Harvard Scientist: "There is No Quantum Multiverse" | Jacob Barandes [Part 3]

We don't have a single interpretation of quantum mechanics that doesn't suffer from serious problems. I traveled to the oldest laboratory in the United States to meet with theoretical physicist Jacob Barandes at Harvard University. He's the co-director of the graduate studies department there. We delved into the technical depths of his innovative reformulation of quantum theory based on more fundamental mechanisms called indivisible random processes. My name is Curt Jaimungal, and this was part of my three-day tour of Harvard, Tufts, and MIT, where I recorded five audio files. One of them you see now, with Jacob Barandes. It was actually over seven hours long, so we're splitting it into two parts, and this is part two. Part one is also linked in the description. The others are with Mike Levin, Anna Chunikina, Manolis Kellis, and William Hahn. Subscribe to get notified.

In this episode, we talk about what are the misconceptions about wave-particle duality and entanglement? Is gravity actually quantized? What about counterfactuality and Bell's theorem, and what exactly are indivisible random processes? Curt, it's good to see you again. It's good to see you. It's been a long time. Wave-particle duality. What is that? Okay. When Schrodinger introduced the idea of the wave function in that 1926-ish paper, based on Hamilton Jacobi theory, and his wave theory of mechanics, and this wave function living in a high dimensional configuration space, he had introduced a new methodology, a technique for calculating things in quantum mechanics. He used the wave function as an indirect way of calculating energy levels. What are the energy levels of atoms that then correspond to frequencies of radiation coming out of atoms? Einstein had a lot of problems with this. So did Heisenberg. One of the few things Einstein and Heisenberg agreed on is that they didn't really like Schrodinger's wave mechanics, metaphysically. I think Einstein said that physics had been completely Schrodingered at this point. And part of the reason why Einstein in particular was worried is that Schrodinger was embracing a kind of what we call wave function realism, that the wave function is a real thing, a physically and metaphysically real thing in a high dimensional configuration space whose meaning is somehow projected down into three dimensions of physical space, and that everything that's really happening was in this high-dimensional abstract space of possibilities, this configuration space. That's where the waves were. And eventually, Schrodinger retreated from that view in one of our previous conversations. I talked about how Schrodinger, in his 1928 fourth lecture, titled Wave Mechanics, expressed some doubts about wave function realism. He indicated that maybe you could think of the wave function as representing all the possible realities of what could happen to the system in a kind of very embryonic version of the many worlds interpretation. But Schrodinger retreated from that view in 1928 in the face of things like Born who said that the wave function should be understood as a tool for calculating measurement probabilities. But in the period from 1926 to 1928, when Schrodinger was still pushing the idea of the wave function as some kind of physical fundamental, Einstein was very puzzled. There's a very famous letter dated December 4th, 1926, from Einstein to his colleague, Max Born, the same Born rule, where Einstein said his famous line that he doesn't believe God plays dice. That's famous, I do not believe God plays dice. What people often don't know is that the very next sentence in that letter is a critique of Schrodinger's wave function realism. And he says that the waves in three-dimensional space are like rubber bands. And he also has similar dots, as if he's writing an ellipsis in the letter. He's like, doesn't even know what to say. What's interesting is that in the canonical translation of the Einstein-Born letters, the collection of letters of correspondence between Einstein and Max Born, the letters translated into English, were translated by Irene Born, and the letter N is missing. Einstein just says, waves in three-dimensional space as if rubber bands, the N is missing. And without the N, you don't realize that his concern isn't waves per se, but his concern is 3N dimensional wave functions in configuration space. That's what he was stressed about. But if you look at the original German, you'll find the N is there. So, Einstein had a lot of doubts about this idea. But the idea has earlier origins, doesn't it? The idea of matter waves introduced by de Broglie is that particles like electrons and waves were linked by an analogy to how light is classically considered a wave. And then came the evidence, starting with Planck and Einstein, that light has particle-like properties. This idea that some phenomena have both particle-like and wave-like features became known as wave-particle duality. And when people study, for example, the double slit experiment, and they do the double slit experiment in the traditional way, one particle at a time, the wave function that we can pretend is moving in three-dimensional space, but that's really just an artifact of the fact that the configuration space for a single particle looks three-dimensional. It seems like you have to treat the particles as a wave as it goes through the slits to get the right pattern across many repetitions in landing locations. We don't actually see a wave on the other side. What we see are dots, and many, many landing locations across many repetitions of the experiment. The wave is inferred. But when you measure where the particle is at the end of the experiment, or you measure which slit it goes through, you get a definite result, and that's what makes it seem more particle-like. So this is the idea that things are sometimes particle-like, and sometimes wave-like, depending on which feature of the system we're trying to study. This has become known as wave-particle duality. And what complicates matters further is the fact that there are different kinds of waves in physics. Electromagnetic waves for example. Light is a disturbance in the electromagnetic field that propagates like a wave through three-dimensional space. And those are waves. I mean, as I said, I teach electromagnetism from Jackson. We talk about waves moving through three-dimensional space. It's very easy to confuse field waves, like the electromagnetic field, with wave functions or Schrodinger waves in quantum mechanics, but they're not the same thing. And this has led to wave-particle duality. When Planck in 1900 and Einstein in 1905 and many other people proposed that light comes in quanta, particle-like discrete quanta called photons, the wave they were imagining, the wave corresponding to the photons, was a three-dimensional electromagnetic wave. A wave of the familiar kind of waves. The wave functions introduced by Schrodinger in 1926 were not like those waves. They were not three-dimensional waves in physical space of the field. They were these abstract, complex-valued functions in a high-dimensional configuration space. And when you measured them, they collapsed. Now, if you're in an MRI machine, and they turn on a very strong magnetic field, don't worry that if you make the wrong measurement, you're going to collapse the magnetic field in the MRI machine. It's not that kind of field. The waves they're sending to you aren't those kinds of waves. So you have to distinguish between the old waves, the field waves, and the Schrodinger waves. And I want to make it perfectly clear that in the indivisible random approach to quantum mechanics that we've been talking about, I say that Schrodinger waves are not real things. These abstract things living in this high-dimensional configuration space, are not physically real. But classical waves or field waves, which are a conceptually different and distinct kind of wave, those are perfectly fine. And if you study a system that's not made of particles, but a system made of fields, you'll see wave-like behavior as well, but those are a different kind of wave. And these are the kinds of subtle details that I think get lost when someone says wave-particle duality. So again, to summarize that, the relationship between a photon and a light particle and an electromagnetic wave is not like the relationship between an electron and the Schrodinger wave function of the electron. And what makes this even more confusing is that electrons have fields as well. There's something called the Dirac field that plays a very important role in the standard model. And that's a field, a three-dimensional field of the electron, but the Dirac field of the electron is not the Schrodinger wave of the electron. These are very subtle distinctions, but it's important to keep them in mind. What makes this even more confusing is that particles like electrons, which are called fermions, are particles that have intrinsic half-integer spin. They are the particles that obey the Pauli exclusion principle. You can't put them all in the same energy state. They make chemistry possible by not having all the atoms collapse to the ground state. Electrons are like that, quarks, protons, neutrons. And even though they have fields associated with them, the fields associated with them aren't classical fields like the electromagnetic field. The fields are much weirder and stranger. And I won't have time to talk about them very much except to say that one of the limitations of Bohmian mechanics is that it has a very hard time dealing with the kinds of fields associated with fermions. And that's one of the reasons why Bohmian mechanics has difficulty, Bohm's pilot wave theory. I'm getting ahead of myself a lot, but I just wanted to clarify what's going on in wave-particle duality. So, in the indivisible random approach, there are no Schrodinger waves as part of the fundamental physics. Of course, you can, when you go to the Hilbert space picture, you can write down wave functions mathematically and use them, and write down Schrodinger waves, but they're not actually there. You don't need them to explain interference patterns. The indivisible random dynamics itself generally predicts that you will have what looks across many repetitions of the experiment points that look like they're following some kind of wave equation, but there's no wave actually involved in those experiments. But I'm not saying that field waves, the waves that exist in fields are not there. That's a different kind of wave.

So, talking about these waves, you indirectly mentioned quantum field theory with Dirac. Does your approach shed light on any aspect of quantum field theory or the standard model? We've certainly talked about quantum mechanics, especially in part one and part two. What about QFT? Yes, one of the nice things about Bohm's pilot wave theory is that it works really beautifully with systems with fixed numbers of non-relativistic infinitely many particles. That's a lot of qualifiers. It doesn't work so easily for fields. You end up either having to do extremely complicated things or maybe even introducing randomness of some kind. It becomes kind of messy, and there's a significant difficulty in dealing with fermionic fields in particular, the fields associated with particles like electrons. One of the advantages of this approach is, well, let me say something really quickly about Bohmian mechanics now. And this is different because this is also related. In Bohmian mechanics, again, for systems of fixed numbers of a finite number of non-relativistic particles, we have deterministic equations. There's a pilot wave that guides the particles. The wave function, the pilot wave obeys the Schrodinger equation. Then there's another equation called the guidance equation which is how the wave works, where the pilot wave guides the particles. And everything is deterministic. There are no fundamental probabilities. There is some initial uncertainty in the initial configuration of the system. And these evolve to become Born rule probabilities later. But the dynamics is fundamentally deterministic and doesn't generate probabilities in a law-like way. That picture is very elegant in some ways, provided you're okay with having a pilot wave that lives in a high-dimensional configuration space. Although I should say that Goldstein and Der and Zangi have actually proposed the idea that the Bohmian pilot wave is law-like and not a physical thing. So there are other ways of reading that theory. The problem is that it helps itself to a lot of very special features of models that consist of fixed numbers of non-relativistic infinitely many particles, which aren't available when you go to more general systems like fields. So you end up writing down something completely different looking model, including in some cases models that you now need to deal with randomness and non-deterministic dynamics. And it doesn't work very well when you try to go beyond that. One other thing that Bohmian mechanics requires is a preferred foliation of spacetime. So last time we talked, we talked about that in special relativity, there's no preferred way of taking spacetime and slicing it into moments of time, like different ways of doing that. The guidance equation, the equation that takes the pilot wave and explains how the pilot wave, obeying the Schrodinger equation, and how the pilot wave guides the particles, they call it the guidance equation, relies on having a preferred foliation of spacetime, a slicing of spacetime into moments of time. And that's also not really great. It works fine in the non-relativistic case, but we want to deal with relativistic physics as we often do when we want to do quantum field theory, which is the kind of models we use when we want to deal with special relativity and quantum mechanics together, like in the standard model. It's very difficult to deal with preferred foliation, not impossible, but… it would be nice if we didn't need it. In the indivisible random approach, there's no guidance equation. There's no pilot wave. That doesn't mean you solve a Schrodinger equation, and you get a pilot wave, and then you take the pilot wave and put it into a guidance equation, which relies on preferred foliation, and then guide… none of that happens. There's just the indivisible random dynamics, which can be represented in the Hilbert space language, but the dynamics happens directly. There's no intermediary. There's no pilot wave and guidance equation in the middle. And that means the theory won't be deterministic. I think one of the questions in the comments is, is this fundamentally deterministic or not? It's non-deterministic. It's not a deterministic theory. Because there's no guidance equation, there's no preferred foliation. Because we don't rely on all of these special features of the particle case, it's now quite straightforward to generalize this to more general kinds of systems. Did you do it? Did you do it? Good question. There's this thing called time, and time is finite and limited. Is it? It's surprisingly. In your framework? At least in my lifetime. Okay. And when we get to open-ended questions like directions of research, which maybe people watching this might be interested in, because, I mean, the best part of formulating or picturing or modeling something new or anything else, are there things people can work on? There are things people can work on. That's one of the things that people can work on. So, the term here is straightforward and principled in terms of generalizing this to quantum fields, because there's no, there's none of the obstacles as before. One of the problems of Bohmian mechanics is that your wave function has to live in a space, configuration space. And fermionic particles don't have a familiar kind of configuration space. And that makes it very difficult to do Bohmian mechanics. But there's no pilot wave here, so you don't even have that obstacle. A lot of the things that would have prevented us from applying this to any kind of system are no longer there. So, if you want to deal with field theory, you just replace the particle locations with the local field density. Those become your degrees of freedom. And then you just apply the random laws to them, and it works in the usual way. A problem with quantum field theory is that quantum fields in general are that they have infinitely many degrees of freedom, infinitely many moving parts at every point in space, you know, I mean, that's a whole renormalization story, and effective field theory, but as in the simplest bird's eye view kind of thing, you have a degree of freedom at every point in space, infinitely many of them. And that makes them extremely difficult to deal with mathematically. Even in the traditional Hilbert space formulation or path integral, quantum field theories are extremely difficult mathematically. And there are very few, if any, I think there are no precisely defined quantum field theories that are also suitably experimentally applicable. Like any of the quantum field theories that make up the standard model are not precisely defined. That means that anytime you mention quantum field theory, you're going to run into mathematical difficulties and that's just because quantum field theory is extremely mathematically complicated. So I think there's a research direction for adventurous students to not only formulate quantum field theory in this language but also to see, does it make any of the mathematical difficulties easier? Does it make any of them harder? Like what exactly does it look like when you do this with extreme care? And that, I would say, is an open research question. But many of the obstacles that stand in the way, for example, Bohmian mechanics are no longer standing in the way here. 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If you're passionate about expanding your knowledge and gaining a deeper understanding of the forces shaping our world, I highly recommend subscribing to The Economist. It's an investment in intellectual growth, an investment you won't regret. As a TOE listener, you get a special 20% discount. You can now enjoy The Economist and all it offers for less. Head over to their website, www.economist.com, and put in TOE, TOE, to get started. Thanks for listening, and now back to our explorations of the universe's mysteries. In, for example, Bohmian mechanics is no longer in the way here. What makes quantum field theory not precisely defined besides path integral? Because there are other ways to quantize other than path integral. How much time do we have? So, what makes it difficult? It's not difficult. It's not precisely defined. It's not precisely defined. So, okay, I mean we have precisely defined quantum field theories, but they tend to be precisely defined quantum field theories with very low numbers of spacetime dimensions, where you can, for example, precisely define all the integrals and take all the limits. We have precisely defined quantum field theories with what are called the Wightman axioms, but those axioms are very strong and they rule out kinds of quantum field theories that seem more suitable for describing kind of nature. There are many different angles I could take on this. Let me just, I'll just pick one. So, here's one way of seeing what can go wrong. If you take quantum electrodynamics, which is the quantum field theory that describes electrons best, and if you want, you can add some heavier cousins of electrons, like muons, that interact with photons, with the electromagnetic field. I should say, by the way, that most of what we do when we do quantum field theory isn't looking at particles dancing around. What we do is we posit in the distant past, the non-asymptotic past, what's called the state, which is a quantum state vector consisting of some list, some variety of particles that are supposed to go into the experiment, and then we write down some list of outgoing particles. You might ask, how do we know that particle will come out? Well, we don't. We're going to calculate the probability that this goes to that. So, we start with some incoming particles. We start with some proposed outgoing particles. And then, using either path integral or, you know, other calculational methods, we calculate what's called a complex-valued scattering amplitude. It's the complex number that you get. When you add these things together, the complex number that when you modulus square it, is supposed to be related to the probability that you get that particular result. Practically, what we do is calculate what are called scattering cross sections, which are like a fraction that comes out one way, and a fraction that comes out another way. Notice that all of these things are phrased in a way that's perfectly consistent with the textbook formulation of quantum mechanics. We don't ask what happens in between. We don't deal with macroscopic systems. We do exactly what the textbook axioms tell us to do, which is you prepare, and you calculate the probabilities of measurement outcomes. All the averaging and numbers you do are as if the experiments are repeated a large number of times. So, you will not, most of the time, encounter any of the fundamental paradoxes or ambiguities of quantum theory. So, it's very easy to apply quantum field theory and think there's no problem. Everything's great. We're doing quantum field theory. What's the problem? That's because most of what you do doesn't encounter any of those mysterious things that you encounter with the axioms. Now, this theory is very useful, and we can calculate lots of things. We can't calculate everything. There are some ingredients that you have to take from experiments, right? What are called the physical coupling constants you have to go out and measure, and plug into the model. Because if you naively try to calculate everything from first principles, what you discover is that some quantities you might like to calculate depend very sensitively on some kind of upper cutoff that you've put into the theory. So, when you study a theory like this, you realize that you cannot arbitrarily access high-energy physics. Our experiments don't pump in more than a certain amount of energy. So, we shouldn't extrapolate the theory to arbitrarily high energies. We're going to put a cutoff on the theory. We're only going to discuss what happens in the theory up to a certain level of energy, or some energy cutoff. The point is that some things you might like to calculate from first principles depend sensitively on the cutoff, and those are things that your theory cannot provide for you. So, we have to take some things from experimental data and plug them in. And we plug them in. And they become some parameters in our theory. The standard model has about 20 or so such parameters that you have to take from experiment and plug in. And once you have those, you can now make a huge number of non-trivial, extremely precise predictions about what happens. But you still have this upper cutoff. And if you try to calculate things at arbitrarily high energies, eventually, your calculations stop working. So, one of the dirty secrets of physics is that a lot of calculations we do are very approximate. A lot of them, when we do it by hand, we use a tool called perturbation theory, which I cover in some of my courses. Perturbation theory is a systematic recipe for predicting and calculating things. And that recipe doesn't work well once you start trying to push your predictions beyond a certain energy level. There's a trick you can do to change the shape of the theory as you study different energy levels. It's called renormalization. And what you find is that some parameters in the theory, stop having values that make it possible to do a consistent perturbation theory. Now, if you want to precisely define a quantum field theory, what you want to do is to take some kind of limit where you can study the theory at arbitrarily high energies. And that roughly corresponds to being able to arbitrarily assign degrees of freedom to arbitrarily small points in space. And you see that there's immediately an obstacle here. For most of our theories, there's a cutoff. There's a limit we can't go beyond. The theory simply doesn't allow us to go to arbitrarily high energy levels. And so, we're not going to be able to write down what's called a complete and perfectly precise ultraviolet version of this theory. We can only use a theory up to some cutoff. For example, it's not expected that the standard model holds at arbitrarily high energy scales. We think the theory is only reliable up to a scale of ten electron volts. And that's one of the reasons why we build experiments, or try to build experiments, or attempt to do experiments, to explore the physics that happens above those scales, where maybe the standard model no longer makes the correct predictions. All of this takes us very far afield, unintentionally, far afield from what we were talking about before. But these are the kinds of things, like, maybe quantum field theories in the real world, real life, out there in the wild, quantum field theories are never completely defined. Maybe all we have are a series of what are called effective field theories which are all well-defined within some limits. And there's no ultimate theory that's perfect and precise, and, you know, perfectly precise and ultraviolet complete. Maybe there's just, like a tower of these theories. And that makes questions about existence and what exists physically, I think, very mysterious. Because if we think that there's not going to be some fundamental theory at the bottom of all of this, then what's really there in nature, I think that's an open question. I don't know if you want to rephrase that question in the language of this kind of…

