Sean Carroll
Show: Sean Carroll's Mindscape
Cleaned and reformatted from the auto-generated YouTube transcript — punctuation added, sponsor reads removed, restructured for readability. Not verbatim. For exact quotes, refer to the original video.
Hello everyone, and welcome to the Mindscape podcast. I'm your host, Sean Carroll. You might remember that about a year ago we had an episode with Niayesh Afshordi and Phil Halper. Niayesh is a well-known, respectable, working cosmologist at the Perimeter Institute, and Phil is a science communicator who makes YouTube videos explaining ideas in physics. The reason we had them on the podcast is that they had a book out, Battle of the Big Bang, based in part on surveys they'd done. Rather than pushing their own view of what happened at the Big Bang, they surveyed all sorts of physicists and came up with a way of thinking about the possible views people have proposed.
More recently, in the last few weeks, Phil and Niayesh came out with another survey result. They were asked by the American Physical Society, and they teamed up with some other people to survey physicists on a whole bunch of questions that are not yet settled — controversial, if you like, though science always has controversies; that's not a flaw in the system. Everything we understand goes in the bucket of things we understand, and everything we don't, which is what's interesting and what we talk about, is somehow controversial. So they asked physicists about big questions: what's making the universe accelerate, what happened at the Big Bang, and of course, interpretations of quantum mechanics — one of the most famous unsolved issues in the field. If you've followed surveys of this kind before, you won't be surprised to hear that among physicists the Copenhagen interpretation gets more votes than any other single interpretation. It doesn't get a majority — it's about a third of the people surveyed — but all the others are split, with many-worlds in second place and a whole bunch of support for other possibilities.
Now, if you read the survey's definition of the Copenhagen interpretation: an object's behaviour is described by a multi-state wave function, which collapses to one state when the object is measured. I don't entirely agree with that way of stating what Copenhagen says, but I think it's fine for the survey, in the sense that most physicists who chose that option probably had something like that in mind. The problem is that it's hilariously ill-defined. It's not a good scientific theory — it's not even a scientific theory, not because it's wrong (there are plenty of scientific theories that are wrong but are still scientific theories), but because it's simply not defined. Right there in the definition, you say the state collapses to one state when an object is measured, but you don't say what it means for an object to be measured. No one in the Copenhagen world has ever said that. Some have tried to invoke decoherence and so on, but that doesn't tell you when the wave function is supposed to collapse.
The reason I bring this up is that there are people who are serious about the foundations of quantum mechanics and still lean toward something like Copenhagen — it's possible to take it seriously and think it through. I just don't think most physicists have. If you do think it through, you end up going down the road of people like Niels Bohr, Werner Heisenberg, and John Wheeler, who deny the reality of the wave function and go so far as to deny reality entirely until you have a measurement outcome. That's a very philosophically radical view, and I suspect most of the people in the survey who called themselves Copenhagenists don't actually hold it — mostly because they haven't thought about it very carefully.
All of this is an overly long-winded way of saying that when we talk about the different approaches to quantum mechanics, there are pros and cons on every side — or better, good reasons why people might prefer one approach over another, and good reasons why people might reject any single approach. I'm on record saying that every formulation of quantum mechanics asks you to believe something you really don't want to believe. It pushes you somewhere you didn't want to go, if you want to accept what nature is trying to tell you. That's true of my favourite theory too, the Everettian or many-worlds formulation. One of the frustrating things about talking about many-worlds in the popular landscape is that there are so many bad objections to it — philosophically bad ones, like "that's just too many worlds and you can't observe them." I don't take those very seriously, because they're very easily answered. But there are things about many-worlds that are less easily answered. The theory itself, I'd say, is more or less completely understood — what it says is clear — but how to apply it to the world we see becomes a little trickier.
So today I'm going to fulfil a promise I made during an AMA not long ago, and do a solo podcast about my own ideas — my favourite ways of taking the bare-bones postulates of many-worlds, or Everettian quantum mechanics, and connecting them to the real world. Not because I think this is really an objection to Everett, but because it's an open question, and open questions are important. They're opportunities to learn new things, to go beyond what you already understand — you shouldn't avoid them. If you have a new theory, or even an old one, and you think it's promising, you should be the person most upfront about its open questions, because it's not a problem to have them; it's an opportunity. You might learn something, or even solve puzzles that predate your theory. To say it very quickly, because we'll say it at length soon enough: in the case of Everettian many-worlds, there's a big puzzle that basically comes down to the fact that the theory is too simple. People say Everett is complicated — it violates Occam's razor because of all those extra worlds — but if you know what the theory actually says, it's an austere, simple formalism. So austere that you don't recognise the real world in it when you look. I'll explain what I mean by that, and why I'm nevertheless optimistic that we can find the real world lurking in the Everettian quantum state — at least, I think we have reason to believe the project will turn out well, though it's not done yet. If I'm wrong, we'll still learn something. So let's go.
I want to start with two caveats, which is never a good way to begin a talk — I always tell people not to start with apologies, and then I do it myself; do as I say, not as I do. The first is that this will get a little technical at times. This solo episode grew partly out of my episode with Daniel Harlow, where we talked semi-technically about quantum mechanics and then got fully technical at the end, just for fun. Some people liked that, some tolerated it, but I'm not going to aim for that level here. I'm not going to lecture you the way I'd lecture professional physicists. I'll try my best to make everything understandable. But the issues we're discussing aren't like Schrödinger's cat, or the things you're used to from popular discussions of quantum mechanics or many-worlds. They're very specific research-level questions, and I'll try to explain them as best I can, though I may not always succeed.
The second caveat: people have asked, in response to the AMA, that I steel-man the objections to many-worlds — since I keep telling everyone how great it is but never really say why it isn't. I have to confess that steel-manning isn't really my vibe. I do think that if you want to understand a difficult issue, you should understand the arguments on both sides — that's fine. But I'm not interested in setting up a contest between the best argument for a theory and the best argument against it, putting them in the arena to see who wins. I don't think that's how things work. Rather than the steel-manned version of an argument, I want the correct version — the best version of every argument, not made to sound stronger or weaker than it is. I'm more interested in getting things right than in steel-manning or straw-manning. Your mileage may vary as to whether I succeed at that.
With that throat-clearing out of the way, let's remember what quantum mechanics says. Some of you have heard about it a lot; some of you might be new — this might be your first ever Mindscape episode, which is great. If so, let me tell you about quantum mechanics very briefly, because it could take hours all by itself. Back in the early twentieth century, we knew about electrons — always the example physicists use, because they're heavy enough and electrically charged enough to manipulate, but light enough to push around easily. Chemistry and much of material science are based on what electrons do. There are also protons and neutrons in atomic nuclei, but they mostly sit there unless you're considering nuclear fission, fusion, or radioactivity; in your body and the table in front of you, the nuclei mostly just go along for the ride while the electrons do the interesting work.
