Tag Archives: relativity

At New Ideas in Cosmology

The Niels Bohr Institute is hosting a conference this week on New Ideas in Cosmology. I’m no cosmologist, but it’s a pretty cool field, so as a local I’ve been sitting in on some of the talks. So far they’ve had a selection of really interesting speakers with quite a variety of interests, including a talk by Roger Penrose with his trademark hand-stippled drawings.

One thing that has impressed me has been the “interdisciplinary” feel of the conference. By all rights this should be one “discipline”, cosmology. But in practice, each speaker came at the subject from a different direction. They all had a shared core of knowledge, common models of the universe they all compare to. But the knowledge they brought to the subject varied: some had deep knowledge of the mathematics of gravity, others worked with string theory, or particle physics, or numerical simulations. Each talk, aware of the varied audience, was a bit “colloquium-style“, introducing a framework before diving in to the latest research. Each speaker knew enough to talk to the others, but not so much that they couldn’t learn from them. It’s been unexpectedly refreshing, a real interdisciplinary conference done right.

The Undefinable

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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.

The Only Speed of Light That Matters

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A couple weeks back, someone asked me about a Veritasium video with the provocative title “Why No One Has Measured The Speed Of Light”. Veritasium is a science popularization youtube channel, and usually a fairly good one…so it was a bit surprising to see it make a claim usually reserved for crackpots. Many, many people have measured the speed of light, including Ole Rømer all the way back in 1676. To argue otherwise seems like it demands a massive conspiracy.

Veritasium wasn’t proposing a conspiracy, though, just a technical point. Yes, many experiments have measured the speed of light. However, the speed they measure is in fact a “two-way speed”, the speed that light takes to go somewhere and then come back. They leave open the possibility that light travels differently in different directions, and only has the measured speed on average: that there are different “one-way speeds” of light.

The loophole is clearest using some of the more vivid measurements of the speed of light, timing how long it takes to bounce off a mirror and return. It’s less clear using other measurements of the speed of light, like Rømer’s. Rømer measured the speed of light using the moons of Jupiter, noticing that the time they took to orbit appeared to change based on whether Jupiter was moving towards or away from the Earth. For this measurement Rømer didn’t send any light to Jupiter…but he did have to make assumptions about Jupiter’s rotation, using it like a distant clock. Those assumptions also leave the door open to a loophole, one where the different one-way speeds of light are compensated by different speeds for distant clocks. You can watch the Veritasium video for more details about how this works, or see the wikipedia page for the mathematical details.

When we think of the speed of light as the same in all directions, in some sense we’re making a choice. We’ve chosen a convention, called the Einstein synchronization convention, that lines up distant clocks in a particular way. We didn’t have to choose that convention, though we prefer to (the math gets quite a bit more complicated if we don’t). And crucially for any such choice, it is impossible for any experiment to tell the difference.

So far, Veritasium is doing fine here. But if the video was totally fine, I wouldn’t have written this post. The technical argument is fine, but the video screws up its implications.

Near the end of the video, the host speculates whether this ambiguity is a clue. What if a deeper theory of physics could explain why we can’t tell the difference between different synchronizations? Maybe that would hint at something important.

Well, it does hint at something important, but not something new. What it hints at is that “one-way speeds” don’t matter. Not for light, or really for anything else.

Think about measuring the speed of something, anything. There are two ways to do it. One is to time it against something else, like the signal in a wire, and assume we know that speed. Veritasium shows an example of this, measuring the speed of a baseball that hits a target and sends a signal back. The other way is to send it somewhere with a clock we trust, and compare it to our clock. Each of these requires that something goes back and forth, even if it’s not the same thing each time. We can’t measure the one-way speed of anything because we’re never in two places at once. Everything we measure, every conclusion we come to about the world, rests on something “two-way”: our actions go out, our perceptions go in. Even our depth perception is an inference from our ancestors, whose experience seeing food and traveling to it calibrated our notion of distance.

Synchronization of clocks is a convention because the external world is a convention. What we have really, objectively, truly, are our perceptions and our memories. Everything else is a model we build to fill the gaps in between. Some features of that model are essential: if you change them, you no longer match our perceptions. Other features, though, are just convenience: ways we arrange the model to make it easier to use, to make it not “sound dumb”, to tell a coherent story. Synchronization is one of those things: the notion that you can compare times in distant places is convenient, but as relativity already tells us in other contexts, not necessary. It’s part of our storytelling, not an essential part of our model.

