Harvard Scientist Rewrites the Rules of Quantum Mechanics | Scott Aaronson Λ Jacob Barandes

I don't see every day a new formulation of quantum mechanics. This is exciting. For nearly 100 years, quantum mechanics has split physics into competing interpretations, each with different consequences for reality.

In this lecture, Jacob Barandes, of Harvard University and co-director of the graduate program, developed a revolutionary framework called Indivisible Random Processes which suggests there is no underlying wave function. He joined Scott Aaronson and they contend with other interpretations like Many Worlds and Bohm, as well as discussing: Do quantum computers derive their power from other universes? If so, why don’t quantum computers provide speedups for all problems instead of just a specialized subset? From Jacob’s perspective, what gives quantum computers their power over classical computers is their indivisibility, because the class of indivisible processes is simply larger than the class of all the kinds of processes that classical computers use.

My name is Curt Jaimungal and I use my background in mathematical physics to analyze different theories of everything. Can we finally understand quantum mechanics without invoking mysterious wave functions, or are we forever bound to a world of mathematical abstractions divorced from physical intuition? The audience is in high spirits. I've previewed the questions you have for each other and I'm excited to host you. Thank you. Welcome Scott Aaronson and Jacob Barandes.

It's great to be here. It's nice to be here. Thanks for the invitation. It's good to see you Scott. Yes, good to see you too Jacob. Does the utility of quantum computing offer evidence for many worlds? Scott.

I would say there’s a philosophical argument, for example, made by David Deutsch, right, that says that, and this was very closely tied because he invented the idea of quantum computing in the first place in the early 1980s, right, which says, well, look, suppose you use a quantum computer to factor a number that’s 2000 digits long, right, you know, and Deutsch said this very explicitly, you know, in the 1990s, right? Suppose you run Shor’s factoring algorithm and it factors the number, you know, far more efficiently than we think can be done using any classical algorithm. And he says, you know, if you don’t believe that quantum reality is somehow something vastly bigger than classical reality, then where did the computations happen? You know, where did that take place, right? And so, you know, I think that illustrates, you know, why quantum computing is interesting to many of us in the first place, right? It seems like this is a test that’s really hard to fake, yeah, there’s some kind of reality to these abstractions we talk about that involves these vectors and this hugely high-dimensional space, right? But now I would say the philosophical part, the part where people can reasonably disagree with each other is whether you should describe that in terms of parallel universes or not, you know, is that the right language to use to talk about this huge thing, right? The problem is, you know, what do we mean by a thing being a different universe, right? Usually, you know, we mean it evolves independently of us, right? It’s, you know, its own separate thing. I mean, in TV shows, in movies, there’s always some portal or wormhole through which you can visit the other universe, because, you know, if there isn’t, what’s the plot, right? But somehow it’s separate from our universe, okay? But the problem is that if it’s separate, and for that very reason, we don’t see the evidence for it. You know, as if we do a quantum computation, at the point where the two branches really become separate, then, you know, we don’t see the interference between them. We only see, you know, our branch. And to the extent that you do see interference, you know, as you do in Shor’s factoring algorithm, for example, or other algorithms for quantum computers, you could say that the fact that these things can interfere means that they never really created separate identities as parallel universes at all. They were all just part of this giant entangled quantum mechanics bubble, right? So I think that’s a philosophical objection. But I agree that a quantum computation would be dramatic evidence that the state of the universe, you know, is this somehow much bigger thing than classical physics assumes it to be, right? And that’s a big deal. Now, you know, I get annoyed when, you know, people will take the latest quantum computing experiment, like what Google did, you know, with the Sycamore chip last December, and they’ll say, oh, you know, this is new, you know, evidence for the reality of parallel universes. Like, no, you know, no, it’s not. It’s just evidence that quantum computing works as the theory said it would. And you know, if you buy into the philosophical argument that it’s only explainable by many worlds, you had to believe that way before this experiment, right? And if you didn’t believe that, you still should not believe it. So it’s not, you know, that these experiments change things that much. But, you know, there’s this philosophical argument that I think lies at the heart of why we’re interested in quantum computing, and why Deutsch invented it in the first place.

Before you answer briefly, Jacob, I want to know, okay, what would David Deutsch say to your counter-argument about universes having to be independent? How does that manifest in this universe? Oh, oh, what would he say? I mean Deutsch would say you don’t even need quantum computing to see the obvious truth of the many worlds interpretation. He might say that even the double slit experiment, you know, from over 100 years ago, you know, where you see interference between two paths a photon can take, even that settles the issue and is only explainable by the many worlds interpretation and everybody denies that. And then he’ll say, well, but for those who are too dense to see that, you know, building a quantum computer might help them psychologically, right? Maybe, you know, make it more undeniable. But he thinks you don’t even need it.

There’s some interesting history here. And Scott, I’m sure you’re aware of this, but many people watching probably don’t know. But Deutsch’s development of quantum computing is really a fantastic example of how philosophical and foundational thinking about physics in general and quantum mechanics in particular has borne enormous fruit.

I agree. My understanding is the story is that Wheeler had him to dinner with Hugh Everett when Hugh Everett came out of retirement in the 1970s. Yeah, I can almost see the building where that happened. Right. Yeah, yeah, yeah. And they sat next to each other. And initially, apparently, Deutsch was skeptical or whatever. But by the end of the dinner, he was completely convinced. And as Scott said, I mean it’s in the papers. It’s amazing, isn’t it? There’s this foundational paper in quantum computing from 1985. It’s quantum theory, the Church-Turing principle and the universal quantum computer. And Deutsch makes no bones about citing the Everett interpretation. It’s as in the abstract and throughout the paper, it’s like, and this only makes sense under Everett’s picture and Everett, you know, is and he says very explicitly, you know, one of his motivations for developing quantum computing is to demonstrate that Everett’s approach must be correct.

The interesting thing, and I mentioned this Scott, and it’s entirely accurate. The kind of prevalent modern ideology among people who think and work on Everett’s approach, which is reflected in books like David Wallace’s 2012 book, The Emergent Multiverse, is that you really need decoherence, meaning the gradual disappearance of interference effects between branches in order for the appearance of macroscopic world branches and distinct universes. And that’s precisely not what happens in the middle of a good quantum computation.

Yeah, that’s what I would say. But my point is, that that’s what Scott’s saying, is actually the standard way most Everettians think. So Everett this approach doesn’t really help you much in quantum computing because those other universes, don’t exist specifically in the state that’s being used, you know, so to speak for a good quantum computation. And I’ll just say a couple of things about this. The first is that there are many situations in quantum mechanics where if you. Take a certain philosophical viewpoint seriously. At first glance, it might seem a little revealing, you know. You know, quantum computers can in some circumstances do things much more efficiently than we think is possible with classical computers. And the actual existence of multiple universes might seem to be what gives these systems their advantage. But upon further reflection, it gets kind of weird because if these universes are actually there in some sense, either in the microscopic case where, again, there’s no agreement that we should think that way or or in the macroscopic case, you might think that you could get speedups in far more circumstances where the speedups would be far more general. As Scott wrote at the top of his blog, write a slogan. If you take one thing away from this blog, it’s that quantum computers don’t get speedups because they try to execute all possibilities at once. And this is very puzzling because if you think that those universes exist, you might think that you could get speedups all the time. It’s really amazing that you seem to be able to get a speedup in only very special circumstances. And if those. For me, that’s almost evidence that we shouldn’t think that way. And Scott, you put this really beautifully. I forgot when you said this, but you had this beautiful quote where you say that these other universes aren’t quite as real as actual universes. They’re not quite because they live in some kind of intermediate regime between being real and being unreal. Forrest Sorrenson, who said that. But yes, I mean, I’ve been, you know, having a pedagogical problem about how to explain quantum speedup for 25 years. Right. And you know, I would say quantum computing is more bizarre than any science fiction writer had the imagination to invent. Right. Right. It’s not just classical exponential parallelism. Right. But, you know, it’s related. I mean, you know, in order to explain that to people, we usually say, like, yes, you can create this superposition over a vastly large number of possible answers. But then you’re only going to get this small window to observe something about this. Right. You have to make a measurement. Measurement is a destructive thing in quantum mechanics. It collapses the state. And then your only hope of getting a speedup is to exploit the way amplitudes work in quantum mechanics, being complex numbers, differently than probabilities we’re used to, in particular, that they can interfere with each other. So, with every quantum algorithm, you’re trying to engineer a pattern of interference where the contributions to the amplitude of every wrong answer cancel each other out. They interfere destructively, whereas the contributions to the amplitude of the right answer all add up. They interfere constructively. Right. So this is not something. And this means that I could say that if you gave me a few minutes. Right. But this is not something that’s easily translated into any pithy English phrase that we previously had. Right. Right. Well, let me say a few things about this. The first is that using the branching tree like graphical structures isn’t unique to quantum computation. That’s right. In a probability theory course, we draw like outcome trees, and probability trees, and decision trees all the time to explain things. So, I mean I’m perfectly willing to grant that drawing branching trees is a useful pedagogical exercise. But I want to then move on to the point you raised, which is that the key to quantum computing is the ability to exploit the fact that these amplitudes are complex and that different probabilities interfere and you can use them to cancel each other out. Interference is a very important property in making quantum computation work. So and in fact, I think this is kind of the key because if you think it’s all about parallel universes, you might think you get a speedup all the time when you realize that it actually requires this very careful use of interference. You realize that the class of problems where you’ll be able to get speedups for won’t actually be entirely obvious and will require a lot of careful thinking. We’ve been working on that for 30 years. Exactly. What is that class exactly? Right. Now. But yes, I mean, I kind of like the analogy between the Everett interpretation and Darwinian evolution where you have, you know, these populations of species that can interfere with each other, you know, i.e., sexually reproduce. Right. But, you know, that’s only when the populations, you know, remain relatively close to each other. And it's DNA sequence. Right. Once you have two isolated sub-populations that drift far enough apart, they’ll never merge again. Right. Then they’ve really branched off into separate branches. What, you know, biologists call different species and what we call in quantum mechanics separate Everett branches. Yes. Yes. It’s a beautiful and very useful metaphor, especially pedagogically. Of course, the question is, what is interference and how do you explain interference to students if it’s not, you know, and if these aren’t really universes, if they aren’t really big universes yet, because if they were well-defined microscopic facts, they would have decohered and we couldn’t do quantum computations with them. So what are these things that we’re dealing with? And there’s a kind of quiet that one practices. Let’s not talk about what they mean. Let’s draw them on paper and work with them. And I think we can do better. I mean we don’t have to do better. If somebody’s goal is to build better, more efficient quantum algorithms to build quantum algorithms that can do more things, then I think that’s probably a good thing. But of course, we all think about quantum theory and quantum foundations and the philosophy of physics for many reasons. And I think there are certainly many people who would like to have a more concrete physical picture behind this. And that’s where my style comes in. And I’m happy to say a little bit for those who may not be familiar with my work and how it relates to the power of quantum computation. And I completely agree with the desire to understand the world, not just predict the outcomes of experiments. And then we can talk about how to do that.

So Jacob, before you go on to explain your new formulation, I want to hear Scott Aaronson’s performance of it. But first, before Scott Aaronson, before you talk about Jacob’s theory to have Jacob tell you yes or no, I want you to tell the audience then where do you think this efficiency comes from in quantum computing or where does the interference happen? If it’s not these multiple worlds, if you’re not a believer in many worlds, where do you personally think, Scott, that the efficiencies come from?

I mean, quantum speedup, you know, really, if you think about it, just means classical slow-down, right? It means that our quantum computer can do something that cannot be efficiently done by any classical algorithm, right? And so what that really means is that among all the different ways you might imagine that a classical computer could efficiently simulate these quantum computations, none of them work. And so by its very nature, you know, there won’t be a single explanation for that, right? There might be a different explanation for every possible way of classically simulating the thing, right? Quantum speedup is inherently a negative statement, right? None of the classical methods work. And so I think the exponential size of quantum states, you know, when we write them in the usual way is part of the story. You know, the entanglement of the qubits is part of the story. If there were no entanglement, there would be a classically fast simulation because I could just track the state of each particle separately in my classical computer. Interference is a big part of the story because without interference, I could use a classical computer with a random number generator, and that would do the simulation, right? So it’s really a mixture of all these elements, you know, the very large Hilbert space, as we call it, the entanglement, and the interference that rules out all the different ways you could efficiently simulate this thing using a classical computer. Actually, you need more than that. There are examples of quantum computations, for example, what we call post-selective quantum computations that have all those elements, and yet they can still be efficiently simulated by a classical computer for some other reason, right? Okay, but, you know, if you combine all these elements, the very large Hilbert space, and the entanglement, and the interference, then at least there’s a chance that you will escape any way of efficiently simulating what you’re doing using a classical computer. And I think that’s really what’s going on.