Electrons were understood reasonably well in the early twentieth century, but they had a funny property. We all know the picture of an atom as a little solar system, with a nucleus at the centre and electrons orbiting — but it was instantly realised that this can't be right, because orbiting electrons would give off light, lose energy, and spiral into the nucleus. They don't: atoms are stable, matter is stable, and our continued existence in the universe is evidence of that. How could you explain it? People came up with fairly ad hoc ideas — Niels Bohr suggested that only a discrete set of orbits was allowed, not every possible way an electron could circle the nucleus, without explaining why that would be the case. It was finally Louis de Broglie and later Erwin Schrödinger who elaborated the idea that we should think about electrons as waves rather than particles, giving us what's called the wave function of the electron — a bad name, not nearly evocative enough for such a centrally important concept, and a little misleading too, for reasons I'll get to. But let's first give the true, if somewhat misleading, story: think of the electron as a kind of wave living in the vicinity of the nucleus. Schrödinger provided an equation for this wave — a complex-valued function, though that won't matter for anything we do — and Schrödinger's equation tells us the allowed solutions for how electrons can behave. If you've taken chemistry and learned about atomic orbitals, those are really just different solutions to Schrödinger's equation. It fit the data very nicely: electrons could go from one energy level to another and emit certain amounts of light, and we observed exactly those amounts in the spectra of various substances. Quantitatively, it was a huge success.
The problem is that when we look at electrons, we don't see the wave function — we see a dot, the electron located at a point. That's the whole mystery of quantum mechanics. The way we explain what electrons, or anything quantum, actually are is different from how they appear to us when we measure them. So we teach students something like the Copenhagen interpretation I mentioned: electrons behave one way when you're not measuring them — obeying the Schrödinger equation, settling into orbitals — and a whole different set of rules applies when you look at them. When you measure them, you see a dot. You can't predict exactly where the dot will be; you can only predict the probability of it being there, and that measurement radically changes the state of the electron. We call that the collapse of the wave function. As I said, these concepts aren't well defined, but they were well defined enough to get physics through the twentieth century. When do you make a measurement — what counts as one? You know it when you see it. We've still never developed, in the Copenhagen view, a fully well-defined notion of when and how wave functions collapse — but it works. If you just say, "when I look at it, it collapses," that turns out to work really well. That's why physicists didn't spend much time on the foundations of quantum mechanics through the twentieth century: they had a version of the theory that worked.
Things get more complicated once you go from one electron to two. You might not think it should be — Isaac Newton went from the gravitational field of one planet to two without much difficulty, and in the world of Newton, Einstein, or Maxwell there's no special problem in going from a theory of one object to a theory of two objects. You just have two things happening: one electron doing its thing, with its own wave function, and the other electron with its own. It turns out that's not how it works — there are justifications for this, but I'll just tell you the answer: if you have two electrons, they can be entangled.
What that means: remember I said to think of an electron as a little wave? That's not exactly right. A better way of thinking about it — closer to reality — is that the electron's wave function is a superposition of every possible measurement outcome. When you see the picture of an electron in an orbital, shaped like lobes or balloons, that picture is the wave function — but you won't see the wave function when you look. You'll see a dot, and if you take the function in that picture and square it (take the absolute value squared), that gives you the probability of the measurement outcome being the electron located at that position. So that wave function is really a superposition of every possible answer to "where will the electron be if I look?" — and even if you don't look, the wave function still has that status.
What's the difference between thinking of it as a wave located in space — the picture we're used to from things like the electric or gravitational field, which have a value at every point in space — and thinking of it as a superposition of measurement outcomes? The first sounds unnecessarily fussy: maybe it's true, but what are we learning by putting it that way? The answer comes from asking what happens with two electrons. Your guess might be that there'd be a field for electron one and a different field for electron two, but that's not what quantum mechanics says. It says there's a single wave function for the combination of the two electrons — and if you're worried about the subtlety of identical particles, just think of an electron and a proton, two distinguishable particles. So what does it mean to say there's only one wave function for two particles? If you think of the wave function not as a field living in space, but as a superposition of every possible measurement outcome, then with two particles this becomes distinguishable: the possible outcomes are every possible location of particle one and every possible location of particle two, considered together. For those of you who like the notation, the correct Greek letter for the wave function is psi — and instead of a psi for electron one and a separate psi for electron two, there's only one psi: the wave function of the universe, in this case a function of the position of electron one and the position of electron two. That's radically different from classical mechanics, where you'd just have whatever particle one is doing and whatever particle two is doing, independently. Quantum mechanics says this superposition of both electrons at once is the state of the system — and that's why it implies entanglement: there can be relationships between the probability of seeing one electron here and another electron there.
Let's switch to an electron and a proton to keep things simple. Say the wave function of this two-particle system is: the electron is probably in box A or box B, and the proton is in box A or box B — but they're never in the same box. So part of the superposition says "electron in box A, proton in box B," and part says "proton in box A, electron in box B," but no part says they're both in box A or both in box B. That's entanglement. Nothing like it happens in classical mechanics, but if you think of the wave function as a superposition of every possible measurement outcome, it makes a kind of sense: when you look to see where the electron and proton are, you'll see them somewhere, and that particular wave function I described is just one possibility among many — you could have a wave function that puts them both in the same box, or both definitely in box A. What's new is that quantum mechanics opens up the possibility that you don't know which box the electron's in, but you know it's not in the same box as the proton. Or, to be precise: it's a superposition of both possibilities, and there is no such thing, in that wave function, as where the electron is. This is the crucial feature of quantum mechanics that the wave function is a real thing — precisely what the Copenhagen interpretation denies. There are good reasons not to deny it, and that's one of the reasons why the more you think about the foundations of quantum mechanics, the less you like Copenhagen. Not everyone agrees, of course, but I'm giving my own views — this is a solo podcast, no guest to argue with. So in my view, the wave function is the real thing, and if it says the electron has some possibility of being in box A and some possibility of being in box B, then there's no fact about where the electron really is — there's only the wave function, a superposition of all those possibilities.
That's quantum mechanics, in brief — the basic ontology, what the theory says really exists. For the purposes of this podcast we're working in a realist ontology for the wave function: we think it represents reality. The Copenhagen interpretation then says you don't measure all of reality — when you measure, you see one version of it, and you can only predict the probability of seeing a given version. Many-worlds, by contrast — and we're not going to get much into the worlds aspect, because it's not really relevant to what we're discussing today; I've often said many-worlds isn't mostly about the worlds. They come along, no doubt, but what many-worlds is really about is saying there's no such thing as collapse, no special cordoned-off notion of measurement. There's just the Schrödinger equation, letting the wave function evolve as it will. Everett's brilliant idea was that if you count the observer as part of the quantum system, you get a very different answer from the Copenhagen story. People like Heisenberg and Bohr weren't dummies — they were very smart, and thought about this deeply and carefully, and they knew that if you treated the observer as part of the quantum system, you'd quickly go down a strange road.