Is it from the non-local, non-separable stochastic approach or not? Or is it possible that these theories draw upon some final quantum field theories or a completely different kind of theory, like string theory or something like that? I mean, there are many proposals about where this might end up. But I don't know. But what I will say is this. There is a view that nature is fundamentally described by Hilbert spaces in quantum mechanics, the Hilbert space formulation of quantum mechanics. And if that is fundamental, then we already know what nature is fundamentally. Nature is fundamentally some wave function. That's it. Some wave function in some Hilbert space. We don't know exactly the features of the wave function. We don't know whether it is best described in terms of fields or anything else. But we already know the fundamental ontology of nature. It's a wave function. So we're good. I think that's extremely ambitious.

In the non-local, non-separable stochastic approach, there is no wave function. So the wave function is not the ontology. The wave function is whatever your choice of configurations is. And if you're modeling particles, you use particle configurations. If you're modeling fields, you use field configurations. If there's some fundamental underlying system that underpins everything else, some system at the bottom, some system, if we understood it and understood its laws, we would have a unified theory of all physics. Presumably there are some configurations for that, and we'd use those instead. But we don't know that theory yet. And so I think it's premature to believe that we know the right fundamental degrees of freedom.

Therefore, if someone asks me, what do I think exists fundamentally? I don't know. But then I'm just where we were 100 years ago or 150 years ago. We don't know the final theory of nature yet. And I think it's premature at this stage to guess what the final ontology will be until we get that theory, if we get it. Okay, I'm interested in final theories. Theory of Everything is your podcast name. Sorry, I don't have one for you. Okay, I'm interested in your thoughts on how to unify quantum field theory with gravity. I know we have a large number of audience questions, and we will get to them, but they will have to wait because I have these questions first. These are close to what I wanted to talk about as well. So go ahead. Yes. Great. Great. Okay, there are two questions here. People say, okay, we have Heisenberg uncertainty and that applies even to QFTs. Therefore, spacetime is jittery. Okay, but spacetime in QFT is definite. You can perfectly well pick an X comma. And the values of the particle configurations in the fields themselves are jittery or uncertain. But spacetime itself exists and is given. However, some people say that if you zoom in and you follow QFT because of Heisenberg uncertainty, then thereby you get to uncertainty in spacetime itself. Is this argument correct?

Now, I imagine one way they arrive at this argument is to say that you have energy-time uncertainty in general relativity. Spacetime itself has energy, and therefore spacetime itself must have some uncertainty. But you could also say, well, in QFT, you don't know whether the energy you're talking about is the same, well, well. If you have a statement that applies to all natural numbers, you can't just say any of them, so x squared will always be a natural number if you're drawing from the natural numbers, but not every square number is a natural number. So it depends on the scale of what you're measuring. So can we, in QFT, apply energy-time uncertainty to QFT? I don't know. Okay, that's one question. We should answer that question first before we bring up any other questions. So it's important to backtrack here and make sure that we all know what we're talking about. So it's a quantum field, just because maybe not everybody knows what that is.

So in the typical Hilbert space formulation of a quantum system, we have things that are observable. The observables are these self-adjoint operators. And in quantum field theory, we have operators associated with all points in space, right? And if we work in a formulation where we shift the time evolution from state vectors to observables, we have what's called the Heisenberg picture. And then our field operators depend on space and time. It's a fancy way of saying everywhere in spacetime, we have these kinds of local operators associated with points in spacetime. Quantum field theories like QED, we talked about quantum electrodynamics. They assume this classical background of spacetime. There's no gravity. Spacetime is usually treated as flat. We call ordinary special relativity flat spacetime. We call it Minkowski spacetime. You can do quantum field theory in a fixed curved spacetime. We're still not treating gravity as dynamical, but it gets extremely complicated. Let's start with quantum field theories like QED on the non-dynamical spacetime of special relativity. In that case, you're right. X, Y, Z, coordinates of where you are and T don't fluctuate. They're fixed features of the background architecture of spacetime. They're the stage upon which the event happens. Your question about the uncertainty principle and about the fluctuations of fields is an interesting question.

In the Dirac-von Neumann formulation of quantum mechanics, nothing fluctuates between measurements because nothing happens between measurements. The only things that happen are measurements in the Dirac-von Neumann formulation. So to say, oh, when you're not measuring it, the fields are like dancing all around. The Dirac-von Neumann axioms don't say that. They don't say anything about that. They don't say that particles are wandering around. The Dirac-von Neumann axioms don't allow you to say, oh, the reason that happened is that a photon was emitted from an electron. All that's for color. I said this in one of our previous conversations that physicists often talk that way. They say, oh, this happened because the electron emitted that and did this and the field was fluctuating. If you're just working on the Dirac-von Neumann axioms, all of that is nonsense. None of it's really legitimate through the axioms. Now, if you're frustrated by that, you'll say, well, but surely something is happening. I want to be able to say something is happening. Well, then you're on my side, which is that we need to do something to the Dirac-von Neumann axioms. You're making my case for me.

So the uncertainty principle, the traditional one, we talked about before, is that an observable commutes with a certain basis. And when the state vector of your system is aligned with one axis of that basis, you definitely get that outcome when you measure it. If the state vector is not aligned with that basis vector, it has components along multiple basis vectors, you will get probabilistic measurement outcomes given by Born's rule. And you can be aligned along the axis of something observable and get a definite outcome, but not along the axis of another observable. And you don't have a definite outcome. And if you change the state vector so that it's aligned along one axis, it will not be aligned along the other axis. And that's the uncertainty principle, which says that some observables will have sharp values, and when you measure them, you always get a definite outcome and others won't. And if you try to make one observable sharp, others will become unsharp. That's the uncertainty principle. But notice again that these are all statements at the level of measurements. We're not saying that between measurements, anything is fluctuating. So frankly, there's no way to really talk about what, or to say that the field is fluctuating over spacetime, or to say anything more about Heisenberg's theory principle, other than this is the pattern of measurement outcomes we get when we do measurements on the system.

Now, if you want to do something like Bohmian mechanics or the non-local, non-separable stochastic approach, or many-worlds approach, or something like that, now we can start talking about what happens between measurements because these are all theories that describe things that happen that are not just a narrow class of measurements. In some theories, as in the non-local, non-separable stochastic approach, there's stochastic behavior. The fields really fluctuate. In Bohmian approaches, it kind of depends on whether you're trying to put the fields into a deterministic kind of Bohmian approach or whether you're going to allow the fields to be somewhat stochastic. There are many different formulations of Bohmian mechanics for fields, and I can't do justice to all of them. Some of them, the fields will be fluctuating. Some fields won't be. In some, you deny the existence of fields and try to do everything with particles somehow. Many-worlds is more subtle because in many-worlds, there isn't a single reality where things fluctuate. It's more subtle. And we'll talk about the many-worlds approach in a little bit. So I wanted to clarify that before we then talk about the more subtle question about, does spacetime fluctuate?

So when you go from a field theory, like a quantum field theory, like QED, where again, the thing you're basically calculating are scattering amplitudes. You set up the setup, you get measurement outcomes, and you calculate cross sections, decay rates, things like that. Now you want to talk about gravity. So in general relativity, gravity is a manifestation of changes in the curvature of spacetime. Spacetime doesn't stay flat. It curves. People often wonder where does it curve? Is it curving into some other dimension? There's a way of defining curvature called intrinsic curvature that doesn't refer to other dimensions. You can define it just in terms of the four dimensions of space plus time. So you don't need an extra dimension for curvature. But there's the idea of intrinsic curvature. And if gravity is quantum mechanical, does that mean that the curvature or the shape of spacetime or the geometry also fluctuates to some extent? Now there's this discussion about, well, if you zoom in, I mean I don't know exactly what zoom in means. Do you mean if you're doing measurements or something like that? I mean, if we do very precise measurements on a quantum field on a spacetime background, we might get large variations in the outcomes. But those are measurement outcomes. It's not the field doing anything between measurements, because again, without augmenting the Dirac-von Neumann axioms, we can't talk about what the fields are doing. Does spacetime fluctuate? Well, according to the Dirac-von Neumann axioms, we can't say that. We can only say something like if you measure the metric, it's fluctuating. But I don't quite know how to measure the metric in the way that we measure the intensity of a field. It's kind of subtle, because the relationship between the gravitational field and the curvature of spacetime and the behavior of test particles, for particles that move in spacetime, looks really subtle. And even the notion of energy is very subtle in general relativity. There's also no constant and non-trivial definition of local energy density in the gravitational field itself in general relativity. So, you know, it's really, really hard to even pin down what we mean by all of this. And we're not going to be guided by experiments, because we expect to clearly see the quantum mechanical features of the gravitational field. Unless there's some miracle, we don't expect to see that until you're talking about Planck scale physics. Planck scale physics is the physics associated with distance scales that are like 10 to the minus 43 meters, right? I mean they're as far from an atom as an atom is from the visible universe, something like that. I mean, they're very far from, maybe not, I have to calculate the precise order of magnitude, but like the Planck scale is really small. I think that's equal to 10 to the -43 seconds. That's the Planck time. The Planck scale, the length scale is 10 to the minus 35 meters. So such incredibly tiny and fiddly scales of distance. And we can't do experiments there. So we don't have experimental data to guide us.

So this is exactly the situation where we need the kind of careful and rigorous scrutiny that one gets from, yes, from understanding physics as best we can, but also from having a strong background in philosophy. Because it's very easy to make extremely speculative statements, which build speculation upon speculation, to make what I call speculative metaphysical hypotheses, SMHs, and the abbreviation is not coincidental, just to stack them on top of each other and then not know whether what you're saying is something real and reliable. So I don't have any idea whether we should think of spacetime as really fluctuating. The non-local, non-separable stochastic approach, like all approaches to quantum mechanics, faces fundamental conceptual difficulties of the first order in dealing with fluctuating spacetime, like dynamical curved spacetime. Let me explain why. In order to talk about stochastic probabilities and partition functions and all that stuff, you need a notion of what you mean by time, by slices of the universe at a fixed time. You need to be able to talk about which directions in spacetime are space-like directions and which directions are time-like directions. When you want to specify the configuration of your system, you do that at one time over a certain space. And so you really need to know which slices of spacetime represent space slices. And that's all well and good when you're dealing with Newtonian or non-relativistic spacetime, even in quantum mechanics, not necessarily Newtonian, or even special relativistic spacetime. In special relativistic spacetime, you're given which directions represent time and which directions represent space, and they're perfectly fixed.

But when you think about dynamical spacetime, that is, spacetime where what's called the metric tensor, which is a kind of thing associated with spacetime and general relativity, the metric tensor is the thing that tells you what are the time-like directions and which are space-like directions. If that itself is fluctuating, you don't know a priori which directions are space-like directions and which directions are time-like directions, so you can't even formulate a probabilistic theory clearly. And that's extremely strange. For one reason, this means it's very hard to understand whether spacetime is fluctuating, even in a non-local, non-separable stochastic theory, because it's hard to even specify where do I put my probabilities? What's primary, you know, these probabilities are conditional, they relate one configuration to another at one time to another, but if I don't know which directions are time-like directions, how do I do that if spacetime itself is fluctuating? That's fun. But also interesting is that it highlights a gap in the scientific study of quantum gravity.