Okay, now let’s hear your summary of Jacob’s theory. And just for background for the audience, Jacob has a theory or a formulation of quantum theory, a reformulation of quantum theory which gives an ontological interpretation of what’s going on. And it’s been covered on Theories of Everything, this channel, at least three times, and I’ll put each segment on the screen now, and the links will be in the description. If you want to learn more about my work philosophy, alongside my personal thoughts, you’ll find all that on my Substack. Subscribers get first access to new episodes, new posts as well, behind-the-scenes insights, and a chance to be part of a thriving community of like-minded reasoners. By joining, you’ll directly support my work and help keep these conversations at the forefront. So click the link that’s showing on the screen here, hit subscribe, and let’s continue to push the boundaries of knowledge together. Thank you, and enjoy the show. Just so you know, if you’re listening, it’s CURTJAIMUNGAL dot org, CURTJAIMUNGAL.org. You know, Bohmian mechanics has been around pretty much since the 1950s, with minor tweaks to branding, formulations, and improvements since then. And you know Jacob says he has something different. In fact, when I talked to physicists about this, they said, oh yeah, Jacob Barandes, isn’t he the guy who has something somewhat like Bohmian mechanics? But I think it’s not, and I think I understand better than I did a month ago, what’s going on, and that it’s not quite. So basically, just for a little bit of support, you know, I would say, what Jacob wants to do is, you know, give a new interpretation that reproduces all the experimental predictions of quantum mechanics. So it won’t change the experimental predictions, right? That’s what it means for something to be an interpretation, or a formulation rather than a new physical theory, right? But he wants to do that, you know, using something that’s like classical mechanics, where you have particles that have, you know, or some things that will have definite classical configurations, you know, like the positions of the particles in three-dimensional space, okay? And you know, and this puts him in a long tradition, people who’ve tried this, including Bohmian mechanics, okay? But the difference is, in Bohmian mechanics, you keep the wave function, the quantum wave function in your ontology. So you still have this, you know, giant wave of amplitudes, you know, just like many worlds, okay? But then you use that wave to guide the particles along trajectories, right? So suppose you have particles that have some actual positions in three-dimensional space, and then those particles are guided, they’re pushed around by the wave function in a way that’s precisely engineered to reproduce the standard quantum mechanics predictions for what you would see when you measure those particles. Right? Okay, that’s Bohmian mechanics. And now Jacob, the magician, is going to get rid of the wave function, and he won’t have the wave function in his ontology, and he won’t have trajectories for the particles either, not in general, anyway, okay? What he will have is just, you know, as in Bohmian mechanics, you pick the basis, such that you have what we call the preferred basis, which might mean, like, the positions of the particles in three-dimensional space, or something like that. And then at any time, you know, he wants to say that the particles, you know, have a real position, you know, the system has a real configuration, a real state on that basis, even if you’re not looking, okay? But now, what he’s going to give up is the trajectories of those configurations, okay? So in general, we’re not going to be allowed to ask, given that the particles were in this configuration at time t, you know, what’s the probability that they’ll be in this other configuration at time t plus one, right? Or, you know, somehow we’re only going to be allowed to ask that question, you know, in the cases where it usually makes sense, right? When, you know, in quantum mechanics, you know, we would say it’s in a superposition state, Jacob would just say, well, you’re allowed to ask at any single time, right? You know, what’s the probability that the particles are here or that they are there, but you’re not allowed to ask, given that they’re here now, what’s the probability of them being there at that time, right? And so, this is what he means by talking about indivisible random dynamics. So he wants to reformulate, for example, you know, what in the standard picture would be Schrödinger’s equation, you know, governing the evolution of the wave function as a differential equation governing the random evolution of these, you know, this, what we could call a hidden variable, except it’s not really a variable. Except it’s not really hidden, right? The classical positions of these particles. So he’s going to give you an equation of evolution for that, but it’s indivisible. In the situations where we say, in the standard account, that quantum interference is happening, you know, you’re not allowed to ask about transition probabilities. You’re not allowed to ask about the full trajectory that these particles follow, or you know, given that they’re here now, what’s the chance that they’ll be there then? It’s just an indivisible random evolution. So, that’s my understanding of it, and now Jacob can tell me where I went wrong.

Thanks, yes. So let me say a few things about this. The first is that there’s kind of a model that we all operate under. It’s a model that I grew up with and I learned when I took my undergraduate courses in quantum mechanics. You know, I ended up getting a PhD in theoretical physics, and we used quantum theory all the time. I used a tremendous amount of quantum theory applied to fields, and so we learned quantum field theory. So there’s a certain way of thinking about quantum mechanics and thinking about how it works, starting from the textbook axioms, the so-called Dirac, from Paul Dirac, and von Neumann from John von Neumann axioms which you get, respectively, 1930 and 1932. This is written in all the textbooks, and these axioms, you know, are quickly summarized. Every quantum system has a Hilbert space. Every system has a definite quantum state in some mathematical terms, either as a state vector or a density, some object that lives in this Hilbert space. This object, when the system evolves through time in a way that it’s not exchanging interactions or information with any other systems, it evolves according to a rule called smooth unitary time evolution, which can usually be expressed in some systems as a differential equation. That’s Schrödinger’s equation. And then you have all these measurement axioms, all these axioms about, you know, what are the mathematical objects that represent the things that we can observe about the system? How do we get probabilities from the theory for the outcomes of those measurements? This is called Born’s rule. And then we’re supposed to collapse the quantum state to reflect the outcome of the measurement and give strong reliable predictions for subsequent measurements. That’s the standard picture, and this picture is built around the idea of the quantum state. You know, there’s this model. I call it the wave function model where you start quantum theory by talking about wave functions or some appropriate generalization of wave functions that live in Hilbert spaces. And then we’re supposed to somehow know what we’re supposed to do from there. When you start from this picture. It might seem very complicated to build a different picture, because you start with all the components of Hilbert space, like, okay, we have Hilbert space, Hilbert space is a kind of vector space, vector space, vector space can be described using what are called different orthonormal bases. So what you have to do is you have to pick a natural orthonormal basis for some reason, and then from that natural orthonormal basis, you have to do this and do that and you have interference and you have Hilbert space, you know, and you have Schrödinger’s equation, which has to be translated back. I mean, when you start from this model, it makes everything seem complicated.

To the extreme. And you see this all the time when you’re talking about, you know, different models of a theory maybe from a newer model, you know, the new model can seem extremely complicated when one tries to express it in terms of the older model, or even very hard to understand. And there’s this whole theory, this whole story in the history of philosophy of science about the incommensurability of different models. So let me start from the beginning. I don’t think models are truly incommensurable. But, you know, that’s a separate discussion. That’s fine. I’m not going to take a stand on that. I’m not ideological about this. I’m just saying that there is in the history and philosophy of science this idea that models can be incommensurable. I’m not going to take a stand on it. Yes. What I would say Jacob is, you know, if you say that this is, you know, a new model of quantum mechanics, and that, you know, we shouldn’t try to express it in terms of the old model, then the task for you, the next task would be to explain, you know, take all the successes of quantum mechanics, you know, all the phenomena we know, including, you know, Shor’s algorithm. Grover’s algorithm, you know, quantum teleportation and show how they succeeded. Show how they have simpler explanations in terms of the indecomposable stochastic dynamics. Right. And what you’re not allowed to do when you do that is to say, well, just translate it back into the usual, you know, cat notation, the usual Hilbert space picture. And then, you know, just invoke this theorem that says that it has an equivalent representation in my picture, because, you know, if that’s your answer, then you’re telling me that operationally I should just keep using the standard picture. Right. And I should keep thinking about it. Right. If you want me to switch to thinking in terms of a different picture, you have to show me how all the specific successes of quantum mechanics that I care about are actually easier to explain in terms of that new picture.

So let me say a few things about that. Yes. So one thing I’m going to do is explain what this approach is on its own terms. But of course one of the important things about this approach is that it leads to the ability to reconstruct the standard axioms and the Hilbert space picture within its own framework and to say a little bit about why there is this kind of limited framework and how one might extend that. But I’m not saying to be very clear. Right. I’m not saying that we should stop using the Hilbert space picture any more than, you know, if you want to, you know, study a problem in classical physics using action-angle variables or if you want to do Jacobi’s theory of quantiles or you want to help yourself to canonical transformations or basic perturbation theory or one of a million other things you might want to do. Path integrals and phase space. You’re going to use Hamiltonian phase space reformulation of classical physics. So if somebody comes along and says, oh, you know about the Hamiltonian, Hamiltonian phase space formulation, you have variables that represent positions or some generalization of positions and variables that represent a generalized notion of momentum, so-called canonical variables. And you have this phase space picture and you have the dynamics, the equations that describe how things evolve according to Hamilton’s equations of motion. And you have these beautiful symmetries. You have this ability to check canonical changes of variables, so-called canonical transformations that can scramble what the picture looks like, you know, and somebody comes along and says, actually I think there’s a physical picture here. The thing you’re describing is a thing that moves. You know, maybe it’s attached to a spring or a pendulum, you know, and the person says, well, well, that’s a useful picture. That’s helpful. But is that going to help me do canonical perturbation theory? Is that going to help me do action-angle variables? I would say, well, no, we have this beautiful Hamiltonian framework to do that. You should use that still. Or another example is that we have general relativity. General relativity, I’ve been teaching general relativity for 10 years. But when we do orbital calculations like sending a spacecraft, we still use the Newtonian model. It’s still incredibly useful.

I understand the point, Jacob. I mean, but general relativity, at least, you know, there’s a class of situations where, you know, this new language is better. Right. So I think that in that case you have to at least show that there’s a certain class of problems in quantum mechanics that are better handled using your new formulation than using the old formulation. Otherwise other people can rightly say, what’s the point of learning it? Or even that can only be handled using your formulation. Right. Right. Right. So let me start with that. I want to explain what it is, but let me quickly move to that. Yes. So if what you’re doing is, again, developing algorithms for quantum computing, I don’t think there’s any obvious sense in which this gives you the ability to do anything differently than you would have done in the old model. The tools we have are extremely good for those situations. You’re studying kinds of tabletop systems where the Dirac axioms work really wonderfully. But those aren’t the only kinds of systems that physicists care about. So physicists care about applying quantum mechanics in astrophysical situations to the early universe cosmology. And people are trying to apply quantum mechanics in the context of quantum gravity. They’re trying to apply quantum mechanics to black holes. They’re trying to do quantum. And now you’re in situations where the Dirac axioms are very vague about what you’re supposed to be able to say. And that’s where I kind of cut my teeth. I mean I got my Ph.D. here at Harvard University in high-energy theoretical physics. Those are the kinds of problems I studied. And I was often puzzled, when we got the legitimacy in using the textbook version of quantum theory. And again, I wasn’t alone. I mean we routinely run into situations. And somebody will say, well, can we do this particular thing? Does this make sense? We have some kind of nonlinear dependence on this or that. And what happens with black holes? And people were puzzled about how to apply quantum theory to situations. But these situations are different from what you find in tabletop experiments. It would be like saying, why do I need general relativity on Earth? Newtonian gravity works fantastically. Well, there are systems off the Earth where we might need a better theory because things become more extreme. Let’s agree that if you can say something new about quantum gravity, that would be fantastic. Right. No argument there. Now if we think of you, you know, you’re kind of hawking a new product that rests on the foundations of quantum mechanics. Strange. Right. Well, well. Quantum gravity theorists are potential customers. Right. I’m also a potential customer. Right. I’m in the market for just a reformulation of existing quantum mechanics that would help in coming up with new quantum algorithms. Right. Or understanding problems that quantum computers will provide and problems they won’t. If somebody can give me that, that’s fantastic. I’ll buy it. Right. But there are a lot of things one might want to do in reformulating quantum theory. The first is, you know, the current approach that we have, and the current formulations and interpretations, if you will. Frankly, I know the terms don’t mean exactly the same thing. And there are some people who really like to be very precise about what they mean. But I’m happy to call this a formulation-interpretation. That doesn’t bother me. But at some point that might be the heart of the matter. For example, are you making a new ontological claim or are you just making a new mathematical reformulation? But both. So I’m very clear to everybody. It’s both. There’s an ontological statement about what actually exists and also a kind of new mathematical formulation. And to be clear, just like what happened when Paul Dirac introduced the path integral in his 1932 paper, Lagrangians and quantum mechanics, he was just curious about how Lagrangians show up in quantum mechanics. This is the classical Lagrangian idea, because the theory at that stage had only been developed in the Hamiltonian formulation. And it took 10 years before Richard Feynman came along and incorporated this idea into his Ph.D. thesis, and then six more years in 1948 in Reviews of Modern Physics. And when he explained the idea to a broader physics audience, even then he said in the paper, there’s nothing you can do here you can’t do using the usual methods. It took decades for people to realize that there are situations where you never want to do things according to the basic Hamiltonian formulation. In particular things like Yang-Mills theories, right? And the Standard Model was formulated in the Lagrangian path integral formulation for very good reasons. Sometimes ideas take a while to bear fruit. And another good example is the work of David Bohm. So decoherence goes back to the work of David Bohm in 1951. He was doing foundational work, trying to understand the fundamental questions of the measurement process in his textbook, Quantum Theory from 1951. And in chapter 22, he studies the measurement process, and in the famous section 22.8, the destruction of interference in the measurement process, he introduces this idea about how decoherence works. And it takes decades for that to become a central part of how we think about quantum computing, right? I mean decoherence timescales are now something people talk about constantly. Things take time, but you have to start with a new idea. And I think it’s interesting to have a new idea that isn’t obviously wrong or inconsistent. So the first thing I’ll say is, certainly if there are any inconsistencies or problems with this new formulation, that’s fair game. But if the only thing is to say, well, I don’t know what it should be used for yet, I think that’s already pretty good. We don’t always know what things should be used for at the beginning. In this case let’s dig into the idea. So I still want to know, did I miss anything important in my summary of what you’re claiming? Okay. First, I commented earlier, does this thing make any new predictions? Yes. I’ll get to that point. Okay. Last, I talked about whether this thing has any trajectories in it. I’ll get to that point again. Okay. But overall, I think that if you’re starting from the Hilbert space picture and trying to explain in a reverse way, how to get from the Hilbert space model, if you want this model, I think generally, your picture is correct. But I think it seems extremely complicated for people who are hearing this for the first time. So let me just explain. I mean I’m just thinking of somebody who already knows quantum mechanics and what’s the fastest way to get them to understand what you’re claiming. Right, right, right. But again, it would be like starting with somebody Hamiltonian phase space formulation and saying, we’re going to choose a canonical basis. I mean what choice do we have? We have to meet people where they are. Right, definitely. Well the choice is, you know, for the new people coming to quantum theory, right, who are, you know, yes. But, well, let me start from the beginning. I’ve listed all the Dirac-von Neumann axioms. They involve all these strange ingredients. We’re not going to do that. Here are the starting assumptions. Here are the axioms. The first is that the physical system has a configuration, and that configuration comes from a list of configurations that we’d like to call, if it’s a nice continuous set of possible configurations, the configuration space, not a real space. And that’s what we call the kinetic part of the theory, which is very similar to what you might do in classical theory. In classical theory you have to start by choosing a suitable set of configurations or configuration space that you want to use to model the system in question. If you want to study particles, you have to choose particle arrangements in space. If you want to do fields, you have to, you know, think about field strength configurations translated to locations in space. Or, you know, a discrete system like in a computer, you can choose arrangements or patterns of on-off switches and memory registers or whatever. So this depends on the model. You choose whatever you need for the model you want to do, and that’s the first axiom. We just choose a set of configurations. And the second is the dynamics. Dynamics means the dynamical laws, the mathematical laws that describe how the configurations are supposed to change. And as you know, in physical theories so far, you know, under this kind of Laplacian model, the idea is that we have some kind of differential equations that take our current configuration and then tell us the subsequent configurations in a smooth way. Usually, in the language of some giant differential equations, we don’t do that. The new dynamical postulate is that there’s a family of conditional probabilities, right? This family of conditional probabilities of the form, given that the system is in such and such a configuration at this conditioning time, this is the conditional probability that the system will be in such and such a configuration at a certain target time. The conditioning time has to be a special time, right? We’ll talk about, yes, we’ll talk about. So this is a sparse family of conditional probabilities. It’s not completely comprehensive. It’s not, you know, it doesn’t exist for all conceivable things, you know, that you can pick for targets and conditioning times. In particular, the conditioning times are somewhat special. And that’s what makes this a sparse family of conditional probabilities. And because they’re special, these processes are called indecomposable processes. And indecomposability means there’s a failure of iteration. You can’t do some process over a certain amount of time and act iteratively using some maps or rules that then give you for each successive time because that assumes that each time is a time when you can restart and condition. If you give up this assumption, you’ll have a simpler family of conditional probabilities. These processes entered the research literature in 2020 in a preprint by Simon Milz and Kevin Modi in a kind of quick comment in figure six in their research paper, which was a beautiful review article about classical and quantum stochastic processes that I highly recommend. It’s on PRX Quantum. It’s, you know, available to everybody. It’s, you can also get an archive version of it or whatever. But, you know, it was eventually published, as I said, in PRX Quantum. And that was the next year. So in 2021, this seems like a relatively new idea. It hadn’t been explored by people working in statistics and in the theory of stochastic processes. These processes are not Markovian. So Markov processes are processes that have this nice iterative behavior. In general, I mean it’s slightly more precise than that. But even, you know, when people considered traditional non-Markovian processes, as in textbooks, when people think about non-Markovian processes, they imagine these extremely complicated structures with these towers of higher and higher order conditional probabilities that are all different from each other. They become extremely complicated. They’re very hard to formulate and characterize. And that’s why people usually, when they can, try to write down Markov processes. These indecomposable processes are simpler than Markov processes. They fail to be Markovian, not because they’re more complicated than Markov processes, but because they’re actually simpler than them. They’re so simple that people stumbled over them and didn’t realize they existed. And I’m talking now to people who work in the theory of stochastic processes. And they say, oh, yeah, well, that’s actually a new idea. And new ideas are always exciting, right? I mean, when you realize that there’s something very simple that was there and people hadn’t noticed it. I mean there’s new mathematics to be done. There are new ways to think about things. And remarkably, you know, you might just have thought, well, if there’s this new kind of process that’s simpler and more general than the processes we’ve been dealing with, can it do anything? Does it have any applications? And it turns out that it seems perfectly right to get back quantum theory. So again, the two assumptions are configurations and configuration spaces. And the dynamical laws are these sparse conditional probabilities that will generally not be decomposable. Sorry, will generally fail to be decomposable. They’re called indecomposable processes. And then there’s a mathematical correspondence, a map, very much like the map between the classical Newtonian system and the Hamiltonian phase space formulation, which is this mathematically abstract formulation with all these symmetries and all these calculational tools. And that correspondence is called the quantum stochastic correspondence. And it lets you go back and forth between the two pictures. So, you know, once you leverage this map, you can just systematically reconstruct all the axioms. But now you know where they came from. And you get these very nice ways of understanding the source of some of the strangeness of quantum theory. So let me take, for example, complex numbers. When you want to use this quantum stochastic correspondence, what you generally find is that it only works when complex numbers are introduced at this step. So, or some algebraically equivalent or isomorphic structures to what we call complex numbers. And that’s actually really nice. You need some negative numbers. Yes, definitely. Right, right. But you can imagine, for example, representing complex numbers by two-by-two matrices or something like that. But my point is that the stochastic process you start with doesn’t have any complex numbers in it. It’s written in the language of just old-fashioned probability theory, right? There are no Hilbert spaces. It’s just systems moving around. And the probabilities are old-fashioned probabilities that have all the usual rules of old-fashioned probabilities. And when you want to write it in this Hilbert space picture, what you find is that in most cases, complex numbers are necessary to write that description. And this gives a very satisfying explanation of why we need complex numbers in quantum theory.

