280 - David Albert & Jacob Barandes: Debating the Foundation of Quantum Mechanics

33:24Of course, we can't be using eigenstates of configuration because there are no such mathematical objects. But I suspect that there are various ways to soften that up by analogy with what's done in the GRW theory, for example, where we don't have collapses to eigenstates of position. We have collapses to something like Gaussians centered on a certain position that are relatively narrow, so on and so forth. So I don't want to detain us there. And I suspect that Jacob will have much more to say about that later on. Let me skip to Section 5, which I guess is, I think, the important one and the one that will be worth talking about a lot here.

34:15So section five of my commentary, which is called The Incompleteness of Jacob's Theory. What we expect of a fundamental physical theory, I take it, is that it tell us what fundamental stuff there is and that it tell us what that fundamental stuff does. Jacob's theory does the former, but it only does a part of the latter. It gives us in particular probabilities that the configuration of the world will be this or that at any time t, given its configuration at the initial time, t0. But unlike, for example, Bohmian mechanics, it tells us nothing about what path the world may have taken through the space of possible configurations to get there.

35:09Here's another way to put it. Jacob's theory, as it stands, gives us probabilities that the configuration of the world is this or that at any time t, given its configuration at the initial time t0. But for any two times TA and TB, neither of which is the unique and metaphysically privileged initial time T0, Jacob's theory is going to tell us nothing whatever about how the configuration of the world at TB depends on the configuration of the world at TA. one might think that this is not a particularly egregious or particularly worrisome omission one might think for example that the probability that the world has this or that configuration at this or that time must already include everything there is to say about the probability that this or that experiment has had this or that outcome since those outcomes must presumably supervene on those configurations.

36:15And it might be argued that any theory that gets those probabilities right must be empirically adequate. And it might be argued that insofar as Jacob's theory does get those probabilities right, it has already delivered everything that we have any legitimate right to expect of a fundamental physical theory, and that the business of telling ourselves stories about what path the world might have taken from one of those times to another, once those probabilities are already in place, is idle, speculative, unconformable fluff. But this is much too fast. Consider, for example, the following way, you might call it the minimal way of completing Jacob's theory.

37:03Here is the minimal completion. One, the probability that the configuration of the world at any time t is this or that, given its configuration at t0, is the one we get from my original version of Jacob's theory. Two, second postulate of this minimal completion. Given any two times, TA and TB, neither of which is T0, the probability distribution over possible configuration... Tomorrow morning is knocking. Stock your fridge now. How about a creamy mocha frappuccino drink? Or a sweet vanilla? Smooth caramel, maybe. Or a white chocolate mocha. Whichever you choose, delicious coffee awaits. Find Starbucks frappuccino drinks wherever you buy your groceries.

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38:26On this minimal completion of Jacob's theory, the configuration of the world jumps discontinuously around from instant to instant, and the only constraint on the way it jumps around is that at each new instant, the probability that the world has some given new configuration is the one prescribed by my original version of Jacob's original theory. The configuration of the world at any one instant, so long as it is at any instant other than the initial instant, exerts no influence whatsoever over its configuration at any other instant. The configuration of the world at any one instant contains no record or trace or memory of its configuration at any other instant, the traces and records and memories of the past that seem to present themselves at any single instant, although they are all consistent with one another, are all completely unreliable as indicators of actual past configurations.

39:34Let me make this a little bit more explicit. Let P sub C star as a function of C and T represent the probability according to the minimal completion of Jacob's theory that I've been talking about, that the configuration of the world is C at time T, given that it was C star at the initial time T0. and conditionalize P, C star as a function of C and T on the existence at time TB of a certain book in a certain extant library, existent library in a certain existent city that describes, say, the life of Napoleon. That conditionalized distribution will assign a high probability to the existence at TK of other books and of paintings and of videos and of memories and so on that describe the life of Napoleon as well.

40:34And this is an example of the phenomenon that I referred to earlier on as the statistical vestige in Jacob's theory of the Bohmian mechanical phenomenon of effective collapse or of the Everettian phenomenon of branching. That is, at each moment, the world will contain a whole bunch of what appear to be records of earlier situations of the world, which the linearity of the quantum mechanical equations of motion are going to guarantee are all consistent with one another. But note that this same distribution, the distribution that we attain, that is, by conditionalizing P sub C star as a function of C and T on the existence at time TB of a certain book in a certain existent library in a certain existent city that describes the life of Napoleon.

41:28this, the existence of all these things is going to assign an astronomically low probability to the very existence of the earth in 1804, or for that matter, 10 minutes ago, or for that matter, at the present minus one nanosecond. Okay. It's going to be extremely unlikely given all these books, not only that Napoleon existed, but that the earth even existed a second ago. and consider whether there are really any measurements or observers or experiences at all in a world like that. Isn't it absolutely of the essence of what it is to be an observer or a measuring instrument, after all, that the system in question, that is the observer or measuring instrument, responds in certain more or less reliable ways to certain features of its environment, isn't absolutely of the essence of what it is to be an observer or a measuring instrument, to put it slightly differently, that the system in question, that is the observer or the measuring instrument, is possessed of certain more or less reliable behavioral dispositions.

42:41And the problem is that there are no such dispositions, none at all, in this minimal completion of Jacob's theory. And there will presumably be similar worries about the existence of observers or experiences or measuring instruments in other imaginable completions of Jacob's theory on which the variations in the configuration of the world from moment to moment are not completely random, but nevertheless, whatever this means exactly, too wild. And perhaps it's worth repeating at this juncture that the fact that the positions of macroscopic material bodies are being measured millions of times per second by their environments is completely irrelevant to the considerations of the last few minutes.

43:34Those measurement events are going to give rise to probability distributions over possible configurations of the world, which display all of the instantaneous statistical vestiges of Bohmian effective collapses or Everettian branches that I was talking about before. But the facts about which branch the world is apparently on, or about which outcome apparently emerged in some past experiment, or about which quasi -classical macroscopic trajectory the world is apparently following, are going to jump around with no pattern and no continuity and no rules and no limits at each new instance. And so the incompleteness of Jacob's theory as it currently stands is, in fact, it seems to me, a very egregious omission and a very serious word.

44:35It seems to me that in the absence of any particular suggestion for completing the theory with a law governing these trajectories through configuration space, the question of its empirical adequacy and the deeper and prior question of whether it has any empirical content at all remains at best radically unsettled. Good. I'm going to make this shorter now. I have an additional section on some very preliminary suggestions for completing Jacob's theory with the dynamics. This may be only a testament to my own lack of imagination, but the suggestions that I was able to come up with, although they'll be in some strict sense empirically adequate, are really ugly and grotesque and suggestions that nobody in their right mind would take seriously as a fundamental physical theory, but we'll have to see how that develops.

45:39So that's this next section. Let me just say one more thing, and we can get into discussions about this. Two, I don't have much to say about this. Jacob has frequently made claims of locality on behalf of his picture. And I guess there are two things I want to say about it. One is, Jacob, and I think Jacob probably agrees with this, Jacob should have been much clearer at the outset about what he meant by locality. Because what an average listener who's familiar with discussions in foundations of quantum mechanics would have thought about the claim that he's got a way around quantum mechanical non-locality might have been that he's got a way around Bell's theorem.

46:38And that's not what he has. What's going on here is that Jacob is working with a different notion of what it means for a fundamental physical theory to be local than Bell was working with. This implies that Jacob thinks that the notion of locality that Bell settled on isn't really the good one or the ideal one or the important one to think about. I don't have too many opinions about that because I haven't studied very closely what Jacob's competing notion of nonlocality is. Let me just say this for people who are familiar with, say, Bones theory. Jacob says that on his notion of locality, the question, or at least he has said to me in the past, that on his notion of locality, the question of whether or not Bones theory is non-local can't unambiguously be settled.

47:43that seems on the face of it like really really bad news for whatever jacobs notion of locality might turn out to be because because on anything that seems related to our ordinary english notion of what locality or not non-locality might amount to it's really really vivid as all students of Bohm's theory know that Bohm's theory wildly violates our intuitions about things only affecting other things directly that are immediately spatially and temporally adjacent to them. But there may be much more to discuss on that score. And I think, let me just sum up I'm sorry to have taken, maybe I didn't take that much longer than I said I would.

48:45Let me sum it up this way. I think this is an interesting proposal. I think it should be very welcome that somebody is putting on the table a way of getting rid of all of the mishegas that investigators of the foundations of quantum mechanics have put themselves through over the past 30 years or so, trying to figure out what to do with the wave function as a fundamental feature of the furniture of the universe. If there's a way of getting rid of that, I think that's exciting. That having been said, at least insofar as I've investigated it so far, I think the theory faces daunting challenges. And I'll be interested to see how and whether those challenges get worked out.

49:44That's all I have to say. Excellent. That was absolutely amazing. One thing you did that's very helpful for me, David, is you gave a roadmap for this discussion going forward. and we can kind of break it up into chunks because time is limited and we can make sure that we touch on a lot of the big points first i think before getting into jacob whether you agree with david's formulation of the theory i think the first thing to touch on is whether or what your thoughts are on realism and whether david is right to treat your account as making straightforward realistic claims about the world. I'd like to start, first of all, by thanking you, Robinson, for organizing this discussion.

50:33And of course, immense thanks to David for engaging so much with my work and providing so much incredibly detailed and helpful input and feedback. David, I have benefited immensely from all this feedback, and there have been some developments to share. So I think this is going to be a very substantive discussion. And I think by the end, if you're not fully convinced that this is the right way to go, I think you'll maybe acknowledge that there's been some real productive work in directions that I think you'll find very amenable. So my view of realism, I think, is quite compatible with David's view.

51:12maybe it would be helpful for me to explain how I would describe what's going on in this theory and then I'll touch on what I mean by realism as I explain it. There's more structure to it than the version that David was describing. The version of the theory that David was describing has a lot in common with a proposal by John Bell in a paper in 1981 called Quantum Mechanics for Cosmologists. Bell was grappling with Everett's theory, the many worlds theory. And he was a little uncertain about exactly what the many worlds theory was trying to say and how it dealt with probability. So he described what he called the Everett question mark theory, which Everettians would not say describes their theory properly.