Duality and Emergence: When Is Spacetime Not Spacetime?

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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.

(I’ve made arguments like that in the past too.)

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.

Classicality Has Consequences

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Last week, I mentioned some interesting new results in my corner of physics. I’ve now finally read the two papers and watched the recorded talk, so I can satisfy my frustrated commenters.

Quantum mechanics is a very cool topic and I am much less qualified than you would expect to talk about it. I use quantum field theory, which is based on quantum mechanics, so in some sense I use quantum mechanics every day. However, most of the “cool” implications of quantum mechanics don’t come up in my work. All the debates about whether measurement “collapses the wavefunction” are irrelevant when the particles you measure get absorbed in a particle detector, never to be seen again. And while there are deep questions about how a classical world emerges from quantum probabilities, they don’t matter so much when all you do is calculate those probabilities.

They’ve started to matter, though. That’s because quantum field theorists like me have recently started working on a very different kind of problem: trying to predict the output of gravitational wave telescopes like LIGO. It turns out you can do almost the same kind of calculation we’re used to: pretend two black holes or neutron stars are sub-atomic particles, and see what happens when they collide. This trick has grown into a sub-field in its own right, one I’ve dabbled in a bit myself. And it’s gotten my kind of physicists to pay more attention to the boundary between classical and quantum physics.

The thing is, the waves that LIGO sees really are classical. Any quantum gravity effects there are tiny, undetectably tiny. And while this doesn’t have the implications an expert might expect (we still need loop diagrams), it does mean that we need to take our calculations to a classical limit.

Figuring out how to do this has been surprisingly delicate, and full of unexpected insight. A recent example involves two papers, one by Andrea Cristofoli, Riccardo Gonzo, Nathan Moynihan, Donal O’Connell, Alasdair Ross, Matteo Sergola, and Chris White, and one by Ruth Britto, Riccardo Gonzo, and Guy Jehu. At first I thought these were two groups happening on the same idea, but then I noticed Riccardo Gonzo on both lists, and realized the papers were covering different aspects of a shared story. There is another group who happened upon the same story: Paolo Di Vecchia, Carlo Heissenberg, Rodolfo Russo and Gabriele Veneziano. They haven’t published yet, so I’m basing this on the Gonzo et al papers.

The key question each group asked was, what does it take for gravitational waves to be classical? One way to ask the question is to pick something you can observe, like the strength of the field, and calculate its uncertainty. Classical physics is deterministic: if you know the initial conditions exactly, you know the final conditions exactly. Quantum physics is not. What should happen is that if you calculate a quantum uncertainty and then take the classical limit, that uncertainty should vanish: the observation should become certain.

Another way to ask is to think about the wave as made up of gravitons, particles of gravity. Then you can ask how many gravitons are in the wave, and how they are distributed. It turns out that you expect them to be in a coherent state, like a laser, one with a very specific distribution called a Poisson distribution: a distribution in some sense right at the border between classical and quantum physics.

The results of both types of questions were as expected: the gravitational waves are indeed classical. To make this work, though, the quantum field theory calculation needs to have some surprising properties.

If two black holes collide and emit a gravitational wave, you could depict it like this:

where the straight lines are black holes, and the squiggly line is a graviton. But since gravitational waves are made up of multiple gravitons, you might ask, why not depict it with two gravitons, like this?

It turns out that diagrams like that are a problem: they mean your two gravitons are correlated, which is not allowed in a Poisson distribution. In the uncertainty picture, they also would give you non-zero uncertainty. Somehow, in the classical limit, diagrams like that need to go away.

And at first, it didn’t look like they do. You can try to count how many powers of Planck’s constant show up in each diagram. The authors do that, and it certainly doesn’t look like it goes away:

An example from the paper with Planck’s constants sprinkled around

Luckily, these quantum field theory calculations have a knack for surprising us. Calculate each individual diagram, and things look hopeless. But add them all together, and they miraculously cancel. In the classical limit, everything combines to give a classical result.

You can do this same trick for diagrams with more graviton particles, as many as you like, and each time it ought to keep working. You get an infinite set of relationships between different diagrams, relationships that have to hold to get sensible classical physics. From thinking about how the quantum and classical are related, you’ve learned something about calculations in quantum field theory.