Here's what happens: say you have an electron in a superposition of box A and box B, so there's no fact about where it really is. You can solve the equations for what happens when an observer measures its position — and solving the equations isn't optional; the equations say what they say. What you get is that the wave function of the universe turns into a superposition of "the electron was in box A and the observer measured it in box A" plus "the electron was in box B and the observer measured it in box B." Bohr and Heisenberg didn't want to accept that — and, to be fair, they had a bit of experience on their side: no experimenter has ever felt like they were in a superposition, as if they'd measured both spin-up and spin-down of some particle. You always seem to get a single, definite outcome. Everett's genius philosophical jujitsu was to say: the problem isn't that you need to change the equations, adding in wave-function collapse and so on. The problem is that you need to think carefully about identifying yourself within the wave function of the universe. He said: treat those two branches — one where the electron is in box A and the observer saw it in box A, the other where it's in box B and the observer saw it there — as separate worlds. You, the observer, are not the superposition of both; you're one or the other, and there's another observer, sharing a past with you, in what we call the other branch of the wave function. That's many-worlds. I didn't mean to get into it this much, but the point is that its formalism just says: there are wave functions, and they obey the Schrödinger equation; everything else is derived from that. In the Copenhagen view, you postulate a whole bunch of other things — measurement, wave-function collapse, a probability rule (the Born rule) for how often collapse happens — extra postulates. In Everett, there are no extra postulates. That's good for the traditional scientific virtue of simplicity: the fewer postulates, the fewer axioms, the better. It's bad for the philosophical task of connecting the formalism to reality, because whatever it's saying is, essentially, "I trust the equations; they tell me what happens, and as long as I correctly interpret who I am within them, I'll fit the data." But that interpretation of who you are in the wave function is a highly non-trivial thing, requiring real work. So Everettian quantum mechanics involves much more philosophical heavy lifting than Copenhagen or any other version — though I should say, Copenhagen has its own different philosophical heavy lifting: you have to disbelieve in reality until you actually measure something, arguably an even heavier lift, just of a different kind.
That's the minimal introduction to Everettian quantum mechanics, but it's not where I want to dwell. I want to talk about good old textbook quantum mechanics, because I've been saying something over and over that maybe you've noticed, maybe you haven't, but should think about. I said the wave function assigns a number — a complex number, as it happens — to every possible measurement outcome. But then what I actually described was measuring the position of the electron. That's not the only thing you could measure. Even setting aside spin, I could measure the velocity, or equivalently the momentum, of the electron. So naively — or at least taking my words too literally — you might think the wave function is a superposition of every possible measurement outcome, including both position and momentum at once. That's not right. If you parse my words carefully, they're compatible with that, but I didn't make it explicit, so let me do so now.
As Schrödinger himself noted, if you give me the wave function as a function of position — which makes sense if you're thinking of it, a little incorrectly, as a field — you're done. You don't separately need to give me the wave function as a function of position and as a function of momentum. You can calculate the probability of a momentum measurement outcome from the wave function as a function of position alone. In fact, this is deeply, intimately related to the uncertainty principle: Heisenberg's uncertainty principle says you don't have quantum states that are simultaneously definite in both position and momentum, because position and momentum are two different angles you can take on looking at the same thing — the quantum state, the wave function. Once you know the wave function as a function of position, you can do something called a Fourier transform and turn it into a wave function as a function of momentum, and vice versa. So you only need the wave function as a function of position or as a function of momentum — not both. That's the origin of the uncertainty principle.
To get a little technical: imagine a two-dimensional vector space with X and Y axes. I could rotate the axes to X+Y and X−Y, the two diagonals through the origin. Momentum is a bit like those diagonal axes, and position is like the original horizontal and vertical ones. If I have a vector specified by a point in X and Y, I don't need extra information to specify it in the rotated axes — it's already implicit there; there's a formula for finding the components in the new axes. That's exactly how position and momentum relate in quantum mechanics. The jargon, if you want to throw it around at cocktail parties, is that an entire quantum wave function can be expressed as a function of some complete set of commuting observables — observables you can measure one after the other without one interfering with the other. Position and spin, say, commute; the position and momentum of the same electron do not. So you don't need to include both: people talk about expressing the wave function "in position space" or "in momentum space" — the same information about the state of the system, just expressed in different variables.
This isn't a minor technicality — it's the essence of everything we'll discuss in the rest of this podcast, so pay attention. Classically, if I tell you a particle's momentum, you know nothing about its position, and vice versa. Quantum mechanically, if I give you the wave function as a function of momentum, I know everything about the wave function as a function of position, and vice versa. That's part of why quantum mechanics is hard to accept: position and momentum, in this realist view of the wave function, aren't what exists. What exists is the wave function. Position and momentum are projections of what really exists onto different possible axes — different possible questions you can ask of the wave function, with different possible answers. This points toward the idea that position and momentum aren't all that fundamental after all. There's something called the wave function, which we had to invent to explain the data, and we invented it in a world where, in our heads, position was very fundamental — things are located in position. The very existence of a quantum-mechanical wave function tells us things aren't quite located in position; they have wave functions as a function of position. But then there's this extra fact: the wave function isn't necessarily a function of position — it could equally well be a function of momentum, without ever mentioning position. Position is implicit, and you can transform it out, but it isn't necessary. That's a deep fact: position isn't necessary to talk about the wave function of the universe.
So what is necessary, what is fundamental, where is the wave function living? Here's where there's a slightly confusing discourse about the difference between wave functions and fields. A field is something that lives in space — a function of good old three-dimensional space, where we all live. At every point in space there's a value for the electric field, a little arrow pointing somewhere; likewise for the magnetic field, the gravitational field, the Higgs field. Wave functions aren't like that, partly because of entanglement: if I have two particles with positions x1 and x2, the wave function is a function of what we call the configuration space of the two-particle system — x1 and x2 together. And if x1 is really three variables (x1, y1, z1) and x2 likewise three more, that configuration space for two particles is six-dimensional, not the three-dimensional space we live in. So wave functions live as functions of configuration space, and some people take that very seriously indeed — configuration space is a giant thing. Avogadro's number, the number physicists and chemists use for the approximate number of particles in a gram of something, is about 6×10²³ — a big number — so six times that is the number of dimensions of configuration space for that many particles. Configuration space is enormous, and this is one of the points at which people get off the bus about the realism of the wave function, because people feel a deep-seated need to think that things live in space. That was one of Einstein's convictions — I'm very pro-Einstein, I think he had a lot of good ideas about quantum mechanics, but one where I'd disagree with him, if we could conjure up his spirit, is that he was devoted to things having locations in space. I think that's exactly what quantum mechanics says doesn't happen. The closest you can get is to say wave functions have values as functions of configuration space for many particles — and that's already weird. But there's an extra weirdness: even with a huge number of particles, you can still cast the wave function as a function of momentum space instead, and in fact there's an infinite number of combinations of position and momenta that work equally well as coordinates on some giant-dimensional space where the wave function lives. So this is already a demotion of our notions of the fundamentality of space, and velocity, and things like that. What it's really pointing at — and I'll finally say this out loud — is that what you call position and what you call momentum are choices of what questions to ask.