So this is something extremely interesting. We can take classical Newtonian physics, and we can simulate it numerically on a computer, and we can also model many Newtonian systems probabilistically like Markov processes. Often, a Markov approximation is perfectly good and can be used all the time to model Newtonian systems, and to model other kinds of systems. And there are stochastic approaches, stochastic formulations of other physical theories outside of Newtonian mechanics. There isn't one for general relativity. So Einstein's general relativity is not a probabilistic theory. Einstein's general relativity is a deterministic kind of theory. It's more subtle. There are some questions about whether it can always be formulated in a Markovian way. So there's some evidence from general relativity, even ordinary general relativity, that suggests that the Markovian picture is maybe not quite the right picture. And there are some brilliant people like Emily Adlam, from Chapman University, a philosopher of physics, and Eddy Chen from UC San Diego, and Shelly Goldstein from Rutgers, who are trying to think about the laws of physics in a different and more globally spacetime-sensitive way that might fit better with theories like general relativity. And there might be some connections to non-Markovian non-local laws. But anyway, general relativity has been formulated in a deterministic and non-probabilistic way. And people are trying to work on quantum gravity now, but you might ask, shouldn't we work on an intermediate step first? How about just a probabilistic version of general relativity? Like a stochastic formulation of general relativity, we take Einstein's field equations, the equations that describe the deterministic shape of spacetime, and we replace them with a probabilistic version. Not a quantum version, but just a probabilistic version, as a stepping stone. You might think that's the natural thing you should do before trying to go to a full quantum version of the theory. And to my knowledge, very little work has been done in this area. I could be missing something. I don't think so, I haven't seen everything that's been written, and maybe people will see this and chime in in the comments and say, wait a minute, there's a theory that suggests this is happening. And there is current work. I mean, I know Oppenheimer's working on a stochastic version of general relativity, but that's recent, right? Like that's not 50 years ago. So I think that's a big goal for research, and it makes sense that this should happen.

I mean general relativity, you know, was finished, the full Einstein field equation level was formulated in November of 1915. You know, Einstein gives these super important lectures to the Prussian Academy of Sciences, and he's scrambling to finish the theory between lectures, and he managed to do it. And then, you know, shortly thereafter, Schwarzschild comes along and writes down the Schwarzschild solution very shortly thereafter, you know, at the beginning of 1916. But there's the whole story that Schwarzschild was doing it in the trenches of World War I. And he wasn't in the trenches. Yes, there's a really great research paper, I believe, by Dennis Lehmkuhl, who's a historian of science, he's great. He was like, Schwarzschild was actually stationed in this very nice house, and he was in the war, but he wasn't in the trenches. I see. He was doing that. But anyway, people, this whole theory was developed in 1915 and 1916. And stochastic process theory wasn't developed then, right? I mean, even like Kolmogorov's axiomatization of probability theory, which came in 1933, right? That means 17 years, 18 years after general relativity, and that's not even stochastic. I mean, stochastic variables don't start being used prominently until the 1940s and 1950s. And I think like a sophisticated theory of stochastic processes, if I'm not mistaken, and again, my history in stochastic process theory might be somewhat mistaken, so people can correct us, but I think it wasn't until later, like the 1950s and 60s. I mean Markov already introduced Markov matrices in about 1906, but like the full construction of an actual comprehensive theory of stochastic processes, that came decades later. And people had already been working on quantum gravity for decades by this stage. I mean people started trying to quantize general relativity especially by the 1920s. I mean Pauli is already trying to quantize general relativity in the late 1920s. And people already give up and pull their hair out and say, you can't do it, right? Already like decades before there's a theory of stochastic processes. So it's not historically surprising that nobody said, maybe before we study quantum gravity, we should do a probabilistic general relativity and see if we can do that.

And there have been many proposals for doing that. Maybe what you do is you want an ensemble of spacetimes, or of multiverse or maybe, but it's not clear that any of these are the right way to do it. I have some suspicions. And now I'm doing something I don't want to do, which is just speculation. But you know what? Let's just speculate. Speculate away. I think it's a fully probabilistic version of general relativity, and I don't mean taking general relativity and adding some little noise terms, like small corrections. I mean like a full probabilistic generalization of general relativity. I think that would teach us a lot about quantum gravity or even quantum gravity. Because remember the non-local, non-separable stochastic approach doesn't start with Hilbert spaces. It's just probability, just fully non-Markovian probability. There's a sense that general relativity in its most general formulation is not exactly, I mean, depending on the nature of spacetime, if you have certain kinds of spacetime, certain properties, you can formulate it as some kind of initial value problem. But it's as if there's something about general relativity that is a little bit different from the laws of our other theories. And I suspect that if you could fully probabilize the theory, you would basically be doing non-local, non-separable stochastic mechanics, but for the gravitational field, and that would actually be a quantum gravity theory. Now that's extremely speculative. I want to be very clear. I haven't worked on this to any depth. It would be interesting to study this problem more. But that's the kind of question that you can start asking. Because if you think you have to start with Hilbert spaces, you'll go, well, quantum gravity must be something of a Hilbert space or a generalization of Hilbert spaces. But because we didn't have to start with Hilbert spaces, we can now ask more fundamental questions like what is just probabilistic general relativity, non-local, non-separable probabilistic general relativity, and is that all we really need? That doesn't mean it's easy, because again, when you have dynamical spacetime, it's very difficult to talk about where you put the conditional probabilities, but it at least focuses the question on something more fundamental. And I think this accords with two other principles that I think one gains from philosophical reflection on the practice of physics. The first is that it's usually better to isolate problems as much as possible and deal with them in the simplest circumstances. I'd rather try to deal with probabilities and general relativity first before I try to deal with quantum gravity. Let's study problems in their simplest pristine embodiment. Let's not teach people quantum mechanics by starting with quantum field theory. Let's start with the simplest kinds of systems and add complexity step by step rather than doing it all at once. That's one thing. And the other thing is the idea that when dealing with conceptual problems or confusion or trying to make progress on a very thorny set of theoretical questions that involve one of our best physical theories, sometimes you don't want to build things at the end. Sometimes what you need to do is go deep into the deep programming of the model and do some debugging. So for people who have done computer programming, you know that sometimes when your program doesn't work, it's not because the end of your code is wrong. Sometimes it's because you made some mistakes at the beginning of your code. And to debug that, you have to go back to the beginning and really start with the definitions, like how you define certain variables or how you define certain functions and make sure that all of these definitions are really good before proceeding. And that's kind of what I'm doing here. Instead of trying to slap quantum gravity onto Hilbert space quantum mechanics, I say maybe we need to go and ask some foundational questions first. Debug this program all the way down to the roots of the axioms. Make sure that the axioms are really sensible. And I can give a very concrete example of where this breaks down. So we talked about the uncertainty principle. The other thing you calculate in quantum mechanics is expectation values. Now in a previous conversation we talked about that expectation value is an average. It's, you know, you have something observable and you want to measure it and you know the quantum state of the system and you can compute its average. And there's a way of thinking about these averages, they're averages of things that happen, phenomena that happen, but they're not. They're defined by the Dirac-von Neumann axioms as statistical averages of numerical measurement outcomes weighted by the probabilities of the corresponding measurement outcomes, and that's it. If you're not measuring things, there's no average there. But there are lots of physicists who think that when you put angle brackets around something, which is the expectation value symbol, we don't have to think about measurements anymore. We can just think about it as things that happen. So people will say something like, well, you know, quantum mechanics predicts measurements and if you measure something you'll get one of the eigenvalues, and you'll get it with Born's rule. How do we get the classical limit? Oh, what we do is we take expectation values. We average everything and then show that these averages evolve in time in the way that classical observables evolve in time. And that's how the classical limit happens. But that's clearly wrong because at least if you don't believe that everything is a measurement, I mean, if you want to say that every phenomenon that happens is some kind of measurement, you can do that, but then the burden is on you to try to show that. If you're not willing to say that everything that happens is a measurement, then you have a problem because things are happening everywhere. Bodies exist on Mars and don't fall apart and primordial gases mix. And you can't just put angle brackets around it and between quantum mechanics things and say these are things that happen because those angle brackets just denote measurement averages. And if there are no measurements,

These things don’t happen. The only thing that happens is the confusion between the expected value of a quantum mechanical measurement and just the average. The confusion between these two things, averages of measurements and averages of things that happen in a certain way, is rampant in the literature. So, if you take, for example—I’m sorry to mention this because I really like this book—it’s Shankar’s book, Principles of Quantum Mechanics. I wrote a book; it’s a wonderful book, it’s a big pink book on quantum mechanics. And chapter six is called the classical limit, and the whole chapter is based on this fallacy. That you put parentheses around things and then you can treat them as classical variables that just happen and nobody measures them. But that’s just wrong. Now, at least according to the Dirac picture axioms.

Now, if you’re willing to augment or change the Dirac picture axioms and turn quantum theory from just a theory of measurements into a theory of phenomena that happen in general, as in the consistent histories approach or Bohmian mechanics or Everett, the many worlds interpretation, you’re free to do that. But you need something to take averages of measurements and turn them into just averages of things that happen. This is just a category mistake again, where we’re just referring Dirac picture axioms to this very narrow category of measurement outcomes and not the larger category of things that we want to be able to happen. So how does this impact quantum gravity? In quantum gravity, we often take quantum mechanical things, put parentheses around them, and then put them into Einstein’s field equation and treat them as if they are classical things. So one of the primary assumptions of semiclassical quantum gravity, where we’re trying to mix a little bit of quantum, is to take the matter distribution, broadly interpreted. Matter broadly interpreted is like massive particles, massive bodies, but also electromagnetic fields are considered a form of matter. In fact, anything that’s not the gravitational field can source gravitational fields or respond to gravitational fields we call matter. And what we do is we take the observable quantum mechanical things, these expectation values, put parentheses around them, call them averages, pretend that they’re classical averages, and then put them into Einstein’s field equation. And a lot of what we do is like that in quantum gravity, but it doesn’t make any sense from the outset.

Something else people often do is they will take functional integrals, this is the Feynman path integral approach where you take all possible paths, okay, this picture, and they will stick a bunch of operators into one of these integrals. Sometimes, to make things better defined, they’ll take time and give it an imaginary part and even rotate the time axis in the complex plane to imaginary time to make the integrals better defined, and they’ll compute these things called correlation functions. And sometimes I’ll have a conversation with somebody who does this and I’ll say, what is this correlation function? They’ll be like, oh, it’s a correlation function, it’s an average. And I’m like, but there are no observers. And you’re describing a situation in quantum gravity where there are no planets or people or measurements. So what is this average? Are you saying that these quantities just do things and we’re calculating an average of them? And that’s not legitimized by direct Feynman axioms. So what is the physical meaning of these quantities that you’re writing down? And sometimes I have a very long complicated conversation about this, and actually we make some progress on this, but often people say, I don’t actually even know what I’m doing, do I? So that’s what I mean when I say that applying rigorous scrutiny to the things we calculate, beyond the mathematics, what do they mean, is actually important because otherwise you might find yourself writing things down and not even knowing what exactly you’re writing down.

I think what this expresses is that the difference between quantum mechanics and general relativity is actually much deeper than I think we all appreciate. I mean, we all know that there are differences. Quantum mechanics is supposed to be this kind of probabilistic, fluctuating theory, and general relativity is supposed to rely on smooth spacetimes and things like that, and how can we reconcile them? But I think the difference between them is deeper. General relativity is a theory of things that happen. General relativity is a theory where you have Einstein’s field equation, you impose suitable boundary conditions, you put in whatever distribution of matter and energy and sources you want in your spacetime, and then you find a spacetime with the right geometry that satisfies all the constraints and obeys Einstein’s field equation. And that is the spacetime where things happen. Projectiles follow what are called geodesics. If they are subject only to gravitational forces, geodesics can cross, they can meet, they can intersect five times. People can, you know, calculate various conserved quantities. Not everything in general relativity is relative. Some things don’t change. They’re just like things that happen in this universe. In quantum mechanics, at least the direct-picture textbook version, all you have are measurement outcomes. The beginning and the end of your measurements. Nothing in between. No picture. So if you try to take general relativity and stick it into quantum mechanics, at least in the traditional Hilbert space direct-picture version, you lose all the phenomena that happen. You lose all the flesh, all the substance of general relativity. There’s like a much deeper problem here. And I think one of the tendencies is, well, but it works well with QED, quantum electrodynamics. But remember, quantum electrodynamics is just a theory like, you set things up and you take measurements at the end. Asymptotic past, you set up your initial state, asymptotic future. We take times that are infinite in the past and in the future, clearly that’s just an approximation. And we just calculate measurement outcomes, cross sections, scattering, you know. But in general, in quantum gravity, we’re trying to describe what spacetime does. We’re trying to understand like what happens to spacetime. And these are questions that go beyond the scope of the things that we usually do when we do quantum field theory. We’re demanding more from quantum gravity. We’re demanding more of a picture, more of a description than textbook quantum mechanics is designed to provide. And therefore I think that if you want to do quantum gravity and really tell the story, and tell a picture, and paint an accurate picture of what happens in spacetime, you’re not going to be able to do it using Dirac, von Neumann, Hilbert space textbook quantum mechanics. You’re going to need a theory for something so that you can describe the spacetime where something actually happens. I hope that makes sense. So I think there are reasons why a conceptual shift in the way we think about quantum mechanics is necessary before we can address some of the deep problems in quantum gravity.