That’s why these papers caught my eye. A chunk of my sub-field is needing to learn more and more about the relationship between quantum and classical physics, and it may have implications for the rest of us too. In the future, I might get a bit more qualified to talk about some of the very cool implications of quantum mechanics.

Stop Listing the Amplituhedron as a Competitor of String Theory

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The Economist recently had an article (paywalled) that meandered through various developments in high-energy physics. It started out talking about the failure of the LHC to find SUSY, argued this looked bad for string theory (which…not really?) and used it as a jumping-off point to talk about various non-string “theories of everything”. Peter Woit quoted it a few posts back as kind of a bellwether for public opinion on supersymmetry and string theory.

The article was a muddle, but a fairly conventional muddle, explaining or mis-explaining things in roughly the same way as other popular physics pieces. For the most part that didn’t bug me, but one piece of the muddle hit a bit close to home:

The names of many of these [non-string theories of everything] do, it must be conceded, torture the English language. They include “causal dynamical triangulation”, “asymptotically safe gravity”, “loop quantum gravity” and the “amplituhedron formulation of quantum theory”.

I’ve posted about the amplituhedron more than a few times here on this blog. Out of every achievement of my sub-field, it has most captured the public imagination. It’s legitimately impressive, a way to translate calculations of probabilities of collisions of fundamental particles (in a toy model, to be clear) into geometrical objects. What it isn’t, and doesn’t pretend to be, is a theory of everything.

To be fair, the Economist piece admits this:

Most attempts at a theory of everything try to fit gravity, which Einstein describes geometrically, into quantum theory, which does not rely on geometry in this way. The amplituhedron approach does the opposite, by suggesting that quantum theory is actually deeply geometric after all. Better yet, the amplituhedron is not founded on notions of spacetime, or even statistical mechanics. Instead, these ideas emerge naturally from it. So, while the amplituhedron approach does not as yet offer a full theory of quantum gravity, it has opened up an intriguing path that may lead to one.

The reasoning they have leading up to it has a few misunderstandings anyway. The amplituhedron is geometrical, but in a completely different way from how Einstein’s theory of gravity is geometrical: Einstein’s gravity is a theory of space and time, the amplituhedron’s magic is that it hides space and time behind a seemingly more fundamental mathematics.

This is not to say that the amplituhedron won’t lead to insights about gravity. That’s a big part of what it’s for, in the long-term. Because the amplituhedron hides the role of space and time, it might show the way to theories that lack them altogether, theories where space and time are just an approximation for a more fundamental reality. That’s a real possibility, though not at this point a reality.

Even if you take this possibility completely seriously, though, there’s another problem with the Economist’s description: it’s not clear that this new theory would be a non-string theory!

The main people behind the amplituhedron are pretty positively disposed to string theory. If you asked them, I think they’d tell you that, rather than replacing string theory, they expect to learn more about string theory: to see how it could be reformulated in a way that yields insight about trickier problems. That’s not at all like the other “non-string theories of everything” in that list, which frame themselves as alternatives to, or even opponents of, string theory.

It is a lot like several other research programs, though, like ER=EPR and It from Qubit. Researchers in those programs try to use physical principles and toy models to say fundamental things about quantum gravity, trying to think about space and time as being made up of entangled quantum objects. By that logic, they belong in that list in the article alongside the amplituhedron. The reason they aren’t is obvious if you know where they come from: ER=EPR and It from Qubit are worked on by string theorists, including some of the most prominent ones.

The thing is, any reason to put the amplituhedron on that list is also a reason to put them. The amplituhedron is not a theory of everything, it is not at present a theory of quantum gravity. It’s a research direction that might shed new insight about quantum gravity. It doesn’t explicitly involve strings, but neither does It from Qubit most of the time. Unless you’re going to describe It from Qubit as a “non-string theory of everything”, you really shouldn’t describe the amplituhedron as one.

The amplituhedron is a really cool idea, one with great potential. It’s not something like loop quantum gravity, or causal dynamical triangulations, and it doesn’t need to be. Let it be what it is, please!

Lessons From Neutrinos, Part II

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Last week I talked about the history of neutrinos. Neutrinos come in three types, or “flavors”. Electron neutrinos are the easiest: they’re produced alongside electrons and positrons in the different types of beta decay. Electrons have more massive cousins, called muon and tau particles. As it turns out, each of these cousins has a corresponding flavor of neutrino: muon neutrinos, and tau neutrinos.