52:04But the Everett question mark theory is basically, you know, many worlds imagine, you know, all the different branches, everything happens. But on this view, only one of the branches is somehow really happening. And which branch is happening more or less randomly fluctuates from moment to moment. But in line with the Born rule, the probability distribution at any given moment specified by the Born rule. So there's no connection between what's going on at one time and what's going on another time. At one time, there can be a world filled with books about Napoleon and artwork about Napoleon and Earth and all of that stuff.

52:46And I love the reference. If I recall, this is from, I think, chapter four of Time to Chance, the Napoleon story, which is really great. And then at another moment, the world could be completely different, drawn again from the Born Rule probability distribution. some other branch of the wave function and then in the next moment some other branch and although at any given moment there's sort of a consistent picture of the world there's no consistency from moment to moment so this is the everett question mark theory and this is very much like the the picture of my theory that david has expressed so i should say just for if it's okay just to make sure we're understanding of course um that that isn't of course the way i was understanding your theory i was understanding your theory as something without this is a theory with the dynamics it's a it's a jumping around i was understanding your theory is having no dynamics at all and this and this was a way of making it vivid how how limited the constraints imposed by your theory on a dynamics that one might add would be.

53:57Right. So to be fair, the way you described the theory was that it simply lacked dynamical structure and you gave it a particular dynamical structure just to show the lack of structure could admit something like the Everett question mark theory. That's a much sharper way to characterize what's going on here. And that's, yeah, that's a reasonable thing to say. So let me describe to you how I would explicate the foundations of this theory, this indivisible theory. And some of this was sort of always implicit. It was sort of how I had been thinking about how the theory worked. But, you know, when you come up with an idea, sometimes you need to talk to people because you need people to push you to make some of your implicit understandings explicit.

54:43So some of this was from talking with people and some of it was also from people who've, you know, made the theory more rigorous. So the theory helps itself to a mathematical theory, the theory of stochastic processes. And the theory of stochastic processes is not, I think, a part of the standard curriculum for folks working in many areas of philosophy, even philosophy physics, with some exceptions. And even many physicists, I think, don't spend a lot of time with the comprehensive theory of stochastic processes beyond simple examples. So some of this work that's helped me understand what I've been trying to say has come from people who come from the mathematical theory of stochastic processes.

55:27And so this has really helped me sharpen the kinds of things that I want to say. I should add that this has not only been about people helping me reveal what I already knew by any stretch. I've also, you know, had new ideas or people have contributed new ideas to this program. So it's been a mixture of all of these things. Now, with that said, let me explain how I would describe the theory now. So to begin, for every system we would like to describe, every physical system in the world in some sense, whether we would call it an open system or closed system, doesn't matter. There is some menu of possible configurations the system could have.

56:09and configurations meaning some kind of way that the system is in some ontological or physical sense at a given moment, let's say, in something like physical space or whatever happens to physical space in our modern physical theories. So if you want to think of a simple model, and David considers a simple model of a non-relativistic system consisting of finitely many, a fixed number of finitely many particles, the configurations would just be the different arrangements, the different snapshot arrangements of the particles. Those are the different configurations. If you wanted to model a system of fields, the configurations would be patterns of field intensities and directions and polarizations in space.

56:55If you wanted to model a discrete register of switches instead of a computer, each configuration would be a snapshot of configurations. So the ontology is as straightforward as I can make it. It's basically classical-like ontology. And by realism, I'm saying that we're describing a world in which physical systems have configurations in a somewhat flat-footed sense, akin to how we might think of configurations in classical physics. Now, this isn't because I have some absolute unwavering commitment to classical-type ontology. It may be that in some future physical theory, we really have to abandon this.

57:38I see this as an intellectual, a form of intellectual exploration. Can we make such a flat-footed ontology work and still get an empirically adequate theory? The answer may be no, but I think there's still this question, can we make that work? And if we can, well, that would be an interesting thing to do. So that's the first part of the theory. And that's my realism, right? Can I get a clarification about that? Sure, please. Yes. I just want to press you a little harder on the question of realism.

58:15I would have thought, and this isn't just an academic remark, I guess this is the kind of theory I'm looking for when I say I'm looking for a realistic theory. I would have thought that it's part and parcel of realism that one takes there to be an objective, determinate fact of the matter at all times and under all circumstances about the situation of the entirety of existence, of the entirety of the universe. Okay. That's something that I always took to be part and parcel of what it is to have a realistic attitude towards the world. Of course, that leaves all sorts of epistemic questions unanswered.

59:09How much can we know about that? Blah, blah, blah. But part of what I mean by a realistic theory is a theory that tells us what physical situations the entirety of existence could or could not be in, and how those situations evolve with time. Is that your picture of realism, or is there someplace you would get off that train? Well, David, here's just a problem we have with standard quantum mechanics. It's not clear we have a place to stand if you're trying to approach a system that's right in front of view. Every system we have any contact with that we know about is an open system, and open systems are very difficult to work with in quantum mechanics, very difficult to give them dynamical rules.

1:00:00So we do this move where we just look to the nearest enclosing closed system, and then we apply the dynamical axioms of quantum mechanics, whether that's the orthodox Dirac von Neumann axioms or something like the Bohm theory or Everett or whatever. And then we apply some rule to how that closed system evolves. And then we look down into the innards, the smaller subsystems, the little Russian dolls inside of our bigger system. Jacob, is that different from what we do in, say, Newtonian mechanics? Yes. Yes, it's different. Say something about that. Yeah, yeah. So, yeah, so Newtonian mechanics, if you hand me an object in front of me, so just a body in space or on a table or whatever.

1:00:51In general, that's not going to be a closed system. It'll be an open system. And I can believe on the Newtonian world picture that there is some fact of the matter about the position of the body, its constituent particles. There's some fact of the matter about the velocities of the body and its constituent particles modulo, all the usual concerns about what do we mean by a velocity? Is that really an instantaneous property? Let's put that aside. And I could also believe there's a fact of the matter about what the forces are on that body. Now, I may not know all this information. I may not have full epistemic access for practical or principled reasons.

1:01:26It may be that I simply don't know everything that could be acting on this body. But I can believe if the Newtonian picture were true, I can believe there is a fact of the matter about the position, the velocity, and what all the forces are. And that means that on the Newtonian theory, I can believe there's a fact of the matter about what the next infinitesimal next moment configuration of this body will be. And then I can believe at that moment that there's some new set of forces maybe on the body. It's got some new position, some new velocity. And so I can believe, again, that there's some fact of the matter about what its next position will be and so on and so on.

1:02:02That seems a little bit misleading. The forces, first of all, at the initial moment, and even more so at the next moment, may well depend on the state of everything that there is. So it's still appealing to some notion of the totality of what there is. Well, that may be the case, but let me come back to this mere logical question. This is important. So, of course, one view could be that there are background forces and forces that don't come from particles. I mean, one can take a view. Maybe they are forces that come from, but we need to know about all the particles that there are. That's true.

1:02:44That's true. But my point is, if there's an object in front of you, it is an open system. And whether or not you want to talk about what's going on the rest of the universe, there's a fact no matter what those forces are. And I have a law that tells me, well, not a law I can necessarily use because I don't know all the details, but in principle, there's some law that dictates what it will then do. Now, in practice, I don't know all of the forces. I don't know everything exactly. So I make approximations. I come up with an idealized model of this Newtonian system with fewer simpler forces, with some truncation on the decimal places of the initial position of velocity and so forth.

1:03:24And then I use this model to predict what it's going to do. And I'm aware, even before I've done an experiment, there's going to be some error bars around my predictions. That is, there's an actual, the actual system as represented, according to Newton's laws of nature. And then there's my model. They're both phrased within commensurate theoretical frameworks. They're both in Newtonian mechanics. And I can talk about how much deviation there is between them. For example, I could put an estimate on how many, I could say, I'm going to ignore all forces that are less than some amount or whatever.

1:04:02And then I can just theoretically begin to estimate how far my deviation is going to be. Let's compare the situation to quantum mechanics. If you give me a system, an open system in front of you, and it's open, it's an open system, what is its dynamical rule supposed to be? In general, there is actually no dynamical rule at all. There is none. This is true even if I have a closed system it's inside of, and even if I know the Hamiltonian of a closed system, There will be no rule at all for the subsystem. None. Jacob, there will be a rule if I suppose that the subsystem state is separable from the rest of the world.

1:04:46contingently wait wait wait wait but that seems to me exactly analogous to supposing that that in the newtonian case the influences of other distant parts of the world i can safely assume to be minimal um or something like okay but so there's a there's a the confusion here is again i have two models one is the way things really are the facts the matter and then there's my idealization. In the Newtonian case, I have both of these things. I can believe that the object in front of me, there's some fact of the matter, but the force is on it, its state, what it's going to do. And then I have my idealization of it.

1:05:24And they both live within Newtonian mechanics. In the quantum case, you're right. I can make idealizations. I can assume as a simple idealization that the initial state of my system cleanly factorizes off of this environment. I have my idealized model, and that will have some dynamics. It'll have some rules. But it's not approximating any dynamical model for which there's a fact of the matter. The open system, right, without those idealized assumptions, the open system doesn't have laws. So again, OK, let me wait, Jacob. Yeah.

1:06:03I thought I asked a straightforward, regular guy question, and I'm not sure what answer I've been given yet. Here's the question. Yes. Is it part and parcel of what you mean by a realistic scientific description of the world? OK, that it is committed to the claim that there is invariably a determinate fact of the matter about the physical situation of existence in its entirety. OK, in its principled entirety and that the task of physics, the fundamental task of physics is to is to describe how that state of that entirety changes. And then we can derive everything else we want from that. Is that your picture of a realistic theory?

1:07:01Here's what I would say. On. That's not a yes or a no. The answer is nuanced. OK. If we're taking a metaphysics in which we believe that there is a maximal system that's well-defined, then yes, I would prefer physical theory. And I would say it is an ideal feature of a realist physical theory that it would be able to give us a description of that. But this is contingent on whether that is metaphysically the case. So the only reason I brought the quantum mechanical example was just to show that there is already a problem in quantum mechanics with this. where we need to go to a, to have any dynamics at all, we have to go to a sufficiently big system.