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Thank you and enjoy the show just so you know if you’re listening to it, it’s curtjaimungal.org CURTJAIMUNGAL.org Problems in Quantum Gravity Great answer Okay so let’s get to some questions about Bell, yes people have questions about Bell inequalities and how they’re represented in your framework okay well ultimately Bell’s theorem is about entangled systems so I should say a little bit about entanglement, we should talk about entanglement first, what is entanglement according to usual textbook quantum mechanics this is what entanglement means entanglement is what happens when you take superpositions of states and you extend them to include composite systems where you have two systems and not one system anymore you can have a superposition of two states but two systems so suppose I have system a which is in state one and I have system b which is in state one prime and that’s all I have okay we’ll say okay the composite system is in state one one prime a is in state one system b is in state one prime that’s all that can be said I can also imagine that system a is in state two and system b is in state two prime and the composite system is in state two two prime okay fine I can also imagine that system a alone is in a superposition of one and one prime let’s say one over root two times one plus one over root two times one prime because in quantum mechanics when we superpose we put a number in front and that number when squared is supposed to be associated with the probability of measuring one over root two has the property that when you square them you get one half and add them you get one these are probabilities you can imagine system a is in the state one over root two one plus one over root two one prime you can imagine system b is in the state one over root two plus one over root two two prime and you can imagine that these are the two states the two systems now the composite system is also in so the composite system is in the state okay it’s a little bit hard to say let me call the state one psi the Greek letter psi is the state one over root two one plus one over two one prime and let me sorry I got the numbering wrong it’s one plus two and two and sorry because a can be in state one or one prime oh one but one or two and the state and system b can be in state oh oh oh one prime or two prime I got it wrong my apologies okay yes so oh so psi will say the Greek letter psi the trident symbol psi will be one over root two state one plus one over root two state two and psi prime which corresponds to system b is psi prime which is the state one over root two one prime plus one over root two two prime and I can say that the composite system is in the state psi comma psi prime then I say if I multiply everything I’ll get four terms there’ll be a term that’s equal to one half one one prime plus one half one two prime plus one half two one prime plus one half two two prime okay we’ll say that this is not an entangled state because it’s factorizable I can factorize it into psi next to psi prime psi for system a psi prime for system b we’ll say that this is unentangled okay and you can show that when they’re unentangled they also have statistical independence if you make measurements on them and calculate the probabilities of the measurements you’ll find that they are statistically uncorrelated but now let me propose a different quantum state and this quantum state will be one over root two one one plus one over root two two two prime and these are only two terms notice that this is a superposition but over both systems now I have one one prime in one term and two two prime in the other term and I don’t have all these I don’t have one two prime I don’t have two one prime they’re not there I only have one one prime plus two two prime I can’t factorize that into two different states there is no psi for system one and psi for system two that allows me to describe them as having their own states we can now say that they’re entangled just quickly the question here so people who are driving and listening to this or maybe they have a pen and paper and they’re thinking okay I’m going to try multiplying some states to get that and then they don’t and then they’re wondering well but just because I tried some states and I couldn’t get there is there a way that I can look at this and then prove that there is no factorizable component yes there is and this is the way to think about this it’s just a matter of forgetting to get frustrated when you do it computationally if somebody gives you for example I have x plus y here and I have w plus z here and I multiply x plus y as a quantity times w plus z as a quantity I get four terms I get xw plus xz plus yw plus I get four terms if I see these four terms I know that I can refactorize it and write it as something x plus y times something else oh z plus w but if I just give you xy plus sorry not xy xw plus zyi I just give you these two you cannot factorize them into something times something that’s like a computational example of entanglement basically so now entanglement is usually formulated as something that doesn’t have any classical correspondent there’s no such thing as classical entanglement actually in a 1935 paper Schrödinger wrote that entanglement was but a feature of quantum mechanics which imposed its distinction from the classical state you can also associate with this paper I’ll send you a link to it now you might be okay there are certainly things that resemble entanglement for example you know John Bell has this Bertlmann’s socks paper and he talks about this fellow Bertlmann who has socks and the socks are always different if you know the color of one sock you’ll know what the other one is you’ll know that the color is not the same there are systems where you know for example if I have somebody setting up coins and they always set up the coins the coins such that when one is heads the other one is always tails always and you find that one is heads and you know that the other one heads tails are correlated even if the coins are very far apart when you look at them if you set up the coins and send them far apart you look at one coin it’s heads you know that the other coin far away is tails this is called correlation and if you do this on many coins you flip the coins you don’t always know what you’re going to get heads or tails but you know that the outcomes will be correlated statistically correlated so certainly statistical correlation happened classically but entanglement is stronger than that and that’s one of the things that Einstein Podolsky Rosen and Bell were trying to get at in this feature of entanglement that’s somewhat stronger you get stronger correlations than you would think were possible in the usual way we think about oh classical probability theory for systems that are spatially separated far apart oh to explain bell’s inequality I should start from where it came from so Bell’s theorem in 1964 is in a paper called on the Einstein Podolsky Rosen paradox he’s referring to a 1935 paper written by Einstein Podolsky and Rosen so I should talk about that paper and what they did and then what Bell was supposed to do people should associate with a copy of that paper people should read it I don’t know how many physicists have actually sat down and read that paper very carefully but it’s and even Einstein wasn’t very happy with it he was a little bit upset about how it finally appeared but it’s a very important paper to read you mean the epr paper that’s the famous epr paper right epr paper yes it’s a very subtle argument but it basically boils down to this if I have two quantum systems and they’re entangled I set them up I set them up in some entangled state and in order to make them entangled there must be something local between them either they must be together initially or you have to send something from one to the other but at some point something local must happen in order to make them entangled with each other oh then you send one of the systems very very far away that’s a weird thing about entanglement when I measure the first system usually people do these thought experiments they imagine Alice and Bob Alice has the first system and Bob is very far away with the second system where Alice makes a measurement on her system and she can measure a variety of different observables she can measure some observable and when she does that if you have the right kind of entanglement you’ll know exactly what Bob will get when he makes his measurement she’ll measure an observable and an observable and she’ll get some answers and then she’ll know I got this answer because of entanglement I know what Bob will get she’ll definitely get this other answer but Alice didn’t have to measure that thing she could have instead measured a different observable she could have measured a different initially incompatible observable incompatible in the same way this position is not momentum compatible which is what they originally used in the epr paper oh that the original epr paper is written in terms of position momentum but these are incompatible observables they obey the uncertainty principle if you know one you don’t know the other with certainty and so she measures she can make Bob’s system collapse he has a definite answer for a different observable okay so you can steer Bob’s system this is called quantum steering and the word quantum steering was coined by Schrödinger shortly after the EPR paper because it looks like Alice’s choice of which measurement she measures or prime like steers Bob’s system now steering doesn’t send signals back there’s this theorem called no-signaling theorem and no-communication theorem that shows that Alice cannot send deliberately controllable messages in this way steering is a subtler thing and it cannot be used to send signals or communications and that can be rigorously established because of this theorem however there is some sense in which you’re somehow steering Bob’s system she will measure an observable she doesn’t control the answer she gets she’s not sure she can get this she can get that depending on what she gets Bob will get a certain similar thing but because she can’t control what she gets she can’t control what Bob gets she knows that once she’s finished her measurement and got a certain outcome she knows that Bob if he decides to measure the same thing will she know exactly what he will get if Allison says she’s measuring a prime she will collapse Bob’s system into a different basis and whatever outcome she gets she’ll know Bob if he measures that corresponding observable she’ll know exactly what he’ll get now Bob’s system and Bob’s system when they do the experiments could be a light year apart and it seems like this superluminal unacceptable thing happening faster than light can happen but if Bob’s system didn’t already know the answer that he would get if he measured the first observable and what the answer he would get if he measured the second observable because Alice could measure either one and depending on what she measures she can make Bob’s system have a definite value for one measurement if one has a definite value for the other and if Alice didn’t really change Bob’s system then Bob’s system must have known all along what they were going to be asked to call their paper “Can Quantum Mechanical Description of Reality Be Considered Complete” they say that unless you allow for something faster than light to happen Bob’s system must already know the answers that it should give to all its measurements because Alice can’t perhaps by her choice of measurement steer it so EPR basically establishes that there’s a logical fork either you allow for some kind of faster than light effects or some kind of causal effects or there are additional hidden parameters and the wave function is the standard approach to quantum theory is incomplete there’s more to the story than just the wave function where Bell came in in 1964 he says okay here’s what they said either you have some kind of non-local or some kind of superluminal causal effect happening you know the steering goes from Alice to Bob or there’s more to the story than just the wave function there are some hidden variables Bob’s system already knows the answers that it will produce what Bell wanted to do was show that that fork was actually in fact there wasn’t really that there wasn’t a way out of non-local causality if you tried to escape non-local causality the way EPR argued you had to assume that there were more hidden variables in the story additional things that don’t actually allow you to escape and what Bell did in his 1964 paper was prove his theorem which is Bell’s theorem which is an inequality that in his opinion any theory of hidden variables that’s claimed to be local satisfies and then write a simple example of a quantum mechanical system that violates it you can go out and do an experiment and check that it violates it in other words Bell is trying to close off a possible way out of non-local causality EPR says there’s either non-local causality or hidden variables and Bell says okay even with hidden variables you still get non-local causality therefore quantum theory is simply a non-local theory and that’s the end of the story that’s what he did and this theorem has gone through a giant game of telephone so I should say first that the paper as it was published Bell it wasn’t and he was a particle physicist doing this foundational work on the side and he was cautioning people against doing foundational work because it was considered very bad for your career which is really shameful I mean physics is supposed to be an intellectual project and shutting down avenues of intellectual inquiry of exploration is just anti-intellectual that’s unfortunate but his research somehow eventually became more widely known as if through a game of telephone and eventually people started thinking that what he did was prove that there couldn’t be hidden variables and people would say oh you have a hidden variable theory that’s ruled out Bell said there couldn’t be hidden variables actually the Nobel prize was given for experimental tests of violation of Bell’s inequality there’s this Nobel prize that was given to Clarer and Zeilinger and was aspe I think it was aspe also and they say if you look at the press release for the Nobel prize they say that Bell showed there couldn’t be hidden variables and this Nobel prize was given because they showed that hidden variables are impossible that’s not at all what Bell showed in fact not only did Bell not show that but he said in his paper that that’s not what he was showing actually he started the paper by talking about Bohmian mechanics and he says that Bohmian mechanics is at least for systems of fixed finite numbers of non-relativistic particles is empirically adequate to quantum mechanics and it’s blatantly non-local the words he used are can there be a better behaved hidden variable theory than Bohmian mechanics when it comes to locality and what he was showing was that there wasn’t but his argument wasn’t it wasn’t as if he was saying okay it’s hidden variables or locality he was saying EPR it’s non-local or hidden variables and actually hidden variables are still non-local non-locality is all you get that’s what he thought he was doing and this paper has been widely misinterpreted and Bell himself complained in his later writings about how people kept misinterpreting his paper either by not reading it carefully or getting it second hand or I think as in the opening what we talked about the textbook that said oh Bell Bell proved that the orthodox approach is the only correct approach I mean that’s not what Bell said okay but then where do we go from here oh Bell claimed that he showed that quantum mechanics wasn’t just a local stop gap but the epr paper and the original epr paper and Bell’s 1964 paper these are arguments they’re mathematical arguments and especially Bell’s paper which is a theorem and you have to be very careful when you talk about theorems in a physics context so we were talking earlier about inductive reasoning all these different arguments in pure mathematics a theorem starts with premises the premises must ultimately be grounded if you have to in anything axioms they are from the domain that you’re working in maybe they go back to the axioms of set theory who knows then you go through a series of logically correct mathematical arguments that culminate in some conclusions that are a mathematical proof and once you’ve proved that as long as you had good good premises and your logic was valid you have a sound proof you have a valid deductive argument and you’re done and if anybody wants to claim that there’s something wrong they’ll have to

He also challenges your premises or challenges your reasoning, and if both are good, you are very good. Therefore, Euclid proves the infinitude of primes, and that's a great example. You start with certain premises about how natural numbers work. Then you have this logical argument that leads to the conjecture that there can't be a largest prime number, as long as you're willing to adopt the axioms, the standard axioms that we use in arithmetic.

But physical theories, like Bell's theorem, Bell's theorem theories related to physics, Spekkens' theorem, PBR theorem—oh, that's the Pusey-Barrett-Rudolph theorem—there are all these other theorems that are called physical theories. They can suffer from another problem. They can succeed like mathematical theorems; they start with mathematically formulated components that you use in the setup, and proceed through rigorous logical deductive reasoning, which you finally arrive at. This is the theorem that you claim to prove. Everything might be fine, but your theory floats in the mathematical world unless it connects to something in the physical world. This connection is where there can be a problem.

So, your mathematical components are not supposed to be pure mathematics anymore; they're supposed to have a physical reference. I'm sorry that the way that the singular is the reference, the singular reference, is the plural, and they're supposed to have things in the world that they represent. And the things they represent need a sufficiently rigorous definition, and the relationship between those referents and the mathematical representations must be sufficiently rigorous connections. If either of those things breaks down, we have a problem of connection. I call it the connection problem. So let's take Bell, let's take—yes—Bell's theorem of 1964 is a good example of this. Okay, okay. Let's go back to EPR. Let's go back to the EPR paper. EPR is a good example of this. The EPR paper has premises. There are premises to the EPR paper. One premise is that wave functions collapse when we make measurements on them. Another premise is, of course, the axioms of Drachmann, which incorporate the collapse. Another premise is that we have a notion of causal influence that can be cashed out in terms of interventions by agents. I needed Alice and Bob to talk about this. Alice is an agent who intervenes in her system; we call it a measurement in this case. Bob is also an agent who intervenes. The interventionist account of causality is one particular way of talking about causal influences. According to the interventionist account of causality, to say that something causally influences something else, thing B, is just to say that if an agent comes along and intervenes in some way in A, there will also be a change in B. That's what it means to say that A causally influences B.

But if there are no agents and there are no interventions, what do we do with this causal influence theory? It might go fine; there are observers. But if you want a theory of quantum mechanics or a theory of physics where observers and measurements and measuring devices are not part of the fundamental axioms that you want, we're going to have a lot of trouble talking about causality in that kind of theory. If you try to do EPR and leave out the agents and leave out the interventions and leave out the wave function collapse, it's really hard to talk about what's going on in the thing. So the extent to which all these things are certain that you have this rigorous statement, some kind of rigorous statement about what's going on, might fail because the reasoning is bad, but it might also fail because there are no agents there. And there are no interventions. It might go fine again. What I mean is, there are people, Alice and Bob. But the thing is, people are made of atoms. And we think that formulating that to meet the level of atoms is atoms intervening as agents, actually faces a kind of deep problem. As if you're really asking me to formulate this not with people, who don't have measuring devices, but the level of atoms, individual atoms that don't make decisions and freely choose to do things and make interventions and act as agents, I don't even know what this causal theory is supposed to mean. And if you don't have a theory of causality, you don't have a theory of causal influence, and you don't have a theory of nonlocal causal influence, and the whole argument collapses. And that's a thorny problem, because causality is just like a nightmare topic in metaphysics, where people have been trying to understand causality for a very long time.

Causality is one of these things that we feel like we understand intuitively. In fact, even Kant argued that cause and effect were built into the structure of our brains, that we needed to think about the world in this way. But it's really hard to pin down exactly what you mean by cause and effect, especially if you're trying to start from physics. So there's a view of physics at the turn of the nineteenth century, which is kind of a Laplacian view of physics. All there is is just the state of the universe and all the particles in it, the universe with their positions and velocities. This is the state at one snapshot of time. And then there's just a giant differential equation, the laws of physics as a giant Markovian differential equation. It takes this state of the whole universe, all the positions and velocities of the particles, and it tells you what the next infinitesimal state in time is, the next state and also the previous one. Oh, and that's all there is. That's all there is in physics. That's all there is in the evolution, the evolution of physical systems. From this, from this point of view, there's no sense in which that rock over there is causally responsible for the motion of that rock. Right? Because it's as if you don't need to have the general state. It's just kind of propagating this giant differential equation forward and backward. There's no role to be played by having these extra components, these idle wheels, notions of causal influence. Now when we teach Newtonian mechanics, we talk a lot about why that rock started accelerating, because that other rock exerted a causal influence, the force that that other rock exerts on this rock, oh, exerted a force on this rock and therefore caused it to move. But if you step back and look at the whole universe, you just have a giant state that's evolving forward through some differential equations. And there doesn't seem to be any place for causality in this picture, at least at the fundamental microphysical level. Pearson Russell, at the beginning of the twentieth century, said that, you know, causality is a leftover. I think he said it's like the British monarchy. It's something that continues to persist under the false assumption that it doesn't cause any harm. He thought you didn't need causality in physics anymore, at least at the microphysical, physical level, and we should just get rid of it. Of course, if you get rid of causality, there's no nonlocal causality. Then what is Bell's theorem? What is EPR even? If there's no causality, there's no superluminal causality, and then the problem is solved.

