Theories of Everything with Curt Jaimungal - Harvard Scientist Rewrites the Rules of Quantum Mechanics | Scott Aaronson Λ Jacob Barandes

Episode Date: March 4, 2025

Join Curt Jaimungal as he welcomes Harvard physicist Jacob Barandes, who claims quantum mechanics can be reformulated without wave functions, alongside computer scientist Scott Aaronson. Barandes’ ���indivisible” approach challenges the standard Schrödinger model, and Aaronson offers a healthy dose of skepticism in today's theolocution. Are we on the cusp of a radical rewrite of reality—or just rebranding the same quantum puzzles? As a listener of TOE you can get a special 20% off discount to The Economist and all it has to offer! Visit https://www.economist.com/toe Join My New Substack (Personal Writings): https://curtjaimungal.substack.com Listen on Spotify: https://tinyurl.com/SpotifyTOE Become a YouTube Member (Early Access Videos): https://www.youtube.com/channel/UCdWIQh9DGG6uhJk8eyIFl1w/join Timestamps: 00:00 Introduction to Quantum Mechanics 05:40 The Power of Quantum Computing 36:17 The Many Worlds Debate 1:09:05 Evaluating Jacob's Theory 1:13:49 Criteria for Theoretical Frameworks 1:17:15 Bohmian Mechanics and Stochastic Dynamics 1:18:51 Generalizing Quantum Theory 1:22:32 The Role of Unobservables 1:31:08 The Problem of Trajectories 1:39:39 Exploring Alternative Theories 1:50:29 The Stone Soup Analogy 1:56:20 The Limits of Quantum Mechanics 2:01:57 The Nature of Laws in Physics 2:14:57 The Many Worlds Interpretation 2:22:40 The Search for New Connections Links Mentioned: - Quantum theory, the Church–Turing principle and the universal quantum computer (article): https://www.cs.princeton.edu/courses/archive/fall04/cos576/papers/deutsch85.pdf - The Emergent Multiverse (book): https://amzn.to/3QJleSu Jacob Barandes on TOE (Part 1): https://www.youtube.com/watch?v=7oWip00iXbo&t=1s&ab_channel=CurtJaimungal - Scott Aaronson on TOE: https://www.youtube.com/watch?v=1ZpGCQoL2Rk - Quantum Theory From Five Reasonable Axioms (paper): https://arxiv.org/pdf/quant-ph/0101012 - Quantum stochastic processes and quantum non-Markovian phenomena (paper): https://arxiv.org/pdf/2012.01894 - Jacob’s “Wigner’s Friend” flowchart: https://shared.jacobbarandes.com/images/wigners-friend-flow-chart-2025 - Is Quantum Mechanics An Island In Theory Space? (paper): https://www.scottaaronson.com/papers/island.pdf - Aspects of Objectivity in Quantum Mechanics (paper): https://philsci-archive.pitt.edu/223/1/Objectivity.pdf - Quantum Computing Since Democritus (book): https://amzn.to/4bqVeoD - The Ghost in the Quantum Turing Machine (paper): https://arxiv.org/pdf/1306.0159 - Quantum mechanics and reality (article): https://pubs.aip.org/physicstoday/article/23/9/30/427387/Quantum-mechanics-and-realityCould-the-solution-to - Stone Soup (book): https://amzn.to/4kgPamN - TOE’s String Theory Iceberg: https://www.youtube.com/watch?v=X4PdPnQuwjY - TOE’s Mindfest playlist: https://www.youtube.com/playlist?list=PLZ7ikzmc6zlOPw7Hqkc6-MXEMBy0fnZcb Support TOE on Patreon: https://patreon.com/curtjaimungal Twitter: https://twitter.com/TOEwithCurt Discord Invite: https://discord.com/invite/kBcnfNVwqs #science #theoreticalphysics Learn more about your ad choices. Visit megaphone.fm/adchoices

It is not every day that I see a claim for a new formulation of quantum mechanics. That's exciting. For almost 100 years, quantum mechanics has splintered physics into competing interpretations, each with a different consequence for reality. In this theolocution, Harvard's Jacob Barandes, co-director of the graduate studies department, has developed a revolutionary framework called indivisible Stochastic Processes that suggest there is no fundamental wavefunction. He's joined with Scott Aronson as they dispute other interpretations like many worlds and bolems, as well as discussing do quantum computers get their power from other universes? If so, why don't quantum computers provide speed ups for all problems instead of just a specialized subclass? In Jacob's view, what actually

gives quantum computers their power over classical computers is indivisibility, and that's because the class of indivisible processes is simply larger than the class of all the kinds of processes used by classical computers. My name is Kurt J. Mungle and I use my background in mathematical physics to analyze various 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 for a huge treat. I've had a preview of

the questions you have for one another and I'm excited to be hosting you both. Thank you. Welcome Scott Aronson and Jacob Barndes. Great to be here. It's lovely to be here. Thanks for the invitation. Nice to see you, Scott. Yeah, good to see you too, Jacob. Does the benefit of quantum computing provide evidence for many worlds? Scott. I would say that there is a philosophical argument that, for example, David Deutsch has made, right, that says that, and this was very closely related to why he invented the idea of quantum computing in the first place in the early 1980s that says, well, look, suppose that you use a quantum computer to factor a 2,000-digit number.

Deutsch said this very explicitly in the 90s. Suppose you run Shor's factoring algorithm and it factors the number just vastly more efficiently than we think it can be done with any classical algorithm. And he says, if you don't believe that quantum reality is in some sense a vastly larger thing than classical reality, then where did the computation happen? Where was it done? And so I think that that does get at, you know, why quantum computing is so interesting to many of us in the first place, right?

That it seems like this really, really hard to fake test that, yes, there is some kind of reality to these abstractions that we're talking about that do involve these vectors and this exponentially large space. But now, I would say the philosophical part, the part where people can reasonably disagree with each other, is should you describe that in terms of parallel universes or not? Is that the right language to use for talking about this vast thing? The problem is that,

what do we mean by something being a different universe, right? Usually, you know, we mean that it is evolving independently from us, right? It is, you know, its own separate thing. I mean, in the TV shows and the movies, there's always some portal or some wormhole by which you can visit the other universe because, you know, if there weren't, then what would be the plot? But somehow it is separated from our universe.

But the trouble is, if it's separated, then for that very reason, we don't see the evidence of it. Like if we do a quantum computation, then at the point when two branches are really separated, then we don't see the interference between them. We only see our branch. And to the extent that you do see the interference, as you do in Schor's factoring algorithm, for example,

or other algorithms for quantum computers, then you could say the very fact that these things could interfere means that they never really established separate identities as parallel universes at all. They were all just part of one giant interfering quantum mechanical blob. So I think that that's a philosophical objection. But I do agree that quantum computation would be dramatic evidence that the state of the universe is this vastly bigger thing in some sense than what classical physics posits for it.

That is a huge deal. Now, I get annoyed when people will take the latest quantum computing experiment like what huge 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 its Willow chip this past 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 like the theory said. And, you know, if you agreed with the philosophical argument that that

can only be explained by many worlds, then you should have believed that way before this experiment. Right? And if you didn't believe it, then you still shouldn't believe it. So it's not like these experiments are changing things that much, but there is this philosophical argument that I think is at the heart of why we care about quantum computing, why Deutsch invented it in the first place. Briefly, before you respond, Jacob, I want to know, what would David Deutsch say to your

response about that the universe must be independent, so how would it manifest in this universe? Oh, what would he say? I mean, Deutsch would say that you don't even need quantum computing to see the obvious truth of the many-worlds interpretation. He would say that even the two-slit experiment from more than a hundred years ago, where you see interference between two paths that a photon can take, even that clinches the case and can only be explained by, you know, the many-worlds interpretation and everyone else is just in denial about it. And then he would say, okay, but for those who are too dense to see that, you know, building

a quantum computer may help them psychologically, right? It may, you know, make it even more undeniable, but he thinks you don't even need it. There's some very interesting history here, and Scott, I'm sure you're aware of this, but many of the people who are watching may not know, but Deutsch's development of quantum computing is really a fantastic example of how thinking philosophically and foundationally about physics in general and quantum mechanics in particular has borne tremendous fruit. I agree. My understanding is the story is that Wheeler had him sit down at a dinner with Hugh Everett

when he ever sort of came back out of retirement in the 70s. Yeah, I can almost see the building where that happened. Right. Yeah, yeah, yeah. And they sat next to each other. And at the beginning, apparently, Deutsch was skeptical or whatever, but by the end of the dinner, he was quite convinced. And then he, and just like Scott said, I mean, it's in the papers, it's kind of amazing, right?

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 is not shy about citing the Everett interpretation. It's like in the abstract and throughout the paper he's like, and this only makes sense under the Everett picture. And he says very clearly that one of his motivations for developing quantum computing is to make just completely clear that the

Everett approach has to be correct. What's interesting, and Scott, you mentioned this, this is exactly on point, the sort of modern ideology that is dominant among people who think about and work on the Everett approach, and this is typified by books like David Wallace's 2012 book the emergent multiverse Is that you really need? decoherence meaning the gradual disappearance of interference effects between the branches in order for

Macro world branches and distinct universes to emerge And and that precisely doesn't happen in the middle of a good quantum computation. Yes, that's what I'm going to say. Right, exactly. So, but my point is just that, like, this is, what Scott's saying is really that the standard way that most Everettians think about it. So the Everett approach doesn't really help you so much with quantum computing because those other universes, they don't exist precisely in the case when they're being used, so to speak, for a good quantum computation. And I'll just say a couple of things about this.

One is there are a lot of situations in quantum mechanics where if you take seriously a particular philosophical perspective, at first glance it may seem a little bit, you know, helpful revealing, oh, quantum computers in some circumstances can do things more efficiently than we believe is possible with classical computers and the actual existence of multiple universes seems like maybe this is what gives these systems their advantage. But then on further reflection, it gets kind of strange because if these universes are just really there, in some sense, whether in the microscopic case where, again, there's not agreement that we should be even thinking that way or in the macroscopic case, you might

think that you can get speed ups in far more circumstances, that speed ups would be far more generic. As Scott has at the top of his blog, his tagline, if you take one thing away from his blog, it's that quantum computers don't get speed ups because they're trying out all the possibilities at once. And that's very confusing because if you think those universes are there, you might just think you can get speed ups all the time. It's actually kind of amazing that you only seem to be able to get speed ups in very special circumstances.

And if those... So for me, this is almost evidence that we shouldn't be thinking that way. And Scott, you put this really beautifully. I forget when you said this, but you had this lovely quotation where you're like, these other universes are not quite as real as actual universes. They're not quite as... They live in some sort of, you know, intermediate regime between being real and being not real. Or it's Saralson who said that. But yeah, I mean, I've been, you know, banging my head against the pedagogical problem of

how to explain quantum speed up for 25 years, right? And you know, I like to say that like quantum computing is a weirder resource than any science fiction writer would have had the imagination to invent. It's not just classical exponential parallelism, but it's related. In order to explain it to people, usually we say, yes, you can create this superposition over exponentially many possible answers, but then you get only this tiny portal for observing something about it, 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 speed up is to exploit the way that amplitudes in quantum mechanics, being complex numbers, work differently from the probabilities that we're used to, in particular that they can interfere with each other. So with every quantum algorithm, you are trying to choreograph a pattern of interference where the contributions to the amplitude of each wrong answer are canceling each other out. They're interfering destructively. Whereas the contributions to the amplitude of

the right answer are all adding up. They're constructively interfering. That's not a thing that is, I can say that if you give me a few minutes, but that's not a thing that is easy to translate into any pithy English phrase that we had before it. Right, right. Well, let me say a couple of things about this. One is the use of branching tree-like graphical structures is not unique to quantum computing.

That's right. If you're teaching a course in probability theory, we draw outcome trees, probability trees, decision trees, all the time to explain things. So I mean, I completely grant that drawing, you know, trees of branches is a pedagogically useful exercise. But so I want to then jump on the point that you made, which is that the key to quantum computing is the ability to exploit the fact that these amplitudes are complex and that the different possibilities interfere and you can use them to sort of cancel each other out. Interference is this very important property

in getting quantum computing to work. So, and actually I think that's kind of key because if you think it's all about parallel universes, you might think you get speed ups all the time. When you realize that it's actually requires this very delicate use of interference, then you realize the class of problems you're gonna be able to get speed ups for

is actually not gonna be totally obvious and will require a lot of careful thought. Right, we've been working on it for 30 years. Exactly. Trying to figure out what exactly is that class. Right, right. You know, but... I...

Go, yeah. I mean, I kind of like the analogy between the Everett interpretation and just, you know, Darwinian evolution, where you have, you know, these populations of species that can interfere with each other, namely reproduce sexually. But that's only when the population remains relatively close to each other in its DNA sequence. Once you have two isolated subpopulations that get far enough apart from each other, then they're never again going to merge. Then they really have branched off into two separate branches, what biologists would call

two different species and what in quantum mechanics we would just call separate Everett branches. Yeah. Yeah. It's a lovely metaphor and very helpful, especially pedagogically. Of course, then the question is, what is interference and how do you explain interference to students if you're not you know and and and if these aren't really worlds if they're not really macro worlds yet because if they were well-defined macroscopic realities they would have decohered them we can't

do quantum computation with them so like what are these things we're dealing with and there's a kind of quietism that one practices let's just not talk about what they mean let's just 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 the goal for somebody is just to build better and more efficient quantum algorithms, to build quantum algorithms that can do more things, I think this is probably fine.

But of course, we all come into thinking about quantum theory, quantum foundations, and philosophy of physics for a variety of reasons. And I think there are definitely a lot of people who would like a more physical picture that underlies this. And this is where my approach sort of comes in. And I'm happy to say a little bit for those who may be unfamiliar with my work and how it connects with this power of quantum computing.

But let me... Totally on board with wanting to understand the world, and not just predict the outcomes of experiments. So, yeah, and then we can talk about how to do that. So, Jacob, before you go on explaining your new formulation, I want to hear Scott Aronson's rendition of it. Yes. But first, before Scott Aronson,

before you speak about Jacob's theory in order for Jacob to say yes or no to you, I want you to tell the audience then where do you think this efficiency comes from in quantum computing or where does the interference occur? If it's not these many worlds, if you're not a believer in many worlds, then where do you personally, Scott, think the efficiencies come from? I mean, a quantum speed up, you know, really, if you think about it, just means classical slowdown, right? It means that our quantum computer can do something that cannot be done efficiently by any classical algorithm, right?