1:07:41And then this question of like, how do we know that such a big system exists? In the language of the metaphysics of myriology, we would say, how do we know that it is necessarily the case that there is a so-called myriological top system or universal fusion, that people have different language for this? And it turns out this was actually a very jealous question. How about saying it in more pedestrian language, more pedestrian philosophical language? There is an entirety of existence. Okay. And what our fundamental theory is fundamental. David, how do you know that? How do you know that there is an entirety?

1:08:20I don't have a proof of that. And that's part and parcel of my not having a proof that realism is true. I mean, maybe we're just having a semantic argument here. I'm not sure if it's semantic. I think it's substantive. Yeah. Okay. But I mean, there is a, I don't know what to say. What I'm used to wanting from a realistic theory, okay, what I get from Bohmian mechanics, what I get from Newtonian mechanics, what I get from the GRW theory, so on and so forth, is an account of the history of the entirety of physical existence. Of course, that takes it for granted that there is such a thing as the entirety of physical existence.

1:09:15If somebody has a good argument why there couldn't be an entirety of physical existence, why there couldn't be such a thing, why the very notion is incoherent or something like that, that would be interesting. And that would constitute, I would say, a serious challenge to the way we've traditionally understood realism. OK, but in the absence of such a principled argument, I should think that it's a pretty straightforward demand on any scientific account of the world that I would consider that I would be interested in giving the label realistic to. that it constitutes, among other things, and not only among other things, but as it were primarily and in the first instance, an account of how the entirety of physical existence works.

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1:11:18Because Quaker's coming in hot with morning nutrition. 100 % whole grain oats and a good source of fiber to fuel the rhythm of your morning and kickstart your day. And that sounds absolutely delicious. Fuel to start whatever's next. Quaker, official sponsor of FIFA World Cup 26. I, O, let's go! Yeah, so again, we're, so, I don't think we have a semantic dispute, But I'm basically saying that I agree with you. I just don't want to engage in too much a priori metaphysics. That is, Newton's theory has the nice feature that you can be agnostic about whether there is a complete universe and a theory still works just fine for open systems.

1:12:09and what's interesting about when you say you agree with me does that mean that it's gonna that it's gonna be fine if we go on with this conversation assuming at every point that that is true that what we have what we need yeah yeah no that's fine if we're gonna take this discussion there is a mere logical top system then then yes i would say that i would prefer when i talk about a realistic theory, that it be a theory that gives a description of that. So I'm right in reading your theory that way, as a theory of the top system. Yeah. If there is a top system, then we can describe it. But I see it as one of the advantages of the theory that, like Newtonian mechanics, we don't have to make that a priori assumption.

1:12:53I don't know how to do Bohmian mechanics or Everettian mechanics or any of those other theories without something like that assumption. That worries me about those theories. I have to say that I don't know how to do Newtonian mechanics without that. But we've been back and forth about that a little bit. That's fine. That's fine. Okay, that's fine. Yeah, so we're in agreement, actually, I think. OK, so if we're in agreement about that, so then we don't need to debate about that anymore. That's what we're talking about here. A theory of the top system from which all of the features and and and evolutions of the lower down systems can be described, can be deduced.

1:13:34I just need that if people listening are interested in learning more about these questions about whether there's a mirror logical top system, in the terminology introduced by Jonathan Schaffer in 2010 is this question about can there be so-called junkie systems? there's a really beautiful paper by Thomas Mormon 2014 called set theory topology and what is it set theory topology and the and I think the possibility of junky worlds I think that's the name of the paper and he has lots of very simple element or examples for where you have simple sensible mirror logical systems notion systems where there's things that are parts of other things where there just fails to be a top system.

1:14:22So that's all fine. But let's put that aside. If we're, for the sake of argument, going to take for granted that we can assume there's a mere logical top system, then I'm happy to proceed. And I would be, the claim would be that this theory could accommodate that, yes. Good. So then, well, I don't want to direct, but maybe this will help me. My thought is that if it's conceded for the sake of this conversation, that there is a top system, okay, then what I said about your laws constraining the dynamics no more than the bell jumping around theory does, or maybe I should put it as a question. Yes.

1:15:10Assuming that there is a top level system. Yeah. Was I wrong to think that your laws don't constrain the dynamics any more than bells jumping? Yeah, that's that's that's the second point. So the first point I made about the theory is and just to reiterate, systems have configurations in a configuration space in something like physical space. That was point one. Now, point two, there is more structure, more structure than in the version of the theory that you presented. And again, this is a point where I'd say I had always implicitly assumed we had this structure. I agree that I wasn't as clear about it.

1:15:44And conversations like our discussions have helped me see that and be more explicit. So the second point is there's some more structure. There's modal structure. There's probabilistic structure in this theory. And there has to be because we need probabilities to sew things together. Here, I'm very much motivated by my older work on the modal interpretations, which suffered from a lack of the structure and from the effort question mark theory, which lacked this structure. We have this sort of connective tissue connecting one time to another that lets these wild fluctuations happen. We don't like that.

1:16:15Okay. So here's the second point. What I'm saying is that each system we want to consider, whether it's open or closed, in addition to having configurations, forms a stochastic process. Now, a stochastic process is a fairly old idea. Stochastic processes go back the better part of the century. What is a stochastic process? In general, a stochastic process, I can give you the mathematical definition, but I'm not going to do that. It won't be interesting to people. One way to think about a stochastic process is it's some kind of variable maybe representing the configuration of something. And this variable changes probabilistically with time.

1:16:59And this model comes with modal structure. Modal structure meaning like structure beyond just physical, like ontological facts at locations in space. like other structures. Modal structures include things like probabilities and laws and so forth. There's more modal structure here. These stochastic processes come with probability distributions over multiple times, right? So the model comes with a probability distribution that the variable is some value X at a given time. It comes with a probability distribution that the variable is X at a certain time and Y at some other time. It comes with the probability that the variable is x at a given time, y at a given time, z at another time, and so on and so on.

1:17:46There's just this tower of so-called multi-time joint probabilities, just where the system is. That's a lot of additional structure. Now, often simplifications are made when stochastic models are used in practice. We assume that a lot of that extra structure is somehow trivial, or ignorable. And we get a very simple kind of stochastic process called the Markov process. The characteristic feature of a Markov process is that you just have to know what's going on at one time and then you have probabilities that say would happen later and the past is ignorable and it simplifies these stochastic processes to assume they're Markov.

1:18:31Now, I say a little bit about why you might want to go beyond Markov. There's like many different reasons in recent years that have pointed to something very deep and intrinsically non-Markovian going on in quantum mechanics, even separate from the kind of prosaic violations of Markovianity that come from systems being open. There's like situations which even closed quantum systems seems to exhibit various forms of non-Markovianity. But in any event, a generic stochastic process will not have those simplifications. There'll be a huge assortment of these higher order probabilities. And you can understand why physicists have not been terribly interested in touching these theories with a 10-foot pole, because it seems like if you were to somehow take all of those multi-time joint probabilities to be laws, it would be a huge amount of information you'd have to specify, in principle, an infinite amount of information.

1:19:23And we don't want laws that are infinitely complicated. You end up - Wait, Jacob, I'm getting lost again. Let's go to a very simple case. Once again, we consider a world which in its entirety is a collection of particles with positions. Yes. Okay, at every time. Yes. Good. I described a law that gives the positions at any time, the configurations at any time, assigns a probability distribution to the configurations at any time as a function of an initial configuration. Yep. Was that law false or incomplete? Incomplete. So say a little more. So stochastic process has a lot more probabilities in it than that, a lot more joint probabilities.

1:20:18There are probabilities, you know, given that the system is in X at configuration X at one time and that it's at Y at some other time. And it's either there's all these additional probabilities that do something. They're doing work. So it's not just that there's just sort of disconnected standalone probabilities every time or even one conditional probability at some initial time T naught. that gives you a conditional distribution over all the times and nothing else. For a generic stochastic process, there are going to be way more probabilities. Yeah, but I'm not interested in the generic stochastic process.

1:20:53I'm interested in the theory you can... Right, but that's just step two. In order to reproduce the predictions of... I understand, David, but I need to, first of all, say what a stochastic process is, because I'm claiming that quantum systems are stochastic processes. That's all I needed to say. Stochastic processes come with some collective... Do you claim that quantum systems are stochastic processes a way of negating, a way of saying that the way I described your theory was false? Yes, that it was incomplete. Oh, okay. The way you described it had too little modal structure. There's more modal structure in the theory.

1:21:30Oh, wait, wait. So the probabilities are something other than what I said in that initial introduction? The only probabilities are numerically different from the ones that I specified? So you specified some of the probabilities, but there's more. And those other probabilities are doing work. Give me a simple example of an additional one and of how we calculate it in your theory. That's the next step. Good. So now that I've told you the ontology and I've told you that it's some stochastic process, which means that in principle, there are all these two and three and four time joint probability distributions.

1:22:04That's a lot of modal structure. And you might think this theory is non-predictive. Okay. So now we have the third step. Okay, here's the third step. The third step is we imagine, and here, like explicit models can be written down, so this isn't just speculation, but you can imagine you take one of these stochastic processes, it's not Markov, it's got all these multi-time probabilities, we don't know what they are, and you imagine that there is some particular time. t prime call it time t prime and at time t prime something interesting just happens with this theory at t prime the among all the probabilities this system has it has many two three four times probabilities conditional probabilities all that at this time t prime the first order conditional probabilities that means that among all these probabilities the ones of the form probability the system is at X at some time T, given that it was at Y at time T prime, those probabilities, and those are called rooted at T prime.

1:23:07That means they're conditioned at T prime. They're rooted at T prime. Suppose there's a time T prime at which those first order conditional probabilities become independent of the standalone probability distribution at T prime. Okay. So there's a sequestration between these first order probabilities and the standalone probabilities of T prime. That means just to make this super clear, what I'm saying is there's a time T prime at which on the one hand, we have the standalone probability distribution, just unconditioned, the probability of what configuration Y the system is in at T prime. And we have a conditional probability, the probability that it is X at T given that it was at y at t prime we have these two things the standalone probabilities and the conditional probabilities and they neatly separate the conditional probabilities do not depend on the instantaneous conditions at t prime anymore they do you mean do you mean that the dependence is exactly zero ah no let me come back to that in a moment it's not exactly zero but let me come back to that because it's very important.