I think if one takes the viewpoint as some philosophers do, John Norton, for instance, has a paper you should also link to, what's called causal holism, which states that there's no fundamental causality in nature. This holism, in the early days, was all about looking for cause and effect, but we've become more sophisticated where we don't try to formulate things in terms of cause and effect anymore. You know, cause and effect is a language that we can only introduce later to simplify how we describe things. But we shouldn't look for physical theories that are fundamentally formulated in terms of cause and effect anymore. That's a leftover from the old days. I think if you want to take that viewpoint, that's a viewpoint that's consistent with itself. But then you won't be able to appeal to Bell's theorem and say that there's nonlocal causal influence going on in theories of hidden variables. If you want to talk about nonlocal causality, you need a theory of causality. You need to bite the bullet and say we're going to talk about causal influences. And if you rely on interventionist causality, you're going to face the problem that interventionist causality doesn't seem like the kind of fundamental, basic, physical definition of causality that we should talk about, when we're talking about precise physical theories like quantum mechanics. A lot of the no-go theorems related to Bell's original 1964 theorem, that theorem itself, the EPR paper, and the GHZ argument, a lot of them help themselves to interventionist causality. They end up involving agents fiddling with things and making interventions. In a fundamental, precise physical theory that's just atoms doing the things that they do without agents, and no fundamental role for agents or interventions or measurements, it's not clear what these theorems are saying. Bell wrote another version of his theorem, a generalization in 1975. It's a wonderful paper, and I think it's not widely read by physicists. I think a lot of people tend to focus on the 1964 paper. The 1975 paper is much more subtle. I'll put the link on the screen. Yes, you should put the link. It's a great paper. It's beautifully written. And he tries in this paper to deal with this problem. And he doesn't use the word intervention, but he tries to get away from relying on measurements and on collapse. He retreats to a more primitive idea. He just said, look, even standard quantum theory is committed to some ontology, things that actually exist. Measurement outcomes, quantum theory says there are measurement outcomes. And that's something that it's committed to. Those are the beables, the things that actually exist there. According to quantum theory, there are actual facts about how the measurements come out, that actually exist in the world. He calls them beables, not observables, but beables, things that are. Maybe that's all you have beables. Maybe there are more possibilities in your theory, but standard quantum theory only contains those. To be clear, what is a beable? An ontological entity? Yes. A beable is what you think is real, and what you think actually truly exists. According to quantum theory, you're at least committed to measurement outcomes. Now, this of course raises some questions. If the measuring devices exist and they're really real, what are they made of? In quantum theory, there's nothing. You can't say, well, they're emergent, because emergence requires a substrate. Water, liquid water emerges from water molecules. Things that the emergence is composed of must exist. In quantum theory, you can't say that the measuring devices are emergent without mentioning what are the things that they emerge from. In a theory like Bohmian mechanics or many worlds or the no-collapse stochastic formulation, you have those components that the emergence is supposed to be from, but in standard quantum theory, you don't. Putting all that aside, you're at least committed to measurement outcomes. Measurement outcomes are the boundaries of the theory. Bell just—he reformulates the premises of his theorem differently. He doesn't rely on intervention. He doesn't even propose a theory of causality. He just said, look, I don't have a good theory of causality. I'm not going to give you a full and complete theory of causality, but I think any good theory of causality should have a certain feature. It should have a feature, which we call today Reichenbachian common cause analysis. This is just the statement that if A is something that's correlated with something else, B, they go up and down together statistically, in some statistical way, A and B don't causally influence each other directly, perhaps because they're too far apart when they occur to be able to communicate with light. Then there must be some other variable, C, that causally influences both of them. For example, if people have one medical condition, and some other medical condition, and it was clear that neither medical condition caused the other, but they seem to be correlated, you might think, oh, there must be something they ate, or something they did that was responsible for both of them. There's a thing like Nicolas Cage movies being released when people tend to die from drowning in swimming pools. Certainly. I don't know if that's an interesting suggestion. Well, it turns out that the reason is that Nicolas Cage releases movies in the summer. Oh, good. Yes. It's a common cause of summer. Good. Yes, exactly. It would be like saying, okay, barometers show low pressure, and that's correlated with hurricanes. But it doesn't seem like barometers are causing hurricanes. Okay. Or that hurricanes, which haven't happened yet, are causing the barometers. But there's a low-pressure system that happens first, and that leads to both of them. Right. And that's what's called the common cause principle. What Bell asserts is that any good theory of local causality must have the property that local beables, whatever they are—they could be measurement outcomes, they could be other beables—it's very general in this respect. But local beables that are correlated that are far apart, there must be other beables in the past, in the causal past, in what's called the intersection of their light cones. That's the fancy way of saying it. And there must be a sufficiently rich set of those things, a sufficiently rich set of them, such that if you condition on all of them, and you know all of them, they explain the correlation in a very rigorous mathematical sense. They lead the joint probability distribution of the two things, two beables, A and B, and they lead the joint probability distribution to factor cleanly when you condition on the local beables in the past, which is the common cause of the local beables. And that's called Reichenbachian analysis. I don't know that Bell was aware of Reichenbach's work. Reichenbach formulated this idea in the 1950s. And it's certainly something that you could imagine that a good theory of causality should possess. Bell needed this analysis to derive his inequality. With these weaker and more general assumptions, the 1975 theory was general enough to include probabilistic theories, theories with hidden random variables, where the hidden variables don't uniquely determine the measurement outcomes, but only probabilistically determine them. So this is a more general theory, but he changed his premises. And he now takes on this premise. In order to consider the theory locally causal, his principle of local causality is, again, it's locally causal if we have statistically correlated local probabilities, A and B are sufficiently far apart when they occur that they cannot causally influence each other. There must be a sufficiently rich set of causal variables in the past that when you condition on them, the correct joint probability distribution factors in this neat way, and this is necessary to get the theorem. Now I'm not the first one to suggest that Reichenbachian analysis is a very strong requirement, and a strong enough requirement that it cannot be imposed on a theory of causality. Others, you know, Bell Unruh, for example, in a 2002 paper, which I can also link to, he has this longish explanation. He says, well, yes, I mean the things were entangled. There was some interaction that entangled them. But in quantum mechanics, interactions aren't variables or beables. They're not things that you can condition on. There was a common cause, which was the interaction in the past, but it's not the right kind of common cause to get the factorization, so there's no problem here. And many philosophers of science have made this argument as well. There's a bunch of papers by Jeremy Butterfield, who's a philosopher of physics at Cambridge University, who has also questioned Reichenbachian analysis. Why do we think Reichenbachian analysis is good? Well, it kind of works with the joint probabilities of the macroscopic world, but that's not a strong argument that it should also apply to precise physical probabilities. And there are actually good reasons to doubt that it should hold in fact. But that's just setting the stage. If you deny that Reichenbachian analysis is a good requirement for any good theory of local causality, then Bell's theorem has no teeth. It simply doesn't work anymore. Now, in a lecture that Bell gave in the early 1990s called La Nouvelle Cuisine, which is in his collected works, Speakable and Unspeakable. It's a collection of all his papers, but not the first edition, the second edition of my Speakable and Unspeakable. And he has this lecture called La Nouvelle Cuisine, which we'll also link to. He recounted the story of the 1975 theory again, and he tweaked its premises a little bit. I've corresponded by email with the philosopher of physics, Ivana Lukic, about this. She's working on a paper where she's looking at all the different formulations of Bell's theorem. And in 1991, he changed some of the premises slightly, so he doesn't rely on the same kind of Reichenbachian analysis, but he still needs all this kind of assumptions about what a good theory of causality could be. He doesn't propose a theory of causality. There are many theories of causality historically. There are regularity theories that say A causally influences B means that when A happens, B happens, or later, or counterfactual theories that say A causes B only if B would not have happened if A had not happened. And there's conservation law causality, and there's increase of probability causality. There are all these causal theories. Bell doesn't propose a theory of causality. He just said, I think a good causal theory should have this feature. And if you assume this feature, you get this inequality. The inequality is violated by quantum mechanics. Therefore, whatever quantum mechanics is, it doesn't have this feature. Therefore, it cannot have a good theory of local causality. But he didn't propose a theory of local causality.

So this is a very long way of saying, in the no-collapse stochastic approach, we replace differential equations. We don't have the Schrödinger equation anymore as the fundamental equation, or Newton's laws, or Maxwell's equations, or any of that. We don't have those things anymore. Instead, we have these conditional probabilities, this set of what I call directed conditional probabilities. I'll explain the directedness in a moment. But these directed conditional probabilities are exactly the kinds of components that show up in the literature related to causal modeling. When you do probabilistic causal modeling, you have random variables. These are things that can change, and they have links between them that describe the causal relationships. And these causal relationships take the form of conditional probabilities. The probability of having certain values of B, given that these other variables have their values, and thereby we can say that those variables causally influence B. This is exactly the language in which the laws are formulated in a no-collapse stochastic formulation of quantum mechanics. So you might think, well, it's formulated in a way that provides a very hospitable setting to talk about causal relationships. Perhaps we should read those conditional probabilities through a causal lens. And now you have the opportunity to build a microphysical causal theory out of these components. You're no longer relying on a Laplacian model of differential equations. It's now relying on the kinds of conditional relationships that we might think have causal meaning to them. So in one of my later papers, this is the paper, New Prospects for a Locally Causal Formulation of Quantum Theory, I run with this. I say, okay, okay, let's take this and use it to talk about causal influences between things. And now let's suppose that what it means for a theory to be locally causal is that when you have two systems in space-like separation, they're far enough apart that they can't influence each other, then there's a clean factorization of the conditional probabilities between them. And I formulate this very vaguely, because it's hard to write down, but you can read the paper. But this essentially proposes a—it takes a position. It proactively proposes a microphysical theory of causality, and then it asks the question, of microphysical theory of causality, do we get nonlocal causal influences in EPR experiments in particular? And the answer is that we don't. So you can read this. That's in the paper. I also have some online talks. People can go and they can watch the talks where I go through all the technical details. I very precisely define what I mean by causal influences built on these conditional probabilities. Then I carefully define what I mean for two things to be causally independent of each other. And I precisely define what I mean when I say that two things don't exert nonlocal causal influence on each other. And then I carefully study EPR experiments and show that in EPR experiments, there's a causal influence that comes from the creation of the entangled pair. So the two particles, which is sensible, because that instance lies in their past light cone, but there's no causal influence that propagates from anything Alice does to anything Bob does. So I'll put a link to all your talks on the screen and in the description as well. And maybe at some point when you have another talk planned, I'd like you to present it on TOE so people can see some of the mathematics behind what you're saying. That would be very cool. I hope all that is somewhat clear and understandable. Okay, many people have questions about Bell, so I'm glad that you were able to give this clarification. Yes. This is a brief summary of how to think about Bell's theorem. But it's general; it's the kind of care that one must take when approaching any theory about physics, any physical theory. It's not enough to check that the theory is mathematically sound as a mathematical argument. You have to ask, are the things that it refers to in the world, the referents, are they precisely defined? And in Bell's case, he needs a local causal relationship. Are those terms well enough defined? And I contend that in fact, they aren't. And then you have to worry about the relationship between those referents and the mathematical components. Is that sufficiently established? That's where the weakness lies. If Bell's definition of causality is not rigorously enough defined, the theorem has no teeth. And if you can give a precise physical theory of causality and a theory of what that precise physical theory of causality means for things to not be able to nonlocally causally influence each other, that's all you have. If people still don't like that and they still think, well, it still seems like there's a lot of correlation. Okay, maybe that doesn't seem great. Maybe that's unintuitive, but it's not a source of breakage. Right. Now all this leads to the question, what do we even mean, what is entanglement in this picture? So this no-collapse stochastic picture, what's going on in entanglement? If there's no state vector, if there's no superposition actually happening, what do we mean by entanglement? There's actually a very nice picture of what happens with entanglement now. Let's suppose I start with two systems. Think of two particles, for instance, or two qubits, two simple systems. And let's suppose that these systems are initially independent of each other. They have their own configurations. They're not interacting with each other in any way. Well, according to the no-collapse stochastic approach, by definition, what it means for them to be independent and non-interacting is that they have their own separate stochastic laws. Now, let's suppose that there's a certain time. We'll call this time t prime. At this time, they interact in some way. And because interactions happen locally, whether you're working in quantum mechanics or not, they have to be close to each other or share some intermediaries in order to communicate. But somehow they start interacting. What does this interaction mean? Well, even in Newtonian physics, when two systems interact, they don't have their own separate potentials anymore. There's one joint potential for both of them that can't be factored. In the no-collapse stochastic approach, the interaction is represented by the fact that there's now a joint stochastic dynamics for the two systems, and that the joint stochastic dynamics does not factor during their interaction. Now, what you might imagine would happen is that once the systems separate and are taken to far distances in space, they'll have their own separate stochastic dynamics now. And that's what would happen in the Newtonian case, in the Newtonian case. But that doesn't happen here. That doesn't happen here because the joint stochastic map is non-factorizable. It goes all the way back to the first time, before they interacted. It cumulatively encodes all the statistical effects between the pre-interaction and all future times. And if there's a moment where it stopped factoring, it won't start factoring again. So the two systems won't have their own separate laws. There will be one joint, non-factorizable stochastic dynamics for the two systems. But there is a common cause. And the common cause was their interaction. But the common cause is not the kind of common cause that can be incorporated into a Reichenbachian principle of common cause. Now, if you have an agent, if you will, Alice or Bob, or the environment, or even just one of those little qubits that we talked about, a detection unit that we had when we were talking about the double slit experiment, that interacts with one of the systems and reads its configuration, at a later time, t double prime, t double prime, later on, when they're far apart, it will produce a splitting event. This splitting event will allow us to restart the joint stochastic dynamics, but the systems are separate now. And so when the stochastic dynamics restart, and start cleanly, they stop interacting. It will start factoring, and it will remain factored. And that's disentanglement.

Therefore, the two systems do not interact initially. They have their separate, non-entangled, random dynamics. We can say they are not entangled. They begin to interact for some time during the interaction. And then, until the next division event, they no longer have their separate, non-entangled, random dynamics that are analyzed. Then when there is a later division event, once they are completely separate and we can restart the random evolution, we can stop and look at the configurations that they are in, and then write new laws for them. They have now separated. Now they will have their independent laws again. This is disentanglement.

Note that this is a picture of entanglement that is formulated entirely in terms of ordinary probability theory without Hilbert spaces. That is the claim that is being made. And that’s what happens under entanglement. And this picture of what happens with entanglement is consistent with this microphysical theory of causality that I was describing before, a theory that doesn’t allow any agent or environment or measuring system acting on one system to have a causal influence across a spacelike separation on the other. So that's what I would say entanglement is. It’s a picture of entanglement at the level of ordinary probability theory. Whether you call it classical probability theory is a fine point. It depends on whether you think non-entanglement is a classical property or not, but it’s certainly ordinary probability theory and doesn’t require Hilbert spaces and so on.

So this is one way of thinking about how entanglement happens ultimately at a deeper level than the non-entangled random process. I mentioned that the entangled random dynamics somehow contains memory. I know you don’t like the word memory, but somehow encodes what happened before in itself. So if I think of that as information being encoded, well, information, if you pack enough of it, you form a black hole in a small enough region. Does that mean that if entangled particles remain entangled for long enough, they will form a black hole because the dynamics between them encodes so much information? Help me unpack this question. Yes, so I think there is a sense in which the overall non-entangled random map does encode a kind of cumulative statistical correlations. But even that, I mean I am fishing for metaphors here somewhat when I say that because it's not memory in the traditional sense. Again, a traditional non-Markovian process, in the way we usually talk about non-Markovian processes, we have this hierarchy, this tower of higher and higher and higher order or conditional probabilities conditioned on more and more facts that are all different and contain a huge amount of information. A Markovian process is what happens when you assume that all of those are equal to first-order processes. They are there, but they are all equal to first-order elements, so they don't contain any really interesting information. And in a non-entangled random process, they are not there at all. We don’t have all this stored information. The statement is simply that the probabilistic description of the later configuration of the system depends on its initial configuration, and that can happen again - it can happen in the past. It can be the configuration of the system sometime in the past. That doesn’t mean that information is literally encoded. It's not the kind of information that could saturate the maximum amount of information that can occur in a region of space, as Bekenstein bound says, and would lead to the formation of it – it exceeds the amount of information you can have and would require the formation of a black hole. So I just want to say I don’t think this information – it’s not information I think that’s encoded on physical qubits in space that would interact with spacetime and have gravitational effects. It’s just that the laws are a little bit weird and weirder than we thought.