I think there’s something nice happening there, as in the axiomatic reconstruction of quantum mechanics, is something that people, you know, Lucien Hardy and many others, you know, and Giulio Chiribella has been trying for many years, you know, which I think is a slightly different game than interpreting quantum mechanics. Yes, yes. I should say that those approaches, for example, Hardy’s approach, right, has this. And I recommend this to everyone listening because it’s a beautiful piece of research. It’s quantum mechanics from five reasonable axioms. But these approaches are clearly instrumental. They’re part of a larger idea called generalized probabilistic theories, the other GPT, is the original GPT, which is just aimed at treating quantum theory as a kind of instrumental tool where agents or observers make measurements on things. So they’re not intended to be an ontological interpretation. So to be very clear, that’s a completely different picture. But let me go further. Right. One question people have is, you know, why? Why interference? Why linearity? Where do these features come from? And interference is extremely strange, as we talked about earlier in this conversation, and it’s something that relates if you take a certain kind of stance on many worlds. We have different realities, but they’re not really different realities yet because they haven’t been detected with the naked eye and haven’t been decohered yet. You know, and somehow, they’re complex numbers and they can cancel each other out. Right. But like what physically happens? There’s no kind of clear physical picture here. But because you now have this correspondence between Hilbert space, this Hilbert space story, and this stochastic story, you can translate back and forth to get a physical picture. And if you translate interference back into this picture, what you will find is that it’s literally just indecomposability. If you do a process and you start from a certain conditioning time and go to a certain target time, you will get some data about the conditional probabilities, and the system will end up where it ends up. If you manually ask that we can decompose this process and write down kind of closest decomposable approximants to this process, simply splitting it on paper at this intermediate time and then trying to treat it as a process with a split in the middle, you will get the wrong answer. But the amazing thing is that when you compare the right answer with the indecomposable dynamics to the wrong answer, you just subtract the two, subtract the expectations of one from the other. The formula that pops out is exactly the formula for interference. So interference now has an interpretation. This is just if you want to go to a formalism, not a non-decomposable formalism with laws that are kind of hard to apply, but you want to go to the nice and beautiful and clean and smooth Hilbert space formalism where you can do time evolution in steps. You use unitary time evolution. It’s nice and decomposable. It looks Markovian. Then the cost you pay. The indecomposability doesn’t go away. It manifests itself in this extremely abstract and confusing kind of interference. But now interference has a physical meaning it didn’t have before. I mean, I mean it better be the case, right? Oh, yes, of course. It better be the case. We produced quantum mechanics. Absolutely. But let me answer your question. I think we’re pretty much on the same page about what’s being claimed, you know, and if we are, then, you know, I can now explain, I think, very clearly why, you know, as an interpretation of quantum mechanics, why I don’t buy this product. I have two points I should make first and they might change. Okay. Okay. Let me get to these. Yes. Yes. Yes. So. So the first thing before let me say, because you’re reconstructing the postulates of quantum theory, you don’t have to go through one by one and make sure everything comes out. Oh, you can. And some people do that. Yes. So I’ve done two things. The first is this question about the absence of trajectories. I want to be a little bit more precise about this. Yes. The statement here is that there isn’t that we’re saying there are no trajectories. What we’re saying is that the theory doesn’t give you a precise description of which trajectories are taken. So, you know, there is in the system at any moment a probability distribution for the configuration of the system. And these probabilities, and these distributions are where the system changes. In some circumstances you can give conditional probability statements about where the system is. And in other circumstances you can’t. But that doesn’t mean the trajectories don’t exist, but we don’t have the theoretical tools to tell us what they do. Now you can say that this makes them unobservable. And then we can get into a discussion about the theory of unobservable things. Let me turn this over to Scott. Yes Stan, are you committed to the existence of the trajectories, even if you can’t compute their probabilities? Yes, you’re right. Yes. Yes. So you’re saying that there are actually trajectories. Yes. The system really does things. I mean your theory doesn’t tell you their distribution. Right. Yes. Yes. And that is that this is different from what I thought. Excellent. Good. I thought so, I thought you were denying the existence of trajectories. No, no, no, no, no. There are trajectories. The system follows some trajectory. We just don’t know what it is. If you have God’s eye view and you can see the whole universe unfolding, you will see all these funny trajectories. You won’t need the probabilities. We’re limited cognitive beings. But okay, but it’s not just that your theory doesn’t tell us the trajectories. It’s, you know, within the experimental framework of quantum mechanics, it seems that we can’t even in principle, you know, only God himself can literally know that. That’s correct. I take the experiments. The experiments seem to indicate that when you make a measurement, you get one outcome. The outcome is probabilistically obtained. And there are certain things that we cannot know, like the trajectories of the systems. And my approach says that’s what nature says. Why don’t we just believe nature?

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Right. There are some things, you know, where there will be I don’t know exactly about them. Right. So to be clear, we are not providing a probability distribution over paths. That’s kind of the thing. You’re not. You’re not. I understand. Excellent. Yes. Okay. Yes. But that’s not so. I mean, there’s one objection one can always raise if you’re not providing individual paths. And I’ve done a lot of early work in conditional interpretation. Okay, okay, interpretations, the failure to provide path information can lead to very severe existential instability, where, like, macroscopic systems can fluctuate between like a live cat, a dead cat, a live cat again in somewhat uncontrollable ways. And, you know, what you don’t want is to not be able to specify paths for things to go to microscopic systems. But what you can show is precisely that as systems get bigger and bigger, they have more and more of these branching events that just arise from interactions with the environment, and for macroscopic systems, you get really nice and clean evolution. As you know, when you properly handle collective variables and corresponding degrees of freedom, you find that macroscopic systems, move in highly predictable ways, even though deep down, their individual elementary particles or elementary constituents, whatever, behave in ways that cannot be assigned within a specific path theory. So it’s very important that we bridge the gap between the unpredictability of paths of microscopic things and the emergence of nicer paths for big things. And that’s something I’m very sensitive to, again, because of my early work in typical interpretation. So I just want to say something quick about paths. I’m glad we touched on that.

The other thing I wanted to say is this question about does this lead to different predictions? So the Dirac-Feynman axioms are ambiguous about what should happen when you have very large systems that you want to treat quantum mechanically, right? This is the heart of systems that include us. They include us, but Schrödinger’s cat, Wigner’s friend experiment, right. And so there’s just ambiguity and particular, I mean, I mean, to some extent, as long as the cat or the friend or whatever is outside of you, right, as long as you’re willing to treat them as just a collection of atoms, you know, even a huge atom, you know, evolving by Schrödinger evolution, it’s clear what to do. But if you yourself are part of the system, I think that’s when the experimental problem arises. I mean, you know, I think there’s a way to phrase it, and I have this, this flowchart that maybe Kurt can, can, can hang up, but I call it the Wigner’s friend flowchart. And it’s as in the Wigner’s friend thought experiment, which again, if people haven’t heard about this very quick summary, there are now two observers. Very important now for Hugh Everett, who first introduced it in the literature is a long-form thesis in 1956, where he phrased it in terms of two observers. You know, in the simplest case, one observer is outside a sufficiently sealed box for the duration of the experiment, such that we can pretend that nothing leaks out of the box or comes in. And then Wigner’s friend is a second observer inside this perfectly sealed box, along with some quantum system and some kind of superposition that Wigner’s friend will measure, or perform a measurement on. And the question is, now that we have two observers, there’s this ambiguity, do we invoke the collapse or measurement axioms? Do we not invoke them? Do we invoke them for everybody or for one? And you can just build out the details. When I have this conversation with Wigner’s friend, people tend to equivocate and weasel, right? I’ll say one thing, and then they’ll go one way. I’ll say, but if you just draw a complete flowchart and just say, this is the flowchart, and here are all the options available to you. You have to pick one. Yes or no to this, yes or no to that, yes or no to this, yes or no to that. And they all end at some kind of problem or end at some kind of interpretational sense. If you believe that Wigner’s friend inside, actually collapses the quantum state by this measurement, then you run into the measurement problem, right? Heading to what counts as measurements, and what doesn’t count as measurements. If you think that the collapse happened, but it wasn’t due to measurement, then you’re talking about dynamical collapse or some other theory about why collapses happen. If you don’t think that the overall wave function has collapsed, that means that whichever of Wigner’s friends actually got a result. There was actually a result even though it’s not reflected in the overall wave function, and that by definition is a hidden variable approach. And a lot of physicists implicitly follow this approach if they don’t want to be mind-body dualists. They say, well, we just have to be perspectival. There are different perspectives. Wigner on the outside assigns one wave function. Wigner’s friend inside has a definite outcome, but that’s literally a hidden variable approach. Or you deny that there was, in fact, a definite outcome, and you either accept that more than one outcome has ever happened, which is kind of a many-worlds type of thing, or that nothing happened, and Wigner’s friend inside somehow yielded nothing whatsoever. And then you adopt some kind of anti-realism, which would be radically self-undermining. And those are your options. You have to pick something. And I know you can kind of try not to, but it’s just kind of guiding you there. I’m clearly adopting the option of the overall wave function, okay, on the Hilbert space side of things, we can say the overall wave function. On the stochastic side, we can just say that there’s this continuous, indivisible stochastic process that hasn’t been broken. That’s what happens to the system as a whole. And at the same time, Wigner’s friend got a definite outcome, so you can think of this, if you want, as a hidden variable approach, even though, as Scott pointed out, these variables are certainly not hidden from Wigner’s friend, and they are not additional or extra variables because the wave function is not a physical object. These variables are the only things that exist. So I’m clearly adopting this part of the flowchart, and that makes the prediction different from the Dirac-Feynman axioms, which either run into the measurement problem or are ambiguous about what’s supposed to come out.