1:24:21Okay. Let's suppose just for the second that it's zero, but then I'll come back and explain what we don't need to be zero. If it were exactly zero, what we would suddenly have in this model is what we call in the physics philosophy of physics parlance, a good initial value problem with a clean separation between initial conditions, just meaning the instantaneous conditions at T prime. In this case, represented by the standalone probability distribution at T prime on the one hand, and then separately, a dynamical law in the form of first order conditional transition probabilities rooted at T prime that tell you, given the system's configuration T prime, this is the probability distribution for this configuration will be at any later time T, what configuration X will be at a later time T.

1:25:10This is now a good initial value problem. You can counterfactually imagine different probability distributions, standalone probability distributions, T prime, and counterfactually altering them, you've got a dynamical law that then projects those forward and tells you what's going to happen. That's what a division event is. Now, if division events are not exactly perfect, all that means, it doesn't mean that we had nothing and that there's no modal structure and everything falls apart. It just means that the initial value problem is slightly imprecise. and that the behavior of the system will deviate ever so slightly from the predictions that you make if you assumed it was a perfect initial value problem.

1:25:56Now, to be clear, these division events, as I prove in the paper, they emerge out of decoherence. And so the discrepancy... Not exact ones, of course. Not exact. No, not exact. But they're exact to like one part in 10 to the 40. Yeah, yeah, yeah, yeah. But that's not the... But the point is, it's not that without them, the system has no modal structure. This is the key thing. So that's what I'm not understanding. Yeah. So look. Now this is akin to the Newtonian case where there's like an exact statement of what the forces are that we don't know. And yet there is something that really does happen.

1:26:29And then there's our idealization that we can make predictions with and there'll be tiny discrepancies. This is exactly the same thing. Look, you got to help me out a little. Okay. Yes. I gave in the first, in the opening, beginning of my remarks, a one sentence, complete statement of a theory of the entirety of physical existence. OK, now, maybe that theory was wrong. Maybe that theory was not the one that you intended. Right. It's not. It is a theory that's going to be in this trivial and useless sense empirically adequate in the way that the bell jumping around theory is and so on and so forth.

1:27:17But good. What you need to give me, I don't think it's going to help me to hear hear a lot of stories about all the varieties of stochastic dynamics there are and so on and so forth. Can you give me a succinct statement like F equals MA in the Newtonian case or like the statement I gave you in the beginning of my remarks about what on your picture the complete laws of the world are? I gave a succinct statement of those. I gave it in one sentence. I was proud of the simplicity of this one sentence. you obviously you it's clear that your reaction is no that's not my theory right um good is there a is there um um a theory with is there a way of stating what your theory positively is that rivals my statement for succinctness i mean as long as i'm allowed to assume that people know what a stochastic process is no you're not no no i didn't but like i didn't assume that i i gave such a simple claim okay but the claim is that the universal stochastic process i don't know how to nation of the world here's how you calculate the probabilities of future configurations period end of story let me try my best here okay okay so uh there's a set of possible configurations of your system yeah there is as part of the theory although we don't have epistemic access to it a whole bunch of joint probabilities for all the goings-on of the system and at certain moments these division event moments the t primes we get a nice emergent initial value formulation where you can imagine counterfactual initial conditions at that time and then projected them forward what are the rules of doing the calculation what are the rules for calculating all these probabilities excellent that's the next point good so um there are two nice ways to think about this the first is uh very general if you have one of these division events just spontaneously occurs.

1:29:43Oh, wait, wait, wait. You've got to tell me what a division event is. A division event is not an exact division event because - It doesn't have to be exact. No, no, no. What does it have to be? It just has to be - We're talking about fundamental laws. I understand. There is a fundamental description. If you want a so-called, there's an exact description in which what we have is a configuration of the system changing in time and a bunch of multi-time joint probabilities capturing what it's doing. We don't have access to that. And we shouldn't have to talk about anything else but that. That's fine.

1:30:12That's fine. That's good. But a system like this will simply, in the generic case, occasionally have times where things simplify. But forget about that. Yeah. Just tell me what the basic universal rules are. I did. That's the rule. The rule is that there's... That's... And then in some situations, they'll simplify... No, no, no. Start at the beginning of a sentence. Don't say and then in some situations. What's the rule? So I think you may be thinking a little too narrowly about rules. I'm saying that what nature is is a stochastic process. That means that there's configurations and there's also probabilities.

1:30:55And in general, that's all you got at a fundamental level. But in. So the question is, like, where are the laws? Where are the laws for a completely generic open system, not at a division event? there aren't any. This is the structure you've got. Now, what can happen, and of course, what you have to assume, the past hypothesis of this sort of picture, is that there was a time, T naught, if you will, where that complicated set of probabilities has this nice feature that at T naught, we get a nice separation between the standalone probabilities and the first order transition probabilities, the first order conditionals that are rooted there.

1:31:36And we assume that happens. We don't assume it happens anywhere else. But here's what's really cool about this. If there is such time, then there's a simple mathematical transformation you can do that turns this whole system into a Hilbert space description. Not only a Hilbert space description, but it turns out you can represent how the system is behaving using unitary time evolution operators, all the usual familiar

1:32:10appurtenances that we know and love from quantum mechanics. And so as long as there's one such moment, we're going to have something like a representation of which we have unitary time evolution. Now, here's the next thing to say. If this system is really big, and again, you can construct very concrete models of this. One of them is constructed in the paper. If you had a big system with lots of degrees of freedom, that just means its configurations are very complicated, a lot of moving parts. We could talk about subsystems. Subsystems would just be some sub-collection of those degrees of freedom.

1:32:46And if you set up a, if you imagine that the overall structure of this whole thing, the Hamiltonian, the Unitary Evolution, whatever, You set it up so that something like a measurement-like interaction takes place. Now, I said the word measurement. I'm not treating measurements as primitive. Just two systems happen to bump into each other, and the configuration of the one very closely changes in a way that corresponds to the configuration of the other. Just two systems being treated as part of this overall system. What you can show, and this is done explicitly in the paper, is that when that happens, the marginalized probabilities for the subsystem being measured, its own marginalizing over the environment, its own probabilities, which in general are just going to be all over the place, multi-time, whatever, they will develop a division event of this kind.

1:33:40That is, when that interaction happens, the subsystem being measured will suddenly have a clean separation between its standalone probabilities at that time and the first order conditionals. And that means that we have an initial value problem at that moment for that subsystem. It arises emergently. So what you're looking for, David, is - This level of accuracy. Sure, sure. So what's exact is the configurations and the modal structure. What's inexact are the emergent dynamical laws and initial value problems. But I don't want the emergent dynamical laws. I want the fundamental dynamical laws. So this is, I think, where there's a substantive metaphysical difference between us.

1:34:23And that's fine. I don't think that at the end of the day, on a theory like this, we're going to have as a fundamental statement that there is just some initial value problem phrased in terms of dynamical laws that take the form of conditions on freely adjustable counterfactual initial conditions as a general statement. So what I'm proposing is that there is a more primordial modal structure from which that picture of dynamical laws and initial value problems emerges to a very good approximation in various circumstances. And I see this as an asset in the sense that we explain what is a mysterious fact about the nomological structure of our physical theories.

1:35:07I mean, one big question that people have had a long time is, why do our best physical theories have this clean nomological law-like structure? We have this nice, clean separation between initial conditions and inimical laws. here I'm giving you an account with a much more primordial structure, modal structure, from which that clean initial value formulation with clean laws, separate of minical conditions, emerges to a very good approximation in real world cases. So I'm trying to get at that structure from a more primordial structure. And my argument is that in order to get quantum mechanics to make sense, we have to make that move.

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1:36:45um um well in order to make it make sense without a wave function sure ways of making it make sense sure yeah but anyway i'm although i would argue you can't make sense of it with a wave function anyway so that i wanted to get to this also it's not just that i think but wait hold just hold on one second before we move on sure look um i started out my little remarks by apologizing profusely about how much they were going to take for granted um in terms of the knowledge of the listener. But you're, I mean, you're going way beyond that. Okay. There's, there's, it feels like I'm asking a very flat footed question.

1:37:34Okay. I shouldn't be asking things then. If I hear you, I shouldn't be asking questions like, what are the fundamental dynamical laws or what are the fundamental laws under which the probabilities? What do you mean by laws? I mean, do you want to get into a whole human? Not the metaphysics of laws. I don't mean like our laws human. So what are you asking? Do you think that? Here's what I, here's the picture that I had. Okay. Yes. We need initial value formulation. You have a law. Well, I don't know if it's right to call this an initial value formulation because it doesn't assign states at every time.

1:38:21I'm asking you if you think it's necessary for laws that there be an initial value formulation. No, no, no. You think it's a necessary condition? It depends what you mean by an initial value formulation, but I'm pretty sure the answer is no. It's fine with me if you have other kinds of boundaries. You know, there are laws of electrostatics, okay, which have boundary conditions. I'm sorry, boundary conditions. Do you believe that it's necessary that laws be dividable into boundary conditions? But it doesn't have to be that either. I mean, F equals MA doesn't refer to particular boundary conditions unless you're setting up a particular way of solving it.

1:39:00So, no, there's no attachment to anything like that. I just want to know exactly what it is. And I'm hoping for a simple statement of it, like the one sentence statement I gave of what I took to be your theory in the beginning of my presentation. OK, I want to I want some kind of a simple claim. OK, about I don't know how to put this generally sufficiently generally. No, it certainly doesn't have to be an initial value formulation. I don't even see why it has to be a boundary value formulation or something like that. But some simple statement of exactly what the rules are that determine which histories of the world or which totalities of the world are physically possible and which are not.

1:39:55The rules are? And in other versions of quantum mechanics, and in the version of quantum mechanics that I proposed for you, there turned out to be a very simple such statement. So far, I'm not hearing a statement like that from you. Yeah. So the rules are the universal stochastic process. That's the rule. No, but Jacob, that's not enough. There are lots of those. Yes, there are. Good. What are the rules of this one? What are the rules? Really big. And we assume at some time, the past hypothesis, is there some time in which we get this clean separation? That's it. We get an initial value problem at some time.