And so what it really means is just that of all of the different ways that you might have imagined that a classical computer could efficiently simulate this quantum computation, none of them work. Right? And so by its nature, you know, there's not going to be just one explanation for that, right? There might be a different explanation for every possible, you know, way of simulating the thing classically, right? It's fundamental. Quantum speedup is a negative statement at its core. None of the classical approaches work. And so I think that the exponential size of quantum states, when we write them down in the usual way, is part of the story.

The entanglement of the qubits is part of the story. If there were an entanglement, then there would be a fast classical simulation because I could just keep track of the state of each particle separately in my classical computer. The interference is a huge part of the story because if it weren't for interference, then I could just use a classical computer with a random number generator, and that would do the simulation. It's really the combination of all of these elements,

the exponentially large Hilbert space as we call it, the entanglement, the interference that is ruling out all of the different ways that you could simulate this thing efficiently with a classical computer. Actually, you even need more than that. There are examples of quantum computations, for example, what we call stabilizer quantum computations, that have all of those elements and yet still they can be efficiently simulated by a classical computer for another reason, right? So, it's, but you're, you

know, if you combine all of those elements, exponentially large Hilbert space, entanglement, interference, then at least there's a chance that you're going to evade any way of simulating what you're doing efficiently using a classical computer. I think that's really what's going on. Okay. Now let's hear your recapitulation of Jacob's theory.

And just for a background for the audience, Jacob has a theory on or a formulation of quantum theory, a reformulation of quantum theory that gives an ontological account as to what's occurring. And it's been covered on theories of everything this channel at least three times. And I'll put each part on screen right now and the links will be in the description. Hi, everyone. Hope you're enjoying today's episode. If you're hungry for deeper dives into physics, AI consciousness, philosophy, along with my personal reflections, you'll find it all on

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Kurtjaimungel.org. Yes. So it is not every day that I see a claim for a new formulation or interpretation of quantum mechanics. So that's exciting. I tend to think that the basic options on the table, like Copenhagen or many worlds interpretation, Bohmian mechanics have pretty much been around since the 1950s, with minor rebrandings, combinations, elaboration since then.

Jacob is saying something different. Actually, when I talked to physicists about this, they said, oh yeah, Jacob Berandes, isn't he the guy who has something that's kind of like Bohmian mechanics? But I think it's not, I think I understand better than I did a month ago what is going on and that it's not quite that. Basically, just to back up a little bit, I would say what Jacob wants is to give a new account that reproduces

all of the empirical predictions of quantum mechanics. He's not going to change the experimental predictions. That's what it means for something to be an interpretation or formulation instead of a new physical theory. But he wants to do it with using something that looks more like classical mechanics, where you have particles that will have, or some objects that will have just definite classical configurations,

such as just the positions of particles in three-dimensional space. That puts him in a long tradition, and people who have tried that, including Bohmian mechanics. But the difference is, in Bohmian mechanics, you retain the wave function, the quantum wave function in your ontology.

So you still have this gigantic wave of amplitudes, just like many worlds does. But then you use that wave to guide the particles along trajectories. All right, so you have, let's say, particles that have some actual positions in three-dimensional space, and then those particles are guided, they're nudged around by the wave function in a way that's been

precisely constructed to reproduce the predictions of standard quantum mechanics for what would you see when you measure those particles. Right? Okay, so that's that's Bohmian mechanics. Now Jacob, a contriest, is going to get rid of the wave function, to not have the wave function in his ontology, and he's not going to have the trajectories for the particles either, not in general anyway.

What he's going to have is just, like in Bohmian mechanics, you pick a basis, so you have what we call a preferred basis, which could mean positions of particles in three-dimensional space or something like that. Then at any given time,

he wants to say the particles have a real position. The system has a real configuration, a real state in that basis, even if you don't look. But now, what he's going to give up on is trajectories for these 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, what is the probability that they will be in this other configuration at time t plus 1?

Right, or we're only going to be allowed to ask that question in the cases where it would normally make sense. In quantum mechanics, we would say that it's in superposition. Jacob would just say, well, you're allowed to ask at any individual time, what is the probability that the particles are here or that they're there, but you're not allowed to ask given that they're here now, what is the probability that they are there then? So this is what he means in talking about indivisible stochastic dynamics. So he wants to reformulate, say, what in the standard picture would be the Schrodinger equation that

governs the evolution of the wave function as a differential equation that is governing the stochastic evolution of this, what we might call a hidden variable, except it's not really hidden, right? The classical positions of these particles. So he's going to give you an evolution equation for that, but it's not divisible. In the cases where in the standard account,

we would say that quantum interference is happening, you're not allowed to ask for transition probabilities. You're not allowed to ask for the whole path that is followed by these particles. Or given that they're here now, then what's the chance that they're there then? It's just all one indivisible stochastic evolution. So that's my understanding of it and now Jacob can tell me what I got wrong. Thanks. Yeah. So let me just say a couple of things about this. The first is there is a kind of a paradigm that we all work under.

It's a paradigm that I grew up learning about when I took my university courses in quantum mechanics. You know, I ended up doing 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. And so there's a certain way of thinking about quantum mechanics and thinking about how it's supposed to work, starting from the textbook axioms, the so-called Dirac for Paul Dirac, von Neumann from John von Neumann axioms that you get from respectively 1930 and 1932, that's written in all the textbooks.

And these axioms are quick to summarize. Every quantum system has a Hilbert space, every system has a quantum state defined 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 is evolving through time in a way where it's not mutually exchanging interactions or information with any other systems,

evolves according to a rule called smooth unitary time evolution, which can usually be for some systems expressed as differential equation, that's the Schrodinger equation. And then you have all these measurement axioms, all these axioms about what are the mathematical objects that represent the things that we can observe about the system, how do we get probabilities out of the theory for those measurement outcomes that's called the Born Rule,

and then we're supposed to collapse the quantum state to reflect the result of the measurement and give robust, 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 paradigm I call the wave function paradigm that quantum theory begins by talking about wave functions or some suitable generalization of wave functions that live in Hilbert spaces. And then we're supposed to sort of figure out

what we're supposed to do from there. When you start from this picture, it sounds very complicated to construct a different picture because you start with all these Hilbert space ingredients are like, well, we've got a Hilbert space. Hilbert space is a kind of vector space. Vector spaces can be described using what are called different

orthonormal bases. So what you have to do is you have to pick an orthonormal basis for some reason and then from that orthonormal basis you have to do this and do this and you have interference and you have the Hilbert space and you have the Schrodinger equation which has to be translated back. I mean when you start from this paradigm it makes everything sound very complicated. And you see this all the time when you're talking about you know different paradigms for a theory that from maybe a newer paradigm, you know, a new paradigm can look very complicated when one attempts to express it in terms of an older one, or even very difficult

to understand. And there's this whole theory, this whole story in the history of philosophy of science about the incommensurability of different paradigms. So let me just start from the beginning, okay? I don't believe that paradigms really are incommensurable, but you know, that's a separate discussion we could have. That's fine. I won't take a stand on this. I'm not ideological about this. I'm only saying that there is in the history

and philosophy of science, this idea that paradigms can be incommensurable. I won't take a stand on it, yeah. What I would say, Jacob, is that, you know, if you say that this is, you know, a new paradigm for quantum mechanics and that, you know, we shouldn't try to express it in terms of the old paradigm, 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 that we know about, you know, including, you know, Shor's algorithm, Grover's algorithm, quantum teleportation, and show how they have simpler explanations in terms of indivisible stochastic dynamics.

And what you won't be allowed to do when you do that is say, well, just translate it back into the usual Kett notation, the usual Hilbert space picture, and then just invoke this theorem that says that it has an equivalent representation in my picture. Because if that's going to be your answer, then you're telling me that in practice, I should just continue using the standard picture,

and I should continue to think in terms of it. If you want me to switch to thinking in terms of a different picture, right? And I should continue to think in terms of it, right? If you want me to switch to thinking in terms of a different picture, then you have to show me how all the specific successes of quantum mechanics that I care about actually are simpler to explain, present in terms of that new picture. So let me say a couple of things about that first, and then I'll get to it.

Yeah. So one of the things 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 an ability to reconstruct the standard axioms and the Hilbert space picture in its regime of validity. And say a little bit about why it has this sort of limited regime of validity and how one might extend that. But I'm not saying, to be super clear, I'm not saying that we should stop using the Hilbert space picture any more than if you want to study

a problem in classical physics using the action angles formulation, or you want to do Hamiltonian Jacobi theory, or you want to help yourself to canonical transformations or canonical perturbation theory, or one of a million other things that you might want to do visualize trajectories in phase space. you're going to use the Hamiltonian

phase space reformulation of classical physics. So if someone comes along and says, oh, you know about Hamiltonian, the Hamiltonian phase space formulation, you've got Qs representing positions or some generalization of positions and Ps representing some generalized notion of momenta, the so-called canonical momenta, and you have this phase space picture and you've got 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 like ability to do changes of canonical variables, these so-called canonical transformations that can scramble what the whole picture looks like. And someone comes

along and says, actually, I think that there's a physical picture here. The thing you're describing is an object moving around, maybe it's stuck to a spring or a pendulum. And the person says, well, okay, that's a useful picture that's helpful, but will it help me do canonical perturbation theory? Will it help me do action angle variables? I would say, well, no, we have this beautiful Hamiltonian framework for doing that. You should use that still. Or another example is we have general relativity. So general relativity, this is,

I've been teaching jealousy for 10 years, but when we do orbital calculations in like, you know, sending spacecraft around, we still use the Newtonian paradigm. It's still very useful. I understand the point, Jacob. I mean, but general relativity, at least, you know, there is some class of situations where, you know,

this new language is better, right? So I think in this case, you at least have to show that there is some class of problems, of quantum mechanics problems that are better treated using your new formulation than using the old one. Or else other people could justly say then what is the point of learning it? Or even can only be treated using your formulation.

Right, right, right. So let me start with that. I want to get to explaining what it is, but let me just quickly jump to that, okay? So, if what you're doing is, again, developing algorithms for quantum computing, I don't think there's no obvious sense in which this gives you the ability to do anything differently from what you would do in the old paradigm. The tools that we have are extremely good for these situations. You're studying tabletop kinds of systems where the Dirac, Vitamin, and Axioms work

really great, but those are not the only kinds of systems that physicists are interested in. So, physicists are interested in applying quantum mechanics in astrophysical situations to early universe cosmology, and people are trying to apply quantum mechanics in the context of quantum gravity. They're trying to do quantum mechanics applied to black holes. They're trying to do quantum mechanics, you black holes. They're trying to do quantum, you know, and now you're in situations where the Dirac-Vitamin axioms

are very ambiguous about what you're supposed to be able to say. And this is where I sort of cut my teeth. I mean, again, I did my PhD here at Harvard in high energy theoretical physics. These are the kinds of problems that I studied. And I was often very confused about, you know, when we were legitimated in using the textbook version of quantum theory. And again, I wasn't the only one.

I mean, we would routinely run into situations in which people would say, well, can we do this particular thing? Does this make sense? We have this sort of nonlinear dependence on this or that and what's going on with black holes and people were genuinely confused about how to apply quantum theory to these situations. But these are situations that are different from what you'd find in table-top experiments. It'd be like saying, why do I need general relativity on Earth? Neutroning gravity works fantastically.

Well, there are systems that are beyond Earth where we may need a better theory because things get more extreme. Let's agree that if you could say something new about quantum gravity, that would be great. No argument there. Now, if we think of you as, you know, you are sort of hawking a new product at the foundations of quantum mechanics bizarre, right? Well, okay, the quantum gravity theorists are potential customers, right?

I am also a potential customer, right? I am in the market for even just a reformulation of existing quantum mechanics that would help in coming up with new quantum algorithms, right? Or understanding for which problems quantum computers will give a speed up and for which they won't. If someone can give me that, that's great. I'll buy it. Right. But so there's like a lot of things that one might wanna do with reformulating quantum theory. One is, you know, the existing approaches that we have, the existing, if you want, formulations, interpretations.

Honestly, I know that the terms don't exactly mean 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. Okay, but at some point that might actually be the crux. Are you making a new ontological claim or are you just giving a new mathematical reformulation?

Both. But both. So I'll be very clear for everybody, it's both. There's both an ontological statement about what is actually out there and also sort of a new mathematical formulation. And to be clear, like when Paul Dirac introduced the path integral in his paper in 1932, Lagrangians and quantum mechanics, he was just curious how Lagrangians show up in quantum mechanics, this classic idea of Lagrangians, because the theory at that point had been developed only in the Hamiltonian formulation.

And it took 10 years before Richard Feynman came along and incorporated this idea into his PhD thesis. Then six more years in 1948 in reviews of modern physics. And when he spelled out the idea for a broader physics audience, and even then he said in the paper, there's nothing you can do here that you can't do using ordinary methods. It took decades for people to realize

that there are situations in which you would never wanna do things in the canonical Hamiltonian formulation. In particular, things like Yang-Mills theories, right? And the standard model is formulated in the Lagrangian path integral formulation for very good reasons. Sometimes ideas do take a while to come to fruition. And another good example is David Bohm's work. So, decoherence goes back to David Bohm's work in 1951. He was doing foundational, trying to understand foundational questions of the measurement process in his textbook, Quantum Theory from 1951. And in Chapter 22, he studies

the measurement process. And famously in Section 22.8, Destruction of Interference in the Process of Measurement, he introduces this idea of how decoherence works. You know, and it takes decades for that eventually to become a major part of how we think about quantum computing, right? I mean, decoherence, decoherence timescales are now a thing that people just talk about constantly. Things do take time, but you have to begin with a new idea. And I think it's just interesting when you have a new idea that isn't obviously wrong or inconsistent. So the first thing I'll just say is, like, certainly if there are any inconsistencies or problems with this new formulation, that's, you know, fair game.