For the sake of the listeners, I think we should say that the problem with using the Wigner’s friend thought experiment to get predictions is that at the end of the experiment, Wigner’s friend doesn’t actually have a memory of what happened, which is what we can use to test this prediction. By the time we finally ask the friend at the end, what did you experience, and then write it down and publish it in a journal, then we all know how to do the calculation for what the friend will say. Will that follow the usual Born rule in quantum mechanics, unless there is something of a dynamical collapse going on or something like that. But otherwise, you will see the same quantum mechanics that we’ve known for 100 years. If there is any experimental difference, it can only be in what Wigner’s friend experiences while conducting the experiment. But once that’s done, they will have no memory of it. Just for the benefit of the viewers, I will put the picture that Jacob was referring to on the screen. Then I also want to mention that I asked you, Jacob, last time, what’s the difference between Wigner’s friend or the thought experiment and Schrödinger’s cat, except that the cat is now a friend? They’re basically the same thing. It’s just a question of, are we worried about just putting a large system in a superposition state? Are we worried about the fact that it’s alive? Are we worried about the fact that it’s conscious? And in a sense, we can be. Cats usually can’t report experimental results. Right. You just increase the dramatic stakes by going from a very large object to a meowing cat, you know, to a friend you can actually talk to. A cat that can take data and report it would be Wigner’s friend, basically. Yes. Somebody wrote a funny comment that said, no Kurt, you’re wrong because cats are never anybody’s friend. Well, that’s clearly wrong. Yes, I don’t think we can agree on that. I don’t think that’s true at all. Or that cats never treat humans as their friends, something like that. Well, I mean, I think that’s what we know. I mean, I mean, cats can be friendly, but on their own terms. Right. That’s the difference from dogs. Right. But let me quickly say about this comment that we all know what happened. We actually don’t know what happened. And the reason I say that is, according to the Dirac-Feynman axioms, if you read the axioms in one way, then actually there’s an overall unitary evolution. The whole apparatus evolves as far as Wigner on the outside is concerned, there’s no loss of coherence. And we can in principle do interference experiments or even do that reverse unitarity and reverse the system to where it started. But the Dirac-Feynman axioms say that when a measurement is performed, things collapse. And if you take that seriously, then you can’t do those operations. You can’t do interference experiments on Wigner on the box. You can’t reverse the procedure unitarily. And that’s the ambiguity. And I think what you’re basically saying, which is what most physicists do, is that we’re going to resolve this ambiguity in favor of maintaining unitary evolution. But that, strictly speaking, is going outside the Dirac-Feynman axioms. So when a physicist says this to me, they say, we don’t need all this philosophy. We don’t need the foundations of quantum, you know. You know, but in the Wigner’s friend thought experiment, we’ll take this prong of the fork. They explicitly say that they are now outside the bounds of the Dirac-Feynman axioms. They’re making a claim that goes beyond the axioms. As far as I’m concerned, they’re already halfway there, right? As in, when you agree that the Dirac-Feynman axioms are ambiguous or incomplete or insufficient for this experiment, well, then you’re on my playing field. Now we just have to provide a consistent account of when we are allowed to do that, and when we are not supposed to do that or justify that. If the Dirac-Feynman axioms are no longer available anymore, and if we’ve gone beyond them, then we need new axioms, right? Because if you’re outside your axiomatic framework, you’re floating in the void. You need somewhere else to stand. And all I’m saying is that we should have another set of axioms that would legitimately and honestly allow us to be able to make the statement that I just made.

So the audience here has been watching from the beginning and knows that Scott is on the market. Scott is the quantum mechanic who actually wants to buy from you, Jacob. He just wants to make sure that you have something worth buying, but he wants it. So maybe Scott now has some objections like I’ll buy from you, Jacob, but a, b, c. So what is it? Yes. So, at some point in this podcast, I wanted to say, you know, why I, I think I’m not buying this product right now. You know, I, uh, might come back to this product in the future, uh, if, uh, you know, uh, uh, I’m very happy that Jacob has marketed this product to other people, but I can explain why, why, why the sale didn’t close with me today. Okay. And the reason is, you know, if you’re telling me that there are, you know, particles that have real locations in space. And now you’re also telling me that those particles have paths, right? But the paths are unknown to us, right? You know, you can only, through quantum theory, you get this indivisible stochastic dynamics, right? That tells you kind of, you know, you know, we’re not allowed to ask, right? And so, for example, if I’m Wigner’s friend in the experiment, I can’t use this to predict, you know, since I’m experiencing this experiment at one time, what’s the probability that I’ll have a different experience, uh, uh, two seconds from now, right? I can’t actually use it for that, you know, it’s unknown, by me, right? Well, guess what? That’s what standard quantum mechanics told me. It told me that it’s unknowable by us, you know, uh, uh, feel, uh, at that point, maybe I might as well say that, you know, what is knowable, what’s within the realm of physics to talk about is the wave function. Which is what, you know, uh, uh, most viewpoints on quantum mechanics have been saying for a hundred years, right? Like, I haven’t improved enough in that regard, right? For me, you know, to say, let’s say, in the double-slit experiment, to say, uh, uh, you know, we can improve, you know, just getting a wave function where there’s some amplitude for the photon to go through the first slit and some amplitude to go through the second slit. You know, uh, that means saying something like, uh, well, well, really the photon goes through one slit or the other and I can tell you which path the photon will take, right? Which is exactly what the Bohmians claim they do, right? If you’re not going to say that, if you’re just going to tell me, well, this indivisible stochastic dynamics gives you the probability distribution where you’ll find the photon if you want to measure it at any average time. Right? Uh, uh, but, you know, if you don’t measure it at average times, then, you know, it can be jumping around and in some way only God knows. Well, I feel, you know, that’s what standard quantum mechanics already told me, right? It already told me how to calculate the probabilities if I measure the photon at any specific time. And it told me that, you know, if I don’t do the measurement, then I don’t get transition probabilities, right? So, you know, just kind of a metaphysical assertion that, you know, there’s this underlying thing on which the transition probabilities exist and I can’t know what those transition probabilities are. You know, I can’t know what the distribution over paths is. It feels like an ontological commitment that doesn’t pay rent for me. You know, it doesn’t improve enough. You know, I, I have a very strong faith. Like, I want to know what’s really there in the world. You know, I’m not a instrumentalist, right? But I want to align my ontology as much as possible with what’s actually observable or at least in principle observable, right? Because I think the history of physics has given us lots of examples where people get themselves tangled up in, you know, let’s say, you know, the embodiment of, you know, things like, you know, general relativity, coordinates, right? Or, or choice of gauge, you know, and correcting things that don’t make a material difference, you know, the global phase of the wave function, right? And, you know, again and again, the right answer has been to try to exclude things that can’t be observed even in principle, right? Get an ontology that’s, you know, as perfectly consistent as possible with the set of all things that are in principle observable. And, you know, whatever my reservations about the many-worlds interpretation, and I do have reservations about it, but it at least tries hard to do that, right? It tries to say, look, you know, the wave function is an encoding of everything that’s in principle observable, so that’s what we’re going to consider to be our ontology, full stop. It’s the wave function, and if we don’t have to add anything extra to it, we won’t. You know, and Bohmian mechanics, of course, tries to add something extra, you know, making it tell a very specific story, right? And of course, you know, one can object, well, why this story versus 100 other stories, but it’s at least a story. Right? At least, you know, there’s a clear story we can stare at and look at and see if we like it, right? Now I feel like we’re adding more ontology without adding a story that goes along with it from Jacob’s point of view, and, you know, that’s something you can do, but, you know, I don’t see that I’m going to get something out of it that’s worth the price of admission, at least not for me, not now. But, you know, I would say, go in peace, you know, if this helps with quantum gravity, that would be great. And that would certainly be one reason to take another look. If this gives new insight into quantum information protocols or quantum computing, that would certainly be another reason for me personally to take a look. And I feel, you know, until something like that happens, I’ll just say, you know, I’ll pass on this product, go in peace.

So I have a couple of points I’d like to clarify about that. First, there are some similar technical aspects. At some point I said, well, Wigner’s friend inside knows the outcome, but he doesn’t know then what he’ll do two seconds from now. That’s actually not true, because, you know, the measurement that Wigner’s friend does generates a branching event. And the branching event is where you can make conditional probability predictions from that moment on. So the scenario that I implicitly had in mind was that suppose Wigner’s friend is in a superposition of two mental states, and then we do a Hadamard operation on that. You know, we do some interference or in your terminology, some indivisible operations that take us from one superposition to another. And then the problem is that, you know, in ordinary quantum mechanics, we wouldn’t get transition probabilities. That’s the scenario I was looking at. That’s good. Right, exactly. But, you know, for Wigner or you or anybody doing measurements like ordinary life, you would be able to make those predictions and those that are consistent with what we see. I understand that. I mean, that’s because real life is largely decoherent. Yes, exactly. But let me now address some of the points that you raised. Yes. And let me say, first, before we begin, not everyone has to agree that this is the path to take. I’m not selling this to you personally, Scott, although it would be great if you liked it. We’re all looking for different things, right? As I said, and you know, when you’re teaching quantum mechanics and we’re snowing the students, we snow them by saying, these are the axioms. And the students stare blankly, they’re like Hilbert spaces, linear algebra, density matrices, self-adjoint linear operators, you know, POVMs. And, you know, you put them in a state where they can’t even be able to ask questions about why. I mean, I introduce these things only as needed. But, you know, I mean, of course, I’m also in the market looking for better pedagogical ways to teach quantum information, you know, to students. I like that. But it seems like even if I believed your philosophical commitments, you know, it seems to me that I would still have to teach the students about Hilbert spaces and unitary transformations. And all that stuff, because how would they, you know, do the calculations? I agree. But there’s a difference between saying I have forces in Newtonian mechanics that push things around. And then through a series of mathematical transformations, I can convert that into Hamilton’s equations of motion or the principle of least action. And then, in contrast, showing up on day one and just saying Hamilton’s equations of motion or the principle of least action with Hamiltonian’s. I mean, there’s a total pedagogical difference there. But let me put all that aside. So let me also add one other point, which I think is important. You know, this old joke, right, that these two campers hear the bear. Yes. And one starts running and the other one starts putting on his shoes. And the first one’s like, you can’t outrun the bear. The guy’s like, I just have to outrun you. I’m not suggesting here that this formulation interpretation is going to satisfy everyone. And I’m not saying that this is necessarily the final word. I mean, we don’t even know if quantum theory is the final word. Right. I mean, if we’re trying to develop a theory of quantum gravity, it’s possible that quantum theory will be modified in a much deeper way than is specified in this approach. But the question is, is this at least an improvement over other interpretations or formulations that we have? And I have a clear set of reasons why I think that’s the case. So if somebody comes to me and says we have enough interpretations already, why do we need another interpretation? I’ll sit down and I’ll sit on many worlds or I’ll sit on Bohmian mechanics or I’ll sit on Copenhagen or whatever else. What I’m telling you is that these aren’t really safe havens. Right. They give us a false sense of security. Here’s a list of criteria that I think are required for any good theoretical framework in physics or formulation. And certainly for quantum mechanics, even irrespective of any aesthetic judgments or preferences. The first is that the thing should be empirically adequate. Right. It should make predictions. The predictions should agree with what we see. That’s the first element, you know, for all kinds of systems that we care about in quantum mechanics. Empirical adequacy is first. And the second is, it shouldn’t be ambiguous. You know, if somebody asks you a question and they equivocate and weasel and are ambiguous, you know, I don’t know what we can say, but I kind of know when we see it, we’ll use our expert intuition. Like, that’s ambiguity. And the third is. It shouldn’t be opaque in making predictions for certain kinds of systems that might be practically impossible to study in principle, but are nonetheless study-able. And that, again, is like macroscopic writing systems like the ones generated by Wigner’s friend. There should be at least a schematic story in principle told about how the classical world is supposed to emerge. It doesn’t have to be. I mean, clearly getting all the fine-grained details is going to be extremely difficult. It’s very hard to do all the details and explain how classical deterministic classical type dynamics emerge from microscopic system mechanics. But there’s at least a schematic story about how that works. And the last thing is that it shouldn’t rely on a long list of what I call contemplative metaphysical assumptions or ad hoc additional empirical axioms in order to get it off the ground. A long list of epicycles like that are the things I think we should reasonably ask for. My view is that none of the interpretational approaches that we have meet the minimal requirements. Right. And I can explain in detail why each of them doesn’t. Bohmian mechanics has proven very difficult to generalize beyond fixed-number systems to find many non-relativistic particles. So it’s proven very difficult to use it to understand how quantum field theories in the standard model are supposed to work. Our best theory of fundamental interactions is written in terms of quantum field theory. In particular, Bohmian mechanics has a lot of difficulty dealing with what are called fermionic quantum field theories, which don’t have conventional configuration spaces of the kind that Bohmian mechanics wants to help itself to. Bohmian mechanics works by positing a new evolution rule, even if it’s a stochastic rule. You might have to pick your preferred frame of reference or things like that. That’s what people do. Maybe this is the core of my objection. I feel that Bohmian mechanics suffers from all these problems because it tries to make a concrete commitment. And you avoid that just by not committing to paths. Once you make that commitment, you’re going to run into the same problems that Bohmian mechanics faces. Yes, you’re right. Bohmian mechanics tries to write extremely complicated, and some might argue stochastic dynamics in such situations. This is the work of people like Shelly Goldstein et cetera, who have tried to generalize this when they need a preferred reference. It turns out to be extremely complicated and seems kind of ad hoc, frankly, right? Yes, I agree. I agree. They have a clear goal to replicate that. That’s not the product for me either. Right. But I mean, look Jacob, once you’ve now told me that you’re committing to the existence of paths, even if we can’t, you know, know their distribution in principle, even

Learn, now, in fact, your viewpoint seems more like Bohmian mechanics than I had thought during this conversation. But it seems to me like a minus minus Boom, you know, it's Boom, except you are omitting the definite commitment about the guiding equation. And you're saying, like, you know, who knows? Which, you know, yes, you can do that. But, you know, you know, just as I would have known before that that was an interpretative option on the table, although I wouldn't have phrased it in the context of non-separable stochastic dynamics. Yes.