1:40:35There's nothing of a dynamical nature. Not that there has to be. But I'm just asking, is there nothing here of a dynamical nature? I thought there was a dynamics here, but it was non-Markovian. You're telling me, no, no, no, there's no dynamics. Dynamics is not the right way to think about it on the fundamental level. so um sounds like you're saying yeah so um if you take a non-markovian process and you imagine all the probabilities of the form what's the probability my system is in configuration x to time t given where it was at time one given where it was at time one and where it was at time two given where it was at time one and time two and time three and so on and so on and so on you'll get a tower of conditional probabilities that you can think of as the dynamics of the non-Markovian process.

1:41:28And those would be something like dynamical laws for the non-Markovian process. So if you want, that's the laws, right? I'm still, okay, I shouldn't, I'm sorry, I'm prolonging. No, but this is actually very good. What may not be useful. I'm making a posit about what the structure of the world is like. I'm saying that the world consists of configurations of things that change with time. And there are probabilities that systems might be described. The world consists of configurations of things and those configurations change with time? Yeah, the configurations change with time, but those changes with time are systematized by some set of joint probabilities.

1:42:10Good, good. Those configurations change with time? Yeah, they do. Wait, wait, wait, wait, wait. Let me finish your sentence. Good. What I'm used to thinking I'm going to be offered by fundamental physical laws about worlds like that is some claim like, here is the set of evolutions of these configurations that are physically possible, and here's the set that aren't. Okay. I'm used to being offered some simple rule which distinguishes between those two. It sounds like you're telling me that's not what I should be hoping for. Well, I mean, you'll have probabilities that are higher for some things happening and lower for other things happening.

1:43:03And probably there are some things where the probabilities are negligibly small. We would say those don't happen. um but yeah i'm giving you that structure i'm saying that there are probabilities over all the you know joint whatever you know configuration system and some of them will have very low probabilities some are very high probabilities no no no but say in the grw theory you also have you don't have deterministic claims of the form this sequence of states is physically allowed that sequence of states is not physically well the grw theory is probabilistic so yeah that's what i mean yeah yeah so but you're not going to have a clean thing where you say these are definitely impossible and these are that's right but what you do have okay are claims about um um well are the kind of thing that you're calling an initial value problem okay right tww has an initial value problem right right um or initial value formulation initial value formulation what i'm saying is we can take an initial value formulation at t t naught to be our past hypothesis, if you will, to get the ball rolling.

1:44:08Wait, wait, wait. Take an initial value formulation or a claim about the initial value to be the past type? Oh, oh, oh. So if you want both, I mean, in the Mintaculous, there's both a statement, the past hypothesis about the macro state being low entropy, and also there's the statistical postulate about, you know, the probability distribution over initial microstates. in this case to get the ball rolling you need there to be a t naught at which you have an initial value formulation you can then argue well okay now that we have this now initial value formulation we we can then maybe ask okay what is the initial distribution need to look like and we might impose something like this distal postulate on that yeah yeah no no no i'm i'm sorry, I'm dragging us off the point here.

1:45:01Look, on this topic here, I feel a bit lost at the moment. I don't understand what it is, what set of claims it is that your theory is making about the entirety of what exists to say that it's a stochastic process isn't enough i i want to know yeah so i i want to know i want you know in the grw case i have precise extremely simple rules saying which which evolutions of probabilities are physically possible and which are not Okay. It doesn't sound like I'm going to get something similar here on a fundamental level until I have a division event. Let me try. Maybe this will work a little better. Let's make the following stipulations.

1:46:03Okay. Configurations, stochastic process, and, and there's a T naught, a time T naught in which the stochastic processes we're going to consider are all going to be ones at which at this time T naught, there is this clean separation between initial conditions. What do you mean by the ones we're going to consider? You mean the entirety, the ones that concern the entirety of the existence? Yes. Yes. Oh, this is exact. Yep. Yep. Well, I don't know if it's exact. It could be. It might not be. I don't know if it is. Jacob, you're making me nervous. My point is I'm not going to make an a priori statement.

1:46:42I'm not asking you to make an a priori statement. There is, so far, the game of fundamental physics has been played within the context of what I'm calling this realistic assumption, that there are these facts about what the entirety of existence is doing. Yes. You say we don't have a proof of that. No, no, no, David. It's not what I'm saying. It's not what I'm saying. I'm saying the facts that you're referring to are facts about configurations and joint probabilities. And I'm saying those are those are facts. But what you would like is something more than those facts. You also want some kind of additional thing.

1:47:30And I'm saying that. So I I'm a realist here in the sense that I'm saying, like, there are configurations at all times. There are joint probabilities. there are configurations of everything of everything at all if you if you if we're going to take for granted there's a mirror logical top system yes system of everything yes i'm saying on this theory that that top system has a configuration at every time and that there are joint probabilities of what its configurations are at all times and those are all statements about what this thing is doing and in the evolution of that top system say what And in the evolution of that top system, are there exact division events?

1:48:09Maybe, maybe not. I'm not assuming that there are. There could be, but I'm not requiring it. It seems like... No, I'm not requiring that there are. We have a well-defined behavior, and I am assuming that there's at least one that's very, very good. And from that very, very good one, we get a nice, clean initial value problem that we can use to make predictions. Okay, okay. That's the same thing, yeah. Okay. I feel like I'm not being helpful here. I'm just lost. I would have, like I say, here's something which, if you're inclined to think about it, would be helpful. have if my initial statement of the fundamental laws of the world on your picture was false okay give me one that is makes makes um predictions that the theory you actually believe in is it's numerically different from those false in that very flat-footed sense if it's false It would be great to have a simple statement of what's true that rivals in simplicity the statement I gave, which you're telling me is false.

1:49:29So it's false in the sense it's incomplete. It is the case that if I give you a stochastic process for a maryological top system, it is the case if I give you this, and if there is a division event at T0, then it will be the case that among the modal structure will be the probabilities you were talking about. Conditioned at T0, such and such with the probability later times. That will be among the probabilities, but it won't be the only probability. I gave a crisp prescription for calculating those probabilities. Yes, yes. What's the prescription for calculating the other probabilities that this one leaves out?

1:50:07Excellent. So in general, we won't have epistemic access to all of them. They'll be beyond our ability to do it or no. But what you can show is that if you have all that extra structure there implicit, even if we don't have epistemic access to it, then what it will entail is that subsystems bumping into each other will develop their own initial value. What are the rules of the extra structure? I gave you the rules of these probabilities of configurations at any one time. It's the Schrodinger equation and the Born rule, period. Okay. What are the rules that determine the extra structure? If you take an initial division event, put a Hamiltonian there.

1:50:53No, but Jacob, I get so queasy when your answers start with if. I'm asking an unconditional question. What are the rules? I don't think there are answers. All questions are conditional, right? Come on. No. Okay. Look, what you're demanding is a level of simplicity that is not going to work. It's not available. And I want to make very clear here, and I want to pivot a little bit because we have more to talk about. But we're going to have to give something up. What I'm giving up is exact initial value problems. That's what I'm giving up. But I'm not giving up modal structure probabilities. Now, what I've argued is that we have no other theories on the table that are going to work.

1:51:40And I want to talk a little bit about why that is. We have Bohmian mechanics. We don't have Bohmian mechanics. No, David, we don't. We have bolemy mechanics only for systems of fixed numbers of finite and many non-rollers. No, I don't agree with that. But that's another story. No, this is actually very important because if you think that there's a way out of this, you'll be like, well, why do we need this crazy idea? We have a suggestion from Bell. Oh, we do? Yeah. You're referring to Beables for quantum field theory, 1984 paper? Yeah. Unfortunately, it doesn't work. What do you mean? Okay. So I have to tell a little bit of history here to explain why it doesn't work.

1:52:14This is actually really important. It's not widely known. So for the background for the listener, Bohm's theory is when dealing with non-dwell-disk particles, it's deterministic. But when you want to generalize the theory to handle fields, it's a little complicated to do for all kinds of reasons. And so what John Bell proposed in 1984 was a stochastic jump model, a Markov-type jump model, where the number of particles and their locations, at least for fermions, they jump around kind of in a stochastic way, probabilistically, but in a Markov way, in the sense that you only need the initial wave function and the initial state, and then you get what comes forward.

1:52:54As best I can tell, this idea was basically accepted broadly as, well, it works, the equations look fine. In 1992, there was a paper by Lucian Hardy at the time he was at Durham and Holm and Squires and Whitaker. It was called something like Realism for the Quantum Mechanical Two-Level Oscillator, something like that. It was in Physical Review A. I don't think they knew about Beables for quantum field theory, or at least it wasn't cited in the paper. What they presented was a simple version, a simplified version of Bell's proposal for a two-level system. Bell was dealing with an infinite-level system.

1:53:32Hardy et al. proposed the exact same model, but for a very simple two-level system. Today we would call it a qubit, but the term wasn't available yet for reasons that Robinson and listeners may remember. We talked about the etymology of qubits. The word qubit wasn't available. They called it a two-level system, but it was basically a qubit. And they said, can we account for what we see in the quantum mechanics of a qubit with this stochastic jump model? It was the same as Bell's model. And they wrote it down. They wrote the equations. Equations are very similar to Bell's equations. You get a master equation, all this stuff.

1:54:02Two years later, Daniel Gillespie, who I don't know if that's a name that's familiar to people here. he was a master stochastic theorist responsible for, among other things, the Gillespie algorithm, which I think is like 13 ,000 citations. He wrote books on this. Anyway, he had an interest in quantum mechanics. And so he read this paper and he said it doesn't work. And because this is a simplified version of what Bell was doing, a fortiori, Bell's model also doesn't work. And so he wrote an article explaining, and the title of the article was 1994, also in Physical Review A. Not widely known, not widely cited.

1:54:40But the title of the paper is Why Quantum Mechanics Cannot Be Formulated as a Markov Process. That's what it was called. And he said, you know, the mathematical equations are great. They look perfectly beautiful. You know, you took quantum mechanics and you tried to write down these equations that formally resembled the equations of a stochastic process, a Markov process, but they couldn't actually describe an actual Markov process. some things were lost in translation. If these equations purportedly describing a Markov process really were describing a Markov process and all the ingredients really had meanings that you would give them if this were really a Markov process, then mixed into some of those mathematical ingredients would be various additional probabilities, various additional transition probabilities and stuff.