For quite some time, physicists thought that all of these neutrinos had zero mass.

(If the idea of a particle with zero mass confuses you, think about photons. A particle with zero mass travels, like a photon, at the speed of light. This doesn’t make them immune to gravity: just as no light can escape a black hole, neither can any other massless particle. It turns out that once you take into account Einstein’s general theory of relativity, gravity cares about energy, not just mass.)

Eventually, physicists started to realize they were wrong, and neutrinos had a small non-zero mass after all. Their reason why might seem a bit strange, though. Physicists didn’t weigh the neutrinos, or measure their speed. Instead, they observed that different flavors of neutrinos transform into each other. We say that they oscillate: electron neutrinos oscillate into muon or tau neutrinos, which oscillate into the other flavors, and so on. Over time, a beam of electron neutrinos will become a beam of mostly tau and muon neutrinos, before becoming a beam of electron neutrinos again.

That might not sound like it has much to do with mass. To understand why it does, you’ll need to learn this post’s lesson:

Lesson 2: Mass is just How Particles Move

Oscillating particles seem like a weird sort of evidence for mass. What would be a more normal kind of evidence?

Those of you who’ve taken physics classes might remember the equation $F=ma$ . Apply a known force to something, see how much it accelerates, and you can calculate its mass. If you’ve had a bit more physics, you’ll know that this isn’t quite the right equation to use for particles close to the speed of light, but that there are other equations we can use in a similar way. In particular, using relativity, we have $E^2=p^2 c^2 + m^2 c^4$ . (At rest, $p=0$ , and we have the famous $E=mc^2$ ). This lets us do the same kind of thing: give something a kick and see how it moves.

So let’s say we do that: we give a particle a kick, and measure it later. I’ll visualize this with a tool physicists use called a Feynman diagram. The line represents a particle traveling from one side to the other, from “kick” to “measurement”:

Because we only measure the particle at the end, we might miss if something happens in between. For example, it might interact with another particle or field, like this:

If we don’t know about this other field, then when we try to measure the particle’s mass we will include interactions like this. As it turns out, this is how the Higgs boson works: the Higgs field interacts with particles like electrons and quarks, changing how they move, so that they appear to have mass.

Quantum particles can do other things too. You might have heard people talk about one particle turning into a pair of temporary “virtual particles”. When people say that, they usually have a diagram in mind like this:

In particle physics, we need to take into account every diagram of this kind, every possible thing that could happen in between “kick” and measurement. The final result isn’t one path or another, but a sum of all the different things that could have happened in between. So when we measure the mass of a particle, we’re including every diagram that’s allowed: everything that starts with our “kick” and ends with our measurement.

Now what if our particle can transform, from one flavor to another?

Now we have a new type of thing that can happen in between “kick” and measurement. And if it can happen once, it can happen more than once:

Remember that, when we measure mass, we’re measuring a sum of all the things that can happen in between. That means our particle could oscillate back and forth between different flavors many many times, and we need to take every possibility into account. Because of that, it doesn’t actually make sense to ask what the mass is for one flavor, for just electron neutrinos or just muon neutrinos. Instead, mass is for the thing that actually moves: an average (actually, a quantum superposition) over all the different flavors, oscillating back and forth any number of times.

When a process like beta decay produces an electron neutrino, the thing that actually moves is a mix (again, a superposition) of particles with these different masses. Because each of these masses respond to their initial “kick” in different ways, you see different proportions of them over time. Try to measure different flavors at the end, and you’ll find different ones depending on when and where you measure. That’s the oscillation effect, and that’s why it means that neutrinos have mass.

It’s a bit more complicated to work out the math behind this, but not unreasonably so: it’s simpler than a lot of other physics calculations. Working through the math, we find that by measuring how long it takes neutrinos to oscillate we can calculate the differences between (squares of) neutrino masses. What we can’t calculate are the masses themselves. We know they’re small: neutrinos travel at almost the speed of light, and our cosmological models of the universe have surprisingly little room for massive neutrinos: too much mass, and our universe would look very different than it does today. But we don’t know much more than that. We don’t even know the order of the masses: you might assume electron neutrinos are on average lighter than muon neutrinos, which are lighter than tau neutrinos…but it could easily be the other way around! We also don’t know whether neutrinos get their mass from the Higgs like other particles do, or if they work in a completely different way.