So let me say earlier, when I mentioned Bohmian mechanics, I talked about pilot-wave physics. I should just point out that when Boom introduced Bohmian mechanics in 1952, he considered the pilot wave to be a material thing. He's very clear about that in his papers. But there are still Bohmians who adopt this view. But I mentioned Shelly Goldstein, but Goldstein and Dürr and Zanghi, you know, they've adopted since the 1990s a viewpoint of Bohmian mechanics where the wave function is not a material object, but it's an expression of what's called nomology. It's a law-like expression, which in some ways takes quantum mechanics back to its roots. When Schrödinger introduced his picture of wave or wavy mechanics, he constructed his wave function from the fundamental Hamiltonians, which are expressions of certain kinds of law-like things. Basically, he took the Hamilton-Jacobi function, and he put it into the phase of the function. And he called that the wave function. And so, in a way, this is kind of bringing things full circle.

There's a sense that what I'm doing, like the closest least-squares approximation I'm doing of existing interpretative frameworks, is that it's very similar in some ways to the nominalistic view of Bohmian mechanics. But without spacetime preferred foliations, and without a particularly contrived set of laws, the laws are simpler. Without the timing equation, with a definite commitment about what the trajectories are, which was for me kind of a hallmark of Bohmian mechanics that, you know, makes that commitment. You just take that out and say there are some trajectories. It's unknown what they are. Okay, okay, okay. And that's what gives you this is simpler laws and greater generalizability as well, because now you can apply this basically to any kind of system. So the generalizability is helpful.

But let me say something else here. So you have this paper from 2004. Is quantum theory an island in theoretical space? But in that paper, you're asking, could we modify any of the features of quantum theory to search for a different theory? Could we, for instance, write down a quantum theory that doesn't use complex numbers? Could we make a quantum theory or modify this feature or that feature or this feature? And what I love about that paper is, you know, you're not taking nature as having handed us, especially you're imagining that maybe there's a different kind of theory out there. And that's worth. Trying to find out where we can generalize quantum theory in anticipation of maybe getting an experimental result that requires a generalization of quantum theory or that there's a lot of things you can do when you start. From Hilbert space formulation, if you. Do a lot or do something, and that's because the problem is the Hilbert Hilbert space formulation has a very precise relationship to the probabilities of experimental measurement. You have to follow a sequence of steps and through Born's rule, and you'll get the probabilities. And if you just say I'm going to take the axioms, and Hilbert space, and Dirac von Neumann axioms, just play around with them, you'll almost immediately get nonsense, right? You get probabilities that don't add up to one or negative. That doesn't make any sense because you risk damaging this very precise bridge or connection to probability theory. If you started from a different axiomatic place, arguably simpler and fewer axioms that are easier to explain to a newcomer that are formulated in old probability theory, there would be no link. You need to get to probability theory and you can imagine generalizing the theory in ways that were hard to imagine starting from the Hilbert space formulation and. You know, I completely agree with the spirit of what you were doing in that paper. I believe in it. One of the advantages of reformulating the theory in terms of different axioms, especially axioms that are less abstract, fewer in number, and less sensitive with less sensitive connections to things like probability theory, is that we have greater flexibility to consider variations of it and to build more general theories. And I think that's exciting. If you're a student watching this and you're wondering. Yes, maybe I'll work on an interesting project. What can I do? And here's something interesting to do. How can we generalize starting from this new starting place? I was about to ask you, I mean, could you leverage that idea? I mean, yes, I can imagine that. But could you, starting from stochastic dynamics, give me any example of something that's kind of like quantum mechanics but not quantum mechanics? Yes, yes. Okay, here's one example. I'll give you a couple. But tell me. Yes, one example of this is that these discrete conditional probabilities, you know, are only conditioned once. Right. They are conditioned on one time, one of these partition times. One generalization might be: Is there a theory where we can condition on two times? Is there a theory where you condition on three or more times? These now describe theories where when it's not clear that the stochastic quantum correspondence works in the same way. You don't necessarily get the standard Hilbert space picture. Now, arguably, you can do tricks. There are all these tricks where you can take a non-Markovian model with conditioning multiple times and write it in a bigger way. So it's possible that there's some way to write this in the usual Hilbert space formulation. But maybe not. So you're just posing this as an open question. Yes. Open question. Well, I think that's going to be fine. And there are lots of these open questions. Right. I might not even know how to ask this question. The Hilbert space viewpoint. Right. And, you know, that's one example. I want to say a few other quick remarks about what you said. So one of these questions is should the theory be formulated in the context of things, you know, more objectively, you know, should we have components we don't like to know what they are? There's this long-standing question about the role that unobservable things play in physical theory. Should physical theory contain unobservable things? And I know you're not a strict operationist here, which is, you know, the only things that have physical meaning, right, are things that we can have some procedure or process to follow and implement or measure or work with. All our physical theories somewhere or other contain unobservable things that play an important role. I'd like to believe the moon is there even when I'm right. Yes, and I would too. And it would be nice to have some justification to believe that even if you know, because, again, from Dirac von Neumann, there's nothing mysterious, but the moon is there, which is kind of the problem. And on the other hand, you know, the global phase of the wave function of the universe. You know, if I have an account where there isn't, I'm not sorry to see it. Right. Yes. But Scott, it's worse. Even in principle. But Scott, it's worse. It's worse than that. And now I know that if I ask you this, you probably won't commit to this. But there are a lot of people committed to the idea that the objects that exist in Hilbert space picture wave functions might be far from the global phase, you know, and, you know, these kinds of components are somewhat like material things, so we should ascribe some idea of physicality or existence to them. But the problem is that there's actually a larger class of gauge transformations and quantum mechanics which actually, as far as I can tell, only goes back to 1999 in a philosophy paper written by Harvey Brown. He's at Oxford University. And it's called Aspects of Objectivity and Quantum Mechanics. And Kurt, you can link to it because he does it on the first page. Sure. He's a philosopher and he identifies on the first page a large class of gauge transformations that apply to all quantum systems. You can think of these gauge transformations as a generalization of change, or a unitary change of basis. These are gauge transformations where you're changing the basis differently at different times. So in the language of differential geometry, which maybe not everyone watching this will be familiar with, but some of you might know it, you can think of quantum mechanics evolving in time as a bundle of Hilbert spaces connected to each other like, you know, when you string together, you know, popcorn on a string or something like that. Right. Each Hilbert spaces are fibers attached to the string and the string is time. We just call it a zero plus one-dimensional manifold. It's just time. And there's a Hilbert space attached at each string. And we can imagine doing an independent unitary rotation on each of the different Hilbert spaces. And this is somewhat analogous to the more traditional language of doing what's called a time-dependent unitary transformation. We're acting with a time-completely independent unitary transformation on the quantum system. And you might say, well, but this doesn't keep things in different quantum mechanics. What are you talking about? But actually it turns out that it does. So you can look at the beginning of that paper. As long as all the commuting operators that represent things that can be observed transform in a certain way, what's called a similarity transformation under the unitary transformations and the Hamiltonian is what's called a flat gauge connection. And again, all this is actually written in Harvey's paper, although he doesn't use all these terms, but that's the case. Anyone who works in non-Abelian gauge theories will immediately see that the Hamiltonian transforms in this very distinctive way. The theory is completely invariant. Now, what's weird about this? And I know this is getting very technical, but this is a technical objection to trying to take Hilbert space seriously, which is that it means that the state vectors can be infinitely reassigned however you want. And any trajectory in Hilbert space that you thought was encoding some kind of invariant information about the system can be literally reassigned to any other trajectory by these time-dependent unitaries. Well, obviously we can't reassign the actual numbers, you know, in some definite representations, which are connected to our choice of basis and so on. But I don't think any world out there, for instance, or anybody who believes in the reality of the wave function is saying anything that naive. Right. Okay, but it's hard because then you have to get into the details of exactly what's being proposed. So when I talk to some people who don't like Kurt, I'm sorry Kurt, because you wanted that. Yes, let me simplify this for everyone. So Jacob, you're in the showroom. You've come in here with some old stuff cards you want to trade in. Okay, and you're looking at the options and someone comes along whose name is Jacob. And is this also Jacob? Yes, I have a handsome guy wearing this great shirt. And you say, I'm not going to be swayed by your smile alone, Jacob. So, okay, let me hear about the benefits. And then Jacob tries to sell you. And I also want the audience not to take anything away unless you end up, Scott, buying from Jacob by the end of this podcast. I mean that would be silly. Most people have to look at a car or anything else seven times before making a purchase. Yes. No, I mean, look, look, I've already decided I'm not going to buy at this stage. I'm happy. I'm happy to chat more. But okay, the point is there are two ways to sell. The first is to talk about your own benefits. So Jacob, from your other card is to talk about the downsides of the competitors. So Scott, you've come with a car. You've also said that you're not a layman. You're not just interested in getting from point A to point B. You want to know what's going on under the hood. So Jacob says, okay, whatever car, all the other cars here will give you some account of what's going on under the hood. Some actually won't. But the ones you care about will give an account. They give a false account or an account that when you actually look under the hood it disappears and turns to dust. So first, Scott, what car are you going to drive away from here? What are you committed to so that Jacob can then say, okay, okay, let me compare my approach to that directly. I should actually say I stopped driving years ago. I didn't like it. I just walk or take an Uber. But my wife's a good driver. Right. So, you know, so, you know, it's all about different cars on different days. And that's analogous in quantum mechanics, I think. Right. I mean I know I know how to think as a scientist a lot. You know, me and if you want me to, you know, to have in ontology, you know, to be as simple as possible, then I would say, you know, it would look like a wave function. And this evolves by unitary transformation. And, you know, the hard part of course is how do I get out of that? You know, my personal experience. Right. Which is about how do you get probabilities out of this deterministic picture? But, you know, at that point, I feel like this would be entangled with, you know, entangled. No pun intended. Yes. Yes. With huge questions like, you know, what is the observer? What is experience? Do you know what consciousness is? Right. And these were incredibly perplexing questions long before quantum mechanics came into the picture. Right. These, you know, Democritus, you know, asked about these things in 400 BC, which is why I titled my book Quantum Computing Since Democritus. Right. And so I feel, you know, if you take consciousness out of the picture, you know, if you take our own observing out of it, and just, you know, just wanted a picture of the laws of physics evolving, you know, where, you know, you would have things that look like observers arising. Not necessarily us, but, you know, you would have stars, and planets, and life forms, you know, living beings arguing about these things, you know, publishing research about it. Right. And then you can get all that, you know, as far as I'm concerned, just from Schrödinger's equation, from unitary evolution. Right. But if you also want to take into account some kind of our own experience, you know, when we're inside the system, then I would say, you know, this has been a big puzzle even before quantum mechanics. You know, the mind-body problem or, you know, things like that, you know, quantum mechanics adds a new twist to that problem. It adds a new dimension to it, you know, without quite solving it. Right. And, you know, so, you know, if you want to be a positivist, you know, if you just want to say or rather, you know, don't deny the reality of anything else, but just say, you know, what can be known is just what we can observe in principle, and, you know, everything else is just speculation. Then you go back to what Bohr and Heisenberg were saying in the 1920s, to the Copenhagen viewpoint. Well, you know, I would say, you know, for me, Copenhagen is basically just shut up and calculate except there's no shut up part. It's, you know, endless philosophy about, you know, why you shouldn't ask, you know, these other questions. And, you know, and of course, it's unsatisfactory not to be able to ask these questions. But we've seen in this conversation that even from Jacob's viewpoint, right, even from this new viewpoint, when I asked him, what are the trajectories of the particles? You know, I can't ask about his theory and get an answer to that. So it always seems that this kind of thing, you know, either I'm not allowed to ask or, you know, maybe I'm allowed to ask, but I don't get an answer from the theory. So I think that's what I'm going to drive my car home in. Okay. So let me say a few things about this. So, yes, yes. The first is that people watching this should read this wonderful paper that Scott wrote in 2013. I think it was called "The Ghost in the Quantum Turing Machine". Yes. Right. Like, if you want to read something by someone I don't think calls himself a philosopher formally, but it's one of the most philosophically interesting things I've ever read, you should read this Scott. Thank you. We used to run a science philosophy club at Harvard University and we invited Scott to come and talk and it was awesome. I mean it's full of interesting ideas, and as with everyone, they're great. I think you wrote that like post-tenure, right? This wasn't you like. Yes, it was, it was like immediate post-tenure publication. Right. It was great. So I want to be clear, people should know that Scott takes these things seriously. He's not like one of these people who considers philosophy a waste of time. I don't care about the mind-body problem, but I'm really glad to have this conversation with Scott about all this. Okay. So let me, let me now say a few quick things. The first is that I really love in the end the way you like correct yourself. You said, well, there are things I'm not allowed to ask, but actually maybe in your style, you are allowed to ask, but the theory doesn't provide you with them. I think that's a crucial difference. So in Copenhagen, you're explicitly not supposed to ask certain things. And when you go to a physics seminar, you learn very early on. There are certain questions you're not supposed to ask. If you ask them, people will groan and roll their eyes. That's not exactly a vibrant intellectually like environment in academia. If you want to ask about trajectories, we welcome you. If you want to think, are there trajectories? I'll say, yes. If you're like, okay, is there some way I can infer or deduce what exactly the trajectories are without making measurements on the system? I would say, well, the theory doesn't provide you with the ability to do that. But of course, you know, there are unobservable features in every formulation of quantum mechanics. I mean one of the weirdest things about many worlds is that there are all these parallel universes full of people, inside them billions and billions of humans. And not only have we never been able to do an experiment that directly confirms their existence, but their own interpretation says we can't because they only exist when they are completely decoupled from our branches. So there's no way whatsoever we would ever be able to test them. There's this grand conspiracy where the vast majority of existence in the universe is completely and forever beyond our capacity. I won't call it a conspiracy because the theory itself explains why we can't communicate with them. Sure, sure, sure. I mean it's just the linearity of quantum mechanics. It's just the linearity of quantum mechanics. Right. But, but, it would be a conspiracy if we had to specially contrive it so that we couldn't communicate. That's right. We don't have to specially contrive it. That's right. Yes. More than I'll have to specially contrive that you can't know what the trajectory will be without making the measurements. But I'll tell you, I'd rather have sometimes microscopic systems that occupy trajectories we can't specify as things we can only know if we measure them, than an infinite number of parallel universes each containing billions or trillions of conscious beings that we have. You know, maybe you prefer the many worlds ontology, even though there are some problems with it. But I'm certainly saying this is definitely not worse than that. Okay, so let me now get to the most important points Scott made. So Scott, you said, okay, look, I can get all this stuff from Schrödinger's equation, from the wave function of Schrödinger's equation. And now I'll put this back to you. What do you say we can just get out of the wave function of Schrödinger's equation? I'm saying that if you program your computer to simulate, you know, a bunch of quantum fields, okay, you know, interacting, you know, according to, you know, let's say the standard model or something like that. Okay, well, you know, first of all, you know, I couldn't do this because, you know, my computer's time would run out. You know, that's why a lot of people want to build quantum computers. You know, that's one of the reasons. But in principle, I can do this. Right. Do a simulation aa aa that would maintain this giant, evolving wave function. You know, I'm saying that, you know, one can then go inside the wave function and one can find branches in it which one can interpret as containing things. You know, containing excitations that look a lot like observers. That's conjectural. To be clear, conjectural. There's no evidence that you get a unique set of decoherent branches from many worlds. Right. Yes. Yes. Yes. But I would say that's just as conjectural as it is conjectural, you know, if you run the equations of classical physics, you know, from the beginning of time, eventually you get planets and life and all these things. And, you know, I mean we believe that and in a sense, because, you know, we have the example of our universe where this seems to have happened. Right. We can't actually do a computer simulation where we see all this happen from the beginning. But, you know, this is what we get down to, you know, does one ever believe in scientific materialism? Right. Or does one think that there was, you know, there must have been some external designer, you know, intelligent to guide things and create, you know, and cause life and intelligence to happen? Right. If one doesn't believe that, then, you know, one believes that this kind of thing can arise from just iterating these equations without intention over and over again. And I see, you know, that there's no fundamental change if the equations are quantum mechanical, they just say that what will evolve is this giant superposition. But within that superposition, I can again find things that look like, you know, planets with primordial soup, you know, from which life will evolve. So I would say, you know, that's why I say that, you know, if we're willing to leave ourselves out of the matter, you know, maybe we shouldn't be right. But if we don't care, you know, about taking our experience into account, then I think Everett actually gives you a pretty nice picture of what happens, how, you know, you can just start with this very simple wave function, let it evolve according to Schrödinger's equation, and then you get, you know, something like what you need. So let me come back to this, because I think this is kind of a central point, right? Yes. So let me put aside the question of whether you get a unique basis by which decoherence distinguishes things. And that, again, is unknown at this stage, certainly not for a theory as complicated as the standard model. But I'll tell you this, if you proposed a theory let's forget about quantum, and if we got all this stuff, let's say I propose that decoherence doesn't happen. And I would say that that's not just a problem for many worlds. Sure, sure, sure, sure. For any no-collapse viewpoint of quantum mechanics. No, no, not necessarily. For instance, you know, if we're living in a world where Bohmians throw this into the universe, which Bohmian mechanics works in, then we don't have to worry about whether there are different rules by which decoherence works. Bohmian mechanics only picks out one picture. Okay, but put that aside. And here's what I'll ask. Forget about quantum mechanics, and forget about all our physical theories. Let's create a library for a Babel version of the universe. People might be familiar with this fictional idea of the Library of Babel. This isn't the exact version of the story. It's going to be the version I'm going to use. Okay, there's a vast library. And you enter the library and what you see is every book, isn't that the one that starts with what was? You see a bunch of doors, a bunch of doors with different letters on them. You go through the letter T, the door labeled T, and then inside there is