1:55:31and what Gillespie showed was that some of those probabilities failed to stay between 0 and 1. Now, if you weren't paying attention to this, and Bell certainly didn't pay attention to this, there was none of this in Bell's work, you got to make sure that every little quantity that's going to end up being something like a probability stays in the right bounds. Bell didn't check that. And what Gillespie shows is some of them diverge enormously. Don't stay good probabilities between 0 and 1 is this couldn't possibly be coming from a Markov process. So Gillespie wrote this paper, and he had a couple of other criticisms.

1:56:07There's a variety of problems that show up. And then Hardy and his colleagues, they wrote a paper, it was published in 1997, responding to this. It was Reply to Why Quantum Mechanics HB. And then Gillespie wrote Comment on Reply to, also 1997. And then it basically just petered out after there. These papers have, I think, a combined, I mean, I think Gillespie's articles got like eight citations. Basically, no one saw them. But you can read them, and they are pretty devastating. I should. Yeah, they're worth reading. And I recommend, unfortunately, Daniel Gillespie died a few years ago. I think he had brain cancer.

1:56:44It was very unfortunate. Now, what did this lead him to? Interesting. Remember, I told you how roads keep leading to non-Markovianity. So what Gillespie decided to try a few years later was to see if he could build a non-Markovian stochastic formulation of quantum mechanics. And he attempted to do this in a couple of papers in 2000, 2001. He gave up. He didn't know how to make it work. And, you know, I'm both very grateful that he tried to do it and also grateful that he didn't succeed because then I wouldn't have had anything to do. But it's worth noting that one of the world's great historical stochastic modelers looked at what Bell, not what Bell was doing, but what Hardy was doing, which is a simple version of what Bell was doing, and said this is not really a valid process.

1:57:25Well, look, needless to say, Jacob, this sounds very interesting. It's very interesting, but it also means we lose that as an additive. I should look at it. I have no idea what to say about it off the top of my head. I wouldn't. Yeah. Little known papers. But I'm just saying, like, if your thought was, well, why do we need this? We could always go to we can't always go to be. Even if all of this is exactly as you're reading it, there's no argument that this is the only way to bowmize quantum field theories. That is Bell's way. That is, even if everything you're saying about the way Bell fails is taken is taken on board.

1:58:03There's no reason to think that's the only available route to bowmizing field theories, quantum field theories. But anyway. Yeah, I would view this as the way to do it. Basically, if you take Bell's approach, which was Markov and show that it doesn't work, you could say, well, is there a non-Markovian way to bow my eyes? Or is there an altogether different approach? But my approach is the non-Markovian version of what Bell would do it. And I think Bell also mentions in this paper, you could do it deterministically with non-Fermion fields. Okay. It's part of the Fermion fields. And it might be, for example, that knowing the value of the gravitational field everywhere in this room is enough to tell me where the tables and chairs are and so on.

1:58:53And maybe that's all I need from such a theory. So there are lots of, Bell didn't go very far with this. There are lots of approaches. The stochastic approach you're mentioning is not the only one that he mentions, even in that paper. Yeah. And, you know, our friends, Shelley and Nino and everybody, they talked about exactly what are the ontological commitments we need at minimum to get a real picture. Maybe we only need bosons. Maybe we only need, you know. Exactly. Right. Granted, granted, right. I have a completely deterministic theory, as in as in Bohm's non-relativistic chronomechanical theory, yada, yada, yada.

1:59:30So there's a lot to say about that. If the if the status of the discussion is obviously none of the existing approaches can work. If the status of the current conversation is obviously all of the existing approaches are at a definitive dead end. That seems wrong to me. OK. And and and then questions can arise. OK, if they're not all at a dead end, how much would be will would we be willing to sacrifice of what kind of thing? So on. Then we get into a delicate balancing act of the time we've been dealing with for a long time. But let me ask you a question. How old is the Bohm theory at this point?

2:00:15How old? I mean, it was first published in the 50s. yeah yeah he's bohm started working on the late 1951 he published it how old was aristotelian physics no but here's my point better yeah but wait wait david and of course if you go back to de broix's formulation in 1930 which was very similar to bohm's theory we're talking about a theory that's almost clear that i didn't understand his theory that uh his book is with objections to his theory, which he should have taken care of with a wave of the hand, okay? And he sort of gave up. So de Broglie didn't understand decoherence, which plays a very important role in Bohm's theory.

2:00:55That's part of what he didn't understand. But my understanding was that Pauli pointed out to him that on his theory, an electron in a ground state orbital would be stationary, which is obviously preposterous, okay? And de Broglie put his tail between his legs and whimpered off instead of saying to Pauli, what exactly would be preposterous? Yeah, what would be preposterous? But in Bohm's theory, that's what happens. Yeah, no, I agree. De Broglie didn't have the courage of his convictions in 1930. He also didn't like the idea that the wave function lived in the configuration space. He was very worried about that.

2:01:34We haven't talked about that yet. But he had basically the structure of the Bohm theory. My point is, you know, it's not that there's a definitive argument that you can't possibly make something like deterministic Bohmian mechanics work. But it's been a really long time. And I'm not going to wait anymore on the hopes that that could happen. It could. It could happen. People have been trying to get probability to work in Everettian quantum mechanics for over 70 years. Right. You know that you and I are both in agreement that that project is not going to succeed. I think that's right. Yeah. And so, sure, there's the GRW theories, which are not ruled out.

2:02:12And to be clear, I mean, some of them are ruled out, but there's still some live GRW theories. And I don't, I regard those as certainly possibilities. But I do think it is entirely reasonable at this point, well into the 21st century, that we should strike out in a new direction, especially if - But of course, I agree with that, Jacob. of and that was exactly the nature of my introduction right i'm just i was happy in the beginning because i thought i had an exact simple statement of what it is that this theory asserts okay and um you're suggesting one that that was wrong and two incomplete yeah okay and And two, that there isn't going to be something to offer me along the lines that I guess I was hoping for.

2:03:07I mean, mind you, mind you, given, mind you. So given what I started with, my version of your theory, I don't think it's by any means at a dead end. One could experiment with adding dynamics to it. OK. In the way I suggested the initial suggestion I had for adding dynamics to it was silly. We didn't talk about it here. Yeah. But there might be better ways of adding dynamics to it. There might be a lot to say there. So let me just say that there's a version of the theory I think you'd be happy with, which is that there is a division of N at T naught, and you can take it to be exact. Let's just – the David Albert version of this theory is there's an exact division of N at T naught.

2:03:58at that exact division event because it's an exact division event we can specify exactly by a formula actual formula what the conditional probabilities will be at later times but that's not all that the theory contains it also contains all these higher order probabilities that which theory that's not all that the theory uh take the theory as i stated it okay that is not that so that's not a version of my theory at all fine is it a theory uh i guess it's a theory it's it's not the theory that i'm proposing that's okay what i'm saying is there's a version of my theory called the david albert version of the indivisible theory right that is the indivisible theory and it contains among its ingredients conditional probabilities conditioned rooted at t naught to the future but it contains more that's all i'm saying it contains more than that The rules of the more stuff.

2:04:58Right. So the other stuff is not fixed by what we have epistemic access to. It's not fixed by the first order rules. We fix the first order rules. The other stuff, I don't know what it is. But the fact that it's there at all has implications for what happens to the universe as a whole and to its subsystems. if you and this now just requires like working through calculations with stochastic processes but if you assume all that stuff is there even if we don't know what it is and you assume that we've got david's law starting from t naught and going into the future then you can do marginalization on those unknown probabilities and the details you didn't know wash out of the predictions for subsystems that's what's miraculous about this is the washing out of the unknown details So here's a version of this.

2:05:57It's not quite the same thing, but it gets a little bit about what I'm trying to say. On the non-relativistic Bohmian theory, there's a lot of information that we humans don't have epistemic access to. Now, the theory does stipulate what they are, let me be clear. Theory stipulates what they are, but we don't have epistemic access to them. Unlike in your case. Right, right, exactly. Yeah. So we don't have access to them. And if we did, if we could somehow see all the hidden trajectories of the Bohmian particles, if we could somehow see them in some sense, sense them, we could sense them, then we could do all kinds of, you know, send signals and you could do all kinds of weird stuff.

2:06:36We don't have access to them. We can't have access to them. Right. Now, in the theory that I'm describing, we don't have access to the true trajectory taken by the system, just like in the Bohm case. We also... In the bone case, the theory does tell us. Yes, that's right. In this case, the theory doesn't fix what those higher probabilities are based on what we've specified. So your law about first order transition probabilities rooted at T naught is not enough to fix what all that other stuff is. Now, the proposal is there is stuff there. It's just not fixed by the law you gave. And so you might ask, well, gosh.

2:07:15No, but is it fixed by some other law that you give? It's partially fixed, yes. And we explain. Is it fixed completely? No, it's not fixed completely. Okay, then I don't know what we're talking about. In the sense that the universe knows what it is, but we don't, is what I mean.

2:07:39So we don't have epistemic access to it. The theory does not specify what it is. Right. the first statement is true of bohm's theory also that's right but it's not the second is false right this is different from bohm's theory that's correct this theory does not the theory doesn't fix what those right higher order conditional probabilities are and so your reaction might be well there's all this probabilistic modal structure that we that the theory doesn't specify exact doesn't fix uniquely can we say anything at all about it the answer is we can because if your David's law, the one rooted at T naught, which is describable by unitary evolution, you can show it's describable by unitary evolution.

2:08:30If that evolution implies, and again, construct exact examples of this, that subsystems will interact in such a way to generate these emergent initial value problems, then that higher information we didn't have access to the theory doesn't specify, it washes out. Except if we're interested in the entirety of what exists. That's right. Yes. If the entirety of what exists, the whole universe as a whole, we're not talking about macroscopic systems like you or me or mesoscopic systems or planets. We want some statement about the entire universe as a whole. Can we fix exactly what the multi-time probabilities are for the universe as a whole, the answer is no.