But if the only thing is to say, well, I don't know what to use it for yet, I think that's actually pretty good. We don't always know what to use things for initially. In that case, let's delve into the idea. So I still want to know, did I get anything importantly wrong in my summary of what you are asserting? So, okay.

One, you made a comment earlier, does this thing make any new predictions? I'm gonna come to that point. Another, you talked about whether this thing has any trajectories in it. I'm gonna come to that point again. But broadly speaking, I think that if you're starting from the Hilbert space picture and trying to explain backward how to go from the Hilbert space paradigm, if you want, to this paradigm.

I think broadly speaking your picture is right. But I think for people who are hearing this for the first time it sounds very complicated. Let me just explain. I mean I'm just thinking of someone who already knows quantum mechanics and what is the quickest route to get them to understand. But you are asserting. Right, right, right. But again it'd be like starting with the Hamiltonian phasespace formulation and saying we're going to pick a canonical frame. I mean, what choice do we have?

We have to meet people where they are. Right, absolutely. Well, the choice is, you know, for new people coming to quantum theory, right, who aren't, you know, yeah. But, okay, so let me just start from the beginning. I listed all the Dirac-Vinom and axioms. They involve all these exotic ingredients. We're not going to do that. Here are the starting assumptions. Here Aumen axioms. They involve all these exotic ingredients. We're not going to do that

Here are the starting assumptions. Here are the axioms. The first is that a physical system has a configuration and that Configuration comes from some menu of configurations that we like to call if it's a nice continuous set of possible configurations a configuration space Not a physical space and this is this is we call this the kinematical part of the theory, and it's very similar to what you would do in a classical theory. Classical theory, you begin by picking up an appropriate set of, or space of configurations that you want to use to model the system in question. If you want to study particles, you would pick arrangements of particles in space. If you want to do fields, you would consider configurations of field intensities localized

at places in space, or in a discrete system like in a computer, you would pick arrangements or patterns of on and off switches and memory registers or whatever. So that's model dependent. You pick what you need for the model you wanna do, and that's the first axiom. We just pick a set of configurations.

The second is the dynamics. The dynamics means the dynamical laws, the mathematical laws that describe how configurations are supposed to change. And, you know, in physical theories up till now, you know, under this sort of Laplacian paradigm, the idea is we have some kind of differential equation that takes our present configuration and then tells us later configurations in some smooth way. Usually in the language of some giant difference equation. We don't do that. The new dynamical postulate is there's just this family of conditional probabilities, right?

This collection of conditional probabilities of the form, given that the system is in such and such configuration at this conditioning time, this is the conditional probability the system will be in such and such configuration at a particular target time. Conditioning time has to be a special time, right? We'll talk about, yeah, that's what we'll talk about. So this is a sparse set of conditional probabilities. They're not completely comprehensive, they're not, you know, they don't exist for all conceivable, you know, things you might, you know, pick for target and conditioning times.

In particular, the conditioning times are a little bit special. That's what makes these a sparse set of conditional probabilities. And because they're special, these processes are called indivisible processes. And indivisibility just means that there's like a failure of iterativeness. You can't just take some process over some amount of time and just act repeatedly with some map or rule that then gives you for each successive time because that would assume that every single time is a time at which you can restart and condition on.

If you give up that assumption, you have a simpler collection of conditional probabilities. These processes entered the research literature in 2020 in a pre-print by Simon Mills and Kevin Moody, in just a throwaway comment in figure six in their paper, which was a beautiful review article on classical and quantum stochastic processes that I highly recommend. It's on PRX quantum,

it's available for everyone. You can also get the archive version of it, whatever. And then ultimately it was published, like I said, in PRX Quantum. That was next year. So 2021, this is a relatively new idea. It hasn't been explored by people who work 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, broadly speaking. I mean, it's a little more subtle than that. But even, you know, when people have considered traditional non-Markovian processes, like in the

textbooks, when people think about non-Markovian processes, they imagine these very, very intricate structures with these towers of higher and higher order conditional probabilities that are all different from each other. They get very, very complicated. They're very difficult to formulate and specify. And that's why people, when they can, typically try to write down Markov processes. These indivisible processes are even simpler than Markov processes. They fail to be Markovian, not because they're so, they're more complicated than Markov processes, but because they're actually simpler than them. They're so simple that people just kind of stumbled over them and didn't realize that

they existed. And you're talking right now with people who work in the theory of stochastic processes and they're like, oh, yeah, well, that's actually like a new idea. And new ideas are always exciting, right? When you realize there's something pretty simple that's been sitting around and people didn't notice it, that, I mean, there's new mathematics to be done, there's new ways to think about things. And remarkably, you know, so you might have just 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 it appears to be exactly right to give you that quantum theory. So again, the two assumptions are configurations and configuration spaces, and the dynamical laws are these sparse conditional probabilities that generically will fail to be indivisible. Sorry, will generically fail to be divisible. They're called indivisible processes.

And then there's the mathematical correspondence, a map, that's very analogous to the map between a classical Newtonian system and the Hamiltonian phase-space formulation, which is this very mathematically abstract formulation with all these symmetries and all these calculational tools. And that correspondence is called the stochastic quantum correspondence, and it lets you go between the two pictures.

So, you know, once you avail yourself of this map, you can just systematically reconstruct all the axioms. But now you know where they come from, and you get these very beautiful ways to understand where some of the weirdnesses of quantum theory come from. So let me take, for example, the complex numbers. When you want to use this to cast a quantum correspondence,

what you find generically is that it only works when the complex numbers are introduced at this step. So, or some algebraic structure that is algebraically equivalent or isomorphic to what we call the complex numbers. And that's actually really nice. It's close, like you need some negative numbers. Yeah, absolutely right, right.

But you could imagine, for example, represent the complex numbers with like two by two matrices or something. Right, absolutely. Right, right. But you could imagine, for example, represent the complex numbers with like two by two matrices or something like that. Yeah, but my point is the stochastic process you start with doesn't have any complex numbers in it. It's written in the language of just ordinary old fashioned probability theory, right? There's no Hilbert spaces, there's no comp.

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, when you want to write it in this Hilbert space picture, what you find is that in most cases, the complex numbers are necessary to write down that description. So this gives a very satisfying explanation

of why we need the complex numbers in quantum theory. The- I do think there's something nice that is going on there. Like in the axiomatic reconstruction of quantum mechanics, which is another thing that people have, you know, Lucien Hardy and many others of, you know, Giulio Chiribella have tried for many years, you know, which I would think of as a somewhat different game from interpretation of quantum mechanics. Yes, yes. I should say that those approaches, for example, Hardy's approach, right, he has

this, and I recommend this to everybody who's listening because it's a beautiful paper, it's quantum mechanics from five reasonable axioms. But these approaches are explicitly instrumentalist. They're part of this larger idea called general, a generalized probability theories, the other GPT, the original GPT, which is just to treat quantum theory as kind of an instrumentalist device in which agents or observers do measurements on things. So these are not intended to be physical interpretation. So this, to be super clear,

this is a very different kind of a picture. But let me go further, right? One question people have is like, you know, why interference, why linear, where do these features come from? And interference is this very bizarre, as we were talking about earlier in this conversation, it's something about,

if you take kind of a many worlds-ish kind of attitude, we've got different realities, but they're not really different realities yet, because they're not macroscopic and they haven't decohered yet. And somehow they're complex numbers and they can cancel each other out, right? But like, what is going on physically?

There's kind of no like clear physical picture here. In that, but because you have this correspondence now between 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 to this picture, what you find is that it's literally just the indivisibility. If you take a process and you start from some conditioning And if you translate interference back to this picture, what you find is that it's literally just the indivisibility.

If you take a process and you start from some conditioning time and go to some target time, you'll get some statement about the conditional probabilities the system will end up where it does. If you by hand just demand that we can slice this process up and write down the kind of nearest approximate divisible counterparts of this process. You just divide it by fiat at this intermediate time and then try to treat it as a process with a division in the middle, you'll get the wrong answer.

But what's fascinating is that when you compare the correct answer with indivisible dynamics to the wrong answer, you just subtract the two, subtract the predictions of the one from the other. The formula that pops out is exactly the formula for interference. Interference now has an interpretation. It's just if you want to go to a formalism,

not an indivisible formalism with laws that are hard to apply, but you want to go to this nice, beautiful, clean, smooth Hilbert space formalism in which you can do time evolution in steps, you use unitary time evolution, it's nice and divisible, it looks Markovian. Then the cost you pay, the indivisibility doesn't go away,

it manifests as this very abstract, very confusing kind of interference. But now the interference has like a physical meaning that it didn't have before. That had better be the case, right? Oh yeah, of course, that had better be the case, right? Oh yeah, of course, it had better be the case. We produced quantum mechanics. Absolutely, but let me get to your question about...

I think we're pretty much on the same page about what is being asserted. And if we are, then I can now explain, I think very crisply, why as an interpretation of quantum mechanics, why I am not buying this product. I have two points to make first that may change your view on this. So let me get to these. Okay. Okay.

Okay. So the first thing before, let me just say, because you're reconstructing the axioms of quantum theory, you don't have to go through one at a time and check that every single thing comes, oh, you can, and some people do that. So you've got a couple of things. One is this question about there are no trajectories. I want to be a little more precise about this.

Okay. The statement here is that there are, it's not that we're saying that there's no trajectories. What we're saying is the theory doesn't supply you with a precise description about what trajectories are taken. So the system at any given moment, there is a probability distribution for the configuration of the system and these probability, these distributions are, where the system is, is changing. In some circumstances, you can make conditional probabilistic statements about where the system will be. In other cases, you can't. But this isn't to say that the trajectories aren't there, just that we don't have the

tools from the theory to tell us what they're aren't there, just that we don't have the tools from the theory to tell us what they're doing. Now, you could say this meets them on observable, then we can run into a discussion about, should a theory have observables in it? Let me pass this over to Scott. Yeah. Stan, are you committed to the existence of trajectories,

even if you can't calculate their probabilities? Yes. You are? Yes. Okay, so you say that there really are trajectories. Yeah, the system is really doing things. I mean, yeah. It's just that your theory doesn't tell you their distribution.

Correct. Yep. Okay. That is different from what I thought. Excellent. Good. I thought that you were denying the existence of the trajectories. No, no, no, no, no.

There are trajectories. The system is following some path we just don't know what it is. If you had a God's eye view and could see the entire universe unfolding, you'd see all these zany trajectories. You wouldn't need probabilities, you would need quantum theory, but we are limited, epistemic limited beings. Okay, but it's not just that your theory doesn't tell us the trajectories, it's that, you know, within the empirical framework of quantum mechanics, it would seem we cannot know them, even in principle. Literally, only God can know them. That's right. I take the experiments. Experiments seem to indicate that when you do a measurement,

you get one result. The result is obtained probabilistically, and there are certain things that we cannot know, like trajectories of systems. And my approach just says, nature says that. Why don't we just believe nature? As you know, on Theories of Everything, we delve into some of the most reality-spiralling concepts from theoretical physics and consciousness to AI and emerging technologies. To stay informed, in an ever-evolving landscape, I see The Economist as a wellspring of insightful analysis and in-depth reporting on the various topics we explore here and beyond.

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get a special 20% off discount. Now you can enjoy The Economist and all it has to offer for less. Head over to their website, www.economist.com slash Toe, T-O-E, to get started. Thanks for tuning in and now back to our explorations of the mysteries of the universe. Nature says that, why don't we just believe nature? Okay. Okay. So then that is a very key difference from Bohmian mechanics, let's say, where Bohmian mechanics will just say, among all the choices that we could possibly make for distributions over trajectories that would

reproduce the predictions of quantum mechanics, we are going to make this one particular choice, right? So, Bohmian mechanics means you're committing to a specific choice. And one of the central objections that I have always had to Bohmian mechanics is, well, why that choice? Why not a thousand other equations that I could have also written down would have been empirically indistinguishable from that one. Agreed. And so you're saying, okay, well, there is some distribution over trajectories, right? There is some, you know, as there would be in the linear mechanics.

And you're just going to be completely agnostic about which. Right. So to be clear, we're not providing a probability distribution over trajectories. That's kind of the thing. Right. You're not. You're not. I understand that. Excellent. Yeah. Okay. Yeah. But this isn't, I mean, so one objection one can always raise if you're not supplying

individual trajectories. And I did a lot of early work in the modal interpretations. Okay. Modal interpretations, the failure to provide trajectory information can lead to ontological instabilities that are very severe, where macroscopic systems can fluctuate between cat alive, cat dead, cat alive again in ways that are sort of uncontrollable. And so what you don't want is for the inability to specify trajectories to bleed into macroscopic systems. But what you can show is precisely because as systems get bigger and bigger,

they have more and more and more of these division events that just arise from the interactions of the environment. That for macroscopic systems, you get a really nice clean evolution. When you work in terms of collective variables and appropriately coarse-grained degrees of freedom, you find that macroscopic systems, they do move in very predictable ways. Even though way down deep, their individual move in very predictable ways, even though way down deep their individual elementary particles or elementary constituents, whatever they are, are behaving in ways that can't be assigned within the theory specific trajectories. So it's very important that we close the gap between kind of the unpredictability of the

trajectories for microscopic things and the emergence of nicer trajectories for big things. And this is something I'm very sensitive to, again, because of my early work in the modal interpretation. So I just wanted to say something quickly about the trajectories, and I'm glad we touched on that. The other thing I wanted to say was this question about, does this make different predictions? So the Dirac, Vondelman axioms are ambiguous about what should happen when you've got very large systems

that you want to treat quantum mechanically, right? This is the heart of- Systems include us. They include us, but short in your cat, Wigner quantum mechanically, right? This is the heart of- Systems include us. They include us, but Schrodinger's cat, Wigner's friend experiment, right. And so there's just an ambiguity and a particular- I mean, in some sense, as long as the cat or the friend or whatever is external to you, right?