Every book that could exist that begins with the letter T. Then what you do is go through the door labeled H. And if you go to that door, there’s every book that begins with the letter T. And in that way you can find your way around somewhat. You can write or find every book that can be written just by going through a series of doors. This library contains all of them. And one says this gives an accounting of the universe. I mean, after all, we just look at the whole library, and somewhere there will be a universe just like our library. But you look at that and go, this is completely empty. This doesn’t get any interesting information. Right. What we want is a theory that somehow lets you know, and some that can put some constraints around what kinds of universes will happen, which won’t happen. And one of the problems, problems, with the many-worlds approach is that it contains many different kinds of universes that differ radically. And one of that when you read about people who write about the many-worlds interpretation, I mean, in the last podcast I did with you, Curt, I had this lengthy explanation of problems with the many-worlds approach. But but but but one problem I didn’t mention in that conversation, but which does appear in the literature is that people don’t take it seriously enough.

So when Bryce DeWitt published his article in Physics Today in 1970, that was 13 years after Everett got his Ph.D. dissertation in ’57 announcing and broadcasting what Bryce DeWitt called the many-worlds interpretation to the wider physics community. I think the article is called Quantum Mechanics and Reality, it’s in Physics Today. It talks about how there are these branches, they seem sort of somewhat reasonable, and there are also these branches that lie at the fringes of probability, the tails of the probability distribution and they are weird and strange things happen in them. I don’t remember whether he introduced in that article the term branching for these, but eventually these became known as branching. But when you read the literature in many-worlds, people who nominate some kind of technical people to use what’s called Dutch book arguments to argue about how to extract probabilities, they still stay within this kind of narrow confines of the normal-looking branches and maybe the branching. But if you take the many-worlds picture seriously, you have to think about the much weirder branches than the branches that conform to whatever game you’re trying to play. I call these the super-branching, you know, they’re just branching, but they’re like branches where whatever rules you’re trying to set up for the game you want to play, use the branches to explain branches that don’t conform to the rules because something completely weird is going on. And once you include all the super-branching, you’re essentially in a Library of Babel situation where you explain everything and you put no constraints on what kinds of worlds we expect to see. And there are no resources in many-worlds interpretations to narrow it down to worlds that at least look like the ones we see among all the possibilities. That’s a big problem.

