argument from (Theoretical) Experience

Everything in this middle category rests on a particular sort of argument. It’s short of a guarantee, but stronger than a dream or a hunch. While the previous category was based on calculations in theories we already know how to write down, this category relies on our guesses about theories we don’t yet know how to write.

Suppose we had a deeper theory, one that could use fewer parameters to explain the many parameters of the Standard Model. For example, it might explain the Higgs mass, letting us predict it rather than just measuring it like we do now. We don’t have a theory like that yet, but what we do have are many toy model theories, theories that don’t describe the real world but do, in this case, have fewer parameters. We can observe how these theories work, and what kinds of discoveries scientists living in worlds described by them would make. By looking at this process, we can get a rough idea of what to expect, which things in our own world would be “explained” in other ways in these theories.

The Hierarchy Problem: This is also called the naturalness problem. Suppose we had a theory that explained the mass of the Higgs, one where it wasn’t just a free parameter. We don’t have such a theory for the real Higgs, but we do have many toy models with similar behavior, ones with a boson with its mass determined by something else. In these models, though, the mass of the boson is always close to the energy scale of other new particles, particles which have a role in determining its mass, or at least in postponing that determination. This was the core reason why people expected the LHC to find something besides the Higgs. Without such new particles, the large hierarchy between the mass of the Higgs and the mass of new particles becomes a mystery, one where it gets harder and harder to find a toy model with similar behavior that still predicts something like the Higgs mass.
The Strong CP Problem: The weak nuclear force does what must seem like a very weird thing, by violating parity symmetry: the laws that govern it are not the same when you flip the world in a mirror. This is also true when you flip all the charges as well, a combination called CP (charge plus parity). But while it may seem strange that the weak force violates this symmetry, physicists find it stranger that the strong force seems to obey it. Much like in the hierarchy problem, it is very hard to construct a toy model that both predicts a strong force that maintains CP (or almost maintains it) and doesn’t have new particles. The new particle in question, called the axion, is something some people also think may explain dark matter.
Matter-Antimatter Asymmetry: We don’t know the theory of quantum gravity. Even if we did, the candidate theories we have struggle to describe conditions close to the Big Bang. But while we can’t prove it, many physicists expect the quantum gravity conditions near the Big Bang to produce roughly equal amounts of matter and antimatter. Instead, matter dominates: we live in a world made almost entirely of matter, with no evidence of large antimatter areas even far out in space. This lingering mystery could be explained if some new physics was biased towards matter instead of antimatter.
Various Problems in Cosmology: Many open questions in cosmology fall in this category. The small value of the cosmological constant is mysterious for the same reasons the small value of the Higgs mass is, but at a much larger and harder to fix scale. The early universe surprises many cosmologists by its flatness and uniformity, which has led them to propose new physics. This surprise is not because such flatness and uniformity is mathematically impossible, but because it is not the behavior they would expect out of a theory of quantum gravity.

The Cool Possibilities

Some ideas for physics beyond the standard model aren’t required, either from experience or cold hard mathematics. Instead, they’re cool, and would be convenient. These ideas would explain things that look strange, or make for a simpler deeper theory, but they aren’t the only way to do so.

Grand Unified Theories: Not the same as a “theory of everything”, Grand Unified Theories unite the three “particle physics forces”: the strong nuclear force, the weak nuclear force, and electromagnetism. Under such a theory, the different parameters that determine the strengths of those forces could be predicted from one shared parameter, with the forces only seeming different at low energies. These theories often unite the different matter particles too, but they also introduce new particles and new forces. These forces would, among other things, make protons unstable, and so giant experiments have been constructed to try to detect a proton decaying into other particles. So far none has been seen.
Low-Energy Supersymmetry: String theory requires supersymmetry, a relationship where matter and force particles share many properties. That supersymmetry has to be “broken”, which means that while the matter and force particles have the same charges, they can have wildly different masses, so that the partner particles are all still undiscovered. Those masses may be extremely high, all the way up at the scale of quantum gravity, but they could also be low enough to test at the LHC. Physicists hoped to detect such particles, as they could have been a good solution to the hierarchy problem. Now that the LHC hasn’t found these supersymmetric particles, it is much harder to solve the problem this way, though some people are still working on it.
Large Extra Dimensions: String theory also involves extra dimensions, beyond our usual three space and one time. Those dimensions are by default very small, but some proposals have them substantially bigger, big enough that we could have seen evidence for them at the LHC. These proposals could explain why gravity is so much weaker than the other forces. Much like the previous members of this category though, no evidence for this has yet been found.

