Why Physics Without Philosophy Is Deeply Broken... | Jacob Barandes [Part 2]

There was no wave function, there was never superposition, there was never any need to make anything collapse. In this picture, some observable quantities reflect things that already exist. The people who gave us the biggest revolutions in modern physics, quantum theory and relativity, were all strongly connected to philosophy. Physicists have struggled with the seemingly bizarre results of quantum theory, where particles are allegedly in multiple places at once, there’s a mysterious wave function that collapses upon measurement, a framework requiring so-called imaginary numbers, and so on.

I’m at the physics lab in the United States to meet at Harvard University with theoretical physicist and philosopher Jacob Barandes, he’s the co-director of the graduate studies department there, where we delve into the technical depth of his groundbreaking book, Reframing Quantum Theory for a More Fundamental Mechanics, called Indivisible Random Processes. My name is Curt Jaimungal, and this was part of my three-day tour of Harvard University, “t Hooft’s,” and MIT, where I recorded five audio files, one with Jacob Barandes whom you see now, which ended up being seven long hours, so we’re splitting it into two parts. The others are with Mike Levin, Anna Sionica and Manolis Kellis. There’s also Professor William Hahn, a computer scientist, who was filmed directly in the MIT Media Lab. Subscribe to get notified.

Jacob’s revolutionary theory raises provocative new questions like, what if quantum waves didn’t exist? Did physics lose its soul by abandoning philosophy? Does time flow differently in quantum physics, and was Einstein right all along? It's good to be here. It's really nice to see you again. The last time we spoke, I enjoyed it very much. Yes, me too. So let's talk about physical philosophy versus the philosophy of physics. People have heard of the philosophy of physics. What is physical philosophy?

Yes, so my research is kind of two-pronged. There’s the physical philosophy side, and there’s the philosophical physics side. Let me start with physical philosophy. So the way I describe physical philosophy, is using the results, the ideas, the discoveries, the theories from physics to address traditional questions in philosophy, particularly in metaphysics. So the kinds of questions we’re interested in here are questions about space and time, philosophy of time, causation. There are interesting links between physics and causation, which we hopefully will have a chance to talk about today. And also philosophy of probability, which is a very subtle and very complicated area. And also metaphysics of laws, which is a very rich and fascinating area of research. So just thinking about what will the best of our current physical theories bring to bear on these traditional questions? How do they constrain what we can say about these kinds of things?

So this is a good example, a concrete example. Philosophers and metaphysicians have been thinking about the nature of time for a very long time, right? It goes back to Parmenides and Heraclitus and people thinking, you know, is time something that flows? Is time something that’s merely an illusion? And there’s this very famous paper, which you might be able to relate to because it’s a beautiful paper and people should read it, written by McTaggart, the philosopher, over 100 years ago about the nature of time. He introduced these terms, the A-series, the B-series, the C-series, these different ways of thinking about time and how it’s structured, right? The A-series is the idea that events that happen in time can be classified as past, present, and future. But that seems like it relies on the notion of presence, and is that really a sensible notion? Then there’s the B-series, which has less structure. This just points out that events can only be classified in terms of their precedence or their subsequence. So there’s just a pairwise relationship between them, and there’s no distinctive notion of the present. And the C-series is even less structured. It just says that there’s a sense of ordering of events, and that given any three events, we can say what happens between any other two events, but without privileging the direction in time. And as you know, he explores all these ideas in the paper. But around the same time, Albert Einstein was developing special relativity, and special relativity has some very serious implications for how we think about the nature of time. In particular, although a lot of people have heard about phenomena like time dilation, the idea that observers moving in different states of motion will have, you know, different senses of how time flows, like the rate at which time flows for one observer might differ from the rate at which time flows for another. And some people might have heard about length contraction or Lorentz contraction, where spatial distances can be distorted in the direction of the change of reference frame. What’s somewhat less well-known is the breakdown of simultaneity, which is the idea that observers in different states of motion will assign different events to be in their present. So for an observer in one frame of motion, a set of events might be in what that observer knows as the present moment. But for an observer in a different frame of motion, his sense of the present seems tilted. It’s like tilted a little bit, such that things that the first observer would say are in the future are in the present of the second observer, and also some things that maybe were in the past of the first observer. And this feature of special relativity, that simultaneity is not a fixedly defined notion, has profound implications for how we think about the philosophy of time. And it was explored by people like the philosopher Hilary Putnam in the 60s, who wrote a really beautiful piece of work, which you should also link to because it’s very beautifully laid out. And he argues for what he calls four-dimensionalism, you can call it eternalism, which is the idea that different observers will disagree about which events are in their presence, if we take the totality of all the things that everybody thinks are in their present, it’s essentially all of spacetime. If you look at observers in different locations, and different frames of motion, does that mean that everything in spacetime is already somehow there? You know, the future is not something that hasn’t happened yet, the future is not something that’s unfolding, but our experience of the flow of time is merely a psychological experience. And special relativity actually tells us, in a very strong sense, that we live in what’s called a block universe where everything is there.