Certainly, I agree that, you know, if a theory doesn’t rule anything out, you know, if it doesn’t tell us that anything is impossible or at least, you know, highly improbable, you know, it’s empty, right? Then it doesn’t do anything for us, right? You know, and that’s why I, you know, that’s part of the reason why I’ve never been a hard-core many-worlds person, right? You know, I’ll use it pedagogically when it’s useful for me. Like, you know, one example of where I find it indispensable is when I’m teaching quantum computing, right? And I want to explain how it’s possible to take a qubit, you know, to do what we call a CNOT gate, a controlled NOT gate, right? Like writing the outcome of the qubit somewhere else, or copying its state to a different qubit. And now the effect on the first qubit is exactly as if somebody had measured it, right? It’s been decohered from the perspective of somebody who’s now only looking at the first qubit, right? And students get incredibly confused about this. They say, you know, why is this, right? They feel, you know, it’s still a superposition, right? And like the only explanation I can give them that seems to work, is to say, look, you can also say if you want that the qubit was measured. It was measured by the other qubit, you know, the other qubit is the one that did the measuring. And you can also say that when you do a measurement, well, what does it mean when you do a measurement? It just means that there’s a giant CNOT gate happening to you from that qubit, to the possible states of your brain, to your measuring apparatus, to your environment, right? You know, for me, that’s the essence of what Everettian says. You know, it’s the best way to explain that, right? And it’s true that I, you know, am ultimately not satisfied with a theory that doesn’t take into account my experience with the world, right? Because, you know, as Democritus said in that famous dialogue, you know, in 400 BC, how can you, you know, disregard the senses when you’re getting the evidence from the senses, right? You know, how can we disregard our own experience when our experience is the only reason why we believe in quantum mechanics in the first place, right? So I would say that, with some, you know, I think, you know, somewhat, you know, additional assumptions that seem reasonable about, you know, what are observers, and how, you know, observers connect to the physical world. So yes, I can get something that, like, looks like the predictions of standard quantum mechanics, you know, from the Everettian picture, but it’s not automatic. You know, I agree that it’s not automatic. You know, I don’t believe any of the so-called derivations of the Born rule, you know, for probabilities from many-worlds, you know, neither Everett’s original derivation nor any of the subsequent ones. You know, they all sneak in some additional assumptions. But I would also say that that’s not just a problem for many-worlds. I would say that, you know, in any account of quantum mechanics, at some point you’re going to run into this problem, where does the Born rule come from, right? Where do the probabilities come from, you know, if you don’t want to have probabilities in your fundamental picture? Of course Jacob, in your account, you have probabilities in your fundamental picture, right? But, you know, if you have a deterministic picture to begin with, you’re always going to run into this problem. And that’s a good reason not to have a deterministic picture, I mean, it’s like – I agree that, you know, there are pluses and minuses, you know, in all the different main interpretations, you know. Then, you know, there are other ones where I only see minuses. We don’t have to talk about those, maybe. But, you know, for that reason, you know, I don’t own a car. I just, you know, I choose Uber, if I want. I just, you know, I drive different cars as needed. You know, I can imagine some future circumstances when I would want to use Jacob’s car, right? I can imagine, you know, if it helps with quantum gravity – Scott, you can borrow my car anytime you want. Oh, thank you, thank you. That’s very kind of you. Look, if it helps me, you know, understand quantum algorithm, I’m willing to take a ride in any car that will get me where I need to go. You know, right now, I don’t see where this car will get me, you know, to where I couldn’t already get. But, you know, I like to keep an open mind. Let me just say a couple of quick things to follow up on that. Yes, okay. So, this is one of the troublesome places where I’ll be the annoying philosopher. I’m sorry. But, you know, one of the things philosophers like to do is to take a claim, an idea, and drill down into it and make sure it really works when you follow it through to all kinds of logical conclusions. When I said, okay, if I have the Schrödinger equation and it evolves into some wave functions and that would be good enough, you’ll notice we ran into problems pretty quickly when I checked on that. Because I asked you exactly how to do that, and you were kind of like this, and then you pointed out this problem with all these weird branches and say a lot, and then said, okay, we add some other assumptions and so on. One of the strengths of the many-worlds approach is that it’s extremely simple. I mean, just take the Schrödinger equation and unitary evolution and maybe one or two other things. I have a book on my desk. You can kind of see it. It’s sitting there in front of an Einstein doll. It’s called Stone Soup. And I think this gives a wonderful metaphor for what happens in an approach like the many-worlds interpretation. So, those of you who don’t know the folk tale of Stone Soup, these soldiers come to a very skeptical town and claim that they can make a delicious and savory soup from just water and stones. And the townspeople are amazed by that, and they give them a pot, and they start boiling the water. And as they’re boiling the water, they say, you know, this is already great, but, you know, it would be better if we had a little bit of spices. And the townspeople come and add some spices. And they were saying, oh, this is already almost perfect, but, you know, it would be better with a little bit of vegetables. And then the townspeople add the vegetables. And eventually, they got this, you know, obviously they added vegetables and spices and meat and broth and all kinds of things. And the townspeople eat it. And there’s this line in some versions of the story where one of the amazed townspeople who wasn’t paying that much attention says, my goodness, all this from just water and stones. Many-worlds interpretation. So Jacob, in your account, the path integral would be the meat and vegetables that need to be added. But I’m very explicit in the beginning, right? I tell you exactly the ingredients. We’re not going to go, you know, and I say this in the podcast with Curt, right? To get many-worlds off the ground, at least to try to get it off the ground, you have to add more and more of these postulates. And I think, I mean, I don’t know, Scott, how much of the literature you’ve read in many-worlds. But, like, the number of additional assumptions you need to add is very large. And many of them are of a certain kind, metaphysical, and it’s very hard to imagine how we could check that they actually work. So, I call this the Stone Soup problem. And I think it’s actually a very serious problem with the many-worlds approach. But basically, I don’t think it can work. And I’ve noticed this, Scott. You said that the derivations of the Born rule from the many-worlds approach, you don’t believe any of them. And I agree with you. And I explained my reasons for skepticism in the podcast I recently did with Curt. But actually, it’s worse than that. Because you could also say, maybe we can’t derive probability or derive the Born rule. So, let’s just agree that it will be an additional axiom that we’ll add, right? Because that’s one way I know that some people go. It’s like, well, you know, if I can’t derive probability from the beginning without probabilistic assumptions, let’s just do many-worlds and then we’ll see all these universes and we’ll somehow connect probabilities to them, let’s say some are probable, some are improbable. There are extremely strong arguments that if you’re going to assign probabilities to the branches at all, any rule for doing so other than the Born rule will lead you to nonsense. And these arguments, by the way, appear in Everett’s original dissertation, right? Even in the shorter version of his dissertation, the one that was on the podcast. I mean there are many different arguments that all lead to the same result. There are many different arguments. Yes. But here’s the problem. Right. So, if your view is that the branches were fundamental things, that is, they’re like the branches themselves that are fundamental constituents, it’s perfectly fine in an axiomatic theory to assign them in the axioms things like probabilities. And this, for example, is what happens in the stochastic versions of Bohmian mechanics or what happens in spontaneous collapse theories or whatever else, right? I mean, if you’re taking certain things to be part of your fundamental constituents, it’s allowed for you to assign features to them in your fundamental constituents. The problem is that in order to overcome this preferred basis problem of the many-worlds approach, there are an infinite number of rules that we could use and what distinguishes one basis from another, the idea is that we rely on the dynamical decoherence process of the macroscopic worlds to pick out these approximate macroscopic worlds. The problem is that if your branches only appear in an approximate way at later stages of the development of the theory, you can’t assign axiomatic features to them like probabilities in the axioms. It would be like taking a theory in chemistry, and saying that I have an axiomatic theory of chemistry where you end up in some situations with tables and chairs, and I’m going to assign properties to tables and chairs in my axioms of chemistry. Like, you can’t do that. The axioms have to apply to the fundamental constituents. But people like Deutsch and Wallace try to do this, they say, well, look, we have observers in the context of many-worlds. They must behave as if the probabilities are the Born probabilities. That’s what rational decision theory means in this context, that’s what we mean by probabilities in this context. Well, so I agree that you have to give – this doesn’t work. Probability. Well – it doesn’t work. I mean, and I talked in my podcast with Curt, I don’t know if I want to rehash all those arguments. Yes, yes, yes. But these arguments are all logically circular, right? Because you can’t say, well – I mean – because you’re using the word should. You should be a rational observer. I don’t know what that means. In many-worlds, there are countless, innumerable parallel worlds with countless copies of observers doing all sorts of things. All these arguments must have a starting point, right? I agree that none of them can get something from nothing. But you can’t derive probability from – none of them can get soup from pure stone, okay? Exactly. Right. But to be fair, there’s a huge precedent in the history of physics for making the fundamental constituents of your theory as simple as possible, even impossibly simple. Atoms in a vacuum, right? Agreed, yes. A bunch of particles going – and then somebody might say, well, but that doesn’t work because you don’t have tables and chairs and trees in your fundamental ontology. And you say: No, but that’s a misunderstanding. We actually don’t need that at all. All of that can be derived. All of that can be explained from these very simple constituents, right? I mean, I think that’s the goal. Now, I agree that to explain the experience of the observer, it seems like there’s something missing. There are some missing additional constituents. And maybe, I feel like I’m talking in circles, and maybe we are at this point. But I think one place where you and I strongly agree is to say that you can ask that question, and I can’t give you an answer, or that there’s no known answer at this point. That’s an improvement over saying you’re not allowed to ask the question. Good. Yes. Let me quickly go back, because I think there may have been… I’m not sure it was a misunderstanding, or if it was just that you’re going a different route. But you said that a theory doesn’t necessarily need to specify chairs as fundamental constituents. I agree. Yes. And I also agree that axioms should be simple. Yes. And I completely agree with that. Yes. So an Everettian might say, you don’t have to specify the branches as fundamental constituents. They would say that branches are like tables and chairs. Right. But here’s the problem, right? You have this fork that represents a serious problem for the many-worlds approach. If branches are fundamental, we can assign probabilities to them in the axioms. But then you’ll run into all these secondary problems about preferred basis and so on. If you make branches non-fundamental, you won’t be able to put axiomatic probabilities on them, because they are not fundamental objects. I’m not saying branches can’t be emergent. Chairs certainly can be emergent tables. But then you can’t specify probabilistic features of those non-fundamental things in the fundamental axioms. You’re stuck between a rock and a hard place, either you give them axiomatic probabilities, but then they have to be fundamental to be things you can specify in the axioms, or they’re emergent approximate things, and then the axioms can’t touch them, can’t assign probabilities to them. And that’s why people don’t give all these rational arguments and decision theory for probabilities just for fun. They’re doing this because they no longer have the ability to put probabilities in the axioms anymore. So they have to take them somewhere else, but you can’t do that, for all the reasons you and I agree on. So I don’t see this as just a pesky feature of the many-worlds approach. I actually claim that the Stone Soup problem is best-case scenario. It’s like I don’t think it survives even Stone Soup. I think that once they try to add all these ingredients, they show it to the townspeople, and the townspeople go, that’s not soup. It didn’t work. Right? So I think that’s actually a very serious problem, and that means the many-worlds approach, and I haven’t seen any viable version of the many-worlds approach that overcomes these problems. And that’s why if it’s off the table, if we look into it and find it doesn’t work. So look, Scott, if you’re coming to this car dealership and you’re saying, you know, I’m here for the car dealership because my friend Curt brought me, but I’m walking, you know, I don’t really, I don’t really drive a car. Well, I don’t know that the car dealership is really going to work. We really have to bring somebody who actually wants a car. And that’s fine. I mean, you know, but, but certainly what you can’t say is that all these other cars are good. If they were, you would have taken a peek at one of these other cars. Yes. Yes. To switch metaphors. I mean, it’s like I can listen to somebody, you know, explaining all the serious and enormous problems plaguing democracy, and you know, I agree with this person. Right. And that still doesn’t mean that I’m persuaded by monarchy or communism or any other system. Right. You know, that still, that, that’s not enough to make the sale for me. Right. There’s this thing, you know, like this, this system is the worst regardless of all other systems. Right. You know, I feel, you know, you know, we, you know, actually know quite well, you know, how to use quantum mechanics in situations where decoherence is strong. Right. Agreed. You know, so, you can say, like, you know, once there are lots of records of something, you know, everywhere, once the information about whether this qubit is a zero or a one has spread into the environment, into the air, into the radiation flying away from us at the speed of light, then, you know, most of us can agree that there’s something real there. Right. And I think even many people who call themselves Copenhagen or instrumentalists will agree at this point that this is real, right? This is, this is now really, you know, this is a real element of reality, even if nobody thought about it or nobody knows about it, you know, it really exists, right? You know, the whole difficulty is when you’re not in that situation, right? When you have branches that can interfere with each other in the standard picture, when you have non-separable stochastic dynamics, according to your picture, right? Then, then we, then we don’t know, you know, how to say what’s real, right? You’re kind of asserting that there is, you know, there’s a basis where something real is happening, but then you can’t really tell me what it is, in the sense of giving me trajectories. And you know, I’m not sure that that’s a sufficient improvement over what I could say before I learned this, which is, yeah, something real is supposed to be happening there. And I can’t tell you what, other than write these equations, write down the wave function, you know, from which I can calculate the probabilities of different things I’ll see when I look. Scott, why is providing trajectories for you so important? You should know Jacob has been on the podcast four times to delve into his technical theory, as well as debunking quantum myths. Scott was also working on debunking quantum myths as well, but he also talked about consciousness and AI three times here once with David Chalmers and twice solo. Links in the description. Well, because in order to improve on the perspective of standard quantum mechanics, right? Like, if I just wanted to say that, you know, there’s this wave function, you know, that gives me probabilities, I already knew how to do that, right? I didn’t need Jacob’s picture for that, right? If I wanted to make a somewhat stronger ontological claim, well, there, you know, the photon really goes through one slit, or goes through the other slit, even when I’m not looking, well, well, now I want to know more. I want to know, you know, you should be able to give me an equation for this photon, right? At least tell me, given that the photon was going through this slit at this time, what’s the probability that it will be, you know, at this other place at this other time, right? If you don’t know that, then, you know, you haven’t really told me anything about the photon, you know, I wouldn’t say that this improves on what I already know about it from standard quantum mechanics. So let me say a few things about all this. The first is this set of phrases about, well, when the records, which are kind of hard to define, are far enough away in the environment, and there are enough of them, and they’re far enough away, and moving fast, like, we all agree, all I’m saying is that in a good physical theory, I think I teach general relativity, I teach Jackson’s electromagnetism, right? I mean these are theories I can be much more precise in. And when we say that, oh, and things get far enough away from enough records or something like that, I mentioned, you know, Zurek’s quantum Darwinism approach, about selection, that kind of thing, at some point, somewhere, we wave our hands, and then it seems like, I’m just trying to get us to be honest and precise about this, right? I think precision is possible. If precision is not possible, if it’s not possible to make quantum mechanics more precise about this, if it’s not possible to remove this very, very great ambiguity, that’s interesting. It would be interesting if that’s not really possible. If it can be reduced to some axiomatic formulation or interpretation or what have you, that’s also interesting, right? And I think that’s worth investigating, even if not everybody feels the need for it. Now, let me say additional things. Up until now, for me, who got a Ph.D. in topics that were very close to or very near string theory, to make the only game in town argue that this is the only game in town. But what I just want to say is that I’ve provided a list of criteria for what I think a reasonable, applicable, empirically adequate, unambiguous, and unambiguous predictions interpretive framework should be like, at least a schematic picture of the classical limit, not an endless list of speculative metaphysical assumptions. Like, these are just minimum requirements that we might put on a theory. I didn’t even add Occam’s razor, but you can add that as well. There are all these things that you can add. My argument is that none of our approaches meet even these minimum requirements. If they did, I mean I’ve spent different points in my career here working in other different interpretive frameworks. As I said, I spent a long time in conditional interpretations, which Scott will remember when I said a lot of weird things about conditional interpretations many years ago. I’ve arrived here because this meets those requirements and the others don’t. Now, it doesn’t do everything you might want. There are aesthetic criteria you might want as well. You might want to be able to say what happens in all circumstances, and what exactly are the trajectories taken. I think the main reason why there is

The debate about interpretation is that for every interpretation, you can state a clear condition that that interpretation fails to meet. In your case, that condition is that for every element the theory postulates to be real, you have to give an equation that shows how that element evolves over time, if it's really fundamental. But Scott, the reason why I think this is an aesthetic thing is that we don't hold any of our other physical theories to this standard. All of our other physical theories contain things that we don't have the ability to describe. And we don't know what the equations are to apply to them. If you take general relativity as a great example of that, we have access, if you think of spacetime as a four-dimensional manifold, we have access to an incredibly thin slice of the entire spacetime manifold. Most of spacetime will be and remain forever inaccessible to us. You can very quickly run into situations where the unobservable components of our various physical theories, we cannot describe what's happening with them, we can't, you know. I don't really agree with this analogy. I mean, I would say in GR, you can put in a space like a slice. Once you put it in, you'll have this field equation that tells you how to evolve it forward, except when you run into singular situations. Or you hit Cauchy horizons, or you hit, I mean, there's, yeah. That's right, that's right, or different, but as you know, in many circumstances, you can just propagate this equation forward, right? And as you know, if you believe in standard quantum mechanics, you say, you know, once you tell me what the wave function is, you tell me what the Hamiltonian is, then I can just take this psi and propagate it by e to the minus iht psi. I can, you know, propagate this equation forward, right?

In your case, you're telling me that something is real, that is, you know, the locations of these particles in space, or you know, the slit that the photon goes through, and you're not giving me an equation of evolution for that thing that you postulated to be real, which well, you know, as I said, every interpretation has a loophole or something that it fails to satisfy, and this is the appropriate one for you. But I don't see that that's necessarily, you know, any worse than the Everett interpretation which has no answer about the source of probabilities. Well, to be clear, I think it's a somewhat more serious problem when the full empirical content of quantum mechanics, which consists of the measurement probabilities, cannot be derived from you. I mean it's one thing to say that some unobservable features of the theory we don't have equations for, right? It's another thing to say that the observable features of the theory and the empirical content we cannot derive, right? I mean, that would be like saying, not that we can't make predictions, but what's outside, you know, our accessible light cones in general relativity, but we can't predict what's inside our accessible light cones in general relativity.

I mean, we can say that every interpretation of quantum mechanics has the property that to actually use that interpretation, you know, to actually connect it to the experiments that we can do, we need some auxiliary assumptions that look like, you know, the real world is incoherent. It has things like records and so on. So every interpretation will have a story of this kind that tells us where some mystery will come in. Right. But the problem, as we've mentioned, with the many-worlds approach is that that doesn't seem to be possible in principle compared to the worlds approach, as if it were a much more serious problem. So let me actually step back and go back to, I'll just say, suppose you went back, and you turned back the clock to 1923, 1924, the time when people like Pauli and Bohr and Heisenberg started to doubt the possibility of a physical picture of the things that are going on. Because at that time, people still thought there were particles going around atoms and things, right? There were fields that were interacting with particles. All this was happening somehow, there was an actual ontological picture. And people started openly doubting the possibility of any picture because nobody could come up with any laws that when combined with any clear picture would lead to the correct experimental predictions of quantum mechanics. Then Heisenberg started his search for matrix mechanics in 1925, in the spring of 1925, with a bold statement that we should abandon these pictures altogether and that we should do everything in a brutally instrumental way. And as you know, people believed that there were no effective laws, and that there were no laws that you could find.