I think these categories are helpful, but experts may quibble about some of my choices. I also haven’t mentioned every possible thing that could be found beyond the Standard Model. If you’ve heard of something and want to know which category I’d put it in, let me know in the comments!

Simulated Wormhole Analogies

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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.

Simulated Wormholes for My Real Friends, Real Wormholes for My Simulated Friends

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Maybe you’ve recently seen a headline like this:

Actually, I’m more worried that you saw that headline before it was edited, when it looked like this:

If you’ve seen either headline, and haven’t read anything else about it, then please at least read this:

Physicists have not created an actual wormhole. They have simulated a wormhole on a quantum computer.

If you’re willing to read more, then read the rest of this post. There’s a more subtle story going on here, both about physics and about how we communicate it. And for the experts, hold on, because when I say the wormhole was a simulation I’m not making the same argument everyone else is.

[And for the mega-experts, there’s an edit later in the post where I soften that claim a bit.]

The headlines at the top of this post come from an article in Quanta Magazine. Quanta is a web-based magazine covering many fields of science. They’re read by the general public, but they aim for a higher standard than many science journalists, with stricter fact-checking and a goal of covering more challenging and obscure topics. Scientists in turn have tended to be quite happy with them: often, they cover things we feel are important but that the ordinary media isn’t able to cover. (I even wrote something for them recently.)

Last week, Quanta published an article about an experiment with Google’s Sycamore quantum computer. By arranging the quantum bits (qubits) in a particular way, they were able to observe behaviors one would expect out of a wormhole, a kind of tunnel linking different points in space and time. They published it with the second headline above, claiming that physicists had created a wormhole with a quantum computer and explaining how, using a theoretical picture called holography.

This pissed off a lot of physicists. After push-back, Quanta’s twitter account published this statement, and they added the word “Holographic” to the title.

Why were physicists pissed off?

It wasn’t because the Quanta article was wrong, per se. As far as I’m aware, all the technical claims they made are correct. Instead, it was about two things. One was the title, and the implication that physicists “really made a wormhole”. The other was the tone, the excited “breaking news” framing complete with a video comparing the experiment with the discovery of the Higgs boson. I’ll discuss each in turn:

The Title

Did physicists really create a wormhole, or did they simulate one? And why would that be at all confusing?

The story rests on a concept from the study of quantum gravity, called holography. Holography is the idea that in quantum gravity, certain gravitational systems like black holes are fully determined by what happens on a “boundary” of the system, like the event horizon of a black hole. It’s supposed to be a hologram in analogy to 3d images encoded in 2d surfaces, rather than like the hard-light constructions of science fiction.

The best-studied version of holography is something called AdS/CFT duality. AdS/CFT duality is a relationship between two different theories. One of them is a CFT, or “conformal field theory”, a type of particle physics theory with no gravity and no mass. (The first example of the duality used my favorite toy theory, N=4 super Yang-Mills.) The other one is a version of string theory in an AdS, or anti-de Sitter space, a version of space-time curved so that objects shrink as they move outward, approaching a boundary. (In the first example, this space-time had five dimensions curled up in a sphere and the rest in the anti-de Sitter shape.)

These two theories are conjectured to be “dual”. That means that, for anything that happens in one theory, you can give an alternate description using the other theory. We say the two theories “capture the same physics”, even though they appear very different: they have different numbers of dimensions of space, and only one has gravity in it.

Many physicists would claim that if two theories are dual, then they are both “equally real”. Even if one description is more familiar to us, both descriptions are equally valid. Many philosophers are skeptical, but honestly I think the physicists are right about this one. Philosophers try to figure out which things are real or not real, to make a list of real things and explain everything else as made up of those in some way. I think that whole project is misguided, that it’s clarifying how we happen to talk rather than the nature of reality. In my mind, dualities are some of the clearest evidence that this project doesn’t make any sense: two descriptions can look very different, but in a quite meaningful sense be totally indistinguishable.

That’s the sense in which Quanta and Google and the string theorists they’re collaborating with claim that physicists have created a wormhole. They haven’t created a wormhole in our own space-time, one that, were it bigger and more stable, we could travel through. It isn’t progress towards some future where we actually travel the galaxy with wormholes. Rather, they created some quantum system, and that system’s dual description is a wormhole. That’s a crucial point to remember: even if they created a wormhole, it isn’t a wormhole for you.