Unlike other mysteries of physics, we’ll likely have the answer to some of these questions soon. People are already picking through the data from current experiments, seeing if they hint towards one order of masses or the other, or to one or the other way for neutrinos to get their mass. More experiments will start taking data this year, and others are expected to start later this decade. At some point, the textbooks may well have more “normal” mass numbers for each of the neutrinos. But until then, they serve as a nice illustration of what mass actually means in particle physics.

QCD Meets Gravity 2020, Retrospective

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I was at a Zoomference last week, called QCD Meets Gravity, about the many ways gravity can be thought of as the “square” of other fundamental forces. I didn’t have time to write much about the actual content of the conference, so I figured I’d say a bit more this week.

A big theme of this conference, as in the past few years, was gravitational waves. From LIGO’s first announcement of a successful detection, amplitudeologists have been developing new methods to make predictions for gravitational waves more efficient. It’s a field I’ve dabbled in a bit myself. Last year’s QCD Meets Gravity left me impressed by how much progress had been made, with amplitudeologists already solidly part of the conversation and able to produce competitive results. This year felt like another milestone, in that the amplitudeologists weren’t just catching up with other gravitational wave researchers on the same kinds of problems. Instead, they found new questions that amplitudes are especially well-suited to answer. These included combining two pieces of these calculations (“potential” and “radiation”) that the older community typically has to calculate separately, using an old quantum field theory trick, finding the gravitational wave directly from amplitudes, and finding a few nice calculations that can be used to “generate” the rest.

A large chunk of the talks focused on different “squaring” tricks (or as we actually call them, double-copies). There were double-copies for cosmology and conformal field theory, for the celestial sphere, and even some version of M theory. There were new perspectives on the double-copy, new building blocks and algebraic structures that lie behind it. There were talks on the so-called classical double-copy for space-times, where there have been some strange discoveries (an extra dimension made an appearance) but also a more rigorous picture of where the whole thing comes from, using twistor space. There were not one, but two talks linking the double-copy to the Navier-Stokes equation describing fluids, from two different groups. (I’m really curious whether these perspectives are actually useful for practical calculations about fluids, or just fun to think about.) Finally, while there wasn’t a talk scheduled on this paper, the authors were roped in by popular demand to talk about their work. They claim to have made progress on a longstanding puzzle, how to show that double-copy works at the level of the Lagrangian, and the community was eager to dig into the details.

From there, a grab-bag of talks covered other advancements. There were talks from string theorists and ambitwistor string theorists, from Effective Field Theorists working on gravity and the Standard Model, from calculations in N=4 super Yang-Mills, QCD, and scalar theories. Simon Caron-Huot delved into how causality constrains the theories we can write down, showing an interesting case where the common assumption that all parameters are close to one is actually justified. Nima Arkani-Hamed began his talk by saying he’d surprise us, which he certainly did (and not by keeping on time). It’s tricky to explain why his talk was exciting. Comparing to his earlier discovery of the Amplituhedron, which worked for a toy model, this is a toy calculation in a toy model. While the Amplituhedron wasn’t based on Feynman diagrams, this can’t even be compared with Feynman diagrams. Instead of expanding in a small coupling constant, this expands in a parameter that by all rights should be equal to one. And instead of positivity conditions, there are negativity conditions. All I can say is that with all of that in mind, it looks like real progress on an important and difficult problem from a totally unanticipated direction. In a speech summing up the conference, Zvi Bern mentioned a few exciting words from Nima’s talk: “nonplanar”, “integrated”, “nonperturbative”. I’d add “differential equations” and “infinite sums of ladder diagrams”. Nima and collaborators are trying to figure out what happens when you sum up all of the Feynman diagrams in a theory. I’ve made progress in the past for diagrams with one “direction”, a ladder that grows as you add more loops, but I didn’t know how to add “another direction” to the ladder. In very rough terms, Nima and collaborators figured out how to add that direction.

I’ve probably left things out here, it was a packed conference! It’s been really fun seeing what the community has cooked up, and I can’t wait to see what happens next.

QCD Meets Gravity 2020

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I’m at another Zoom conference this week, QCD Meets Gravity. This year it’s hosted by Northwestern.