You could tell an alternative history where the theory of stochastic processes was discovered, you know, much earlier than it actually was. Paul Majorov didn't publish his axiomatic treatment of probability theory in 1933, a year after Von Neumann's book on quantum mechanics. He published it in 1833. There were some backward causal loops and he went back and published his axiomatic treatment of probability theory. You know, Markov didn't first introduce the Markov matrix in 1906 in some obscure journal. But all this happens in the nineteenth century. People develop a strong probabilistic theory of stochastic processes starting in the nineteenth century. And then people start exploring non-Markovian processes and somebody mentions, what about non-integrability? And then comes 1923, 1924 and they go, well, I mean, we have these non-integrable processes. Let's try those laws. They try them and they get all the correct experimental results. They are able to derive this beautiful mathematical correspondence in the way that we took Newtonian mechanics and derived the Hamiltonian formulation, right? You can do things much more beautifully and elegantly in this Hamiltonian formulation. I think a lot of the interpretational questions that we ask today wouldn't exist, right? The measurement problem wouldn't have happened. If I imagine myself in that alternative history that I've drawn, I still ask myself, well, you know, what the hell is this non-integrable stochastic dynamics, right? What do we know? How does that even become dynamics at all, right? What are the transition probabilities? What are the paths that these particles follow? And then in your alternative history, if somebody like Schrödinger came along and said, look, you can think of it in terms of this wave of amplitude, right, as Schrödinger did in our history, then in that history, just as in this history, I say, oh, that's nice. That helps me. Right? As a useful picture, just like the Hamilton-Jacobi picture is a very useful picture, right? But it would immediately come along with all these strange puzzles like superposition and the measurement problem. But people would always say, they would say, well, well, this is a really useful mathematical picture. This is a really useful visualization. But ultimately, if we have any question about what happens when a measurement is made, we have this more mechanistic picture, just as in the Hamiltonian formulation. If you've been living in spacetime land for a while and you're confused, you are. That's always the problem of going back in history, right? Many-worlders will also say this constantly. They'll say, well, it's not fair that Copenhagen got there first, right? If only, you know, people had just accepted many-worlds in the 1920s, then this strange instrumentalist Copenhagen, you know, which diverted from which would have, you know, gained acceptance on its own merits and so on, right? Well, you know, well, you know, in this branch of the wave function, you know, history happens in a certain way, right? And then, you know, if you want to get converts to a new viewpoint, you have to meet them, you know, after they've learned everything they've learned from the previous viewpoint and show them why the new viewpoint is an improvement on what they can already do. I mean, and it's interesting that Schrödinger did that, if you read his fourth lecture on wave mechanics, what is it section 15, the interpretation of the generalized psi function. He presents a many-worlds picture in embryo, right? It's not actually that people didn't think of these things. If you read some of the early papers from that time, in the 1920s, people did. And some of them were imagining this kind of thing, but it wasn't accepted because it doesn't work. And what happened, it wasn't that Everett came along and found a way to make it work. Everett found a story he could tell which some people find incredibly compelling, but it's still not effective. Like the people who gave us quantum mechanics, they were incredibly clever. They didn't have everything. They didn't know that you could write the laws in certain ways, but they certainly thought about some of these ideas at the time and rejected them. But Jacob, the people who added more and more epicycles to the Ptolemaic model, they were also incredibly clever, right? You know, they were also, you know, trying to make things work. And you know, and they would say, well, you know, well, yeah, maybe, you know, you can imagine, you know, the Earth going around the Sun. But, you know, that doesn't work because we don't feel ourselves rotating. Yes, which we don't. It actually takes a lot of physics to explain why a pendulum feels the way it does. And the Everettians have a whole story, you know, in which Everett is like Copernicus, right? He's just giving this, you know, reinterpretation like, yeah, we know that we don't feel ourselves in all these different branches. But you wouldn't, you know, if that's what's happening. Well, that's what he said, actually, in response to Bryce DeWitt, because when Bryce DeWitt, the theoretical physicist who eventually maybe spoke to Everett in his letter and said, I'm not branching. Everett said, well, how would you feel if you did? And he actually made this Copernican analogy. The problem, of course, is that the Copernican story says that all the humans on Earth, if the Earth is, in fact, rotating and revolving around the Sun, then all the humans on Earth will see the Sun seemingly moving. And it predicts what all the humans will see. The problem with the Everett approach is that it predicts everything. It predicts every bit as if there will be copies of observers who see absolutely everything. And then you either run into a circular argument, well, the reason why we see the world that we see is that we will be stipulated to be the ones who see the world. It's a completely circular argument. Or you might say something like, well, what would a typical copy of an observer see? But typical is a matter of what's the most probable is a statement of probability. And then you find yourself in a circle about how to get probability out of the Everett approach? Like all this stuff doesn't work. And I think early quantum mechanics, the early people in quantum mechanics, you know, realized that at some level, this is not something that's ultimately going to work without slogans.

But look, history ended up turning out in a certain way. It's hard to know exactly what would have happened if it had come out differently. I would argue that if they had a physical picture, a simple physical picture, simpler than the Hilbert-Dirac-Von Neumann axioms with all the strangeness that you get from those axioms. They would have looked at the Hilbert space picture exactly as we look at the Hamiltonian phase space picture today as a very powerful mathematical device that we can use to do all sorts of amazing calculations and simplify things and identify certain kinds of interactions. But ultimately, when you run into any conceptual confusion, you can go back again to the physical picture in the Newtonian case to bodies moving in space, interacting with fields and in this picture to objects with configurations with more general laws. Now, I want to ask one more quick thing. You said they would maybe say something like, well, what are these laws? What are these conditional probabilities? What are these laws? The question of what are laws is, as Scott, I'm sure you know, a very hot topic in metaphysics today in metaphysics and philosophy of science. I don't follow enough metaphysics to know that, but okay. And that's okay. Nobody's perfect. I'm just kidding. But like, what is a law? Yes. Like, I mean, I don't know what Newton's law is. I mean, I know what the equation is, but I don't have any greater understanding of what it is for Newton, what does it mean to say that there is this law that takes the current configuration of the system and the infinitesimally early configuration or the equivalent of the current configuration, the velocity and then how does that work? And if you're talking to human beings about laws, that's a term introduced by David Lewis to refer to a particular view about the metaphysics of laws which is somewhat connected to David Hume, the philosopher's ideas about the nature. You know, what you're saying is that you don't believe in laws at all, because the notion of a law is a very strange one and strange laws are not primitive things. They're just. Tools that human beings use to summarize phenomena, you know, but the upside of all this is that, yeah, non-integrable laws are strange because they're different from the kind of time differential Markov style laws that we've been using for the last few hundred years. But that's just a historical contingency. There's nothing stranger about a Markov law or Newton's second law, I mean they're all strange. All laws are strange. They're just stranger because we're newer to this idea. Well, what I'm saying is not that law is strange. I'm saying that in a place where I would expect there to be a law in your picture, that is, for the transition probabilities, there is actually no law at all. Yes. In some cases, there's no law in your ghost in the quantum Turing machine. You introduced a great term for unpredictability that is not even probabilistic. You're referring to this book from the 1920s by the economist Frank Knight. You call it Knightian uncertainty. Yes. Right. Conditions where we can't even put probabilities on certain things. And it's interesting that this is certainly not unique to quantum mechanics. So here I can put on my general relativity hat. One conjecture about general relativity is that all reasonable spacetimes should do that. It's called global hyperbolicity from global hyperbolicity, which just means that you don't have Cauchy horizons, and the equations apply to everything and we get it. But that's just a conjecture, right? There are solutions to Einstein's field equation where you get Cauchy horizons. These are places where general relativity simply fails to give any further predictions about what will happen next. And you can't put probabilities on these things. They're not all black hole singularities. There are other situations where you get Cauchy horizons. So like the idea that it's possible that you could have situations where we can't do that. The theory doesn't give a prediction of what comes next. That's not a new idea. Well, look, you know, well, because you, you know, read Ghost in the Quantum Turing Machine, and I'm perfectly willing to consider uncertainty about initial conditions. Right. Right. Because, you know, that's the thing that, you know, in our experience, the laws of physics leave them unspecified. Right. I'm more hesitant to allow uncertainty in the rules of evolution. And that seems to be what you're doing. Yes. Okay. That's good. Although I will tell you that even in standard quantum mechanics, we are unable to assign probability distributions to a variety of things. You can't assign joint probability distributions to non-commuting observables, you know, like that. It all boils down to the same problem of multiple times or transition probabilities. It all boils down to the basic fact that we are cognitively limited beings. We're trying our best in the universe that we're part of, that we're physically embodied in. And we're incredibly lucky that we have a theory that allows us to make many of the predictions that we want to make. But we can't make every prediction that we want to make. And yes, that's a bullet I will certainly bite. I will bite that bullet. But I will say that anytime somebody comes along with a new picture of reality, it opens up potential new connections with new fields, and interdisciplinary connections, and new ways of thinking about old problems and potential new generalizations, and maybe new pedagogical teaching techniques. It even arguably opens up the space for us to rethink certain things that we've taken for granted. I mean, sometimes, you know, John Bell, and this is the only thing I'm going to say about John Bell here. You know, John Bell was very clear that having a physical model sometimes can tell you a lot about things that you thought were true, right? There was a prevailing idea from John Von Neumann that hidden variables had been completely ruled out. And although Bell wasn't the first to notice it, Grete Hermann noticed it almost immediately in the 1930s. Bell independently rediscovered this, rediscovered, this flaw in Von Neumann's proof because he had a model, Bohmian mechanics, which showed that there was a problem here. And of course, Bohmian mechanics also helped with the development, leading to the development of decoherence, which, I mean, that getting physical pictures can lead to rethinking things, including even things like classical theories, like Bell's theorem and related theorems. So I think that's also a useful thing. And you know, in my podcast interview with Kurt, we talked about the potential connections to rethinking how causality works. I think there are a lot of things you can do with this that aren't for everybody. But unless we identify some actual inconsistencies, some real problems, then either one can say that there's just an inconsistency, something doesn't work, or one can say that it's trivial or uninteresting or not useful to me or doesn't do better than things that I already like. And if we basically reach either one of those positions, if we don't reach the position of inconsistency, but we reach the position, well, maybe this doesn't suit me or I like these other things or it's trivial or anybody could say that or whatever. I'm actually okay with that because some people will find it satisfying and some people will not. And that's just the way the world is. Right now, I feel about your account the same way that I feel about category theory, for example, or calculus. Right. I have friends who swear by these things. This is the way to understand everything. And they will gladly take something that I know how to prove in one paragraph naturally, and they will give a proof using category theory that's 20 pages long. With lots of diagrams, all these diagrams. Right, with all these diagrams. I'll say, can't you see that this is much better, that this is more insightful? And I say, well, I guess it is for you. Believe it. Go in peace. Carry on. You know, you haven't yet sold me by showing what this can do for me. But, you know, I'm open to the possibility of that happening in the future. That seems like a great place to wrap this up. Yes yes. I'm still waiting for John Baez to tell me what the dagger-symmetric monoidal categories are supposed to say that's different from just translating something from quantum mechanics and then translating it back. Because usually, the insight comes from translating into a different field and then doing something in that other language that you couldn't do in the previous language, and then translating back. But as far as I can see, you just translate and then translate back without creating anything new. So I'm in a similar boat to Scott. And I think you and I talked about this off air Jacob. Yes, but let me put this properly. There are people who don't know quantum mechanics. And I feel incredibly sad for these people. They don't know what they're missing. Everybody should learn quantum mechanics. It's a beautiful theory. But there are people who work in statistics who don't work in quantum mechanics. And they have developed all sorts of incredibly sophisticated and interesting ways of thinking about statistics. And there's a barrier between them and people who work in quantum mechanics because quantum mechanics is formulated in this very different language. If you hand them a version of quantum mechanics formulated in the language of ordinary probability theory, suddenly some things that might be difficult to apply from statistics become suddenly applicable. And this, I mean, this is very new. It's a case I can imagine you making, but I would say that you haven't made this case. I haven't. No, I agree. This is speculation. And as I said, this is completely new. And if you want to show that this is actually a better way to introduce quantum mechanics to people who haven't seen it before, you need to show that by showing all the phenomena of quantum mechanics, you can explain them better this way. I don't see that you've done that. But that's the thing that if you did that, then yes, that would make me want to go back and take another look at this vehicle. You know, it's rare in science or in philosophy that one finds oneself with a blank page to fill. I find that incredibly exciting, especially in a theory as old and well-tested as quantum mechanics. So I'm enjoying this opportunity. I feel like we've already made a lot of progress, and I'm very excited about the things that we hopefully can explore moving forward. Okay, quantum mechanics courses usually begin either with the double-slit experiment or the Stern-Gerlach experiment and then try to explain that. I would welcome a lecture on the double slit and/or Stern-Gerlach, but only without resorting to the usual Hilbert space picture, only your picture. That would be awesome. So I sent you a document, Kurt. Yes, yes, you already have that in paper form, and so I'll put it on the screen. And Scott, it was great talking to you again. Jacob, thank you so much. This was so much fun. This was fun, and Scott, it's always a pleasure to chat. We hope to find more opportunities. I enjoyed talking to you Jacob. Okay, it's good to see you all. Yes, it's good to see you. I've been getting many messages and emails and comments from professors saying that they recommend their students to Theories of Everything, and that's awesome. If you are a professor or lecturer, and there's a particular featured episode that your students could benefit from, please share it. And as always, feel free to reach out. So my question was that you gave an earlier example about a CNOT gate, and then you used many-worlds to explain how you said some people find that easier. Do you have any other examples of situations where students get confused, and then you use a different interpretation to explain it? Not really. I don't usually use interpretations to explain conceptual points. I certainly talk about Bohmian mechanics when we're talking about Bell's inequality and the CHSH game, but that's partly just for historical reasons to explain why Bell was interested in this in the first place. I haven't yet seen a situation where Bohmian mechanics helps me explain something that I couldn't explain without it. I see. Because you were saying earlier, look, you're willing to use an Uber, which is any car to get from point A to point B, but it seems you're going to use an Uber as long as it's a Hummer, as long as it's the same car. Yes, I mean, usually when we're trying to solve a concrete problem, like what does this quantum algorithm do? We don't need an interpretation for that. We know what this computation looks like. Interpretation mostly comes in handy when we want to insert ourselves into the picture. New update! A substack has begun. The writings currently revolve around language and ill-defined concepts in addition to some other mathematical details. There's a lot being written there. This is content that's not anywhere else. It's not on Theories of Everything. It's not on Patreon. Also, the full transcripts will be put there sometime in the future. Many people ask me, Kurt, you've talked to so many people across theoretical physics, philosophy, and consciousness. What are your thoughts? And while I remain neutral in the interviews, this substack is a way to look into my current deliberations on these topics. Also, I thank our partner, the Economist. Whenever I share on Twitter, or on Facebook, or even on Reddit, etc., it shows up on YouTube, and people talk about this content outside YouTube, which in turn greatly helps with distribution on YouTube. Third, you should know that this podcast is on iTunes and on Spotify and on all audio platforms. All you have to do

He is writing theories of everything and you will find them. I personally benefit from rewatching lectures and podcasts. I also read in the comments that the total listeners also benefit from replaying. So, what do you think of re-listening instead on those platforms like iTunes, Spotify, and Google Podcasts, or any podcast program you use.

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