When you have the wave function, asking "what's the probability of observing it in some position?" is a choice — you're choosing to make a certain kind of observation that will give you a certain kind of answer. You could ask a different question: what about the momentum? Or, if you wanted to, some weirder combination of position and momentum. You're allowed to ask all sorts of questions and get different answers, and the underlying physics doesn't change. This is a very familiar situation in physics: you have a way of describing something, but it's the thing itself that matters, not your description of it. The classic example is coordinates in ordinary three-dimensional space. You might have Cartesian coordinates — X, Y, Z with perpendicular axes — or spherical or elliptical or other coordinate systems. In general relativity, Einstein's theory of curved spacetime, you need crazy coordinate systems, because spacetime isn't flat and simple rectilinear coordinates aren't available anymore — you have to use curvilinear ones. Mathematicians understood from a relatively early time that you shouldn't confuse the real thing with your convenient description of it — you shouldn't confuse what actually exists with your choice of labels, which is what coordinates are. That's easy to say, and you're all nodding along — it doesn't matter whether I express a distance in metres or feet; what matters is the physical thing, the length or distance itself. But in practice it's surprisingly hard to truly internalise this lesson, and Einstein himself failed at it repeatedly. He died in the 1950s, still not really understanding that black holes existed, and confused about whether gravitational waves were real. These days, black holes and gravitational waves are taken as among the most important implications of general relativity, but between 1915, when Einstein wrote down the theory, and the 1950s, when he died, people were confused about how to extract what was physically real in general relativity from what was simply an artefact of one coordinate system versus another. For gravitational waves, you can change coordinates so it looks like the wave isn't there; for black holes, you can change coordinates so the event horizon looks like just a boundary you can't get past. It took a lot of work to figure out how to disentangle what's real from what's merely a coordinate implication. The coordinates are not the territory — a simple motto for a very difficult lesson to truly internalise.
The reason I'm diverting into Einstein and coordinates is that I think — and here I'm in a tiny, idiosyncratic minority, so feel free to disbelieve me — we're facing a very similar problem in quantum mechanics. The choice of position, or the choice of momentum, as a way of expressing the wave function, are just choices of coordinates. We call the set of all possible wave functions or quantum states Hilbert space — a big vector space, so called because you can add wave functions together and scale them by numbers. We understand Hilbert space mathematically very well, and position and momentum, as with our two-dimensional example, are two different choices of basis vectors in this vector space — a particular kind of coordinate system on it. If you take seriously the idea that coordinates aren't what's real, just convenient ways of talking — and you were taking that seriously two minutes ago, when I said it about ordinary space — then position and momentum are not real. Not in quantum mechanics, anyway. They're just choices of coordinates on Hilbert space, choices of basis. They're things you're able to observe, but they're not fundamental to the theory's description. This is another point where people get off the bus, because they'll say: the fact that I can observe and measure position and momentum relatively straightforwardly does give them a privileged status. It's absolutely true that position and momentum are very convenient — easier to observe than other things — but nothing in the formalism of quantum mechanics says these are the only things you can possibly observe. They're choices, and our convenience doesn't define the fundamental nature of reality. So I don't think you can take these particular bases in Hilbert space very seriously when trying to understand reality — and I don't want to undersell the implications of that. They're big: position isn't fundamental, locations in space aren't part of the fundamental description of reality. People don't like that. Einstein would have hated it. Many people working today don't want to go down that road, because they think space is where things are located, and locality — the idea that things happen at locations in space, interacting only with their immediate neighbours — is really important. Einstein was a big believer in locality. John Bell, in Bell's theorem, points out that understanding the quantum measurement problem inevitably involves some kind of non-locality — there's a lot to be written about what kind of sense that is, and in many-worlds there's a sense in which it's true, though a different sense than in other approaches. I don't get too deep into those conversations, mostly because they tend to start from the presumption that we want locality to be there — we like it, we want to preserve it, or find some dance that keeps it around. I don't think that way. If you stare quantum mechanics in the face and ask what it's telling you, I think it's telling you that locality just isn't fundamental. And none of what I've said here involves quantum gravity, string theory, or emergent space — this is just undergraduate quantum mechanics. Already, at that level, you should know that locations in space are not fundamentally real.
So the game we're going to play today — and you might think we're still just warming up, but no, we've actually made some important points — is this: I'm not going to talk for twelve hours, because I'm raising questions and gesturing toward their solutions, not spelling out complete answers to research-level questions we don't yet fully have. The attitude we're taking is: let's stare reality in the eyeball. Let's not impose our precious notions of the world — what some call folk physics, the physics of stuff with locations moving around, which you'd have believed even before Aristotle — or, in Wilfrid Sellars's terms, the "manifest image" of the world, the image we have from everyday life. Or, as Judea Pearl has put it, when we're babies in the crib we're causally mapping the world around us, and as Alison Gopnik has also said, that causal map involves three-dimensional space, even if we don't call it that as babies, and things with locations in it. What I'm saying is: let's abandon all of that. Let's take seriously the idea that we're talking about a bare-bones, austere, fundamental version of reality, and our job is not to impose our folk wisdom on it, but to see how the manifest image of the world emerges from that deep-down austere image. That's the puzzle. That's the assignment the theory gives us. If you take that attitude — as bare-bones as possible, not bringing the baggage of classical, everyday experience and forcing it into boxes where it doesn't fit — what are we left with? What is quantum mechanics actually saying?
My claim is that the wave function, which you might think of as a function of position or momentum or whatever, is what mathematicians call a representation of the quantum-mechanical state. The quantum-mechanical state is a vector in Hilbert space — or sometimes an operator in Hilbert space, details we don't need here. That sounds a little circular, since Hilbert space is the space of all quantum-mechanical states and I'm saying the quantum state is a vector in it — but what it means is that we're positing a mathematical formalism that represents reality perfectly faithfully. So what is the world? It's sui generis, as philosophers say — its own thing. The world isn't something else; it's represented mathematically as a vector in Hilbert space, and you don't need to worry too much about the technical requirements for a vector space to count as a Hilbert space. All you need to know is that there's something called the quantum state, and it exists independently of how you express it — just as a number looks very different in base-ten notation than in base-two or hexadecimal, or as Roman numerals, but it's the same number. It's that underlying essence, independent of representation, that really matters. It doesn't matter whether you're in position space, configuration space, or momentum space; what matters is the vector, the quantum state you're representing. And let me tell you — even many committed Everettians are reluctant to admit this. Space, as we know it, or the configuration space of many particles moving around, is super useful — you can't get through life without talking about it. It's a bit like free will, to relate it to another recent podcast: you can't get through life acting as if human beings don't make choices and don't deserve praise or blame — but those choices are nowhere to be found in the fundamental laws of physics. That's fine; you can still imagine free will is real. You can still imagine that position space and momentum space are real; they're just not fundamental, not there in the most austere, deepest way of talking about reality. People are reluctant to go down that road because space seems super useful, super real — I move through it; how could I possibly imagine a description without space in it? My answer: space can still be there, but it's not fundamental — it's emergent. And that's the puzzle, why we're having this podcast: how do you start with quantum mechanics and find space within it? Is that even a sensible thing to try? I think it is, though I understand if you don't. Everettian quantum mechanics is already pretty far from the manifest image, with all these extra worlds and decoherence — and now I'm pushing it further away, by saying that space, locations, and particles bumping into each other aren't part of the fundamental description either. That makes it even more work to connect the underlying theory to the world we see. To me that sounds like a challenge worth taking up. To others, it sounds like something too unlikely ever to work, and I understand that too — but I want to see what we can do.