QCD Meets Gravity is a conference series focused on the often-surprising links between quantum chromodynamics on the one hand and gravity on the other. By thinking of gravity as the “square” of forces like the strong nuclear force, researchers have unlocked new calculation techniques and deep insights.

Last year’s conference was very focused on one particular topic, trying to predict the gravitational waves observed by LIGO and VIRGO. That’s still a core topic of the conference, but it feels like there is a bit more diversity in topics this year. We’ve seen a variety of talks on different “squares”: new theories that square to other theories, and new calculations that benefit from “squaring” (even surprising applications to the Navier-Stokes equation!) There are talks on subjects from String Theory to Effective Field Theory, and even a talk on a very different way that “QCD meets gravity”, in collisions of neutron stars.

With still a few more talks to go, expect me to say a bit more next week, probably discussing a few in more detail. (Several people presented exciting work in progress!) Until then, I should get back to watching!

The Wolfram Physics Project Makes Me Queasy

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Stephen Wolfram is…Stephen Wolfram.

Once a wunderkind student of Feynman, Wolfram is now best known for his software, Mathematica, a tool used by everyone from scientists to lazy college students. Almost all of my work is coded in Mathematica, and while it has some flaws (can someone please speed up the linear solver? Maple’s is so much better!) it still tends to be the best tool for the job.

Wolfram is also known for being a very strange person. There’s his tendency to name, or rename, things after himself. (There’s a type of Mathematica file that used to be called “.m”. Now by default they’re “.wl”, “Wolfram Language” files.) There’s his live-streamed meetings. And then there’s his physics.

In 2002, Wolfram wrote a book, “A New Kind of Science”, arguing that computational systems called cellular automata were going to revolutionize science. A few days ago, he released an update: a sprawling website for “The Wolfram Physics Project”. In it, he claims to have found a potential “theory of everything”, unifying general relativity and quantum physics in a cellular automata-like form.

If that gets your crackpot klaxons blaring, yeah, me too. But Wolfram was once a very promising physicist. And he has collaborators this time, who are currently promising physicists. So I should probably give him a fair reading.

On the other hand, his introduction for a technical audience is 448 pages long. I may have more time now due to COVID-19, but I still have a job, and it isn’t reading that.

So I compromised. I didn’t read his 448-page technical introduction. I read his 90-ish page blog post. The post is written for a non-technical audience, so I know it isn’t 100% accurate. But by seeing how someone chooses to promote their work, I can at least get an idea of what they value.

I started out optimistic, or at least trying to be. Wolfram starts with simple mathematical rules, and sees what kinds of structures they create. That’s not an unheard of strategy in theoretical physics, including in my own field. And the specific structures he’s looking at look weirdly familiar, a bit like a generalization of cluster algebras.

Reading along, though, I got more and more uneasy. That unease peaked when I saw him describe how his structures give rise to mass.

Wolfram had already argued that his structures obey special relativity. (For a critique of this claim, see this twitter thread.) He found a way to define energy and momentum in his system, as “fluxes of causal edges”. He picks out a particular “flux of causal edges”, one that corresponds to “just going forward in time”, and defines it as mass. Then he “derives” $E=mc^2$ , saying,

Sometimes in the standard formalism of physics, this relation by now seems more like a definition than something to derive. But in our model, it’s not just a definition, and in fact we can successfully derive it.

In “the standard formalism of physics”, $E=mc^2$ means “mass is the energy of an object at rest”. It means “mass is the energy of an object just going forward in time”. If the “standard formalism of physics” “just defines” $E=mc^2$ , so does Wolfram.

I haven’t read his technical summary. Maybe this isn’t really how his “derivation” works, maybe it’s just how he decided to summarize it. But it’s a pretty misleading summary, one that gives the reader entirely the wrong idea about some rather basic physics. It worries me, because both as a physicist and a blogger, he really should know better. I’m left wondering whether he meant to mislead, or whether instead he’s misleading himself.

That feeling kept recurring as I kept reading. There was nothing else as extreme as that passage, but a lot of pieces that felt like they were making a big deal about the wrong things, and ignoring what a physicist would find the most important questions.

I was tempted to get snarkier in this post, to throw in a reference to Lewis’s trilemma or some variant of the old quip that “what is new is not good; and what is good is not new”. For now, I’ll just say that I probably shouldn’t have read a 90 page pop physics treatise before lunch, and end the post with that.

4 gravitons

The trials and tribulations of four gravitons and a physicist