I see. Okay, tell me about the loss of phase information. We talked about this off-air, but explain this on-air. So one of the questions that you might ask is, well, well, when I make this change in representation between the random process that doesn't have complex numbers, doesn't have phases, but non-entangled dynamics and I go to this kind of quantum system where I have phases and all that kind of stuff, right? Phase information seems to be really important. I mean we need it in order to predict interference. How could it be missing from the non-entangled side? Well, the important point is that it’s not missing. The phases that are on the Hilbert space side are just non-entanglement on – so they are there. They just manifest themselves in a somewhat different way. But even then you might say, well, but hey. I mean I can measure those phases indirectly. If I like using the unitary time evolution matrix that I use to describe the evolution on the Hilbert space side and I like to modify the entries and lose all the phase information, how can that still capture the same information? How can it do that? And the answer is in this picture, when you design a measurement process, you have to bring in the measuring apparatus just as Bohm did when he was writing those later chapters in his textbook in 1951 on the measurement process or in his papers on Bohmian mechanics in 1952. You have to bring in the measuring apparatus. And when you do that and you describe the whole thing as a giant non-entangled random process, you don’t need the phases. You just run the overall non-entangled random process including the measuring apparatus, and it will likely end up in one of the configurations of the outcomes of reading the measurement with probabilities that agree with the predictions of Born’s rule. And so the phases are immaterial. You don’t need them. However, if I want to exclude the measuring apparatus from my formal description of the system, if I don’t want to deal with the whole measuring apparatus, if I just want to remove it and look at the system of interest and ignore the measuring apparatus, and treat the measuring apparatus as a kind of background character, not a person in the foreground of the story, then I need the phases to make predictions. And then I will replace the detailed physical measurement process with the von Neumann-Lüders collapse. I will use Dirac’s textbook phenomenological axioms. So what I’m saying is that Dirac’s textbook phenomenological axioms don’t disappear. We just specify that they describe a certain regime of validity. When you are doing a macroscopic measurement using a large measuring apparatus on some microscopic systems, you can design everything and include the measuring apparatus and do everything, and then you don’t need all these phase factors. You can just run the whole thing as a giant random process, and you’ll get the right answer. All of that is spelled out in detail in the first paper, the quantum random correlations paper. But if we don’t want to face all these problems, if we want to simplify our description and ignore the measuring apparatus, and treat it as a background character, and focus only on the system of interest, and the system is microscopic, so we don’t face the messiness that we might face, well, we can ignore the measuring apparatus. We can treat the measurement as an instantaneous collapse process, and then we have to worry about these phase factors. And so the phase factors are a way of encoding not just the non-entanglement but also the invisible measuring apparatus. That's one way of thinking about what happens to those phase factors.

That sounds like Copenhagen still. How is this not Copenhagen? Right. So I mentioned that Heisenberg wrote a lot of philosophy. And he wrote a book called Physics and Philosophy, and there’s a chapter in his book Physics and Philosophy, and we can also link to it. People can find it. And it’s a chapter called The Copenhagen Interpretation, and it describes what he saw as the Copenhagen interpretation. Now, there is no agreement or consensus on exactly what the Copenhagen interpretation means, and different people responsible for what we think of as the Copenhagen interpretation have different views on this topic. Let me just describe how Heisenberg basically described it. He basically said, well, Kant told us that our human brains can only understand the world in certain ways. We understand the world in terms of three-dimensional geometry and cause and effect. There are certain things we just understand. That’s just the way our brain is supposed to work. And the quantum world simply doesn’t work that way. It doesn’t work in ways that our brains can understand. The classical macroscopic world does, and we have good theories for the classical macroscopic world. We have classical mechanics, classical physics. The microscopic world is simply beyond our understanding. Therefore, we use the mathematics of quantum mechanics, Hilbert spaces, wave functions, the Schrödinger equation, not because we believe that the world is literally these things, or that the wave function is real, but simply because they give us a formal apparatus, just a toolkit for predictions. They give us a set of mathematical tools to predict what’s going to happen again on the macroscopic classical scale. A large microscopic system sets up the experiment. It’s measured by a large macroscopic measuring apparatus. What happens in between we don’t have the ability to understand. We use the weird mathematics of quantum mechanics to predict what will happen. But in reality, ultimately, everything has to manifest in some classical outcomes. And that’s the picture that constitutes the Copenhagen interpretation, at least according to Heisenberg. He did have some words about the source of probabilities. He said, well, there’s the uncertainty principle, and for large macroscopic systems, we are all somewhat uncertain. And when microscopic systems interact with microscopic systems, that’s where the probabilities come in. He had a somewhat more complicated picture about all of this. And people can go and read his chapter about all of this. This is not Copenhagen because I don’t practice the same kind of agnosticism about the microscopic world that he did. I don’t say that we don’t know what’s going on in the microscopic world. I don’t say that we basically only have classical physics, and then the microscopic world is mysterious to us. We need this other theory to describe the microscopic world, and all it does is provide predictions. I say the microscopic world has an ontology. I say classical things have physical configurations, and measuring apparatuses have physical configurations. Measuring apparatuses arise from atoms, and that’s fine now because atoms also have an ontology. Atoms really exist. They really have configurations. And when you do the experiment, the particles really do things. They really move in certain ways. The laws are these somewhat non-intuitive non-entangled random laws, but things really do happen between measurements. And now I hope to tell, at least in outline, a picture of emergence, a story about emergence, where we have particles or whatever the ontology is. They could be fields, and then larger-scale things emerge from them, in the way that liquid water emerges from water molecules, at least spiritually. The Copenhagen interpretation doesn’t do that. You can’t talk about how the classical world emerges because the Copenhagen interpretation practices agnosticism about the microscopic world. It doesn’t say what exists in the microscopic world. It doesn’t posit any kind of substrate, or any lower-level reality, or material reality, from which the emergence of classical things is supposed to happen. And these are all ways in which this picture differs from the Copenhagen interpretation. And of course, the Copenhagen interpretation also has this weird undefined boundary between what is quantum and microscopic and what is classical and macroscopic. That’s what’s called the Heisenberg cut. There is a threshold above which you are classical and below which you are quantum. And that’s a blurry line, and people have debated whether it actually exists or whether the idea is that you can move it. But in any case, it’s not part of the non-entangled random approach.

Are electrons single particles? Are they composite or are they point particles in your picture? I don't know what they are made of. Our best theories, the standard model, describe electrons as being non-composite. So I don't know if they are made of anything else. I mean there's also this interaction between electrons and the Higgs field which is, you know, complicated. But they are not any more or less composite in this picture than they would be according to the standard model. Right. So the thing that I'm interested in is the research. What are the open questions that this raises? Where can people come to help you with this theory? Yes. So what I find exciting about this project is that it doesn’t happen very often that you stumble on like a blank slate in an area that you might have thought was settled fundamental physics, where you can ask questions that don't actually have answers yet. And there are many directions people can go in when it comes to research. This project opens up a lot of these directions. One is simply the mathematics of this new class of processes, these non-entangled random processes, which only appeared in the research literature like in 2021 in this review article by Simon Mills and Kevin Modi, which we can also link to, and people can look at it. It appears in these kinds of forms in their paper. There's like Figure 5 in this paper. You know, mathematics has all these very simple ideas like functions and matrices and limits and derivatives that are reasonably easy to define, but have profound consequences. It's not often you see relatively simple ideas, simple mathematical ideas that have wide-ranging applications and ramifications. Non-entangled random processes are a fairly simple idea that I think people haven't really thought about. And so there's some interesting work to be done in trying to understand the mathematics of these processes. That might be interesting work for somebody interested in mathematics and applied mathematics and the theory of random processes. We talked about how to model real-world systems like quantum field theories, like the standard model. There’s a lot of work to be done to take this picture and apply it to systems that appear in condensed matter physics and high-energy physics and the standard model to make sure it works, for one thing, and also to see if it reveals any interesting features of these theories that might be difficult to see in other ways. Dynamical symmetries are a really important topic in physics. Dynamical symmetries appear in a very interesting way in this approach, and so there’s a lot of work to be done there. There are old problems in statistical mechanics. So one of the outstanding problems in the philosophy and foundations of statistical mechanics is where do probabilities come from in statistical mechanics? In classical statistical mechanics, you imagine you have particles, like a gas consisting of particles, and the particles all evolve because they're classical according to Newtonian mechanics, the rules of Newtonian mechanics, but Newtonian mechanics is not a probabilistic theory. There’s this wonderful argument by a philosopher of physics, David Albert, that there is nothing whatsoever in the laws of Newtonian physics that would prevent a bunch of rocks from spontaneously falling together to form a set of little statues of the royal family. You might think that that’s impossible, but it’s not impossible. I mean, after all, you can start with statues of the royal family and turn them into rocks, and because Newtonian physics is time-reversal invariant, the opposite should be possible, yet we can say that this is somehow improbable. But Newtonian mechanics doesn’t come with probabilities, so where do those probabilities come from? One argument is that the probabilities come from the initial state of the universe. The universe started in some initial state, but of course there was one initial state of the universe, not a probabilistic ensemble of initial states. So there’s some work to be done in understanding how we go from some beginning of the universe to the idea of a probability distribution, and it has to be the right kind of probability distribution. On the one hand, it should be the kind of probability distribution that doesn’t lead to rocks forming statues of the royal family because we don’t see that around us. We don’t see that happening. We look around and we don’t see rocks spontaneously clumping together to form statues of the royal family. And so we hope to look for some kind of explanation for why that doesn’t happen. Oh, what I mean is, if you wait long enough, won't you see it? Maybe, but only if the space of probabilities is finite in the right sense. If the number of possible configurations of the universe is infinite, there is no requirement that you revisit or revisit every probability. If there's only a so-called finite space of probabilities, then there are arguments that say that eventually you have to get repetitions or you have to visit everything. But in any case, in the time that we've had since the existence of the universe, we haven't seen that happen. We haven’t seen rocks spontaneously forming. I mean even if we had this infinite space, some events will happen that are going to be extremely improbable. Yes. Of the same size, if not bigger than the royal family. That’s right. But we don’t expect them to happen all the time. Right? We live in a world where these things happen, but rarely, not all the time. It would be very strange if this was happening all the time around us. How do we explain why it doesn’t happen all the time around us? Somehow, this is connected to how the universe started. The universe started in some kind of configuration that was fairly typical. It was very generic. It was very boring. It didn’t have very special arrangements that would lead us to see strange and improbable things happening all the time. But we can’t make it too typical because there is some sense in which the most typical initial configuration is just too random and in a loose sense, too high entropy. We actually need the beginning of the universe to start with a low entropy configuration so that we get a well-defined thermodynamic arrow of time. David Albert calls this the past hypothesis. There’s something mysterious going on about the beginning of the universe if you live in a deterministic world where the laws are deterministic because how can we get probabilities? They must come from some statement about initial conditions, but those initial conditions in the universe have to be such that we started with low entropy and are rising toward high entropy yet are typical enough so that we don’t see surprising things happening all the time. In a theory where the laws themselves are probabilistic and random, we don’t face the same kind of problems. If the laws themselves are random, then we get the probabilities from the laws. And we don’t need to get them from the initial conditions of the universe. And this gives a completely different way of thinking about the source of probabilities in statistical mechanics.

Now, one might ask, well, does that mean that all statistically fluctuating things in statistical mechanics and thermodynamics are ultimately quantum mechanical in origin? That’s not the way I would phrase it. The way I would say it is that we need some source of probabilities in order to ground things like the launching of statistical mechanics. You need some statement, like anything else, all accessible configurations or states of the system are somehow equally probable. The technical term for this assumption is that we assume the microcanonical ensemble. But it's basically saying, if the system can have many states and they're all accessible, the system can reach them. And we should treat them all as equally probable unless we have a good reason to believe otherwise. How do we get that off the ground? There have been arguments for a while that systems might rattle around and change rapidly, even according to Newtonian mechanics in a way that was called ergodic. Ergodic systems are systems that rapidly explore their possibilities or their state space, very rapidly. And very rapidly you can pretend that the system is equally likely to be in any of its states. Unfortunately, proving that systems are ergodic is extremely difficult, and there are many systems that are known not to be ergodic. So it turns out that the ergodic hypothesis doesn’t apply to very many systems. There were some information-theoretic arguments to try to ground this. But then you face some very deep questions like if the probabilities are all just in my head, how can probabilities actually lead to the boiling of coffee or something like that, right? It seems like probabilities have to be somehow out there in nature because they seem to do physical work generally. So the information-theoretic approach to try to derive equal probability of all microstates is extremely difficult. But theories that have probabilities in the laws provide a different way of getting probabilistic behavior at this kind of necessary level. Once you have this probabilistic behavior and you can talk about Boltzmann statistical mechanical systems, you can then take these Boltzmann statistical mechanical systems with kind of all states assigned probabilities with roughly equal amounts. You can combine them together. You can take large, large, large systems called reservoirs that represent the environment and small systems. And you can from these interactions derive concepts like thermal equilibrium at a certain temperature. And then you can derive what's called the canonical ensemble which is the probability distribution that we associate with a system that is strongly interacting with a very large environment called a reservoir. And these systems will exhibit fluctuations which are thermal fluctuations. And those thermal fluctuations are different than quantum mechanical fluctuations. So there's a higher level of thermal fluctuations that you get for these systems. It doesn’t mean that you need the non-entangled random approach to explain this higher level of emergence of thermal fluctuations. The point is that you need these non-entangled random methods or something like them or you need probabilities from somewhere to get statistical mechanics, Boltzmann statistical mechanics. And once you have that launched, you can then use all the tools that have been developed for statistical mechanics to understand the emergence of temperature, the emergence of thermal equilibrium, the emergence of thermal fluctuations.

When you said earlier that it’s not just in our heads because water boils and something happens, did you mean that some people think that randomness is due to our ignorance? Right. Right. Yes. So one way to think about probability is that probability is an objective chance kind of thing. This nature really acts in a random unpredictable way. These phenomena occur in an unpredictable way. Another view is that probabilities are all in our heads. Right? When we assign probabilities to things, we’re talking about what’s called subjective credence. Credence is degrees of belief. When we assign probabilities to things, we’re not saying that the probabilities are really out there in any way. We’re just describing like our belief about whether something is really a certain way or not. And there’s a relationship between objective chance probabilities and subjective credence probabilities. The most famous formulation of it is what David Lewis called his principal principle. The first principal is the principle, PAL. The second is the principle, PLE. And that just means that if you know the objective chance of something, and you condition on that, your credence should be equal to the objective chance. There is a relationship between objective chance and credence. But in this kind of picture, we acknowledge that there are different kinds of probabilities. There are objective chance probabilities. There are subjective credence probabilities. From time to time, people have tried to say that there’s only one kind of probability. Maybe all that exists is just subjective credence probability, and there is no underlying objective chance probability, or the other way around, I suppose. Maybe we’ll talk a little bit about that in the context of Everettian quantum mechanics a little bit, because it shows up in that context. But the question is, if all probabilities are really just subjective credence probabilities, how can subjective credence probabilities in our heads form the basis of Boltzmann statistical mechanics, which underlies thermodynamics and thermal fluctuations and all the things that happen in the world around us? I mean if you know the exact specific state of a system, and now this specific state has a 100% probability or nearly 100% probability, and now that my knowledge has changed, I’ve changed all the probabilities, and therefore make thermodynamics stop working. That’s obviously a very rapid statement, but there’s a little bit of a puzzle here, can it just be all probabilities are in our heads, or is there something somewhat random actually happening in the physical world? The reason why this is so extremely difficult is that coming up with a self-consistent, unambiguous, rigorous theory of objective chance seems to be extremely difficult. And that’s one of the reasons why people retreat to believing that probability is all credence, because if it’s credence, it’s okay if it’s not perfectly rigorous. It is extremely difficult to define objective chance probability. It faces all kinds of foundational problems. What does it mean to say that something in the world has an objective chance of 72% or 0.72? You might say, well, that means that in the long run, if you repeat that many times, 72% of the time it will manifest in a certain way, but that’s not actually true. If you take a coin, for instance, and you think the coin is a 50-50 coin, and you flip it 10,000 times, if it's a fair coin, you will not get heads 5000 times. It will be slightly less than 5000 times. If you think about it hard enough, you will realize that, but there is actually a probability that there will be heads every time. It's improbable that there will be heads every time.