I've called this the problem of structure in Everettian quantum mechanics — though I realised belatedly that's probably not the best phrase, since Simon Saunders and others have used the same label for the problem of branching: when do things branch, where are the branches located, how many are there? That's not what I'm talking about. I'm asking: within each branch, why do things look like stuff arranged in space? Why do we get the particular manifest image we get, and is it uniquely defined, or just a choice we make? Even if objects and their locations in space aren't fundamental, we'd like to think they're not only emergent but that there's a uniquely right way for them to emerge. That's what we're after.
So let's raise the level of technicality a bit to address this. I've called this super austere, bare-bones approach Mad Dog Everettianism — a phrase Ashmeet Singh, a former student and current collaborator, and I coined after what the philosopher Owen Flanagan dubbed Alex Rosenberg, a previous Mindscape guest. Owen called Alex a "mad dog naturalist," meaning that to the extent you can be a mad dog naturalist, you take naturalism as far as it can possibly go — the most extreme version, the X-Games version. Now we're doing that for Everettianism: asking what's the least we can get away with, what's the most fundamental stuff needed to specify a quantum theory.
If you asked physicists on the street — make sure your street is outside the physics department — what defines a quantum-mechanical theory (I don't mean what defines quantum mechanics as a whole, like Everett versus pilot waves versus Copenhagen, but within some particular version, what chooses a model — what tells you this is the simple harmonic oscillator, that's the electromagnetic field, this is the electron in a hydrogen atom), people would say things like: you have a Hilbert space, the space of all possible quantum states — everyone agrees you need a vector in Hilbert space. The other thing everyone's version of quantum mechanics needs is some version of dynamics: the quantum state not only exists, it changes over time, usually phrased via the Schrödinger equation, though there are other formulations — Heisenberg's equations, the von Neumann equation, the path integral — different ways of saying how the state evolves. One way of specifying that is via the Hamiltonian of the theory, a quantum idea descended from an analogous classical one, which basically asks how much energy is in different parts of the wave function. It turns out that knowing the Hamiltonian — how different quantum states are associated with different energies — is enough to fix the dynamics via Schrödinger's equation. I mention this bit of jargon because people use the word "Hamiltonian" a lot in this game, and that's what they mean.
So: you have Hilbert space, you have a state, you have dynamics — but people will also say you need observables, things like position and momentum, and their relationships (they don't commute with each other; that's the uncertainty principle). So maybe you need to specify what all those observables are and how they relate. There's a technicality I won't get into: Hilbert spaces have a nice feature and a sad one. The nice feature is that all Hilbert spaces of the same dimension are the same space — you don't need to say which one you mean, unlike, say, two-dimensional surfaces, where telling me the dimension doesn't tell me whether you mean a sphere, a torus, or something else. The sad feature is that the dimension might be infinite — countably infinite, the same size of infinity as the integers, smaller than the uncountable infinity of the real numbers. When Hilbert space is infinite-dimensional, there's a whole set of new mathematical subtleties, and this is where specifying observables becomes important — people think it's necessary. I suspect it isn't. I'm writing a paper right now with a student, Hongzhu Liu, here at Johns Hopkins, investigating this question — I don't think observables are actually necessary; I think they emerge from everything else, though there are subtleties we'll get into in the paper. For now, that's just a footnote. Let's make our lives easy for the rest of this podcast and imagine Hilbert space is finite-dimensional. It might be — we actually don't know; it's one of the embarrassing things about approaches to a theory of everything that people don't even know how big Hilbert space is. Isn't that sad? But that's the state of the art; we have to work with what we've got.
So my claim is that observables — position, momentum, spin, whatever — aren't part of what defines your quantum-mechanical theory. What defines it is just the vector in Hilbert space, evolving through time. That's all that exists — not that nothing else exists, but at the most fundamental level, that's it. What you need to do is show how that minimal information implies emergent structure at a higher level. To be fair, you also need to know, counterfactually, how different vectors would evolve — that's what the Schrödinger equation tells you: given the set of all possible wave functions, how would each of them evolve. From that, the task is to find space within Hilbert space — to find the manifest-image description of the world, stuff moving around in a three-dimensional universe. Those of you who know me know I've been working on this for about ten years — many people, including me, have their internal sense of time basically frozen by the pandemic, so things that happened ten years ago feel like five — but for roughly a decade, my students, colleagues, and I have been working on some version of this problem on and off, and right now it's very much on: I have a great group of students at Hopkins diving into different aspects of it. How do you get the world to emerge from this bare-bones description of a vector travelling through Hilbert space?
The root of it is something we've called quantum mereology — the title of a paper I wrote with Ashmeet Singh. Mereology is a term borrowed from philosophy, referring to the relationship between a whole and the parts you divide it into. You may have heard the idea that philosophy is about carving nature at its joints — that goes back to Plato, who, in the dialogue Phaedrus, talked about how you understand the world better if you carve it the way a butcher would carve a piece of meat: cutting between the bones, at the joints, rather than artificially carving it somewhere else. So we're asking: how do you carve Hilbert space at its joints? That's what the theory doesn't give you, and it's what we're trying to figure out. In slightly more technical terms, what we're looking for is a definition of subsystems in Hilbert space — which runs very backward from how the game is usually played. If you learn quantum mechanics as an undergraduate, or pick up a textbook, you're usually told: here's an electron, here's its wave function; what if you have two electrons? Here's the recipe for taking two systems and combining them into the system of both — a recipe that, if you want the details, involves tensor products. There's a definite way, in quantum mechanics, to aggregate subsystems into bigger systems. We're trying to go the other way — to reverse-engineer it. We have the whole system, but no one has divided it into subsystems for us. Are there better and worse ways of dividing the whole of Hilbert space into subsystems — of carving Hilbert space at its joints?