2:09:15We can't fix those. However, the fact that we do get fixing of what's going on for subsystems puts strong constraints upwardly on those multi-time joint probabilities. So this is where you just get in the weeds of all these sort of calculations. We discover that if there are subsystems that spontaneously develop division events and have nice initial value statements where there's a clean separation, you can show that that actually constrains what all those higher order probabilities could have been doing, but not completely. They are left somewhat unfixed. There may be a fact of the matter of what they are, but the theory doesn't tell you what they are.

2:09:52And this means that we have a certain degree of epistemic humility about what we can demand. Now, this might not meet your requirement for what an exact theory should be. You might say an exact theory should tell me exactly what all those higher order probabilities are, even if we don't humans have epistemic access to them. As Bohm's theory does. As Bohm's theory does, except that Bohm's theory doesn't handle the relativistic case. No, no, no, that's not what I'm talking about here. Right, but I'm just saying, you're right, it would be nice to have a deterministic theory in which the theory says it's the Schrodinger equation plus a guiding equation and all of that stuff.

2:10:31Be nice. Now, the other thing is that, of course, the Bohm theory has this wave function that we're supposed to somehow make sense of. Now, one of the things that DeBroy, that led DeBroy to abandon his, you know, pilot wave theory, it wasn't the only thing, but it was one of the things was that he was very clear he could not accept that there was an ontological pilot wave in many dimensional configuration space. He is very explicit about this in his 1930 book. When Bohm independently resurrected the de Broglie theory, he was put into touch with Pauli, who issued the exact same objections. What do you mean a physical wave in what he called polydimensional space?

2:11:15And Bohm, and I think maybe Bohm was the first. I can't think of anyone else who I know is prominent. Bohm went all in. He said, that's just prejudice to say that a thing can't exist because it's polydimensional. I believe this thing really ontologically exists and it really exists in a high dimensional configuration space. And at least I'm providing you with anything because the Copenhagen interpretation gives us nothing and I'm giving you something. And they went back and forth about this and Bohm went really hard on this. You see a little bit of this in, of course, his Bohm's two papers, his 1952 papers.

2:11:57But this is really much more well articulated in this correspondence with Cowley. And I recommend people who are interested, I have a paper called Historical Debates Over the Physical Reality of the Wave Function. You can see it on Phil Sire on the archive where I show you this correspondence. It's very interesting. Everett was heavily motivated by Bohm and this view of the wave function in developing of writing quantum mechanics, which also on some views takes the wave function, maybe not in configuration space, but maybe in Hilbert space as being ontological. So if you want to go the Bohmian route, you're not just going to have to deal with all the problems we talked about.

2:12:33You are going to get trajectories. The theory is going to fix the trajectories, but there will be a cost and the cost will be that your ontology is vastly larger because of this. Oh, of course, Dick. This was, first of all, this was my, the ad for your theory that I started out with. Yes, right. Yes. And moreover, the business of what to do with this high dimensional object is something that's preoccupied a lot of my time for the past 15 years and a lot of books that I've written. That's right. But let me give a different view on what this thing is. And this is now from a different paper. And you and I have talked a little bit about this.

2:13:09There were some very interesting developments in the theory of stochastic processes starting in the 60s, but really in the 70s and 80s. Some of this was not widely shared because it was coming out of the Institute for Defense Analysis. And this is people like Lee Neuwirth. And there's a bunch of people who worked on these things in the 70s and 80s. So totally inaccessible to people develop, you know, Bohm, this is decades after Bohm. But they basically noticed, okay, well, suppose you did have a non-Markovian stochastic process. Could you make it into something that looks like a Markov process?

2:13:43Could you just like formally make it into something like that? And they discovered that there was a way to do that. The way to do that was to take all of those additional multi-time joint problems, all that stuff, and write it as a present moment new set of degrees of freedom. And they have characteristic features, David. Very, very characteristic qualities. One is there's a lot of variables you need. That's one. Another is they're abstract. They're usually phrased in very abstract terms. Another is they're highly malleable under redefinitions. Another is they're unobservable. Right. They can indirectly be related to stuff, but you can't ever actually see them.

2:14:24they don't exist in physical space they're not back reacted upon by the stuff that exists this is just a long list of things that are characteristic features of hidden these so-called latent variables you introduce to make it and these are exactly the features the wave functions have like it's hitting all of them they get hit on the nose so when you look at this this is the remember i mentioned there are all these different directions that lead to non-moral vanity this is another one of the directions is looking at the wave function going, what metaphysical category does this fit into? Is the wave function straightforward ontological furniture?

2:14:58It's not quite, maybe, I don't know. You know, I know Tim, this is Tim Maudlin, right? He has a view of the wave function as a distinct kind of ontology. You know, there are many views, right? Maybe the wave function should be understood as purely epistemic. That's got all kinds of problems. There's the view that maybe the wave function is a monistic ontology. It is the only thing that exists in the universe. This is a whole list of views. None of them quite exactly fit. But this other category, that the wave function is a latent variable, ironically enough, sometimes called a hidden variable, that you introduce to get a Markov-looking description, giving you what's called a hidden Markov model, it just nails what the wave function looks like so perfectly.

2:15:44Now, of course, if that's your view of what the wave function is, then your immediate reaction is, well, then what we really have is a non-Markovian process, and the wave function was merely introduced to give us a law-like description. And so what I would say to this, David, is I would say, if the view is that the underlying, the actual metaphysical pictures, we've got some non-Markovian stochastic process, and it doesn't have all the ingredients you want, there's stuff that's unfixed, but I can do a mathematical transformation, take all that stuff that isn't fixed and turn it into something like a latent variable, a wave function that we can't observe and whatever.

2:16:19And now we can turn it into a Markov process. We can write a law down. I would say, if that's what you want to do, go for it. In the non-relativistic case with fixed numbers of finite-mending particles, works great. And I should say that Bohm isn't even the only game in town there. There's another theory. So I just reread. So people may not know, but David just taught another, you know, he taught David and Barry lower. They taught a course this past academic term at Rutgers on statistical mechanics and time and chance, David's amazing book on the difference, the past, the future and all this stuff.

2:16:57So I had an opportunity to reread the book. And also I sat in the course and David will know that I was sitting on the course. and the book talks about how all of the major interpretations they all have a similar kind of deterministic structure, a bilateral deterministic to Everett and Bohm and so forth and this makes it very hard to get statistical mechanics to underwrite thermodynamics you have to work really hard and much of the book is devoted to the project of how how hard is it? How can we do it? And then at the end of the book, last chapter, David's like, well, but maybe we should just take seriously that quantum mechanics should be replaced by a genuinely chancy theory.

2:17:42And the theory that David considers is the GRW theory, which was concocted in the 1970s. G is for Girardi, R is for many, and W is for Weber. And this theory has genuine chances in it. And the genuine chances make a lot of problems simpler to deal with, right? And so if that theory works, it would really make the inter-theoretic reduction of thermodynamics and statistical mechanics much easier. And many of the problems would be simpler. But I should mention that there has been a stochastic theory, not GRW, for a very long time. All the way back, at least as far back as the 40s. In fact, if you read Hugh Everett's unpublished 1956 dissertation all the way to the end to the final section discussion.

2:18:34By the way, I think it's fantastic. Everyone should download it and read it. It's a brilliant piece of writing and a lot of brilliant philosophy. Even if you're not a many-worlder, there's so much really good stuff in there. But the very end, he considers all the alternatives that he was aware of at the time. Bohmian mechanics, he was certainly aware. Bohm's Papers and book were the first three citations in Everett's thesis. He clearly read them all deeply, took to heart all the lessons about decoherence, all that stuff. So he talks about Bohm's theory. He also talks about a theory that he calls the stochastic process interpretation.

2:19:08That's what he calls it. And the stochastic process interpretation doesn't have a wave function in it. It's an attempt to just take the degrees of freedom and give them stochastic laws that will carry them to the right outcomes with the right born rule probabilities without a need for a wave function. And the person he mentions as having worked on this is somebody named Fritz Bopp. There is another Fritz Bopp alive today who's not the same person. He's not just like an infinitely long-lived individual. There was a different Fritz Bopp. He worked on this. Imre Fenya started working on this in the 40s and the 50s.

2:19:40He's more prominent, more well-known. But the most famous person associated with this, and David, you probably maybe know, is Edward Nelson, 60s through the 80s. So 1966, Edward Nelson published a paper in which he claimed to be able to get quantum mechanics with no wave function to get quantum mechanics out of the stochastic process. And he worked on this from the 60s through the 80s. This became known as Nelsonian stochastic mechanics. It's an attempt to get quantum mechanics to emerge from a particular kind of Markov process called Brownian motion. um and this theory i would argue is certainly no worse than bohm's theory it's it replaces bohm's neat trajectories with stochastic trajectories markov type brownian trajectories it's a theory with genuine chance in it and the chance is happening at every moment like in grw so this is a theory i think that would also do what you want grw to do in the sense of making well um just one narrow point and one larger point um jacob what you've been saying might leave the impression i don't know if this is the impression that you mean to leave um but might leave the impression that any kind of stochastic process at the fundamental level is going to be able to do the job for statistical mechanics that GRW does, that's not true.

2:21:20Correct. Yes. Think about, say, something like Penrose's collapse theory, which is also stochastic. That demonstrably will not do the job. Yeah. So so merely having a stochastic process and in particular. I don't see any reason to be confident that having the kinds of stochastic processes that come up in your theory. But I'd need to hear a lot more about this are going to be able to do a job like the GRW stochasticity does for statistical mechanics. anyway just being stochastic is surely not a sufficient condition for that agreed good there's much more to say about than that yeah the larger point and i guess this is the last thing i'll have to say and i'm just repeating something that i've said often in the course of this discussion is, look, I began my comments by saying something about the kind of theory that I think would be a useful contribution to this kind of discussion.

2:22:42And what I meant was a realistic theory in the sense that I was talking about. If one isn't going to demand that, one might as well go with the Copenhagen interpretation or something like that. It gives perfectly good predictions about how experiments are going to come out. So what I was trying to evoke in my initial remarks, in my initial disclaimer, before my real remarks began, was something, was a mood like this. Look, I see in some of Jacob's remarks the outlines of what I would call an unambiguously realist theory, in the sense in which I've always understood realism. And I wrote down the kind of unambiguously realistic theory that I was able to extract from some of Jacob's comments and commented on some of its features, commented on some of the features that make it look promising and other features that makes one worry about it.