Once, but there could be heads every time. If you try to say something like, okay, okay, we need to take some kind of limit, maybe in the limit as the number of flips goes to infinity, it’s exactly 50%, but that’s not how limits work. What if the coin has a tendency to be 50-50? Well, theories of propensities are difficult, because what is a propensity? There’s a propensity to get outcomes 50% of the time, but as you see it’s circular. It’s very difficult to pin down what you mean by propensity. Propensities theories tend to say that it’s just certain things want to do something a certain way, but then what does the 50% mean then? Does it say that they want to do it a certain way during this time, but then we face the same problems that we face here. This probability theory which is about frequencies of repetition, whether it’s a propensity, like coming from something or from laws or whatever, and it’s about how frequently you get certain outcomes is called frequentism, and it’s hard to make frequentism rigorous. You might say, okay, take the limit n to infinity, take the number of trials to infinity, but that’s not how limits work.

A limit, when you say a certain sequence of things has a certain limit, what you’re saying is that if you go far enough out in the limit, you go past some n in the limit, then all subsequent terms are closer to the claimed limiting value than anything else. You give me some error, some epsilon. I can find a distance far enough out along the sequence such that everyone further along is closer to the claimed limit than epsilon. If you make epsilon smaller, I’ll go further out. Make epsilon smaller, I go further out. And as long as I go far enough out, everything later down the line will be closer to the limit than epsilon. Probability doesn’t work that way. Frequentist probability doesn’t work that way. There’s no number of times you can flip a coin that will make its frequencies closer to 50% for sure. I mean you can flip the coin a billion times and it can land on heads every single time. It’s improbable, but it can happen. If you give me some epsilon, you cannot give me any number of flips that will guarantee that it will fall within approximately 50% of that. You might roll your eyes and say, come on, but it’s improbable to do that. It’s likely to be closer than epsilon, but the word likely is probability. What you can say is that if I flip the coin enough times, I can make the probability that it’s further than epsilon from 50% smaller than epsilon. That’s just relating one probability to another. It’s completely circular. The law of large numbers is formulated this way. It’s just circularly relating one kind of probability to another.

The formal way to describe that is that when you’re taking a limit, you need to have a notion of a scale, a metric notion. I’m sorry, you have to have a metric. You have to have a notion of how far something is from something else. For probabilistic systems, the metric itself is a probabilistic metric. That’s what you use for distance. Any attempt to use limits with a probabilistic metric to describe probability will run into the objection of circularity. However, even though we don’t have a rigorous theory of frequentist probabilities, we certainly have an intuition that when we look at a long sequence of coin tosses or a long sequence of ones and zeros, we can distinguish between a highly random sequence and a non-random sequence. If we look at 10,000 zeros and ones and we find that about 50% of them are zeros and 50% of them are ones, furthermore, runs of zeros, three or four or five consecutive zeros, or ones, three or four or five consecutive ones, occur with certain frequencies. This sequence obeys a number of other criteria of randomness, different criteria of randomness. There are the right kinds of lack of correlation as time goes on. All these things you can run on a sequence of 10,000. We will look at that and we’ll say, that to me looks like a random sequence generated by a 50-50 coin. It’s not rigorous. You can’t make it rigorous. There might never be a completely rigorous probability theory at the level of frequentist probability, but when you look at long sequences, there’s at least an approximate notion that some sequences look like they have all the hallmarks of probability. So maybe we don’t need a probability theory for system mechanics. Maybe it’s enough to rely on appropriately defined randomness. There are terms that come up, people talk about Kolmogorov complexity to describe how random a sequence is. Maybe we can rely on those instead of relying on probability. Maybe probabilities are all in our heads, and what’s in nature is something like complexity or Kolmogorov complexity or randomness. Or maybe nature is just inherently random. So there are many ways of thinking about these kinds of problems.

Now, I just mentioned metric, by the way, but there’s the problem of measure in the many-worlds interpretation. We should talk about these other things, why should we bother to come up with a new interpretation of quantum theory at all? Don’t we already have enough interpretations? I mean there are a lot of people who say we don’t need more interpretations. The world keeps adding more and more of them. Why do we need any of them? That’s why I think we need a new interpretation of quantum theory. Existing interpretations suffer from one of the following problems, or more than one of the following problems. Obscurity, they’re obscure about things that they shouldn’t be obscure about. Or they are instrumentalist, meaning that they only talk about what happens in measurements, but then what are measurements and what are measuring apparatuses? And are measuring apparatuses made of things? And all of these run into circularity problems, run into problems of measure essentially. Or they’re obscure when trying to deal with systems of macroscopic size. We’ve talked about the Wigner’s friend thought experiment. Once you get systems as large as macroscopic classical measuring apparatuses, does the theory give unique or unambiguous predictions? Or the theory is empirically inadequate. It works with some systems, like Bohmian mechanics which works very well with systems with fixed numbers of infinitely many non-relativistic particles, but it doesn’t seem empirically adequate enough to be able to deal with the standard model. Or finally, the theory relies on a lot of empirical assumptions and axioms and speculative metaphysical assumptions. That is, in order for the interpretation to work, we have to make a whole bunch of assumptions that are not empirically verifiable, that seem like desperate measures, or seem far-fetched, or are hard to justify, except that they give us the interpretation we want. I think those are the problems that all existing interpretations face. Every single one of them has one of them. I mean, Bohmian mechanics suffers from it, and it doesn’t seem empirically adequate.

A philosopher of physics, David Wallace, who works at the University of Pittsburgh, wrote a paper that I think describes this very accurately. He says, the sky is blue, the sky is blue, and our best theories about why the sky is blue rely on what’s called Rayleigh scattering. Rayleigh scattering is when I teach Jackson electromagnetism, and we cover Rayleigh scattering. When electromagnetic radiation hits charged particles, the charged particles oscillate and re-radiate. And they do that, they radiate energy according to a certain dependence on the frequency that favors high-frequency radiation, and so you get much more scattering of high-frequency radiation compared to low-frequency radiation. Bohmian mechanics doesn’t seem able to explain Rayleigh scattering at this point, and it’s been around for a while. I mean de Broglie first came up with pilot-wave theories in the late 1920s. Bohm rediscovered them independently, and then eventually started talking to de Broglie in the early 1950s. It’s been more than 70 years, and Bohmian mechanics’ inability to explain this kind of familiar feature of our physical world is a mark of empirical inadequacy, and that’s a problem. Copenhagen, well, instrumentalism, obscurity, what’s a measurement, I mean, the Copenhagen interpretation has a lot of problems, we talked about all these problems. There are spontaneous dynamical collapse approaches to quantum mechanics, and I think some of them are still viable and haven’t been ruled out empirically. And some of them have now been ruled out empirically, meaning they’re not empirically adequate. They often involve some ad hoc choices that you have to make, that you have to introduce some kind of ad hoc parameters. What’s the timescale on which the collapse is supposed to happen? But some of these are still live possibilities. People are working on them, and people should work on them. I mean I’m not saying people should stop working on any of these things. We should see if Bohmian mechanics can be made empirically adequate. We should see if dynamical collapse approaches can succeed. But so far, they haven’t, they haven’t yet. Then there are other things further afield from these things, like QBism. So QBism, which comes from quantum Bayesianism, is associated with Chris Fuchs, who works at the University of Massachusetts, Boston. And quantum Bayesianism starts with the idea that probability is really in our heads, and there isn’t really any physical probability. And quantum mechanics, the formalism of quantum mechanics, is really just a methodology for dealing with uncertainty, for dealing with uncertainty about the world. And it’s a particular mathematical framework that you need to use to do that. It claims to be not anti-realist. It claims to be compatible with the idea that there is, in fact, a fact of the matter about what’s going on behind quantum mechanics. But it hasn’t yet been able to formulate what that picture is supposed to look like. And I feel terribly bad, because every time Chris gives a talk, at some point, in the question session, I’ll raise my hand and I’ll ask Chris this question about, well, where’s the picture? What’s the ontology? What’s going on here? And he says they’re not ready to deliver that yet. I feel bad when I ask him that, because he’s very nice and patient with me when I say these things. But I think the problem is that we don’t have a place to stand, right? I think one viewpoint is, what’s the rush? What’s the emergency? Why do we need another interpretation? Just apply quantum theory, or Dirac von Neumann, or Copenhagen, or Bohmian mechanics, or whatever you want. There’s no rush, there’s no problem. There are too many interpretations, actually, and I would say too few. We don’t have a problem of underdetermination with too many applicable interpretations of a single theory. We have a problem of overdetermination, or at least a potential problem. We don’t have one interpretation, in my view, that’s successful, that meets all the requirements that I laid out, and doesn’t suffer from these serious problems. And without one, we’re in danger. We’re like at sea without a life raft. We need something, and that’s why I think it’s time for a new interpretative approach.

I’ve now talked about the unsharp random approach. We’ve talked about many of its advantages. We’ve talked about open questions, and there are more open questions, right? I mean there are potential applications to quantum simulation and quantum computing that people should think about. I mean, after all, if Hilbert space pictures are dual to unsharp random pictures, it might mean that quantum devices could be very good at efficiently simulating certain kinds of random systems. One moment. It’s not exactly dual, because you said it’s many-to-many? That’s right. It’s many-to-many, but the idea is that a given Hilbert space picture can describe many different random systems. That’s good. That might mean that by using quantum devices, we can simulate many kinds of random systems that might be hard to simulate otherwise. So one area of research that people could look into is, and I’m certainly thinking about this, are there applications of this picture to finding new ways to simulate more general kinds of random systems, particularly random systems outside of the Markov approximation, using quantum devices in an efficient way. Then there are more formal things. There’s a whole formulation of quantum theory in the language of C-star algebras, as we talked about in our first talk. What is the appropriate C-star algebraic formulation for this kind of theory, and do we need something like that to talk about certain kinds of physical systems? If we’re no longer starting with Hilbert spaces, we’re not beholden to Hilbert spaces. We’re not trying to build on top of or modify Hilbert spaces. We’re starting in a different place. We’ve just started with ordinary probability theory. Does that allow for generalizations of quantum theory that would have been impossible to reach if we had started with Hilbert spaces? When we start with a Hilbert space, the worry is that if you modify the Hilbert space picture in the wrong way, you’re going to get nonsense. You’re going to get negative probabilities or probabilities that sum to more than one or things that don’t make any sense. But if you start with a theory that’s formulated from the outset in the language of old probability theory, then you’re not in the same danger that your generalizations will lead to nonsensical or inconsistent probabilistic results. You don’t need to get to probability from something else. When you start with Hilbert spaces, the path you take to probability might break down. If you modify Hilbert spaces in the wrong way, the path to getting good probability breaks down. If you start with probability, you’re already there, and you’re not going to be in the same danger of running into inconsistencies in how probability is formulated. And finally, as we’ve already talked about, there might be some potential avenues for rethinking our approaches to quantum gravity. At this point, it would be great to talk about the many-worlds interpretation and what the fundamental problem or problems are associated with it. Okay, open questions, other interpretations. I haven’t said much about Everett quantum theory. What about Everett quantum theory? What about the many-worlds interpretation? Here’s the cartoon story. In the cartoon picture of Everett quantum theory, every time you make a quantum measurement, the universe splits into branches. You have a cat. The cat, as you know, is in a superposition alive and dead. That’s the cartoon version. You measure the cat, and now you’ve branched. There’s a world in which you and a live cat, and there’s a universe in which you and a dead cat are different. Okay, that’s how the cartoon picture is supposed to work. And it seems kind of obvious, and if you want to take wave functions as fundamental, this seems like the natural thing to do with them if you want to take them seriously. But you run into problems almost immediately with this cartoon picture. One problem is that it’s not always 50-50. If the wave function is square root of two-thirds live cat and square root of one-third dead cat, you still have two branches. So in what sense has the probability of one of them now become two-thirds and the probability of one of them become one-third? If they’re two branches, how do we do that? What does it mean to say that one branch has probability two-thirds and the other has probability one-third? How do we connect the branches to the notion of probability that I was talking about before, namely, randomness? If you have a 50-50 random sequence, we expect to see zeros and ones according to some distributions that look random. How do we get the probability picture from the branching probability picture? Like, this, like, is not obvious. Now, one thing you might try to do is to argue that somehow when you have a square root of one-third branch and a square root of two-thirds branch, we should think of the square root of two-thirds branch as actually two branches and there are, like, three branches now. But it turns out that branch counting schemes don’t work very well. There’s a famous 1989 paper in Annals of Physics by Farhi and Goldstone and Gutmann called How probability arises in quantum mechanics. And you can link to it. People can look at it. They’re trying to get this kind of counting picture, you know, all you have to do is think of infinitely many or large numbers of experiments, large numbers of repeated trials of experiments, and somehow argue that some branches in the long run survive and others don’t. And you can kind of count them, and that’s where probability comes from. These kinds of arguments just, are no longer accepted because they don’t work very well. So what do you do? Well, you can just add an axiom. You can axiomatically say that when there are branches, the Born rule tells you their probabilities. The problem is how do we connect these probabilities to the probabilities of randomness that we were talking about? Like, what does it mean to just say there’s a probability here? But there’s actually a deeper problem. As you see, do you remember that we talked about the different rules you can use? In the Everett approach, there’s just one giant universal wave function. And there are infinitely many bases that you can choose. And if you change the basis that you choose, the branches change, right? All components of the universal state vector are the branches. And if you change your basis you change the branches. On which basis do the probabilities refer? If there are, in fact, parallel universes with probabilities assigned to them, on which basis do we do that? That’s known as the preferred basis problem. And I would add something else. Like, probability, when you say something is a certain probability, what you’re saying is that there are n possible ways for that to happen, only one of which is realized. In the many-worlds approach, all of them happen. Is that a probability at all? Is it coherent to talk about this using probabilistic language? And the many-worlds interpretation forces us to doubt some things that we see around us. I mean we do experiments. We get one outcome. Outcomes seem to happen probabilistically. And the many-worlds interpretation denies that, right? If you’re going to do that, you better have good evidence for that.