As long as you are willing to treat it as just a collection of atoms, you know, even an enormous one, you know, evolving by Schrodinger evolution, then it is unambiguous what to do. But if you yourself are part of the system, I think that is when the empirical problem arises. I mean, I think a way to put it,

and I have this flow chart that maybe Kurt can attach, but I call it the Wigner's Friend flow chart. It's just basically like in the Wigner's Friend thought experiment, which again, if people haven't heard about, the super quick summary is there's now two observers. Very important there's now two. Hugh Everett, who first introduced it in the literature in his long form thesis in 1956, he phrased it as two observers. In the simplest case, one observer, Wigner, is outside of a box that is sufficiently sealed

for the duration of the experiment that we can pretend that nothing leaks out of the box or goes 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 this Wigner's friend is going to measure, or do a measurement process on. And the question is, now that we have two observers, there's this ambiguity. Do we activate the collapse or the measurement axioms? Do we not activate them? Do we activate them for everybody or for nobody? And you can just construct a detail.

When I have this conversation with Vigner's friend, people tend to dodge and weave, right? I'll say one thing and then they'll go one way. But if you just draw a whole flow chart and just say, here's the flow chart, here are all of your options, 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 all of them end at some kind of either problem or they end at some kind of interpretive sense. If you believe that Wigner's friend on the inside in fact really does collapse the quantum state by this measurement, then you run into the measurement problem, right? To head on into what counts as measurements, what doesn't count as measurements.

If you believe that collapse collapse happened but it wasn't because of the measurement, then you're talking about what a dynamical collapse or some other theory about why collapses happen. If you don't believe that the overall wave function is collapsed, then either Wigner's friend did in fact have a result. There was in fact a result despite the fact that it's not reflected in the overall wave function, and that is by definition a hidden variables approach. And a lot of physicists implicitly take this approach if they don't want to be meta-worlders.

They're like, well, we just have to be perspectival. There are different perspectives. You know, a vigner on the outside assigns one wave function, the vigner's friend on the inside has a definite result, but this is literally a hidden variables approach. Or you deny that there was in fact a definite outcome, and you're either embracing that more than one outcome has happened and that's kind of a many worlds type ontology

or that nothing happened, that without, that victims from the inside somehow didn't yield anything at all. And then you're embracing some kind of anti-realism which is gonna be radically self undermining. And those are your options. You have to pick something. And I know that, you know,

you can sort of try to not, but it's just sort of steering you right there. I am explicitly embracing the option that the overall, well, on the Hilbrough space side, we would say the overall wave function. In the stochastic side, we would just say that there's just ongoing indivisible stochastic process happening that isn't broken. That's what's going on for the overall system. And at the same time, Wigner's friend did have a definite result. So you can think of this, if you want, as a hidden variables approach, although, as Scott pointed out, these variables are certainly not hidden to Wigner's friend, and they're not extra or additional variables because the wave function is not a physical object.

These variables are the only things there are. So I'm explicitly embracing that part of the flow chart. And that makes a prediction different from the Dirac Phenomenaxioms, which just either run into the measurement problem or ambiguous about what's supposed to come out. For the benefit of listeners, I think we should say that, you know, the trouble with using the Wigner's friend thought experiment to get predictions is that at the end of the experiment, the Wigner's friend doesn't actually have a memory of what happened, which we could use to test this prediction, right?

So like by the time it comes to, we asked the friend at the end, what did you experience, right? And then we write it down and we publish it in a journal. Then we all know how to do the calculation for what the friend is going to say. Is this going to follow the usual Bourne rule of quantum mechanics? Unless there's some dynamical collapse thing going on or something of that kind. But otherwise, you're just going to see

the same quantum mechanics that we've known for a hundred years, right? If there's any empirical difference, it can only be in what Wigner's friend is experiencing while the experiment is underway. But, you know, once it's done, they've got no memory of it. That's what we have. Just for the benefits of the viewer, I'm going to place the image that Jacob was referencing on screen. And then I also want to bring up that I asked you, Jacob, the last time, hey, what's the difference between Wigner's friend's experiment or thought experiment and the Schrodinger's cat, except the cat is now a friend? Yeah, they're basically the same thing. It's just a question of like, is this,

are we worried about just a large system being placed in superposition? Are we worried about the fact that it's alive? Or are we worried about the fact that it's conscious? And that like, in some sense, we could be it. Yeah, it sounds like it's just that cats can't usually report experimental findings. Right, you can just sort of heighten the dramatic stakes by going from like just a really large object

to a cat that's meowing, you know, to a friend who you could actually talk to. A cat that could take data and report it would be Vigor's friend basically. Someone wrote a hilarious comment which said, no Kurt, you're wrong because cats are never a person's friend. Well that's clearly wrong. Yeah, I don't think we can agree on that. Or that cats never treat humans as their friends, something like that. Well, I mean that's, I guess how we know. I mean, cats can be friendly but on their own terms.

That's the difference from dogs. Right. Let me just quickly say about this comment about we all know it would happen. Actually we don't know it would happen. And the reason I say that is, according to the Dirac-Vinam and axioms, if you read the axioms one way, then there in fact is 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 do in principle interference experiments or even do it reverse unitary and reverse the system to where it started. But the Dirac-Vinod axioms, they say that when a measurement is done, then things collapse. And if you take that seriously, then you can't do those operations.

You can't do interference experiments on Vigners on the box. You can't undo the procedure unitarily. And so this is the ambiguity. And I think what you're basically saying is, which is what most physicists do, is we're going to resolve that ambiguity in favor of maintaining unitary evolution, but that strictly speaking goes outside the dirac varnum axiom. So when a physicist says this to me, they're like, we don't need all this philosophy, we don't need quantum foundations, you know, but in the Wigner's Friend Thought

experiment, we're going to take this prong of the fork. They're explicitly saying that they're now outside of the boundaries of the diraclino axiom. They're making a claim that goes beyond the axioms. And then as far as I'm concerned, they're already halfway there, right? Like once you agree that the diraclino axioms are ambiguous or incomplete or insufficient

for this experiment, well, then you're on my playing field. I, this is, now we just have to give an account that's consistent of when we're allowed to do this and when we're not supposed to do this or justify it. If the drag line of axioms are not available anymore, if we've gone beyond them, then we need new axioms, right? Because if you're outside of your axiomatic framework, you're just flying around 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 allow us legitimately and honestly to be able to make the statement that you just made. So the audiences here has been watching since the beginning and knows Scott is in the market. Scott is a working quantum mechanic who actually wants to buy from you, Jacob.

He just wants to make sure that you have something that's worth buying, but he wants it. So now Scott probably has some objections like I would buy from you, Jacob, but A, B, and C. So what is it? Yeah. So at some point in this podcast, I did want to say why I think I am not currently buying this product. You know, I might revisit it in the future, if it, you know, and I'm very happy for Jacob to hawk this product to other people, but I can explain why I, why you have not closed the sale with me today. And the reason is, if you are telling me that there are particles that have real positions

in space, and now you're also telling me that those particles have trajectories, but the trajectories are unknowable by us. From quantum theory, you can only get this indivisible stochastic dynamics. That just tells you, we're not allowed to ask. So for example, if I am Wigner's friend in the experiment, I cannot use this to predict, given that I am having this one experience at one time,

then what is the probability that I will have a different experience two seconds from now, right? I can't actually use it for that, you know, it is unknowable by me, right? Well, guess what? That's what standard quantum mechanics told me. It told me it is unknowable by us. I feel like at that point, I might as well just say that what is knowable, what is within the ambit of physics to talk about is the wave function, which is what most views of quantum mechanics have been saying for a hundred years. Right? Like, I haven't sufficiently improved over that. Right? You know, for me, you know, to say, let's say in the double slit experiment, to say that, you know, we can improve over, you know, just having 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. It means saying something like, okay, well, really the photon goes through one slit or the other slit and I can tell you the path that the photon will take, which is exactly what the Bohmians claim to do. If you're not going to say that, if you're just going to tell me, well, these indivisible stochastic dynamics give you the probability distribution over where you'll find the photon if you were to measure it at any intermediate time. But if you don't measure it at the intermediate times, then it could be jumping around in some way that's only known to God.

Well, I feel like that's what standard quantum mechanics already told me. It already told me how to calculate the probabilities if I measure the photon at any specific time, and it told me that if I don't make the measurement, then I don't get transition probabilities. Just metaphysically asserting that, you know, there is this basis in which

transition probabilities exist, and I can't know what those transition probabilities are. You know, I can't know what the distribution over trajectories is. It just feels like an ontological commitment that is not paying rent for me. It is not sufficiently improving. I have a very strong belief.

I do want to know what is really out there in the world. I am not an instrumentalist. But I want to fit my ontology as tightly as possible to what is actually observable or what is at least in principle observable. Because I think the history of physics has given us so many examples where people confuse themselves by, let's say, reifying things like the general relativity, the coordinates, or the choice of gauge,

and things that don't actually make a physical difference, the global phase of the wave function. Again and again, the right answer has been try to just cut out from your ontology things that are not observable even in principle. Have an ontology that is as tightly fit as possible to the set of all things that could in principle be observed. And whatever my reservations about the many worlds interpretation, and I do have reservations about it, but at least it tries very hard to do that. It tries to say,

look, the wave function is the encoding of everything in principle that's observable, so that's what we're going to take as our ontology full stop. It is the wave function, and if we don't have to add anything additional to that, then we're not going to do that. And Bohmian mechanics, of course, does try to add something additional, and it tells a very specific story. Of course, one can then object, well, why that story as opposed to a 100 other stories, but at least it is a story. At least there's a clear story that we can stare at and poke at and see if we like it.

Now, I feel like we are adding additional ontology without adding a story that goes with it, in Jacob's view. That is a thing that you can do, but I don't see that I'm going to get something from that, that is worth the price of admission. At least not for me, not right now. But I would say, go in peace. If this helps for quantum gravity, that would be awesome. 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 like, you know, until something like that happens, that I'm just going to say, you know, I pass on this product, go in peace. So I have a couple of points to make about that. Yeah. So just first, a couple of like technical aside. Sure. At one point you said, well, Vigner's friend on the inside knows the result but then doesn't

know what he's going to be doing in two seconds from now. That's actually not right because the measurement that Wigner's friend does generates a division event and the division event is a place at which you can then make conditional probabilistic predictions from that moment. So the scenario that I had in mind implicitly is that let's say Wigner's friend is in a superposition of two mental states and then we do a Hadamard operation on that. So we do some interfering operation or in your terms some indivisible operation that maps us from one superposition to a different one and then the issue is that in normal quantum

mechanics we would not get transition probabilities. That's the scenario that I was looking for. That's fine, right, exactly. Yeah. But for, you know, Wigner or you or anyone doing measurements like regular life, you're going to be able to make those predictions and those comport with what we see.

OK. I understand that. I mean, that's because real life is pretty decoherent. Exactly. But let me now get to a couple of the items you brought up. And let me just say, first of all, before we even get started, not everybody has to agree that this is the way to go. I'm not selling this to you personally, Scott,

although it would be lovely if you liked it. We're all looking for different things, right? Like I said, and when you're teaching quantum mechanics and we just sort of snow over students, we stupefy them by saying, here are the axioms, and the students look on gawking, and they're just like Hilbert spaces, linear algebra, density matrices,

self-adjoint linear operators, you know, POVMs, and you know, you render them in a state where they can't even like, even be able to ask questions about why. I mean why I only introduced those things as needed. But, but you know, I mean, so, so of course, I'm also in the market for better pedagogical ways of teaching quantum information, you know, to students, I would love that. But it sounds like even if I believed in your, you know, philosophical commitments, sounds to me

like I would still have to teach the students about Hilbert's pieces and unitary transformations and all those things, because how else are they going to do the calculations? Yes, agreed. But there's a difference between saying I've got forces in Newtonian mechanics that push on things, and then through like a sequence of mathematical transformations, I can turn that into the Hamilton equations of motion or the principle of least action. And then by contrast, showing up the first day and just saying Hamilton's equations of motion

or principle of least action with Hamiltonians, I mean, like there's a total pedagogical difference there, but let me put all that aside. So let me also, so let me add one other point which I think is important. You know this old joke, right? That these two campers and they hear a bear and one of them starts running

and the other one starts putting the shoes on and the person's like, what are you doing? You can't outrun a bear. And the person's like, I just have to outrun you. I'm not proposing here that this interpretation or formulation is going to satisfy everybody. And I'm not saying that it's necessarily the final word. 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 have to be modified in some even more profound way than is specified by this approach. But the question is, is this at least an improvement over the other interpretive or formulations that we have? And I have a clear set of reasons why I think that is the case. So if someone is coming to me and saying, we've got enough interpretations already, why do we need another one? I'm just gonna sit back and sit on many worlds, or I'm gonna go recline on Bohmian mechanics, or I'm gonna recline on Copenhagen or whatever. What I'm telling you is that those are

not true safe harbors, right? They're giving us a false sense of security. Here is a list of criteria that I would argue are required of any good theoretical framework in physics or formulation. And certainly for quantum mechanics, even apart from any aesthetic judgments or preferences. One is the thing has to be empirically adequate, right?

It has to make predictions. The predictions have to agree with what we're seeing. That's just the first item for, you know, all the kinds of systems that we're interested in quantum mechanics. So empirical adequacy is the first. The second is, it shouldn't be vague. You know, if someone asks you a question

and they just sort of dodge and weave and they're vague and, you know, I don't know what we could say, but we kind of know when we see it, we'll use our expert intuition, like that's vagueness. The third is it shouldn't be unambiguous in making predictions for certain kinds of systems that while may be practically difficult to study in principle, one could study, and this is again, like macroscopic type systems like the Wigner's Friend setup, there should be at least a schematic in principle story to be told about how the classical world is

supposed to emerge. It doesn't have to, I mean, obviously getting all the precise details is going to be very difficult. It's very difficult to do all the details and explain how even classically, classical deterministic kinds of dynamics emerge from classical statistical mechanics. But there's at least like a schematic story about how that's supposed to work.