There are infinitely many possible ways to divide up Hilbert space, but some will be more useful than others, and what we have in the back of our minds is, essentially, space — that's the most important thing to get out of this game. Space doesn't show up as part of the fundamental definition of quantum mechanics, but we want to locate it somewhere. There are actually two different ways space shows up — closely connected, though we don't need to go into how — and this part is not one of the hard things to accept. One is: if you just have something like an electron, or a macroscopic object like Schrödinger's cat, some buckyballs, or a solid superconductor — whatever quantum system you're discussing — you want to cast it as something moving in a three-dimensional world we call space. What you really want to do is divide Hilbert space into "here's the cat, here's the box it's in, here's the vial of gas, here's the Geiger counter, here's the source, here's the observer" — dividing it into subsystems that connect to things we'd identify as objects in the real world. Again, that's not there in the bare-bones Everettian description of the theory; it's something we're inventing, and there might be a good way or a bad way to do it.
The other way space shows up is connected, but presented a little differently, in quantum field theory, which we think is our best way of describing particle physics: things are made of fields. The electron is a vibration in the electron field — that's why all electrons are the same; there's a famous idea of Wheeler's that all electrons are literally the same electron, which is wrong, it doesn't work; the real answer is that all electrons are vibrations in a single underlying electron field, all photons are vibrations in a single underlying electromagnetic field, and so on. Fields take a value at every point in space, or spacetime, so you need the idea of space to talk about fields at all. Quantum mechanically, if you want to talk about the Hilbert space for a field theory — glossing over technicalities — imagine dividing the room I'm in into little cubes a millimetre across on every side: a huge number of little cubes, each locating a different part of the room. Every one of those cubes has fields that can vibrate in it, and I can express the wave function of the field in the whole room as the combination — the tensor product — of what the fields are doing in every box, entangled with each other as much as quantum mechanics allows. The crucially important thing about this way of dividing the field into values at different locations is that the fields' interactions are local in space and in time. This is a point where philosophers of quantum mechanics and working physicists talk past each other a lot: philosophers, remembering that Bell proved some kind of non-locality in quantum measurement, while working physicists mostly think quantum measurement is trivial and spend their time calculating pre-measurement dynamics — Feynman diagrams and so forth — for the electromagnetic field interacting with electrons and quarks, and then, at the end, "we observe it, the wave function collapses, and that's easy." So to a working particle physicist, what matters is the unmeasured, unitary dynamics of the system, and that, as far as we know, is strictly local: if I poke the electromagnetic field at one point, it doesn't instantly change throughout the universe — Einstein told us that's not even meaningful. Instead it changes within its future light cone, with influences that travel slower than or up to the speed of light. In the language of physics, poking the field at one point interacts directly with the field's values right next door — its nearest neighbours. Going back to the picture of subdividing space into little cubes: any one cube only touches and interacts with the cubes next to it; it doesn't immediately and directly influence what's happening very far away, at least as far as the unmeasured quantum dynamics is concerned. So, as much as quantum measurement seems to involve some non-locality, quantum field theory, when it's not being measured, is very local — and we can think of that as an implication of a particular way of dividing up Hilbert space, of carving it at its joints: carving it into the Hilbert space happening in this little cube, and that little cube, and all the cubes around it. All the little lattice subdivisions of space go into Hilbert space, and that's a particular way of dividing it up so that it looks like space, so that it looks local.
So those are two ways in which space is important: a high-level way, when we divide the world into objects — cats, boxes, observers, each getting its own factor of Hilbert space — or a deeper way, in quantum field theory, where literal regions of space have different vibrating fields, local in the sense that they only talk to their nearest neighbours. Both notions of space are intimately related, as I said, but what matters is that they're there — and they're certainly there from the start in the usual way of doing physics, where we start with space and objects and only then ask how to put that into a quantum-mechanical context. Our project runs backwards: how do you start from a big vector in an abstract Hilbert space, with no subdivision into regions of space or objects at all, and find that structure? The question becomes: how do you subdivide Hilbert space so that the subsystems represent useful things in their own right — so that there's some tangible physical meaning to a given subsystem of Hilbert space? That sounds a little weak and fuzzy — like some Copenhagen-style "you know it when you see it." If there are infinitely many ways to divide up Hilbert space, how do we know when we've got the right one? How do we know your right answer is the same as mine? In fact, I think it's not nearly as weak or subjective as it sounds — this is a very common feature of emergence.
Forget quantum mechanics for a second and think about classical statistical physics — statistical mechanics leading into thermodynamics or fluid mechanics. I use this example all the time, so you probably know it. If I have a bunch of atoms and molecules in the air around me, I can coarse-grain them to get things like temperature, density, and pressure — a fluid-mechanical description of the air in the room. But that's not an obvious thing to do. When I perform that emergence, I define quantities like temperature, density, and pressure by averaging over small regions of space, because space is the arena in which interactions are local — just as in quantum field theory. In the particle-physics or kinetic-theory way of talking, atoms bump into each other when they're at the same point in space, not when they're moving at the same speed. So there's a way of coarse-graining the atomic description by averaging over regions of space, and that's one of an infinite number of ways I could coarse-grain — but it's certainly the useful one. It's useful because the variables I get out of it — pressure, density, temperature — are sufficient to give a self-contained, autonomous, emergent theory. I can talk about fluid mechanics, or atmospheric science, without knowing about atoms. Most meteorologists don't need to know about atoms, or the standard model of particle physics, to do their job — that would be weird. This is Philip Anderson's "more is different": I can talk about the emergent level without knowing about the lower level beneath it. They're both interesting, both connected, and need to be compatible with each other, but I don't need to know one to talk about the other. That doesn't mean the relationship between them is arbitrary — fluid mechanics is a coarse-grained version of statistical or atomic physics, but that coarse-graining is a very specific way of getting the emergent description, not just any way.
My claim is that the emergence of space itself works exactly the same way. I can imagine a googolplex of different ways to divide up Hilbert space into subsystems, but one of them has the property that, for example, interactions are local. This was the result of a paper by Jordan Cotler, Jeff Pennington, and Daniel Harlow — one of my favourites — called "Locality from the Spectrum," where the spectrum is a way of specifying the Hamiltonian that gives you the dynamics. They asked: if you didn't already know about locality in quantum mechanics, could you find it? Their answer: among the set of all possible ways to take a big Hilbert space and subdivide it into little Hilbert spaces, hoping they'll represent regions of space, almost all of them have the property that every little subsystem interacts directly with every other subsystem. If you carved Hilbert space badly — carved it at its non-joints — then poking the field right in front of your face would affect the value of the field everywhere in the universe, instantly. So locality is very special: when I have a little quantum field at one point in space and I perturb it, the implications of that perturbation only affect its immediate neighbours, and then their immediate neighbours, and so on — that's a very delicately chosen way of dividing Hilbert space. The implications of the paper are that most Hamiltonians, most ways of writing down the dynamics of a vector in Hilbert space, have no local way of talking about them at all — you can't divide Hilbert space, for a generic set of dynamics, into subsystems that resemble space, where poking one only affects its nearest neighbours. Generically, poking anything changes everything else right away. And they go on to say that when there is a local way of subdividing Hilbert space, it's essentially unique. There's been some pushback in the literature — some people think you need an extra ingredient, which is fine, that's how research goes, we disagree and see how things shake out — but I think it's basically right, morally: you don't get a huge number of inequivalent ways of taking the same Hilbert space and making it look like space in very different ways — like ten-dimensional space, or eight-dimensional space, or a cone. There's some rigidity to the answer of what the right way to subdivide Hilbert space is.