Okay, what do you do with all these problems? One argument is to say, well, the preferred basis problem is kind of a problem. But maybe nature dynamically chooses the basis. Maybe as you let the universe evolve, decoherence works well only on one basis. There’s a particular basis, and a particular way of decomposing the universal wave function. Such that when you decompose it in this way, decoherence gives you branches that no longer significantly interfere with each other. I think this is Sean Carroll’s argument in his Mad Dog Everett lecture, and I think you were there. Yes yes. It’s also the viewpoint that was central to David Wallace’s 2012 book, The Emergent Multiverse. This idea is that we don’t assume a particular basis in which the branches occur. The universe just evolves, and decoherence doesn’t work in most bases. But on a particular basis, we get nice, emergent, decoherent branches that no longer interfere. And that’s the dynamically correct branching. And the branches are not fundamental. The worlds are not fundamental. They are not there fundamentally. They’re just useful and convenient ways of describing the wave function. But now we have a problem. If the branches are not fundamental, and if they’re emergent, then we don’t have the probability axiom that assigns probabilities to them. You see, axioms, the fundamental axioms of your theory are supposed to refer to fundamental things. If branches are emergent, approximate things, not fundamental things, the axioms can’t say, oh, if at some point in the future we develop these approximate emergent branches, by axiom probabilities will be assigned to them. If branches are no longer fundamental, but just emergent, just convenient ways of describing what’s happening, it’s very difficult to think how to create an axiom that says that probabilities should be assigned to them. If we don’t want to get probabilities from axioms, we now have a fundamental problem. And this is where a lot of the work in Everett quantum theory has happened, this problem of probabilities. If branches are emergent things and not fundamental, and we can’t axiomatically assign probabilities to them, how do probabilities arise? Now, I think the argument I would like to make here is that they don’t. If you were forced to believe in a bizarre metaphysical picture like the many-worlds interpretation, because you had to, because it was empirically inescapable, like we look out into outer space and we see galaxies that are many, many, many billions of light years away. We see countless galaxies billions of light years away. And that leads us to believe that there’s a vast universe out there. We see clocks on airplanes moving at slightly different rates, atomic clocks moving at slightly different rates. That’s hard to believe, but we can do the experiments and see this repeated accurately many times. That doesn’t mean that we should never believe in bizarre things, but as Carl Sagan said, extraordinary claims require extraordinary evidence. The many-worlds interpretation says that there are countless universes branching off from every moment, not even just measurements, but all the time. That’s a bizarre statement, and certainly, we can believe it if we had to either through rigorous logical reasoning or through empirically inescapable results. But we don’t. When you formulate many-worlds interpretations, you run into this problem, well, I have a problem for every basis. I think I can deal with that by letting the branches emerge in the case of decoherence, but then I can’t axiomatically assign probabilities anymore. At that point, you should just give up, because you’re no longer forced by rigorous logic or empirical data to believe in many worlds. Why are you still trying to chase it? That is, this bizarre and extravagant metaphysical picture is no longer forced on us by logic or by experiment. Why are we chasing it? Why do we start by assuming that they must be there, and we need to somehow fiddle with our axioms and principles and assumptions to get the many-worlds picture? That’s the impression I get when I see some of the work going on now. We’re not forced to consider many worlds a serious idea. And we can only achieve it by adding a lot of things. Why do we do that? Let me just describe some of the avenues people have taken, and then we can stop, because this is basically the end of the matter. One avenue is the one taken by David Wallace in his book, The Emergent Multiverse. It’s an excellent book that you should list on the YouTube channel, and I recommend it to everyone who’s interested. David Wallace is a wonderful and brilliant philosopher and also trained in physics. The book is a beautiful book. I recommend it to everyone who cares about quantum foundations. He tries in this book to solve this problem of probability. How do we get probabilities assigned to these things? By introducing a large number of extra assumptions. Tell them, and I read them, and then I make a list of all the extra assumptions that he has to make. He assumes that we must have the same metaphysical relationship to many copies of ourselves as if there were only one unique individual we were going to become. That means you have to take a stand on old questions like the problem of metaphysical teleportation in metaphysics. The theory that he uses requires invoking the idea of free will that requires taking a compatibilist stance, because in many worlds interpretations, there’s just a universal wave function evolving deterministically. However, he’s mentioned in his proof agents of the Born rule, which is already a serious idea. Agents, we’re re-agents, we’re making choices about what unitary processes they’re going to perform. And that’s an important part of the proof. He has a little footnote where he acknowledges, yes, this does involve some assumptions about free will, but free will is a big problem. Nobody has solved it. That doesn’t make the case. If you’re relying on a problem that hasn’t been solved, that doesn’t mean that what you’re doing is going to work. And he introduces a number of what he calls richness axioms and rationality axioms. The rationality axioms are supposed to be general good practices of what it means to be a rational observer. And they’ve been developed in a single-world kind of picture, and the assumption is that they also work in a many-worlds picture. Basically, the way one tries to proceed here is to say, what does it mean to be rational? That means you want to use decision theory tools, which are the formal and precise and probabilistic tools for making good decisions called decision theory. People who use decision theory tools, who are rational, will end up assigning probabilities to the branches according to the Born rule. That’s a very rough and sketchy outline of how that argument goes. Now, John Norton, again, philosopher at the University of Pittsburgh, has raised an objection to any such approach to trying to derive probability. In deductive argument, the conclusion can’t be stronger than the premises. If you’re trying to make probability emerge as a consequence, certainly there must be probability already present in your premises. In this derivation of the Born rule, one is trying to get probability, so there must be probability somewhere in the premises. If you don’t assume probability somewhere in the premises, you must somewhere be doing something illicit. You can see how this plays out for the decision theoretic argument, which goes back to David Deutsch as well. There’s an earlier version of it in a 1999 paper written by David Deutsch, it’s the old quantum theory in

Decisions. You can also link to that. The argument is that if you adhere to the rules of being a rational observer and use decision theory, you will end up assigning probabilities according to Born's rule. But you can ask, why is this the definition of rationality? I mean, in a multiverse type of world, there will be observers who act rationally according to what decision theory dictates. Some of these observers will be wildly successful over 10 years, and some will be wildly unsuccessful because, in the many-worlds interpretation, everything will happen in some branch. But there will also be observers who don't adhere to the rules of decision theory. There are some irrational observers who chose not to follow any of the rules of decision theory, and there will be branches where they don't succeed over 10 years, and there will be branches where they do succeed over 10 years. All these observers are out there. And saying that, well, you should just be rational and obey decision theory by fiat doesn't solve the problem of probability.

In a single-world picture where only one future happens, it seems that rational people who think very carefully about their decisions and use something like a decision-theoretic approach, in the long run, over 10 years, tend to make more money or have better health or live better lives, whatever you want. And that gives us a reason why I think these are good principles of rationality. If people who follow these principles tend to do better, I see people who exercise and people who make good financial decisions and hedge their investments, they do better, and I say, oh, well, there are good reasons, therefore, for doing what they do and sticking to their principles. But you can't turn it around and say we're going to start with a fiat, this is the way to be rational, and then work backward and show that that then entails this is how probability must work. That's kind of a backwards argument that's happening.

I should say that not all Everettians adopt this decision-theoretic viewpoint. Simon Saunders, for example, tries to do probabilities in a more Boltzmann-like, statistical mechanical way, by rough-and-ready counting, actual counting to some extent, but it's still in its nascent form. Yes. So, there are many approaches to the many-worlds interpretation, and at present, none of them seem to have found a way to get probability off the ground, and I don't think you can. And to the extent that you can by adopting more and more assumptions, you're doing the thing where you're adding untestable assumptions that can't be verified in experiment. I mean, I don't know how I would experimentally test that I should have the right relationship to many copies of myself. I mean, that's outside of empiricism. If you have to tack on lots of these pictures to get the picture out of reality, I don't know how credible that is. How much credence should I give to a theoretical picture that relies on a tower of contemplative metaphysical assumptions? I feel that if you have to do all this work to get the theory off the ground, that diminishes your credence that we should adopt the outlandish idea that there are all these many worlds.

So that's where I've ended up with the many-worlds approach, and that's one of the reasons why I think there's room for another more conservative interpretation, which says, well, we do experiments, we see one outcome, maybe that's because there's only one outcome. And experiments look probabilistic, maybe because they are in fact probabilistic. Nature tells us it's probabilistic, and we should listen to nature, instead of saying, no, no, no, no, we should be deterministic, there's a universal wave function that evolves deterministically, it should be Markovian, you know, maybe we should just listen to nature and build a theory around what nature tells us. I think that's the conservative, less outlandish approach one should take. I want to know, why have you become awesome at being clear and smooth in your speech? That's a very nice thing to say, and I really appreciate that, and that's really kind of you to say that. I think we all have different strengths. I'm bad at many, many things. There are some things that I've honed through practice, and there are some things that we're all sort of born somewhat good at, and we have nascent things that we're kind of good at, and then we hone those things. I've taught many classes over many years here, and interacted with these wonderful students, wonderful, ideal, and amazing students who ask all kinds of wonderful questions. I think it's just practice, you talk a lot with people about very complicated topics, and over time it becomes easier. That's the best answer I think I can give.

There's an Aesop's fable I like to bring up with people, it's about the deer and its antlers, so there's this deer that's drinking from a pool and it admires its beautiful antlers, it thinks its antlers are so great, so magnificent. And it goes on to say the antlers are really the envy of the animal kingdom, and then it looks at its legs and says, but my legs are bony and ugly, and I wish my legs were as magnificent as my antlers. While the deer is thinking about this, it suddenly realizes a pack of wolves is chasing it, so it gets up and runs from the water, trying to get away from the wolves, and when it sees a forest, it'll run into the forest to hide, and when it runs into the forest, and its antlers start getting tangled in all the vines, and before it knows it, it can't run anymore, it's stuck. And as the wolves are closing in on it, it realizes that the thing that it had been praising, its antlers, was the cause of its demise, and the thing that it thought was its weakest attribute, its legs, were the things that would have saved it. If only its legs, its legs would have saved it. So the reason I bring this up is, besides the fact that I think we're all good at some things and maybe struggle with a lot of things, some things that we think we're bad at, are viewed in another way as the things that we're good at, and sometimes vice versa.

So I'll say something that anybody who knew me when I was young would laugh at, because it's so obvious. I came into this world severely lacking in common sense, okay? Anybody who knew me when I was young would say that's the most obvious statement I've ever made, okay? Severely lacking in common sense. And as you grow up, you know, you get ridiculed, and you make a lot of mistakes, and you do a lot of silly things because you lack common sense, and you view that as kind of a weakness, you view it as something that you're a little embarrassed about. When you delve into philosophy and the foundations of science, philosophy of physics, what you see is that a lot of people who let their common sense take them in directions that they shouldn't be taken. You see a lot of people who make arguments or make conjectures or make claims that seem extremely plausible to them, and sometimes they're not rigorously supported. People can, their common sense can lead them astray. And suddenly, the lack of common sense becomes a great asset, because when I read a paper on philosophy or listen to a seminar or try to formulate an argument, I don't have that kind of common sense that makes the answers obvious to me. So I see every argument, and I have to take it apart, deconstruct it, and understand what each of the pieces is doing, because I don't have the intuition, the common sense of how things work. What that means is that to some extent, and obviously, I mean, we all make mistakes, I make mistakes too, but I feel like some of the mistakes that I might have made if I had common sense I was less likely to make. So the thing that I thought was my weakest point, the deer's legs, in a different context turned out to be really useful, like being on land and only having fins for your arms and legs. And then one day, you discover the ocean, and suddenly, what you thought was your weakest asset is now your greatest asset. So I think that's a general lesson that everybody should take seriously. Many things that we think might be our weaknesses can actually be strengths, in a different way. So if you're the kind of person who has a really hard time paying attention to things but hyper-focuses on some things, and you think that's a problem, well, it might be a problem in some contexts, but in other contexts, it could be a superpower. And we see this all the time with a lot of things that people might be embarrassed about.

Now you're talking to researchers and prospective researchers, people from the younger student perspective, even people from the older student perspective, there are some people who are 70 years old and getting their PhDs watching this. Yes. So what's the way they can use to help discover or distinguish between the actual good trait versus the actual bad trait that they think is good? The best I can say is that there's experience. Put yourself in different contexts. If I never became somebody who works in philosophy and foundations of physics, I probably would have spent my whole life thinking that the lack of common sense is a really bad thing. It might be a really bad thing in some contexts, but I wouldn't have seen that there are, in fact, different facets to it. And I think it's just a matter of talking to a lot of people and asking them, are there any facets of themselves that they see as bad in some contexts and in other contexts they see as very useful? And if you talk to enough people, you'll start hearing them say things that remind you of things about yourself. And you'll go, wow, I have this trait that I don't feel good about, but this person found a way to use it really well. Maybe I should follow their example and do what they do. So yeah, that's maybe my best advice on how to do it. But let me add one final thing in closing, alright?

When I teach a class, I just taught this class this fall. We just finished teaching our fall classes. I said to the students, look, we talked about a lot of physics in this class. This was a physics class. Sometimes I teach physics classes, sometimes I teach philosophy classes. This was a physics class. If you don't remember within a year some or most or maybe all of the physics we talked about, I won't be disappointed. But we have to be human to each other, you know? We have to be human to each other. If you forget to do that, I will be very disappointed. You never know when you're interacting with somebody. Is this the person who five years from now will be the right person at the right moment to play a really important role in your life, and your career, and your well-being? You have to treat everybody as if they might be critically important to you. I mean, obviously, if you're getting 100 emails a day, you can't treat each one—I mean, just the sheer volume. But to the extent that you can treat everybody with basic respect and treat people as human beings and treat them humanely, you should always do that. Because you never know, you know, they can always—I mean, obviously, just for its own merits. I mean, people should be treated as human beings anyway. But it's also just a good strategy because you never know if somebody will eventually become important to you.

When students first start here in our PhD program, one of the things I tell them is that their reputation is one of the most important assets they have. And a lot of people think that the right scientific reputation to have is to be intimidating, to have everybody think you're the smartest person in the room, to have everybody, you know, in awe of your intellect and almost afraid to talk to you, right? People think that's the kind of reputation you're supposed to cultivate. Not everybody does that, but some people think that's what you aspire to, and people can often think of figures in their lives, role models in some cases who have that kind of reputation. I would argue that's not the right reputation you should cultivate, that you should strive for. I talked about treating people like human beings. Your reputation, in science, and this is for anybody, students and researchers who want to go into science, your reputation is worth its weight in gold. The kind of reputation you want to have is somebody that people want to work with, somebody that people want to go to and talk to and ask questions of. You want to be the kind of person where when people come to you and ask you questions and talk with you, and when they leave, they feel smarter than they were before. Because people come to you and leave feeling smarter, and they feel happy, and they feel like they can go out and do things with more confidence. They'll want to come back and work with you again, and talk with you again. Yes, there are people who are wildly successful who don't have that kind of reputation, they're extremely intimidating, and they're successful. But they would be even more successful, in my view, if they cultivated that kind of reputation that makes people want to collaborate with them, work with them, and most importantly, support them. Because everybody in all walks of life will at some point need somebody to help them with something. And if people view you as a collaborative and helpful person, and somebody who builds people up and treats people as human beings, they're more likely to support you when you need help. And that's the kind of investment in your career, and in your future, that I think everybody should take seriously and think about very seriously.

Thank you, Jacob. I appreciate you spending seven hours with me. Curt, it's been a joy. It's been a complete joy. And Adi and Will, it's just been really fun. Great. I've gotten many messages and emails and comments from professors saying they're recommending their students to Theories of Everything, and that's fantastic. If you're a professor or lecturer, and there's a particular highlight episode your students could benefit from, please share it. And as always, feel free to reach out to me. New Update! I started a substack. The writings there currently are on language and ill-defined concepts, plus some other mathematical details. A lot is being written there. This is content that's nowhere else. It's not on Theories of Everything. It's not on Patreon. Also, full transcripts will be put there sometime in the future. Many people ask me, Curt, you've spoken to a lot of people in the fields of theoretical physics and philosophy and consciousness. What are your thoughts? While I remain neutral in interviews, this substack is a way to look into my current deliberations on these topics. Also, thank you to our partner, The Economist.

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