If that were the end of the story, this post would still be full of warnings, but the title would be a bit different. It was going to be “Dual Wormholes for My Real Friends, Real Wormholes for My Dual Friends”. But there’s a list of caveats. Most of them arguably don’t matter, but the last was what got me to change the word “dual” to “simulated”.

The real world is not described by N=4 super Yang-Mills theory. N=4 super Yang-Mills theory was never intended to describe the real world. And while the real world may well be described by string theory, those strings are not curled up around a five-dimensional sphere with the remaining dimensions in anti-de Sitter space. We can’t create either theory in a lab either.
The Standard Model probably has a quantum gravity dual too, see this cute post by Matt Strassler. But they still wouldn’t have been able to use that to make a holographic wormhole in a lab.
Instead, they used a version of AdS/CFT with fewer dimensions. It relates a weird form of gravity in one space and one time dimension (called JT gravity), to a weird quantum mechanics theory called SYK, with an infinite number of quantum particles or qubits. This duality is a bit more conjectural than the original one, but still reasonably well-established.
Quantum computers don’t have an infinite number of qubits, so they had to use a version with a finite number: seven, to be specific. They trimmed the model down so that it would still show the wormhole-dual behavior they wanted. At this point, you might say that they’re definitely just simulating the SYK theory, using a small number of qubits to simulate the infinite number. But I think they could argue that this system, too, has a quantum gravity dual. The dual would have to be even weirder than JT gravity, and even more conjectural, but the signs of wormhole-like behavior they observed (mostly through simulations on an ordinary computer, which is still better at this kind of thing than a quantum computer) could be seen as evidence that this limited theory has its own gravity partner, with its own “real dual” wormhole.
But those seven qubits don’t just have the interactions they were programmed to have, the ones with the dual. They are physical objects in the real world, so they interact with all of the forces of the real world. That includes, though very weakly, the force of gravity.

And that’s where I think things break, and you have to call the experiment a simulation. You can argue, if you really want to, that the seven-qubit SYK theory has its own gravity dual, with its own wormhole. There are people who expect duality to be broad enough to include things like that.

But you can’t argue that the seven-qubit SYK theory, plus gravity, has its own gravity dual. Theories that already have gravity are not supposed to have gravity duals. If you pushed hard enough on any of the string theorists on that team, I’m pretty sure they’d admit that.

That is what decisively makes the experiment a simulation. It approximately behaves like a system with a dual wormhole, because you can approximately ignore gravity. But if you’re making some kind of philosophical claim, that you “really made a wormhole”, then “approximately” doesn’t cut it: if you don’t exactly have a system with a dual, then you don’t “really” have a dual wormhole: you’ve just simulated one.

Edit: mitchellporter in the comments points out something I didn’t know: that there are in fact proposals for gravity theories with gravity duals. They are in some sense even more conjectural than the series of caveats above, but at minimum my claim above, that any of the string theorists on the team would agree that the system’s gravity means it can’t have a dual, is probably false.

I think at this point, I’d soften my objection to the following:

Describing the system of qubits in the experiment as a limited version of the SYK theory is in one way or another an approximation. It approximates them as not having any interactions beyond those they programmed, it approximates them as not affected by gravity, and because it’s a quantum mechanical description it even approximates the speed of light as small. Those approximations don’t guarantee that the system doesn’t have a gravity dual. But in order for them to, then our reality, overall, would have to have a gravity dual. There would have to be a dual gravity interpretation of everything, not just the inside of Google’s quantum computer, and it would have to be exact, not just an approximation. Then the approximate SYK would be dual to an approximate wormhole, but that approximate wormhole would be an approximation of some “real” wormhole in the dual space-time.

That’s not impossible, as far as I can tell. But it piles conjecture upon conjecture upon conjecture, to the point that I don’t think anyone has explicitly committed to the whole tower of claims. If you want to believe that this experiment literally created a wormhole, you thus can, but keep in mind the largest asterisk known to mankind.

End edit.

If it weren’t for that caveat, then I would be happy to say that the physicists really created a wormhole. It would annoy some philosophers, but that’s a bonus.

But even if that were true, I wouldn’t say that in the title of the article.

The Title, Again

These days, people get news in two main ways.

Sometimes, people read full news articles. Reading that Quanta article is a good way to understand the background of the experiment, what was done and why people care about it. As I mentioned earlier, I don’t think anything said there was wrong, and they cover essentially all of the caveats you’d care about (except for that last one 😉 ).