And then the final thing is it shouldn't depend on a long list of what I call SMHs, speculative metaphysical hypotheses or ad hoc extra empirical axioms in order to get it off the ground, a long list of epicycles. Like those are the things that I think we should reasonably require. And my view is that none of the interpretive approaches we have

meet those minimal requirements, right? And I can explain in detail why each of them doesn't. Bohmian mechanics has proved very, very hard to generalize beyond systems of fixed numbers of finding many non-relativistic particles. So it's proved very difficult to use it to understand how quantum field theories are supposed to work. And the standard bottle, our best theory of the fundamental reactions is written

in terms of quantum field theory. In particular, Bohm mechanics has a great deal of difficulty handling what are called fermionic quantum field theories, which don't have traditional configuration spaces of the kind that Bohm mechanics would wanna help itself to. Bohm mechanics- Pick up a new evolution rule,

even if it's a stochastic one. You may have to pick a preferred reference frame or things like that. That's what people do. I mean, look, here's maybe the core of my objection. I feel like Bohmian mechanics has all these problems because it tries to make a concrete commitment, right? And you're avoiding that just by not making a commitment

to what are the trajectories, right? Like as soon as you made that commitment, then you would have the same problems as Bohmian mechanics. Yeah, which, but so you're right. Bohmian mechanics attempts to write down, like very carefully written down complicated, some would argue gerrymandered stochastic dynamics in these sorts of situations.

This is the work of people like Sheldon Goldstein and so forth who've tried to generalize this when they need preferred reference for it. It turns out to be super duper duper complicated and it looks very sort of frankly ham-fisted, right? Cause it looks like they have a clear target that's replicated. That is not the product for me either, right?

But I mean, look, Jacob, once you have told me now that you are committed to the existence of trajectories, even if we can't know their distribution in principle, now actually your view sounds more similar to Bohmian mechanics than I thought going into this conversation, but it feels to me like boom minus minus. It is boom except you're taking away the specific commitment about the guiding equation

and you're saying who knows, which yes, you can do that. I even would have known before that that was an interpretive option that was on the table, even though I wouldn't have phrased it in terms of indivisible stochastic dynamics. Yeah, so let me just say, earlier on when you mentioned Bohmian mechanics, you talked about the physicality of the pilot wave. I should just note that when Bohm introduced Bohmian mechanics in 1952,

he did take the pilot wave to be a physical object. He's very clear about that in his papers. But, and there are still Bohmians who take that view. But I mentioned Shelley Goldstein, but Goldstein, Dürr, Zanghi, you know, they've embraced since the 90s a view of Bohmian mechanics in which the wave function is not a physical object, but it's an expression of what's called nomology.

It's a law-like expression, which actually brings quantum mechanics in some ways back to its roots. When Schrodinger introduced his undulatory or wave mechanics picture, he built his wave function out of Hamilton's principle functions, which are an expression of a certain kind of law-like thing.

Basically, he took the Hamilton-Jacobi function, stuck it into the phase of a function. He called that his wave function. And so in a way that's sort of bringing it full circle, there is a sense in which what I'm doing, like the nearest, the least squares approximation that I'm doing from existing interpretive frameworks is that it's most similar in some ways

to this nomological view of bohmian mechanics, but without the preferred foliation of space time, without a particularly gerrymandered set of laws, the laws are simpler. Without the timing equation, with a specific commitment of what are the trajectories, which to me was the sort of distinctive feature of Bohmian mechanics, that you make this commitment,

you're just taking that out and saying there are some trajectories, it is unknowable what they are. Okay, okay, we can do that. What this gives you is simpler laws and also greater generalizability, out and saying there are some trajectories, it is unknowable what they are. Okay? Okay, and what this gives you is simpler laws and also greater generalizability, because now you can apply this to basically any kind of a system. So the ability to generalize it is useful, but let me actually say something else here. So you have this paper from 2004, is quantum theory an island in theory space? But in this paper, you're like, could we have modified any of the features of quantum theory an island in theory space? But in this paper, you're like,

could we have modified any of the features of quantum theory to look for a different theory? Could we have, for example, written down a quantum theory that didn't use the complex numbers? Could we do a quantum theory where we modify this feature or that feature or this feature? And what I love about that paper is, you're not taking for granted

that nature has bequeathed unto us this particular, you're imagining maybe there could be a different kind of a theory out there. And it's worth trying to see where we can generalize quantum theory in anticipation of the possibility that maybe we'll have an experimental result that will require generalization of quantum theory. Or there are only so many things you can do when you begin from the Hilbert space formulation.

If you do too much or you do something that's it, because the problem is the Hilbert space formulation has this very delicate connection to empirical measurement probabilities. You have to go through a sequence of steps and through the Born rule and you get probabilities out. And if you just say, I'm just gonna to take a hatchet to the axioms, the Hilbert space, the Dirac-Vondeman axioms, just play around with them,

you get almost immediately nonsense, right? You get probabilities that don't add up to one or negative, stuff that doesn't make any sense because you're risking damaging this very delicate bridge or link to probability theory. If you start from a different axiomatic place, arguably simpler and fewer axioms that are more straightforward to explain to the newcomer

that are phrased in old fashioned probability theory, there's no longer a link you need to get to probability theory. And you could imagine generalizing the theory in ways that would have been difficult to imagine starting from the Hilbert space formulation. And, you know, I agree very much with the spirit of what you were doing in that paper. I believe in it. One advantage to reformulating a theory in terms of different axioms,

especially axioms that are less abstract and fewer in number and a little less delicate, with less delicate connections to things like probability theory, is that we have greater flexibility to consider varying them and constructing more general theories. And I think that's an interesting thing to do. If you're a student watching this and wondering, maybe I'll work on some interesting project, what can I do? Here's an interesting thing to do. How can we generalize starting from this new starting place. I was about to ask you, I mean, can you make good on that idea? I mean, yes, I can imagine it, but can you, starting from stochastic dynamics, give me any example of something that looks like quantum mechanics but is not quantum mechanics?

Yes, yes. Okay. Here's one example. I'll give you a couple. All right, tell me. Yeah. One example is these sparse conditional probabilities are only conditioned on one time.

They're conditioned on one time, one of these division times. One generalization would be, is there a theory in which we can condition on two times? Is there a theory in which we can condition on three or more times? These are now describing theories that where the, it's not clear the stochastic quantum correspondence works the same way. You don't necessarily get the standard Hilbert space picture. Now, arguably you can do tricks.

There's all these like tricks where you can take a non-Markovian model with conditioning on multiple times and write it in some bigger way. So it's possible that there's some way to write this still in the usual Hilbert space formulation, but you might not. So you're just putting this out as an open question? Yeah, open question. OK.

This is a thing people work at. And there are a lot of these open questions, right? I wouldn't even know how to have asked this question in the Hilbert space point of view, right? And so that's one example. I want to miss a couple of quick other notes from what you said. So one is this question about should the theory be phrased in terms of things that are more objective, should we have ingredients that we can't know what they are?

There's this long-running question about the role and place of unobservables in a physical theory. Should a physical theory contain unobservable things? And I know you don't subscribe to crass operationalism here, which is the statement that, you know, the only things that are physically meaningful, right, are the things that we can have some procedure or operation to go and implement or measure or work with. All of our physical theories at some place or other

contain unobservables that play some important role. I would like to believe that the moon is there, even when I'm not. Right. Yeah, I would also, and it would be nice to have a justification for believing that even if, you know, because again from Drak von Neumann, there's no, it's ambiguous but the moon is there, which is like a problem. On the other hand, you know, the global phase of the wave function of the universe, you know, if I have an account where it's not there, then I'm not sorry to see it go, right?

Yeah, but Scott, it's worse. Because it wasn't observable even in principle. But Scott, it's worse. It's worse than that. So now I know that if I were to ask you this, you'd probably not commit to this, but there are a lot of people who are committed to the idea that the objects in the Hilbert space picture,

wave functions, maybe apart from global phase, and these sorts of ingredients are like physical things in some sense that we should ascribe some notion of physicality or ontology to them. But the problem is there's actually this larger set of gauge transformations in quantum mechanics that actually, as far as I can tell, only goes back to 1999 in a philosophy paper by Harvey Brown.

He's at University of Oxford. And it's called Aspects of Objectivity in Quantum Mechanics. And Kurt, you can link to it because he does this on the very first page. He's a philosopher and he identifies on the first page a large set of gauge transformations that hold for all quantum systems. You can think of these gauge transformations as a generalization of a change, a unitary change of basis. These are gauge transformations in which you're changing the basis differently at different times. So in the differential geometric language,

which maybe not everybody watching this will be familiar with, but those of you, some of you may know, you can think of a quantum mechanism evolving in time as a bunch of Hilbert spaces strung together, like, you know, when you're stringing together, you know, popcorn on a string or something like that, right? Each Hilbert space is a fiber stuck to the string, and this string is time.

It's just, we call it a zero plus one dimensional manifold, it's just time. And there's a Hilbert space stuck to all the strings. And we can imagine doing an independent unitary rotation on each of the different Hilbert spaces. This corresponds in somewhat more conventional language to doing what's called the time-dependent unitary transformation. We act with a completely arbitrary time-depend dependent unitary transformation on the quantum system. And you might go, well, but that's not, that doesn't keep things in variant quantum mechanics.

What are you talking about? But it actually turns out that it does. So you can look at the beginning of this paper. As long as all of your self adjoint operators that represent observables transform in a particular way, just a so-called similarity transformation under the unitary, and the Hamiltonian transforms as what's called a flat gauge connection.

And again, this is all actually written out in Harvey's paper, although he doesn't use all this terminology, but that's what it is. Anyone who works on non-abelian gauge theories would immediately see that the Hamiltonian transforms in this very characteristic way. The theory is exactly invariant. Now what's weird about this? I know this is getting very technical but but this is a technical objection to try to take Hilbert space object seriously

Is that it means that state vectors can be infinitely remapped? However, you want and any trajectory in a Hilbert space that you thought was encoding some kind of invariant information about the system can be mapped to literally any other trajectory by these time-dependent unitaries. Well, it's clear that we can't reify the actual numbers, you know, in some particular representation, which is tied to our choice of basis and so forth. But I don't take any many welder, for example, or anyone who believed in the reality of the wave function to be saying anything quite that naive. Right, well, but it's tricky then

because then you have to get into the details of exactly what's being proposed. So when I talk to some of the, Kurt, I'm sorry, Kurt, you wanted to? Yeah, let me make this simpler for everyone. So Jacob, you're in the showroom, you came here with some clunker card that you want to trade in. Okay, and you're looking the showroom, you came here with some clunker car that you want to trade in.

Okay. And you're looking at the options and someone's coming up to you, his name is Jacob. And he's this- Also Jacob, yeah, got it. Sexy gentleman with this great shirt. And you're like, I'm not just going to be wooed by your smile, Jacob. So, okay, let me hear about the benefits. And then Jacob's trying to sell you. And I also want the audience to not take anything away from if Scott, you don't end up buying from Jacob by the end of this podcast. I mean, that'd be foolish. Most people have to look at a car or whatever seven times before they make a purchase.

Yeah, no, I mean, look, look, I've already decided I'm not buying. At this point, I'm happy. I'm happy to chit chat some more, but. Okay. The point is that there are two ways to go about selling. One is to talk about your own benefits, so Jacob of your car. The other is to talk about the detriments of the opponents. So Scott, you've come in with a car. You've also said you're not an instrumentalist.

You're not just caring about going from point A to B. You want to know what's going on under the hood. Yes. So Jacob is saying that, okay, whichever car, all the other cars here will give you some accounts as to what's going on under the hood. Some actually won't, but the ones that you're interested will give an account. They're giving a false account or an account that when you look actually under the hood, it disappears into dust. So firstly, Scott, what is the car that you're going to drive away from here? What is it that you're committed to so that Jacob can then say,

okay, well, let me compare my approach to that directly. I should actually say I stopped driving years ago. I didn't like it. I just, I walk or I take Ubers. My wife is a good driver, right? So, you know, so, you know, so it's all the, it's, it's, it's different cars on different driver, right? So, you know, so it's all the, it's different cars on different days, right? And it's similar in quantum mechanics, I would say, right? I mean, I know how to think, like a many-worlder, you know, and if you wanted me to like, you know, have an ontology that was as simple as possible,

then I would say it's going to look like a wave function that is evolving by unitary transformation. The hard part, of course, is how do I get out of that my subjective experience, which is related to how do I get probabilities out of this deterministic picture. But at that point, I feel like that's going to be entangled with, haha, entangled. No pun intended, yes. Yeah, with enormous questions, what is an observer?

What is experience? You know, what is consciousness? Right? And these were incredibly confusing questions long before quantum mechanics even came on the picture. Right? These, you know, a democratist, you know, asked about these things in 400 BC. That's why I called my book, Quantum Computing Since Democritus.

Right? That's why I called my book, Quantum Computing Since Democritus. I feel like if you take consciousness out of the picture, if you took our own observerhood out of it, you just wanted a picture of laws of physics evolving in which you would have things that looked like observers arising, not necessarily us, but you would have stars, planets, life forms, organisms that would argue about these things and publish papers about them. Then you can get all of that, as far as I know, just from the Schrodinger equation,

from unitary evolution, right? But then if you further want to account for sort of our own experience as, you know, being inside the system, then I would say, you know, that was a great mystery even before quantum mechanics, you know, the mind-body problem or, you know, or things like that. Quantum mechanics adds a new twist to that problem, adds a new dimension to it without quite resolving it.