2:24:01Okay. And that was the structure of my remarks. When Jacob started talking, the first thing I wanted to know was whether he was interested in the way that I was in saying, look, if this is going to be an interesting conversation at all, it's going to be a conversation about classically realistic theories. And a lot of the remainder of the discussion was, at least from my point of view, a struggle to see whether what Jacob had in mind was really realistic in this sense or not. And I wish I could say that I came out of the discussion with a clear answer to that question. But I don't feel like I'm coming out of the discussion with a clear answer to that question.

2:24:59As I've said, I see ways of extracting something that I have no hesitation in calling exactly the kind of realistic theory that I'm interested in from some remarks of Jacob. Jacob may regard this as a distortion of his remarks, but I'm able to extract this theory. This is a theory which I find interesting, but also worrisome. And that's the impression that I tried to give. And then most of the rest of the conversation, as I saw it, was an attempt to get to the bottom of whether whatever it was that Jacob actually had in mind, of which my remarks were apparently a distortion, whether what he had in mind satisfied my conception of what it is to be the kind of solution to the problems at the foundations of quantum mechanics that was going to interest me at the end of the day which was a genuinely realistic solution and I can't say and maybe this is just my fault or my lack of imagination that I came out of the conversation with a clear yes or no answer to that question that I understand.

2:26:21So that's where I'd be inclined to leave things.

2:26:39First online real money wager only. Minimum$5 wager required for seven consecutive days. $5 first deposit required. Bonus issued as non-withdrawable bonus spets, which expires seven days after receipt. Restrictions apply. See full terms at fanduel.com slash sportsbook. Gambling problem? Call 1-800-GAMBLER or 1-800-MY-RESET. Choice Hotels gets you more of what you value. Comfort in. It's calling your name. Save on the stay. Oh, and free waffles are yours to claim. Book direct at choicehotels.com. Okay, let me summarize a little bit. And I want to, again, express my appreciation both to David and Robinson for this discussion.

2:27:18As do I, to both of you. Very, very interesting. So let me just start by saying there are other problems to the Copenhagen interpretation, right? I mean, I think Everett spells this out rather beautifully. The Copenhagen interpretation has two different forms of time evolution. and whatever it says is whatever your view about whether you prefer one kind of time evolution unitary evolution or the other linear evolution or the other kind collapse probabilistic evolution you can take whatever side you want the stochastic interpretation that he ever is referring to takes the probabilistic evolution everett himself boom they take the the linear evolution whatever Pick one side, but it's something else altogether.

2:28:05To have a theory in which you've got these two different forms of time evolution and just an ambiguity over when which one applies. This is just a measurement problem, right? And what Everett also points out about Copenhagen is, by assumption, because it takes for granted the classical description of the macroscopic world. That's an input into the theory. Everett points out this theory is by its nature incapable of accounting for the emergence of classical reality. It presupposes it so it can't possibly derive it. And to be clear, those are both out the door with my approach. My approach assigns an ontology to everything.

2:28:48There's only one kind of modal structure, these joint probabilities that define this stochastic process. In some situations, we get the emergence of initial value formulations with nice dynamical rules separated from initial conditions. These just emerge from the theory. That's a picture, and the picture applies up and down. Small systems, big systems. There's only one, there's not two different kinds of laws available. You know, there's not, you know, it's not like you've got probabilistic laws on the one hand. And there's no special status assigned to measures. The measurement problem, not uniquely in my approach, obviously all the different interpretations, they all resolve the measurement problem one way or the other, provides one way to resolve the measurement problem.

2:29:30And it doesn't run into the contradictions we run into with the other theories. So I would say that's progress. Now, would I claim that this is definitely the final theory? Well, absolutely not. For one thing, our universe has gravity in it. and we keep talking about applying a theory to the whole universe, I hasten to point out that the observable universe is, first of all, an open system. We don't know what's beyond it. But secondly, at the scale of the observable universe, cosmological gravitational effects are not negligible. And certainly, if there's anything bigger than our observable universe, which we have every reason to think, quantum gravity is going to be really important there.

2:30:09And I'm not claiming to have a theory of quantum gravity. So this is intended to be a much more modest theory at this point that applies to meso and macroscopic systems ignoring the effects of gravity. And again, I still think that's a form of progress because I don't think the other theories get us there. So I just want to say that as background, why we would think this is an improvement over something like the Copenhagen interpretation, which I think needs to be said as a defense. Now, there were two other very quick things I want to mention before we close. One of them was this question about eigenfunctions, and I think this needs to be said.

2:30:47So in David's remarks, he said there's no such thing as an eigenfunction of configuration, eigenfunction of position. That is actually not correct. So what's true is that in the Schrodinger representation, this is not going to get, it's a technical question, does a certain function exist? in the Schrodinger representation of the so-called Weyl algebra, you're right. There are no eigenfunctions for position. That's true. But this is not the only representation of the Weyl algebra. There's a beautiful paper by Hans Halverson, whose name I cannot immediately remember. I think it was from 2001.

2:31:38So it's, yes, right. So this is the paper 2004, Complementary Representations in Quantum Mechanics. It was in Studies in History and Philosophy of Modern Physics, in which he points out there are other representations. And in fact, there are representations in which there is absolutely a position eigenfunction. Although in such representations, there are not momentum eigenfunctions, but not a problem for me. I don't take momentum to be fundamental anyway. So that's fine. And in fact, the way you deal with David's question, how do we deal with an initial condition phrased at the level of an exact position, is you use a different representation.

2:32:16It's an irregular representation, but that's just a technical thing that doesn't really matter. It's faithful. So you just use that representation and then you can avail yourself of all these beautiful theorems in algebra. Yeah, that's great. And of course, that's not, as I emphasized when we were going along, that's not one of the things. I do feel like it was worth mentioning. Yeah, sure, sure. Then the last point is this question about locality. So I want to just say, I'm going to reiterate what David said. My claim is, to be clear, I am, let me not say too many double negatives. I'm not saying that quantum mechanics is in fact local.

2:32:52If anyone has gotten that impression, that is not what I'm saying. There are varying ways to talk about locality. We can talk about whether correlations are local or non-local, and non-local correlations are perfectly fine classically. We can talk about whether a theory is counterfactually local in the sense that is there some weird non-locality between counterfactual propositions? And arguably, EPR settled that. The quantum mechanics has clear examples of counterfactual non-locality that were then precisified by Bell. Then there's a stronger level. Is there causal non-locality? Is there a well-defined sense in which causes and their effects are linked across distances over sufficiently short periods of time that this would require some kind of super luminal, faster-than-light causal influences?

2:33:40That's a different notion of locality. And then finally, there's signal locality. Can a human, an observer, an agent, send messages faster than light? And we're all in agreement that at least, unless something weird and exotic is happening with closed time-like curves and general relativity, that that's not going to happen. So there's general agreement that non-local correlation is fine and is fine in classical physics. There's agreement that signal locality holds in quantum mechanics. Observers can't send messages to each other faster than light. Those are both in agreement. And the question is, what happens to counterfactual nonlocality and causal nonlocality?

2:34:13I am openly admitting that quantum mechanics exhibits counterfactual nonlocality. The question is, does that mean it's causally nonlocal? That's that question. That's why I was very explicit in the papers. And David was nice enough in his remarks to make this clear. I'm talking about causal locality. And to talk about causal locality, we need to say something about what we mean by causal relations. My theory comes with, very naturally, an account of causation built out of the nomological, these conditional probabilities that link things together. And this is all spelled out in other work, including a paper that today was just accepted in Physical Review A.

2:34:53It's so-called CHization Equality that'll be out soon. but the theory comes with its own very natural notion of causation that's rooted in various parts of the literature i can put people to references it's really good stuff on that definition of causation on that definition you can impose locality you can say that notion of causation is not allowed to go outside the light cones and when you do that what you find is you can violate Bell's inequality, violate it, and you can violate it only up until a very famous bound called the Zrelsen bound. Now, this is really interesting. People know that the Bell inequality is violated by quantum mechanics.

2:35:44We know that. Not a lot of people know that it can't violate the Bell inequality arbitrarily much. There is a tight bound on how much violation you can get. In particular, this bound is called the Srelson bound. It was proved in 1980. And you need the whole apparatus of quantum mechanics, traditionally speaking, the whole apparatus of quantum mechanics to derive it. It says that you can violate Bell's limitation by about 41%. You can go up to 141%. You can, like, violate it by not quite 50%. And it's a very, the 41 % is because it comes from root 2. Root 2 is 1.414. So you can only violate it by so much.

2:36:24And one might naturally ask, is there some principle why we can only violate it so much? It was later work, Sandhu Popescu and Daniel Roerlick in the 90s, they tried to find some intuitive reason. Maybe if you violate it anymore, then humans can send signals, but they proved that wasn't true. You can violate it by way more and still not let humans send signals. So there was this question left over. why can quantum mechanics only violate the bell inequality by by by so little when it could violate it by way more without causing any conceptual or logical paradoxes and this paper that we just just accepted um uses the notion of causation that we've introduced that comes directly out of this theory if you were to ask what good is this notion of causation here it is this notion of causation when you impose locality on that gives you a theory that lets you violate the Bell inequality only exactly up to the Tzarelsson band and that's really very elegant and as far as I know maybe there's something in literature I haven't seen but it's a you give me a theory of causation you tell me what it means to be local how high can I go Tzarelsson band and that's a really nice result that says that this notion of causation is actually doing something for us and that's one reason why again I think that we're on the right track with this project so I think that's worth mentioning and I wanted to clarify my remarks because David's right I don't want anyone to get the wrong impression that I'm saying that quantum mechanics is just local full stop.

2:37:55That isn't what I was saying. I want to be very precise about exactly what I'm trying to say. Well, after two hours and 40 minutes, which I found extremely useful. I mean, thank you to both so much, even though we didn't really move too far past the questions of scientific realism and the formulation of Jacob's theory. I found all of that very, very engaging. I'm sure our listeners will too. So maybe we'll come back to this sometime down the road. But until then, thanks both of you for having this discussion. So lovely. Thank you, Robinson. Thank you, Jacob.

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