Sometimes, though, people just see headlines. They get forwarded on social media, observed at a glance passed between friends. If you’re popular enough, then many more people will see your headline than will actually read the article. For many people, their whole understanding of certain scientific fields is formed by these glancing impressions.

Because of that, if you’re popular and news-y enough, you have to be especially careful with what you put in your headlines, especially when it implies a cool science fiction story. People will almost inevitably see them out of context, and it will impact their view of where science is headed. In this case, the headline may have given many people the impression that we’re actually making progress towards travel via wormholes.

Some of my readers might think this is ridiculous, that no-one would believe something like that. But as a kid, I did. I remember reading popular articles about wormholes, describing how you’d need energy moving in a circle, and other articles about optical physicists finding ways to bend light and make it stand still. Putting two and two together, I assumed these ideas would one day merge, allowing us to travel to distant galaxies faster than light.

If I had seen Quanta’s headline at that age, I would have taken it as confirmation. I would have believed we were well on the way to making wormholes, step by step. Even the New York Times headline, “the Smallest, Crummiest Wormhole You Can Imagine”, wouldn’t have fazed me.

(I’m not sure even the extra word “holographic” would have. People don’t know what “holographic” means in this context, and while some of them would assume it meant “fake”, others would think about the many works of science fiction, like Star Trek, where holograms can interact physically with human beings.)

Quanta has a high-brow audience, many of whom wouldn’t make this mistake. Nevertheless, I think Quanta is popular enough, and respectable enough, that they should have done better here.

At minimum, they could have used the word “simulated”. Even if they go on to argue in the article that the wormhole is real, and not just a simulation, the word in the title does no real harm. It would be a lie, but a beneficial “lie to children”, the basic stock-in-trade of science communication. I think they could have defended it to the string theorists they interviewed on those grounds.

The Tone

Honestly, I don’t think people would have been nearly so pissed off were it not for the tone of the article. There are a lot of physics bloggers who view themselves as serious-minded people, opposed to hype and publicity stunts. They view the research program aimed at simulating quantum gravity on a quantum computer as just an attempt to link a dying and un-rigorous research topic to an over-hyped and over-funded one, pompous storytelling aimed at promoting the careers of people who are already extremely successful.

These people tend to view Quanta favorably, because it covers serious-minded topics in a thorough way. And so many of them likely felt betrayed, seeing this Quanta article as a massive failure of that serious-minded-ness, falling for or even endorsing the hypiest of hype.

To those people, I’d like to politely suggest you get over yourselves.

Quanta’s goal is to cover things accurately, to represent all the facts in a way people can understand. But “how exciting something is” is not a fact.

Excitement is subjective. Just because most of the things Quanta finds exciting you also find exciting, does not mean that Quanta will find the things you find unexciting unexciting. Quanta is not on “your side” in some war against your personal notion of unexciting science, and you should never have expected it to be.

In fact, Quanta tends to find things exciting, in general. They were more excited than I was about the amplituhedron, and I’m an amplitudeologist. Part of what makes them consistently excited about the serious-minded things you appreciate them for is that they listen to scientists and get excited about the things they’re excited about. That is going to include, inevitably, things those scientists are excited about for what you think are dumb groupthinky hype reasons.

I think the way Quanta titled the piece was unfortunate, and probably did real damage. I think the philosophical claim behind the title is wrong, though for subtle and weird enough reasons that I don’t really fault anybody for ignoring them. But I don’t think the tone they took was a failure of journalistic integrity or research or anything like that. It was a matter of taste. It’s not my taste, it’s probably not yours, but we shouldn’t have expected Quanta to share our tastes in absolutely everything. That’s just not how taste works.

Chaos: Warhammer 40k or Physics?

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As I mentioned last week, it’s only natural to confuse chaos theory in physics with the forces of chaos in the game Warhammer 40,000. Since it will be Halloween in a few days, it’s a perfect time to explain the subtle differences between the two.