Then if you wanted to be an instrumentalist, if you wanted to just say, or rather not deny the reality of anything else, but just say what is knowable is just what we can observe in principle, and everything else is speculation. Then you go all the way back to what Bohr and Heisenberg were saying in the 1920s to the Copenhagen point of view. Well, I like to say, for me,

Copenhagen is basically just shut up and calculate except without the shutting up part. It's just endless philosophizing about why you shouldn't ask these other questions. Of course, that's unsatisfactory to not be able to ask these questions. But we've seen in this conversation that even with in Jacob's view, right, even in this new view, when I asked what is what are the trajectories of the particles, you

know, I am not able to ask that of his theory and get an answer to that. So there always seems to be that this sort of thing that I'm, you know, either 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 guess that's what I'm driving home in. You know? All right. So let me just say a couple things about this. So the first is people who are watching this should read this just fabulous paper that Scott wrote in 2013. I think it was called The Ghost of the Quantum Turing Machine. Yes. Right. Like if you want to read something by someone who I guess doesn't call himself officially a philosopher,

but is one of the most interesting philosophical things that you've ever read, you should read this. Scott, we used to run a philosophy of science club at Harvard and we invited Scott to come and talk and it was just fantastic. I mean, it's so full of interesting ideas and like everyone should, it's great. I think you wrote that like post tenure, right? Wasn't that your like-

Yeah, it was like immediately post tenure. Right, it was great. So like to be clear, people should know Scott takes this stuff really seriously. He's not like one of these people who's like philosophy is a waste of time. I don't care about the mind body problem. Like I'm really glad to be having this conversation with Scott about all this. Okay. So let me, let me now say a couple of quick things. One is I really like at the end, how you like corrected yourself. You said, well, there are things I'm not allowed

to ask, but actually maybe in your approach, you're allowed to ask it, but the theory just doesn't supply you with it. I think that's a substantive difference. So in Copenhagen, you're explicitly not supposed to ask certain things. And when you go into a physics seminar, you have to learn pretty early on,

there's certain questions you're just not supposed to ask. If you ask them, people will groan and roll their eyes. That's not a very intellectually like vital attitude to have in an academic environment. If you want to ask about the trajectories, you're welcome to. If you want to think, are there trajectories? I'll say, yeah. If you're like, well, is there some way that I can infer

or deduce exactly what the trajectories are without doing measurements in the system? I would say, well, the theory doesn't supply you 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 that are filled with people,

billions and billions of people in them. 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 exist only when they fully decohered from our branches, and then there's no way ever to be able to test them. There's this grand conspiracy where the vast, vast majority of the ontology in the universe is completely and forever out of our ability to experience.

I wouldn't call it a conspiracy because the theory itself explains why we can't communicate with the other. Sure, sure, sure. It's just the linearity of quantum mechanics. It's just the linearity of quantum mechanics. It's just the linearity of quantum mechanics, right. A conspiracy would be if we had to contrive it specially so that we couldn't communicate. That's right. We don't have to contrive it specially. That's correct.

Any more than I would have to contrive it specially that you can't know what the trajectories are going to be without doing the measurements. But I'll tell you, I would rather have microscopic systems sometimes engage in trajectories that we can't specify as our thing that we can't know unless we do a measurement on them, rather than an infinitude of parallel universes containing in each one billions or trillions of sentient beings that we have. Like, you know, like maybe you'd maybe you prefer the many worlds ontology, although there are some problems with that. But I would certainly say this is certainly no worse

than that. Okay, now let me now get to the most substantive of the points that Scott mentioned. So Scott, you said, well, look, I can get all these things out of the Schrodinger equation, out of the wave function in the Schrodinger equation. So now I'm gonna turn this back to you. What are you saying that we can get just out of the wave function of the Schrodinger equation. So now I'm going to turn this back to you. What are you saying that we can get just out of

the wave function in the Schrodinger equation? I am saying that if I program my computer to simulate a bunch of quantum fields interacting according to, let's say, the standard model or something like that. Okay, well, first of all, I couldn't actually do this because I would run out of time on my computer. This is why so many people want to build quantum computers. This is one reason why.

But in principle, I could do this, run a simulation that would maintain this gigantic evolving wave function. I'm saying that one could then go inside of that wave function and one could find branches in it that one could interpret as containing things, containing excitations that look a lot like observers. That's conjectural, to be clear. That's conjectural. There's no proof that you get a unique set

of decoherent branches out of many worlds, right? That's where the outstanding question is. Okay, okay, okay, but I would say it is only conjectural in the same sense that it's conjectural that, you know, if you ran the equations of classical physics, you know, from the beginning of time, then eventually you could get planets and life and all these things. I mean, we believe that in some sense because

we have the example of our universe where it seems to have happened. We can't actually run a computer simulation where we see all of this happen from the very beginning. But this comes down to, does one believe at all in scientific materialism? Does one believe that there had to be some external intelligent designer to guide things along and cause the life and intelligence to happen?

If one doesn't believe that, then one believes that, yes, those kinds of things can arise from just mindlessly iterating these equations over and over. And I see no basic change if the equations are quantum mechanical. Then they're just saying that what's going to be evolving is this giant superposition, but within that superposition I can again find things that look like planets with primordial soup, out of which life will evolve.

So I would say, this is why I say that if we're willing to leave ourselves out of it, which maybe we shouldn't be, right? But if we don't care about accounting for our own experience, then I think Everett actually gives you a very nice picture of what's going on, of how you can just start picture of what's going on, of how you know you can just start with this very simple wave function, let it evolve according to the Schrodinger equation, and then you get you know what looks like the thing that you need. So let me come back to this because I think

this is kind of a central point right? Yeah. So let me put aside the question over whether you get a unique basis in which decoherence singles things out. That again is not known at this point. Certainly not for a theory as complicated as the standard model. But I'll tell you is this, if I propose a theory in which, forget quantum mechanics, forget all this stuff, let's suppose I propose... The decoherence doesn't happen, then I would say that that is not only a problem for many worlds. Sure, sure, sure, sure. That is a problem for any no-collapse view

of quantum mechanics. Not necessarily. For example, you know, if we lived in a universe in which Bohmian, just as throwing this out, in a universe in which Bohmian mechanics works, you don't have to worry about whether there are different bases in which decoherence works. Bohmian mechanics just picks out one particular picture.

Okay, but we'll put that aside. Here's what I'll ask. Forget about quantum mechanics for a second. Forget about all of our physical theories. Let's do a library of Babel version of the universe. So maybe people are familiar with this fictional idea of the library of Babel. This is this, this is not the exact version of the story.

It's gonna be the version that I'm gonna use, okay? There's a vast library, and you enter the library, and what you see is all the books, right, that begin with, what was it, you see a bunch of doors, I'm sorry, a bunch of doors labeled by different letters. You go through the letter T, the door labeled T, and then inside is every single book that could possibly exist that begins with letter T. And then what you do is you go through the door labeled H,

and if you go through that door, there's every single book that begins with the letter as TH. And this way you can just sort of find your way, you can write or find every book that could ever be written by just going through a sequence of doors, and this library contains all of them. And someone says, this gives an account of the universe. I mean, after all, we just look at the entire library and somewhere in there is gonna be a universe that looks like ours. But you look at that and go, that's completely vacuous.

That doesn't contain any interesting information, right? What we want is a theory that in some way makes, you know, has some constraints about what kinds of universes are gonna happen and which aren't. And one of the problems, the two of the problems the many worlds approach is that it contains so many different kinds of universes that are to happen which aren't. And one of the problems, two of the problems of the many worlds approach is that it contains so many different kinds of universes

that are so radically different. And one of the, when you read about people who write about the many worlds interpretation, I mean, in the last podcast I did with you, Kurt, I had this long explanation of the problems of the many worlds approach. But one problem that I didn't mention in that conversation, but that comes up in the literature, is people don't take it seriously enough. So when Bryce DeWitt in 1970 published

his article in Physics Today, this is 13 years after Everett's PhD thesis in 57, announcing and broadcasting what Bryce DeWitt called the many worlds interpretation to the wider physics community. I believe the article was called quantum mechanics and reality was in physics today. He talks about how there are branches that are sort of reasonable looking in some sense. And there are also these branches that are kind of at the edges of the probability, the tails of the probability distribution that are weird and weird things happen in them. I don't remember if in that article he introduces

the term maverick branches for those, but eventually these became known as maverick branches. But when you read the literature in many worlds, people who, and I'm gonna get kind of technical people to use what's called Dutch book reasoning to argue how you can get probabilities out, they still stay within these sort of narrow confines of ordinary looking branches and maybe maverick branches.

But if you take the many worlds picture seriously, you have to consider branches that are even more bizarre than the branches that conform to whatever game is being played. I call these super maverick branches. You know, they're just maverick branches, but they're like, they're branches in which whatever rules you're trying to set up

for the game you wanna play and use the branches to explain, they're branches in which the rules don't apply because something totally zany happens. And once you include all the super maverick branches, you're basically in the library of Babel situation where you're explaining everything and you're not putting constraints on which kinds of worlds we expect to see. And there aren't the resources

in the many worlds of interpretation to like narrow down to worlds that at least look somewhat like the ones we see among all the possibilities. That's a major problem. So certainly, I agree that, you know, if a theory doesn't rule anything out, if it doesn't tell us that anything is impossible or at least vanishingly unlikely, then it's vacuous, then it's not doing anything for us. This is part of why I have never been a hardcore many-worlder. I will use it pedagogically when it is useful for me. One example of where I found it indispensable is when I am teaching quantum computing.

I need to explain how it is possible to take a qubit, do what we call a C-naught gate, a controlled-naught gate, write the result of the qubit somewhere else, copy its state to a different qubit. Now, the effect on the first qubit is exactly as if someone had measured it. It is decohered from

the perspective of someone who now looks only at the first qubit. Students get incredibly confused about that. They're like, why is that? They feel like it's still a superposition. The one explanation that I can give them that seems to click, that seems to work, is to say, look, you might as well say, if you wanted, that the qubit was measured, and just that it was measured by the other qubit. The other qubit did the measurement,

and you might as well say that when you measure, what does that mean, when you measure, it's just that there's a giant CNOT gate that is happening from that qubit to you, to the possible states of your brain, of your measuring device, of your environment, right? You know, to me, that is the core of what, you know, of readianism is saying, you know,

it is sort of the best way to explain that, right? And it is true that, you know, I am ultimately not satisfied by a theory that doesn't account for my experience of the world. Because as Democritus said in that famous dialogue in 400 BC, how can you ignore the senses when it's from the senses that you get your evidence? How can we ignore our own experience when our experience is the only reason why we believe quantum mechanics in the first place, right? So I would say that, like, with some, you know,

I think, you know, fairly, you know, reasonable-sounding additional assumptions about, you know, you know, what observers are, how, you know, observers connect to the physical world. Like, yeah, I can get something that looks like the standard quantum mechanical predictions out of the Everettian picture, but it is not automatic. I agree that it's not automatic. I don't believe any of the so-called derivations of the Born rule,

of the probabilities from many worlds, neither Everett's original derivation, nor any of the later ones, they all sneak in some additional assumption. But I would also say that that's not just a problem for many worlds. I would say that in any account of quantum mechanics, at some point you're going to have this problem, where did the Born Rule come from?

Where did probabilities come from? If you didn't want to have probabilities in your fundamental picture. Of course, Jake, in your account, you do have probabilities in your fundamental picture. But if you have an initially deterministic picture, then you're always gonna have that problem. So, so-

So it's a good reason not to have a deterministic picture. I mean, it's like- I agree that there are pluses and minuses to all the different major interpretations. Then there are other ones where I only see minuses. We don't have to talk about those, maybe. But that's why I don't own a car.

I just take Ubers, if you like. I just drive different cars as the need arises. I could imagine some future circumstance when I would want to use Jacob's car. I could imagine if it helps with quantum gravity. Scott, you can borrow my car whenever you would. Thank you, thank you. That's so kind of you. Look, if it helps with understanding a quantum algorithm,

I am ready to take a ride in whichever car will get me to where I'm going. Right now I don't see where this car is going to get me, where I couldn't already get. But I like to keep an open mind. Let me say a couple of quick things just to follow up about that. This is one of the annoying places where I'm going to be the annoying philosopher, I'm sorry. But one of the things that philosophers like to do is take a claim, an idea, and really drill down on it and make sure that it really

works when you follow it to all of its logical conclusions. When you said, well, if I just have the Schrodinger equation and it's just evolving, it's a wave function, and that's going to be good enough, you'll notice that quickly we ran into problems as I was probing that. Because I asked you, how do we exactly do this? And you're like, well, kind of like this, and I pointed out this problem with all these weird branches and we're saying too much.

And then you're like, well, we add a few more assumptions and so forth. One of the selling points of the Many Worlds approach is that it is so simple. I mean, just take the Schrodinger equation and Unitary Evolution and maybe one or two more things. I have a book on my desk. You can sort of see it. It's sitting there right in front of my Einstein doll. It's called Stone Soup.

I think this gives a fantastic metaphor for what happens in your approach like the Many Worlds interpretation. So those of you who don't know the Stone Soup folk tale, these soldiers arrive at a very skeptical town and claim that they can make a delicious hearty soup out of just water and stones. And the townspeople are amazed by this and they give them a pot and they start boiling the water.

And as they're making the boiling the water, they're like, you know, this is already great, but you know, it'd be even better if we have a little bit of seasoning. And so the townspeople come to the SMC and they're like, oh, this is already almost perfect, but you know, it'd be even better if we have a little bit of seasoning. And so the townspeople come to the SMC and they're like, oh, this is already almost perfect, but you know, it'd be even better with a little bit of vegetables

and then the townspeople vegetables. And then by the end, they have this, obviously they've added vegetables and seasoning and meat and broth and all kinds of things. And the townspeople are eating it. And then there's this line in some tongues of the story where one amazed townsperson who wasn't sort of paying attention says,

gosh, all this from just water and stones. The manuals interpretation. So, Jacob, in your account, the equation for the trajectories would be the meat and the vegetables that need to be added. But I'm very clear upfront, right? I'm telling you exactly what the ingredients are. We're not going through and we're, you know, and I say this in the podcast with Kurt, right? To get many worlds off the ground, at least to attempt 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 quite large. And a lot of them are very esoteric, metaphysical, very difficult to imagine how we would ever verify that they in fact work. So I call this the stone soup problem. And I think it's actually a pretty serious problem

with the many worlds approach. But fundamentally, I don't believe it can work. And Scott, you noted this. You said that the derivations of the born rule out of the many worlds approach, you don't believe any of them. And I agree with you. And I laid out my reasons for skepticism

in the podcast I did interview with Kurt recently. But actually it's worse than that. Because you might say as well, maybe we can't derive probability or derive the Born Rule. So let's just agree that it's gonna be an extra axiom that we add, right? Cause this is one route that I know some people take. They're just like, well, you know,

if I can't derive probability, have the initial without probabilistic assumptions, let's just do many worlds. that I know some people take. They're just like, well, you know, if I can't derive probability ab initio without probabilistic assumptions, let's just do many worlds and then we'll see all these universes and we'll somehow attach probabilities to them, say that some are likely, some are unlikely. There are extremely strong arguments

that if you are going to assign probabilities to the branches at all, then any rule for doing that other than the Born rule is going to lead you into nonsense. Yeah, and these arguments, by the way, show up in Everett's original dissertation, right? Even in the shorter version of the dissertation, the one that was published.