This is a very common thing in treatments of emergence generally. If you go back to the philosophical discussions of mereology, this debate already happened in the literature: why can't you just divide things arbitrarily? Well, some divisions work and some don't; some notions of subsystems work and some don't. David Lewis, whom we've talked about before, was an advocate of modal realism — believing in the existence of all possible worlds and using that to reason about probability — and he invented an example of a bad way to carve nature: the trout-turkey. Take a particular trout — not the idea of a trout, a particular fish — and take its front half; take a particular turkey and take its back half. Consider the combination of the front half of the trout and the back half of the turkey — don't ask me how philosophers come up with these examples, it's their stock-in-trade. His point is that this isn't a good object. You're allowed to contemplate it if you like, but it doesn't give you a handle on reality; it doesn't teach you anything. There's no fact about the trout-turkey that improves your understanding of the world beyond what you'd get from separate facts about the trout and the turkey.
Another way of making the same point is Dan Dennett's idea of real patterns — Dennett was a former Mindscape guest. There are many, many things happening at the microscopic level, and you might imagine many ways of getting coarse-grained descriptions of them, but some give you real, useful information and some don't. You can average over locations in space; you can't usefully average over locations in momentum space — or rather, you could, but the answer wouldn't be a useful emergent theory. David Wallace, another former Mindscape guest — not to be confused with David Lewis — has emphasised the idea of real patterns in Everettian quantum mechanics, and like his former colleague Simon Saunders, he's talking about the branches, the worlds: David's point is that the worlds in Everett are real patterns, and you can show why they're useful ways of talking about the wave function. What I'm talking about here is a little different: we're asking where the real patterns are within each branch. As I said, I'm not really interested here in the worlds — I'm interested in the structure within the world. I gave you the example of space, from the Cotler-Pennington-Harlow paper, but the overall story is: you propose criteria that we recognise from the manifest image — nothing wrong with knowing what answer you want, since at the end of the day we want to start with this weird abstract thing, a vector in Hilbert space, and locate within it three-dimensional space, cats, boxes, and all the rest. So we can use what we know about the manifest image to help us on that journey: we invent criteria we recognise from the world around us, and ask whether those criteria pin down the right way to divide up Hilbert space. That's the quantum mereology programme.
So the answer — and this is the ongoing research problem, and where we start to fade out on what we can say here — is: yes, I think it can be done. The example of locality is an important step in the right direction. There's also the division in quantum mechanics that some of you may know about, involving decoherence and branching. Something crucially important is dividing the quantum state into what we'd label the system — the thing we're going to study and measure, whether an electron, a cat, a solid, whatever — and the environment. Already, in this picture, there's no special role played by observers or measurement; all that discussion is replaced by the dynamics of systems and environments, leading to what we call decoherence. What matters here is that when a quantum-mechanical system in a superposition of different measurement outcomes gets monitored by its environment — now we can actually talk about Schrödinger's cat: the cat is in a superposition of awake and asleep, and there's also an environment, everything else in the box — the photons of light, the atoms of air. Those environmental degrees of freedom keep bumping into the cat, and the environment becomes entangled with it very quickly. That's decoherence: becoming entangled with the environment, and that's when the wave function branches into two branches, which is why when you open the box, you see the cat awake or asleep, not in a superposition of both. This division of macroscopic reality into systems and environments is central to the story we tell about relating quantum mechanics to the real world, and it was the subject of the paper I wrote with Ashmeet Singh. There's a lot going on here — I think we've only just started thinking about it properly, even though we wrote that paper years ago, and there's a lot more work to be done.
What Ashmeet and I pointed out is that there are actually two things going on when you divide the world into a system and an environment. One is what we teach undergraduates in their quantum classes: a theorem called Ehrenfest's theorem, which says, roughly — there are technical requirements we won't go into — that under good circumstances, the expectation value of a measurable quantity like position obeys the classical equations of motion. If you take the Earth, with its centre-of-mass position, something you could imagine observing — why is it that, even though the world is truly quantum mechanical, the Earth obeys Newton's laws of gravity and celestial mechanics so well? The answer is Ehrenfest's theorem: there's very little uncertainty in the position of the Earth's centre of mass, so it will basically obey its classical equations of motion. So one thing you want, in this game of inventing criteria that should be true in the emergent classical or semi-classical description, is that when a big macroscopic system has a more-or-less localised quantum state, that state should remain more or less localised. If you picked your variables so that localising a system of interest caused it to instantly delocalise, that would be bad — and in fact that generically would happen; it's closely related to the fact that a generic division of Hilbert space has no locality at all, with everything talking to everything else, and likewise no localisability, with anything that starts in one small region instantly spreading out under a bad decomposition of Hilbert space. So: you want a localised system to remain localised.
The other, more subtle thing — and I think this one is genuinely interesting and provocative — concerns the relationship between the environment and the system. I said the atoms of air, or the photons, in the box with Schrödinger's cat interact differently with the cat depending on whether it's awake or asleep — that's the origin of entanglement, and people like Wojciech Zurek have emphasised how it's the origin of decoherence; it's a beautiful story. But there's another fact, equally important: once you're in a single branch — once you've decohered, so now you just have a cat that's awake, the classical world you're familiar with — you don't keep entangling further. Once the cat is in one spatially coherent configuration or another, the atoms of air and photons in the room interact with it, but they interact with it the same way; the cat isn't in a superposition of being here and being there. If the cat were in a macroscopically distinct superposition, its two parts would interact differently with the environment, and it would entangle. But once it's in a single, spatially recognisable configuration, it doesn't interact differently with the atoms or photons around it — every photon gets absorbed or scatters the same way. That's also an important facet of carving Hilbert space into systems and environments: we want a localised system to remain localised, and once it's unentangled — once it's in what we call the pointer state, the classical-looking state of the system — to remain unentangled. We argued that these criteria are enough to help figure out the right way to carve Hilbert space into subsystems.
So those two examples — finding locality in space, and finding the system-environment distinction — just from the bare-bones ingredients of a vector evolving in Hilbert space, seem plausible; there seems to be a right way to do it. I promised you I'd tell you about challenges to Everettian quantum mechanics, and the challenge isn't that this can't be done — it's that it hasn't been done yet. Both of these examples are pretty tiny compared to the full glory of the world we actually want to understand the origin of. The technicality about infinite versus finite dimensionality isn't the main issue; there's a lot still to be done.