Warhammer 40k	physics
In the grim darkness of the far future, there is only war!	In the grim darkness of Chapter 11 of Goldstein, Poole, and Safko, there is only Chaos!
Birthed from the psychic power of mortal minds	Birthed from the numerical computations of mortal physicists
Ruled by four chaos gods: Khorne, Tzeench, Nurgle, and Slaanesh	Ruled by three principles: sensitivity to initial conditions, topological transitivity, and dense periodic orbits
In the 31st millennium, nine legions of space marines leave humanity due to the forces of chaos	In the 3.5 millionth millennium, Mercury leaves the solar system due to the force of gravity
While events may appear unpredictable, everything is determined by Tzeench’s plans	While events may appear unpredictable, everything is determined by the initial conditions
Humans drawn to strangely attractive cults	Systems in phase space drawn to strange attractors
Over time, cultists mutate, governed by the warp	Over time, trajectories diverge, governed by the Lyapunov exponent
To resist chaos, the Imperium of Man demands strict spiritual control	To resist chaos, the KAM Theorem demands strict mathematical conditions
Inspires nerds to paint detailed miniatures	Inspires nerds to stick pendulums together
Fantasy version with confusing relation to the original	Quantum version with confusing relation to the original
Lots of cool gothic art	Pretty fractals

From Journal to Classroom

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As part of the pedagogy course I’ve been taking, I’m doing a few guest lectures in various courses. I’ve got one coming up in a classical mechanics course (“intermediate”-level, so not Newton’s laws, but stuff the general public doesn’t know much about like Hamiltonians). They’ve been speeding through the core content, so I got to cover a “fun” topic, and after thinking back to my grad school days I chose a topic I think they’ll have a lot of fun with: Chaos theory.

Chaos is one of those things everyone has a vague idea about. People have heard stories where a butterfly flaps its wings and causes a hurricane. Maybe they’ve heard of the rough concept, determinism with strong dependence on the initial conditions, so a tiny change (like that butterfly) can have huge consequences. Maybe they’ve seen pictures of fractals, and got the idea these are somehow related.

Its role in physics is a bit more detailed. It’s one of those concepts that “intermediate classical mechanics” is good for, one that can be much better understood once you’ve been introduced to some of the nineteenth century’s mathematical tools. It felt like a good way to show this class that the things they’ve learned aren’t just useful for dusty old problems, but for understanding something the public thinks is sexy and mysterious.

As luck would have it, the venerable textbook the students are using includes a (2000’s era) chapter on chaos. I read through it, and it struck me that it’s a very different chapter from most of the others. This hit me particularly when I noticed a section describing a famous early study of chaos, and I realized that all the illustrations were based on the actual original journal article.

I had surprisingly mixed feelings about this.

On the one hand, there’s a big fashion right now for something called research-based teaching. That doesn’t mean “using teaching methods that are justified by research” (though you’re supposed to do that too), but rather, “tying your teaching to current scientific research”. This is a fashion that makes sense, because learning about cutting-edge research in an undergraduate classroom feels pretty cool. It lets students feel more connected with the scientific community, it inspires them to get involved, and it gets them more used to what “real research” looks like.

On the other hand, structuring your textbook based on the original research papers feels kind of lazy. There’s a reason we don’t teach Newtonian mechanics the way Newton would have. Pedagogy is supposed to be something we improve at over time: we come up with better examples and better notation, more focused explanations that teach what we want students to learn. If we just summarize a paper, we’re not really providing “added value”: we should hope, at this point, that we can do better.

Thinking about this, I think the distinction boils down to why you’re teaching the material in the first place.

With a lot of research-based teaching, the goal is to show the students how to interact with current literature. You want to show them journal papers, not because the papers are the best way to teach a concept or skill, but because reading those papers is one of the skills you want to teach.

That makes sense for very current topics, but it seems a bit weird for the example I’ve been looking at, an early study of chaos from the 60’s. It’s great if students can read current papers, but they don’t necessarily need to read older ones. (At least, not yet.)

What then, is the textbook trying to teach? Here things get a bit messy. For a relatively old topic, you’d ideally want to teach not just a vague impression of what was discovered, but concrete skills. Here though, those skills are just a bit beyond the students’ reach: chaos is more approachable than you’d think, but still not 100% something the students can work with. Instead they’re learning to appreciate concepts. This can be quite valuable, but it doesn’t give the kind of structure that a concrete skill does. In particular, it makes it hard to know what to emphasize, beyond just summarizing the original article.

In this case, I’ve come up with my own way forward. There are actually concrete skills I’d like to teach. They’re skills that link up with what the textbook is teaching, skills grounded in the concepts it’s trying to convey, and that makes me think I can convey them. It will give some structure to the lesson, a focus on not merely what I’d like the students to think but what I’d like them to do.

I won’t go into too much detail: I suspect some of the students may be reading this, and I don’t want to spoil the surprise! But I’m looking forward to class, and to getting to try another pedagogical experiment.

4 gravitons

Stories about physics from someone who's been there