Yeah, well, I mean, there are many different arguments that all lead to that same conclusion. There are many different arguments. Yeah. But here's the problem, okay? So if your view was that the branches were fundamental things, that is, they're like, the branches themselves are part of the,

are considered fundamental ingredients, then it is completely fine in an axiomatic theory to assign them, in the axioms, things like probabilities. And this is, for example, what happens in stochastic versions of Bohmian mechanics or what happens in stochastic collapse theories or whatever, right? I mean, if you're taking certain things

to be part of your fundamental ingredients, you're allowed to assign them features in your fundamental ingredients. The problem is that in order to get around this preferred basis problem of the many worlds approach, there's infinitely many bases we could use and what singles out one basis over the other. The idea is that we rely on this dynamical decoherence process for

macro worlds to sort of pick out these approximate macroscopic worlds. Problem is that if your branches are only showing up in an approximate way in later stages of the development of the theory, you can't assign them axiomatic features like probabilities in the axioms. It would be like taking a theory of chemistry, saying I've got an axiomatic features like probabilities in the axioms. It would be like taking a theory of chemistry, saying I've got an axiomatic theory of chemistry in which in some situations you end up with tables and chairs, and I'm going to assign properties to the tables and chairs in my axioms of chemistry.

Like, you can't do that. The axioms have to apply to the fundamental ingredients. But what people like Deutsch and Wallace try to do then is they say, well, look, you know, we have observers within the many worlds context. They should act as if the probabilities are the born probabilities. This is what rational decision theory means in that context. This is then what we mean by probabilities in that context. So I agree that you have to give-

That doesn't work. The probability. Well. It doesn't work. I talked in my podcast with Kurt, I don't know if I want gonna rehash all those arguments. Yeah, yeah, yeah. But those arguments are all logically circular, right? Because you can't just say, well,

I mean, because you use the word should, you should be a rational observer. I don't know what should means. In the many worlds universe, there are just zillions of uncountably many parallel worlds with uncountably many copies of observers in them who do all kinds of things. All of these arguments have to have some starting point.

I agree that none of them can get something out of nothing. But you can't derive probability from them. None of them can get soup from purely a stone. Exactly. But to be fair, there is enormous precedent in the history of physics for making the fundamental ingredients of your theory as simple as possible, even impossibly simple, just atoms in the void.

Agreed. Just a bunch of particles undergoing. Then someone might say, okay, but this doesn't work because you don't have tables and chairs and trees in your fundamental ontology. And you say like, no, but that's a misunderstanding. We don't actually need that at all.

All of that is to be explained from these very simple building blocks. I mean, that is, I think that's the goal. Now, I agree that to explain the experience of an observer, it seems like something is missing. There's some additional ingredient that's missing. And maybe, you know, I feel like speaking of going around in circles, and maybe we are at this point, but I think one place where you and I strongly agree is that saying that you can ask this question and it just, I can't give you an answer,

or no answer is presently knowable. That is an improvement over saying you're not allowed to ask. Good, yes. Let me quickly just go back because I think there may have been, I'm not sure it was a misunderstanding is presently knowable, that is an improvement over saying you're not allowed to ask. Good. Yes. Let me quickly just go back because I think there may have been a... I'm not sure it was a misunderstanding or if it was just you were going a different way, but you said the theory doesn't have to specify chairs as fundamental ingredients. I agree.

I also agree that the axioms should be simple. I completely agree with that. Yeah. So the Egradians would say you don't have to specify branches as a fundamental ingredient. They would say that branches are like tables and chairs. Right. But here's the problem, right? You have this fork that's a serious problem for the many-wheels approach. If the branches are fundamental, then we can assign probabilities to them in the axioms.

But then you run into all these secondary problems about the preferred basis and so forth. If you make the branches not fundamental, then you can't put axiomatic probabilities in for them because they're not fundamental objects. I'm not saying that the branches can't be emergent. Of course, the chairs and tables can be emergent, but then you can't specify the features of like probabilities of those non-fundamental things in the fundamental axioms. You kind of stuck between, you either give them axiomatic probabilities, but then they have to be fundamental to be things you can specify the axioms, or they're emergent approximations,

and then the axioms can't touch them, can't assign them probabilities. And that's why people, people aren't making all these decision theoretic rationality arguments for probabilities just for fun. They're doing it because they no longer have the ability to put the probabilities in the axioms anymore. So they have to get them somewhere else,

but you just can't. And for all the reasons that you and I agree on. So I don't see this as just an annoying property of the many worlds approach. I'm actually arguing the stone soup problem is the best possibility. Like I don't think it even survives a stone soup. I think that once they try to add all these ingredients,

they show the townspeople and the townspeople go, that's not soup, it didn't work, right? So I actually think it's actually a pretty serious problem and it means the many-wheels approach, I've not seen any viable version of the many-wheels approach that gets around these problems. And that's why if it's just off the table, if we drill down and find that it doesn't work.

So look, Scott, if you're coming into this car dealership and you're like, you know, I'm here for the car dealership because my friend Kurt brought me. But I walk. You know, but I don't really, I don't really, I don't really drive a car. Well, then I don't know that the car dealership is really going to ever work. We really have to bring in someone who actually wants a car. And that's fine.

I mean, I, you know, but, but, but certainly what you can't say is all these other cars are just fine. If they were, I would have glommed onto one of these other cars. Yeah. Yeah. To switch metaphors. I mean, like I could listen to someone, you know, explain all the severe, enormous crippling problems with democracy and, you know, agree with that person, right?

And it still doesn't mean that I am sold on, you know, monarchism or communism or some other system. That's just not enough to make the sale for me. There's this saying of this system is the worst apart from all the others. We actually know very well how to use quantum mechanics in situations where decoherence is strong. Right. Agreed. So you could say, once there are lots of records of something all over know, all over the place. Once the information about whether this qubit is a zero or a one has spread into the environment,

into the air, into the radiation that is flying away from us at the speed of light, then, you know, most of us can agree that there is something real there, right? I think even – Yeah, this is a Zurich science selection science selection quantum draw what is in the picture. Even a lot of the people who call themselves Copenhagenists or instrumentalists would agree at that point that like this is real. Like this is now really,

this is a real element of reality even if no one is thinking about it or no one knows about it. It is really there, right? The whole difficulty is what about when you're it is really there, right? You know, the whole difficulty is what about 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 indivisible

stochastic dynamics according to your picture, right? And then, then we don't know, you know, how to say what is real, right? You are sort of asserting that there is a basis in which something real is happening, but then you can't really tell me what, in the sense of giving me trajectories. And I'm not sure that that's a sufficient improvement

over what I could have said before I learned this, which is yes, something real is presumably happening there, and I can't tell you what, other than to just write down these equations, write down the wave function by which I could calculate the probabilities for the different things that I'll see when I look. Scott, why is supplying trajectories to you so important?

You should know Jacob has been on the podcast four times, going into technical depth in his theory, as well as dispelling quantum myths. Scott has also been on dispelling quantum myths as well, but also talking about consciousness and AI three times here, once with David Chalmers and twice solo. Links in the description. improve over the standard quantum mechanics perspective. If I just want to say that there's this wave function that gives me probabilities, I already knew how to do that. I didn't need Jacob's picture for that. If I want to make a stronger ontological claim, that the photon really goes through one slit, uh... make a stronger ontological claim right that there are you know uh... the

the the the photon really goes through one slit or it really goes through the other slit even when i'm not looking well then okay now i want to know more i want to know you know uh... you should you ought to be able to give me an equation for this photon then right at least tell me given that the photon was going through this slit at this time,

then what is the probability that it's, 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 something about the photon, you know, I wouldn't say that that improves on what I already knew about it from standard quantum mechanics. So let me say a couple of things about all this. The first is this set of statements about, well, when records, which are kind of hard to define, are in the environment far enough and there are enough of them and they're far enough away and they're traveling at this speed, like, then we all agree. All I'm saying is,

that in a good physical theory, like I said, I teach general relativity. I teach Jackson electromagnetism, right? I mean, these are theories in which I can be more precise. And when we say that, oh, and stuff just gets far enough out or enough records or something like that, I mentioned Zurich's quantum Darwinism approach,

on selection, that sort of thing. That at some point, somewhere we wave our hand and then it's like, I'm just trying to make us honest and precise about this, right? I think that precision is possible. If the precision is not possible, if it's not possible to make quantum mechanics more precise about this, if it's not possible to eliminate

this very severe vagueness, that's interesting. It would be interesting if it were really not possible. If it is possible to reduce it in 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 it's necessary. Now, let me say additional things. So far be it for me, who did my PhD in, you know, topics that were in or very close to adjacent to string theory,

to make an only game in town argument, that this is the only game in town. But what I would just say is, I gave a list of criteria for what I thought a reasonable, viable interpretive framework should be. Paragladiquacy, lack of vagueness, unambiguous predictions, at least a schematic picture of the classical limit, not an endless list of speculative metaphysical hypotheses. Like these are just bare minimum requirements we would put on a theory.

I didn't even add Occam's razor, but you could add that too. All these things you could further add. My argument is that none of our approaches meet that minimum set of requirements. If they did, I would have, I mean, I did spend various points of my career here working in various other interpretive frameworks.

Like I said, it's been a long time in the modal interpretations, which Scott will remember when I said lots of strange things of modal interpretations many years ago. I arrived here because this met those requirements and the others didn't. Now it doesn't do everything you might like. There are aesthetic criteria you might further want.

You might want to be able to say what's going on in every circumstance, what exactly are the trajectories of this is taking. I think the whole reason why there's an interpretation debate is that for every interpretation you can state an obvious sounding condition that that interpretation fails to satisfy, right? In the case of yours, that condition would be that for every element that the theory posits as being real, you have to give an equation

that says how that element evolves in time. If it's really fundamental. But Scott, the reason I think that's aesthetic is because we don't hold any of our other physical theories to that standard. All of our other physical theories contain things where we don't have an ability to describe them, we don't know what equations to apply to them.

Like all of our, if you take general relativity as a great example of this, right? We have access, if you think of space-time as a four-dimensional manifold, we have access to an incredibly thin sliver of that entire space-time as a four-dimensional manifold, we have access to an incredibly thin sliver of that entire space-time manifold. Most of space-time is and will forever be completely inaccessible to us.

And you can quickly run into situations in which unobservable ingredients of our various physical theories, we don't have a quake, we can't describe what's going on with them, we can't, you know. I don't really agree with the analogy. I mean, I would say in GR, you can posit a space like slice.

You know, once you've posited it, then you have this field equation that tells you how to evolve it forward, right? Except, you know, when you run into singularities or- Or you run into Cauchy horizons or you run into- That's right, that's right. Or various. Yeah. But in many conditions,

you can just extend that equation forward. If you believe in standard quantum mechanics, you say once you tell me what is the wave function, you tell me what is the Hamiltonian, then I can just take that psi and map it to e to the minus iHT psi. I can propagate that equation forward. In your case, you are telling me that something is real, namely the positions of these particles in space,

or which slit the photon goes through, and you're not giving me an evolution equation for that thing that you have posited as real, which okay. Like I said every Interpretation has some hole or something that it's failing to satisfy and that's the one for you But I don't I don't see that that's necessarily, you know less bad Then let's say the the Everett interpretation not having an answer to where the probabilities come from. Well to be clear

I think it's kind of a more serious problem when the entire empirical content of quantum mechanics, which consists of measurement probabilities, can't be obtained from your... I mean, it's one thing to say that certain unobservable features of a theory, that we don't have equations for them, right? It's another thing to say that the observable features of the theory, the empirical content we can't get, right? I mean, that's, that'd be like saying not that we can't make predictions, but what's outside of, you know, our accessible light cones in general relativity, but we can't make predictions of what's inside of our accessible light cones in general relativity. I mean, we could say every interpretation of quantum mechanics has the property

that to actually use that interpretation to make, you know, to actually connect it to the experiments that we can do, we need some auxiliary assumption that looks something like the real world is decoherent, it contains things like records and so forth. So every interpretation is going to have some story of that kind that it tells where some vagueness will enter. Right, but the problem, as we mentioned,

in the many worlds approach is that that doesn't appear problem, as we mentioned in the Many Worlds approach, is that that doesn't appear to be possible in principle in the Many Worlds approach. Like it's much more severe problem. So let me actually just step back and go back to... I'm gonna just say, suppose you go back, you rewind the clock back to 1923, 1924, which is right around the time when people like Pauli and Bohr and Heisenberg were beginning to doubt that there could be a physical picture of stuff happening. Because back then people still thought there were particles going around atoms and stuff, right?

There were fields interacting with particles. These were all happening in some kind of, there was an actual ontological picture. And people began openly to doubt whether there could be any picture because no one could come up with any laws that when combined with any such clear picture could yield the correct empirical predictions of quantum mechanics. And then Heisenberg begins his matrix mechanics paper in 1925, the spring of 1925, with a bold statement that we should give up these pictures altogether and that we should just do everything

in a crass instrumentalist way. So people thought that there just were no laws that would work, that there was just no laws you could find. You could tell an alternative history in which the theory of stochastic processes was discovered way earlier than in fact it was. Kolmogorov didn't publish his axiomatization of probability theory in 1933, a year after von Neumann's book on quantum mechanics. He published it in 1833. He just, there's some retrocausal loop and he goes back

and he publishes his axiomatic account of probability theory. Markov doesn't, you know, first introduced the Markov matrix in 1906 in an obscure journal, but this all happens in the 1800s. People develop a robust probabilistic theory of stochastic processes starting in the 1800s. And then when, and then people begin exploring non-Markovian processes and someone mentions,

what about indivisibility? And then 1923, 1924 comes along and they go, well, I mean, we have these indivisible processes, let's try those laws. They try them and they get all the correct empirical results. They're able to derive this beautiful mathematical correspondence, the way that we took Newtonian mechanics

and derived the Hamiltonian formulation, you could do things much more beautifully, more elegantly in this Hamiltonian formulation. I think a lot of the interpretive questions we would have today wouldn't exist. The measurement problem wouldn't have happened. If I imagine myself in that alternative history that you have sketched, I'm still asking myself, well, then what the hell are these

indivisible stochastic dynamics, right? What do we know? How is that even dynamics at all, right? What are the transition probabilities? What are the trajectories that these particles are following? And then in your alternative history, if a Schrodinger comes along and says, look, you know, you can think of it, you know, in terms of this wave of amplitudes, right, as Schrodinger came along in our history, then, you know, in that history, just like in this one, I say, oh, that's nice. That helps me, right? As a helpful picture, just like the Hamlet and Kobe picture is a very helpful picture, right? But it would immediately come along with all of these bizarre mysteries like superposition and the measurement problem. People would always say, they would say, okay, well this is a really useful mathematical picture, it gives some visualization. But

at the end of the day, if we ever have some question about what happens when you do a measurement, we have this more mechanical picture, just like in a Hamiltonian formulation. If you're living in phase space land for a while and you get confused. This is always the problem with sort of going back to history, right? The many-worlders will also constantly say this. They will say, well, look, it's not fair that Copenhagen came first, right?