To me, there are only two real, big, looming questions in Everettian quantum mechanics. One is the nature of probability, which I haven't talked about and won't get into in this podcast — I think it's a good philosophical question, but I think we know what the answer should be, and we have quite plausible, even persuasive, arguments that we get the answer we want: the Born rule, probabilities given by the wave function squared. The origin of structure — space, and the things in it — is much less understood. That, to me, is the real frontier in Everettian quantum mechanics, and it's possible it might fail. This is the sense in which it's a genuine problem for the theory: once you have a puzzle you haven't yet figured out the answer to, maybe you'll figure it out, or maybe you'll realise there actually is no good answer. That's entirely possible for this particular programme. If Everettian quantum mechanics doesn't work in some sense — if it needs to be changed, modified, or replaced — this is where I think it will be.
I've been telling you the optimistic version of that story, so is there any reason to think it might not work? I'll give you the single best reason, and then tell you why I still don't think it's a very good reason — if I thought it wasn't going to work, I'd be doing something else. The whole story I've told is about starting with almost nothing — a vector in Hilbert space — and deriving everything: how to divide the world into subsystems we recognise as objects, locations in space, and so on. But surely the most important thing — the constraints, the information that led to certain ways of dividing Hilbert space being good and useful, and others being wastes of time — came from the dynamics, from how the quantum state evolves with time. Clearly. But what if it doesn't evolve with time at all? What if it just sits there, static?
On the one hand, that would be trouble: everything we've said would completely fail if quantum-mechanical systems truly didn't evolve with time, because time evolution was the only thing we had to work with. A quantum state that doesn't evolve with time is just sitting in Hilbert space — it wouldn't even matter that it's in Hilbert space; it's just a vector, and who cares about the rest of Hilbert space it will never visit? In some sense you'd be stuck with the kind of problem Daniel Harlow has raised, where he thinks Hilbert space is one-dimensional at the fundamental level — there's nothing to do in a one-dimensional Hilbert space. You want Hilbert space to be very big; if it's big but we only ever live in a single vector of it, it's effectively one-dimensional, and nothing can happen. You might ask how likely it is that we're stuck in that situation — sadly, it's quite plausible, and the reason is quantum gravity.
Whenever we start talking about quantum gravity we should be humble — there's a lot we haven't understood — but we can do the most obvious thing: take our very successful theory of classical gravity, Einstein's general relativity, and try to quantise it. What you get, as we discussed with Harlow in an earlier episode, is the Wheeler–DeWitt equation — a version of the Schrödinger equation, except that instead of the Hamiltonian telling you how fast the wave function evolves with time, the Wheeler–DeWitt equation's Hamiltonian says the wave function does not evolve with time at all. There's no time variable in it, no T for a time coordinate. This is so obvious and glaring that it's been given a name, the problem of time, which I've talked about before, in other solo episodes about whether time is real and whether it can emerge. In this particular context — figuring out how Hilbert space can be divided — it goes from an annoying anomaly we'll have to find some clever way to deal with, to a real problem: all the ways we found structure emerging in Hilbert space depended on the dynamics of the quantum state. Given the dynamics, we can say things like local systems remain local, interactions only move through nearest neighbours — all of that depends on interaction, change, dynamics. If there's no time, you can't play this game at all. That's another thing we're working on right now.
The good news is that time certainly does seem to exist — in the real world, time seems to be important, and to be there. So for any version of quantum gravity, we're going to need time to emerge somehow, and once it does, we can use that emergent notion of time to play all the games we've just discussed. The possible catch is an order-of-operations problem: what if you need structure to get time to emerge, and you need time to get structure? That would be a legitimate problem. We have some ideas we're trying to work through to fix it. Carlo Rovelli, one of the first-ever Mindscape guests, had an idea with Alain Connes called thermal time, where you think of the quantum state as defined by a density operator on Hilbert space rather than a vector in Hilbert space — there's a lot of complicated mathematics there, but it might be a way to get time to emerge uniquely, or at least in a good way. But these are open questions; I don't know exactly how it will work. We're thinking about it.
I want to close by explaining why this matters — my sales pitch for why physicists generally, especially those interested in high-energy or fundamental physics, should care about the foundations of quantum mechanics. Thinking about quantum states and mereology forces you to confront questions you otherwise wouldn't have to confront. In the usual way of doing physics, you start with something like a classical, structured description of the world, and then you quantise it — helping yourself to a huge amount of structure that's very useful. The suggestion from Everettian quantum mechanics is that this is cheating: you're helping yourself to something that isn't actually there, and you should find out how it emerges. That might help with a whole bunch of interesting questions — maybe fine-tuning questions about the hierarchy, or the cosmological constant, maybe what happened at the Big Bang, or the arrow of time. Maybe there are even experimental implications. A lot of the physics theorising and philosophising I do has no immediate experimental implications, but the word "immediate" is doing a lot of work there — if we think about it carefully enough, we might squeeze some out. For example, if the very notion of locality — that things exist at locations in space — isn't fundamental but emergent, then, like all emergent descriptions, it should break down at some level. You can treat the air in this room as a fluid, but once you're down to a single atom in the box, you can't treat it as a fluid anymore. Maybe locality breaks down too — maybe it's just a good approximation. How would you know experimentally? That's another thing we're working on; I don't even know what experiment you'd do, and the reason we don't know is that the way you normally do science is to come up with a theory, and if it fits the data, you pat yourself on the back. All of our theories have locality built into them, centrally, as a starting point, and it works — so we don't ask how well it works, how it would fail if it weren't there. I think being forced to think about these questions this way leads you to ask other questions you wouldn't otherwise think to ask — questions about possible experimental signatures. What would be the first thing to show up if locality were only approximately true, rather than exactly true? I don't know, but it's an interesting thing to think about.
So, at the end of the day, I hope I haven't disappointed anyone who wanted me to steel-man all the reasons Everettian quantum mechanics is wrong, because I don't think it is. I think it has unanswered questions, and if we become convinced there are no good answers to them, then it would be wrong, and we'd give up on it and move on to something else. I know people want a single, simple experiment that would rule the theory out cleanly, once and for all, but that's not how science works. Science is a complicated interplay between people proposing theoretical ideas, people proposing experimental probes of those ideas, people doing experiments, other people doing experiments just for the hell of it and finding surprising things, and everyone trying to figure out how it all best fits together. You don't have the right to demand a single experiment within a few months or you won't take a theory seriously — you can demand it, but no one has any obligation to listen. Instead, I think what we're going to do is continue developing the theory. We don't have knock-down arguments against Everett, but we have open questions, and we're going to keep thinking about how best to address them. That continued thought — what we call research — will hopefully lead to new, fun ideas, maybe solving some old problems, but also maybe to some obstacles that don't go away, where we realise this didn't pan out, this idea wasn't as good as we thought. That's entirely possible. I'm not betting on it happening — I think we're actually going to discover some cool things. I think taking the foundations of quantum mechanics seriously in general, and this super austere, ambitious version of Everettian quantum mechanics in particular, is going to lead to a lot of progress and a lot of good ideas in physics. We'll see whether I turn out to be right.