If only people had just accepted many worlds in the 1920s, then Copenhagen would have been this bizarre instrumentalist deviation from it that would have had to win acceptance on its own steam and so forth. Well, in this branch of the wave function, history happens a certain way. Then if you want to win converts to a new view, then you have to meet them, you know, having learned whatever they've learned from the previous views

and show them why the new view is an improvement over what they could already do. I mean, interestingly, Schrodinger did, if you read his fourth lecture, Wave Mechanics, what, Section 15, the interpretation of the generalized eye function, he presents an embryonic many-worlds picture.

Yes. Right? He actually, so it's not that people didn't think about these things. If you read some of the early papers at this time, in the 20s, people did, some of them were imagining this sort of, but they didn't embrace it because it doesn't work. And what happened, it's not that people, that Everett came along and found a way to make it work, Everett found a story he could tell that some people found very compelling, but it still doesn't work. Like, the people who gave us quantum mechanics, they were very smart.

They didn't have everything. They didn't know that you could write 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 very smart. They were also trying to get things to work. They would have said, okay, maybe you could imagine the Earth going around the Sun, but that just doesn't work because we don't feel ourselves spinning.

Yeah, which we don't. It actually requires a lot of physics to explain why pendulums can feel earth's rotation. And the Averitians have a whole story in which you know Averit is like Copernicus, right? He's just giving this a reinterpretation like yeah we don't feel ourselves being in all these different branches, but you wouldn't, if that were what was going on, right? Well, that's what he said actually in a response to Bryce DeWitt, because when Bryce DeWitt,

the theoretical physicist who eventually propagated the theory, talked to Everett in his letter and said, I don't branch, Everett said, well, what would it feel like if you did? And he actually made this Copernican analogy. The problem of course is that the Copernican story says that all humans on Earth, if Earth is in fact turning and going around the sun, then all humans on Earth will see the sun apparently move through this.

It predicts what all humans will see. The problem with the effort approach is that it predicts everything. It predicts every pot, like there will be observer copies who see absolutely everything. And then you either run into a circularity of saying, well, the reason we see the world we see is because we're gonna condition on us being the ones who see the world, it's a totally circular argument. Or you say something like, well,

what would the typical copy of the observer see? But then typicality is a question of what's the most probable, typicality is a probability statement. And then you run into the circularity of how do you get probability out of the ever approach. Like all of this stuff just doesn't work. And I think that the early quantum mechanics, the early people of quantum mechanics,

you know, realize that at some level that this is just not a thing that ultimately can work without slogans. But look, history ended up turning out a particular way. It's hard to know exactly what would have happened if it had come at a different way. I would argue that if they'd had a physical picture, a simple physical picture, simpler than the Hilbert space,

Dracvino and axioms with all the exotica that you get from those, they would have viewed the Hilbert space picture just as we view the Hamiltonian phase space picture today as a very powerful mathematical apparatus that we can use to do all kinds of amazing calculations and simplify things and specify particular kinds of interactions. But that at the end of the day, when you run into any conceptual confusion, you can retreat back to a physical picture in the Newtonian case to bodies moving in space interacting

with fields. And in this picture to the object with configurations with laws that are just more general. Now I want to add, ask one more quick thing. You said they would probably say something like, well, what are these laws? What are these conditional probabilities? Like, what are these laws? The question of what laws are is, as Scott, I'm sure you know,

a pretty hot topic in metaphysics today, in the metaphysics and philosophy of science. What kinds of thing? Say what? I don't follow enough metaphysics to know that,. What kinds of things, say what? I don't follow enough metaphysics to know that, but okay. That's okay, nobody's perfect. All right.

I'm just joking. But like, what is a law? Yes. I mean, I don't know what Newton's law is. I mean, I know what it is as an equation, but like I have no greater understanding about what is Newton's, like what does it mean to say that there's this law that takes the present configuration of a system and the configuration infinitesimally

earlier in time or equivalently the present configuration of velocity. And then like how is it doing this? And if you talk to people who are humans about laws, this is a term that was introduced by David Lewis to refer to a certain view on the metaphysics of laws that in some sense is connected with David Hume, the philosopher's ideas about nature. Then what you say is you don't believe in laws at all. Because the idea of a law is just so weird and strange, laws are not primal things. They're just tools that humans use to summarize phenomena.

And, you know, so, but the upside of all this is that, yeah, indivisible laws are weird because they're different from the kind of differential and time Markov-style laws that we've been using for the past few hundred years, but that's just an historical contingency. They're no weirder than a Markov law or Newton's second law. I mean, they're all weird. All laws are strange. They're just stranger because we're newer to the idea. Okay. What I'm saying is not that the law is weird. I'm saying in a place where I might have expected there to be a law in your picture,

namely for the transition probabilities, there is actually no law at all. Yes, in some cases there's no law. In your Ghosts in the Quantum Turing machine paper, you introduce a lovely term for unpredictability that is not even probabilistic. You point to this book from the 1920s by this economist Frank Knight. You call it Knightian uncertainty, right? Circumstances in which we can't even put probabilities on certain things. And interestingly, this is definitely not unique to quantum mechanics. So here I can put my general relativistic hat on.

One of the conjectures about general relativity is just that all reasonable spacetimes have to, it's called global hyperbolicity, they're from globally hyperbolic, which just means that you don't have Cauchy horizons, that the equations apply to everything and we get, but this is just a guess, right?

There are like solutions to the Einstein field equation where you get Cauchy horizons. These are places where general activity simply fails to make further predictions about what's going to 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 you could have situations

in which we just can't, the theory doesn't render a prediction about what comes next. That's not a new idea. Well, look, as you know well, because you read Ghost and the Quantum Turing Machine, I am very ready to contemplate nightian uncertainty about the initial conditions. Right. Right? Because that is the thing that in our experience, the laws of physics famously leave unspecified, right?

I am much more hesitant to allow nightian uncertainty in the evolution rules. And that seems to be what you're doing. Yeah, that's fine. Although I will tell you that even in like standard quantum mechanics, we are unable to assign probability distributions to a variety of things.

You can't assign joint probability distributions to incompatible observables. And, you know, so like- I feel like this all sort of boils down to the same issue of just, you know, multi-time or transition probabilities. It all boils down to the basic fact that we're epistemically limited beings. We're trying to do the best we can

in a universe that we're a part of, that we're physically embodied in. And we're very fortunate that we have a theory that lets us make as many predictions as we'd like to make, but we can't make all the predictions we would like to make. And yes, that is a bullet I'm definitely going to bite. I'm going to bite that bullet. But I will say that anytime someone comes along with a new picture of reality, it opens up new possible connections to new fields, interdisciplinary connections,

new ways of thinking about old problems and possible new generalizations, maybe new pedagogical teaching techniques. And even arguably opens us up to rethinking certain things that we took for granted. I mean, sometimes, John Bell, and there's only thing I'll say about John Bell here, John Bell was very clear that sometimes

having a physical model can really tell you a lot about things that you thought were true, right? There was this prevailing idea from John von Neumann that hidden variables were just ruled out completely. And although Bell wasn't the first to notice this, Greta Herman noticed it almost immediately in the 1930s, Bell independently rediscovered this, and he rediscovered it, this flaw in the von Neumann proof,

because he had a model, Bohmian mechanics, that made clear that there was a problem here. And of course, Bohm mechanics also helped develop, lead to the development of decoherence, which, I mean, having physical pictures can lead to rethinking things, including even things like the classic theorems, like Bell's theorem and its related theorems. So I think that's also a useful thing.

And in my podcast interview with Kurt, we talk about possible connections to rethinking how causation is supposed to work. I think there's a lot of stuff you can do with this and it's not for everybody, but unless we identify some actual inconsistency, some real problem, if either one could say that there is just an inconsistency, something that just doesn't work, or one can say that this is trivial or uninteresting or isn't useful

to me or doesn't do better than the things I already like. And if we're basically arriving at either of those two positions, we're not arriving at the inconsistency position, but we're arriving at the position that, well, maybe this doesn't work for me, or I like these other things, or it's trivial, or Arun could have said that, or whatever, I'm actually satisfied with that. Because some people will find that satisfying, others won't, and that's the way the world is.

Right now, I feel about your account the same way that I feel about category theory, let's say, or calculus, right? I have friends who just swear by these things, right? This is the way to understand everything, and they will happily take something that I know how to prove in one paragraph, like normally, and they will give a proof using category theory that's 20 pages. And then they would say like, can't you see? With lots of diagrams, all these diagrams.

Right, right, with all these diagrams. I'll say, can't you see? With lots of diagrams, all these diagrams. Right, right, with all these diagrams. I'll say, can't you see that this is so much better, that this is more insightful? And I'm like, okay, I guess for you it is. I guess so, right? You know, go in peace, carry on. You know, you haven't yet made the sale by showing what this can do for me.

But, you know, I'm open to the possibility that maybe it will in the future. That sounds like a wonderful place to close. Yes, yes. I'm still waiting for John Bias to tell me what daggersymmetric monoidal categories have to say that is different than just translating something from quantum mechanics and then translating it back because usually the insight comes from translating to a different field and then doing something in this other language that you couldn't in the former, then translating back. But as far as I could see, you just translate and then translate back without anything new being generated. So I'm in a similar boat as Scott, and I think you and I have talked about this off air, Jacob.

Yeah, but let me just put this out right. There are people who don't know quantum mechanics, who, and I feel so sad for those people, they don't know what they're missing. Everyone should learn quantum mechanics. It's such a beautiful theory. But there are people who work in statistics who don't do quantum mechanics, and they've developed all kinds of incredibly interesting and sophisticated ways of thinking about statistics. And there's a barrier between them and people who work in quantum mechanics because quantum mechanics is phrased in this very different language.

If you hand them a version of quantum mechanics that's phrased in the language of ordinary probability theory, suddenly certain things that might have been difficult to apply from statistics are suddenly applicable. And this is, I mean, this is just so new. It's a case that I could imagine you making, but I would say that you have not made that. I have not. No, I agree. This is speculative. Like I said, this is brand new. Right. And if you want to show that this is actually a better way to introduce quantum mechanics to people who have never seen it before, then you need to show that by showing all the phenomena

of quantum mechanics that you can explain them better in this way. I don't see that you've done that. But that is a thing that if you did that, then yeah, that would make me wanna come back to look at this car again. You know, it's rare in science or in philosophy to find oneself with a blank canvas page to be filled in. I view that as super exciting, especially the theory is old

and battle tested is quantum mechanics. So I relish that opportunity. I feel like we've already made a lot of progress and I'm very excited about the things especially the theory is old and battle-tested is quantum mechanics. So I relish that opportunity. I feel like we've already made a lot of progress and I'm very excited about the things that hopefully we'll be able to explore going forward. Well usually quantum mechanics courses start with either the double slit or the Stern-Gerlach experiment and then try and explain that. So Jacob, I welcome a lecture of an account of the double slit and or Stern-Gerlach but

just without referencing the ordinary Hilbert space picture, just your picture. That'd be great. Well, so I sent you a document, Kurt, that you can, yeah. Yes, yes. You already have that in paper form. And so I'll put that on screen. And Scott, it was wonderful to speak with you again. Jacob, thank you so much.

This has been so much fun. This was delightful. And Scott, it's always a pleasure to chat. Well, hopefully we'll find more opportunities. Pleasure. Good talking to you, Jacob. Okay, good to chat. Well, hopefully we'll find more opportunities. Pleasure talking to you, Jack. Okay, good to see you all. Yeah, good to see you.

I've received several messages, emails and comments from professors saying that they recommend theories of everything to their students and that's fantastic. If you're a professor or a lecturer and there's a particular standout episode that your students can benefit from, please do share. And as always, feel free to contact me. So my question was, you gave an example earlier about the CNOT gate, and then you used many worlds to explain that. You said that some people find that easier. Do you have any other examples of situations where students are confused and then you use a different interpretation to explain it? Um, not really. I'm not usually using interpretations to explain conceptual points, right? It's, um, let me think.

I mean, I certainly talk about Bohmian mechanics, like when we talk about the Bell inequality and the CHSH game, right? But that's partly just for reasons of history to explain, you know, why did Bell care about this in the first place? But I haven't yet seen a situation where Bohmian mechanics helps me to explain something that I couldn't have explained without it. I see.

Because earlier you were saying like, look, you're willing to use an Uber, which is any car to get from point A to B. But it sounds like you'll use an Uber as long as it's a Hummer, as long as it's the same car. Yeah. I mean, usually when we're trying to solve a concrete problem, like what does this quantum algorithm do, then the whole point, we don't need interpretation for that.

We know what that calculation looks like, right? You know, interpretation is mostly relevant when we want to include ourselves in the picture, right? And then, yeah. New update! Start at a sub stack. Writings on there are currently about language and ill-defined concepts, as well as some other mathematical details. Much more being written there. This is content that isn't anywhere else. It's not on theories of everything, it's not on Patreon. Also, full transcripts will be placed there at some point in the future. Several people ask me,

Hey Kurt, you've spoken to so many people in the fields of theoretical physics, philosophy and consciousness. What are your thoughts? While I remain impartial in interviews, this substack is a way to peer into my present deliberations on these topics. Also, thank you to our partner, The Economist. Firstly, thank you for watching, thank you for listening. If you haven't subscribed or clicked that like button, now is the time to do so.

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