So that’s a great example where things that we learn from successful contemporary physical theories, which are perfectly empirically established, like physical theories, put some very important constraints on what you might think are purely metaphysical questions. So I call this general topic physical philosophy. On the other hand, I also work in what I might call philosophical physics, and the name is supposed to be analogous to…theoretical physics, mathematical physics, computational physics, it’s a methodology for doing physics, not a philosophy. But instead of mathematical physics, for example, where you do physics by stating axioms and proving theorems, or theoretical physics, where you formulate models and then calculate predictions within the models and compare them to experiments, or computational physics, where you simulate physical processes on a computer and make predictions that way. Philosophical physics tries to make progress in physics using some tools that might be traditionally associated with philosophy. So what are those kinds of tools? Thought experiments, coming up with counterexamples, clarifying definitions, clarifying questions, right? Sometimes you deal with a problem in science, or physics more specifically, where the questions haven’t been sharply enough formulated so that you can subject them to experimental study. Sometimes you have to do some work beforehand to clarify those questions, and that’s the kind of thing that philosophers like to do. Identifying implicit assumptions, hidden assumptions, and that’s something we’ll talk about because some of my work is very closely related to the idea of identifying implicit assumptions. Assumptions that might be hindering scientific progress. Subjecting ideas to logical analysis, and also what I call careful scrutiny. Because in philosophy, we’re not generally guided by experimental data or observations. You might think there’s just, well, if you don’t have experimental data, what do you do? Well, you’re not devoid of any tools at all, right? So one of the things that philosophers like to do is to be really careful in how they talk about things and how they define things. To be extremely careful in every step of their reasoning, and to lay out their premises as clearly as possible so that you can pinpoint where the problem is if you find a flaw in their argument. So just sharpen everything and subject things to rigorous scrutiny. These are all tools and techniques drawn from philosophy, and I call this philosophical physics. And this doesn’t just involve taking ideas from philosophy, like just picking up ideas from philosophy and seeing if they have any use in physics. And I think there’s a proud tradition of this kind of work. I’ve talked to philosophers of science who told me that the greatest philosopher of physics in the 20th century is Albert Einstein. And when you look particularly at Einstein’s earlier work, what does he do? He subjects definitions and ideas to rigorous scrutiny. I mean, how much time did he spend trying to define exactly what we mean by inertial reference frame? You might think inertial reference frames are like a scene from Newtonian physics. Like, what could you really gain by spending so much time doing careful scrutiny, careful definition of inertial reference frame and scrutinizing when you know you’re actually in an inertial reference frame? But think how far Einstein went from thinking about inertial reference frames, and which physical laws should be the same in every inertial reference frame, realizing that the speed of light is one of these physical laws that should be the same in every inertial reference frame. Inertial reference frame. And then, you know, his greatest idea—what he described as his greatest idea ever, which is the realization that, you know, it’s impossible to distinguish between the local short-range effects of a gravitational field from being in a uniformly accelerating reference frame. And this realization is, you know, what eventually developed into the equivalence principle and led him to his theory of general relativity. He had this idea in 1907, and he described it as the happiest thought of his life. So naturally, I’ll get to this later, but Einstein was steeped in philosophy. We’ll talk a little bit about the greats of 20th-century physics and how much philosophy they did. So I think there’s a strong tradition of philosophical physics in history, and I’m certainly not the only one practicing, I think, this specialty, but I think there’s really something to be said about it. I think it really contributes something to how we make progress in physics, and I think that’s the other side of what I do.

So what is the standard view of philosophy of physics or philosophy in general from people who consider themselves scientists or who are actually practicing scientists? So for example, when I was talking to Neil deGrasse Tyson, he was saying, well, philosophy, what did you do? Give me, Curt, an example of something that philosophy contributed to modern physics in the last 30 years. Certainly, in the past, there were thought experiments. That’s a beautiful question. I already know Neil Tyson. We worked together when I was in high school. That’s some interesting history. I grew up in New York City, and I used to go to the Museum of Natural History all the time. It was one of my favorite places. I mean, if anybody listening to this hasn’t been to the American Museum of Natural History before, you’re missing out. It’s like going to a magical wonderland for science, which is amazing. And I was fortunate when I was in high school to intern at the museum. And there was a period of time when I worked in the astronomy department, and I worked with Neil Tyson. He was amazing. I mean, he’s great. So, of course, I disagree with this sentiment very politely. I’ll give you a couple of examples. So these are some things that resulted from philosophical thinking about physics, philosophy. I mean the lines are a bit blurry here, because obviously, if you’re doing philosophy that’s very close to physics, one might accuse you of just doing physics. But, okay, let me think of an example. This is from the 80s, okay? So in 1982, Wootters and then independently, the philosopher of science par excellence, Dennis Dieks, independently formulated what we now call the no-cloning theorem. So the no-cloning theorem in quantum theory is a very simple and very beautiful theorem. What it says is that if you’re given, as it’s traditionally formulated, a quantum state in the form of a wave function or a state vector, just some object in Hilbert space that describes, in the traditional sense, the state of your quantum system, and you don’t make any measurements on it. You’ve prepared it, but you haven’t measured the position or anything else, you just leave it alone. Is there a way to build some kind of device that can put another system into exactly the same quantum state? Meaning, can you, you know, if your first system, um…you know, a simple quantum system and it’s in some state, can you bring in a second quantum system of the same type and run both systems through some kind of machine that will put the second system into the same quantum state of the first system every time? Right, every time? And the answer is you can’t. If you set up the device so that it works some of the time, all you have to do is prepare the first system in a superposition of those possibilities, and what you’ll find is that you can’t get the other system to work into the correct quantum state which is also the same superposition. And this is called the no-cloning theorem. And the no-cloning theorem is useful. I mean, certainly, it shows up everywhere in physics, it shows up in high-energy theory, it shows up in all sorts of places. I think this is 1982. I mean that’s a little bit outside the 30-year limit. What happened since the 90s? And we’re not allowed to talk about your work yet. Oh, yeah, we can’t talk about the work yet. I mean that’s an interesting question. I mean, from the point of view of plausibility, it’s a bit difficult because, as I said, the boundaries here are a bit blurry. If you think about people like Martin Lizord or Eric Uriel or JB Manchek, these are people who work in the foundations of general relativity. And you know, their work is very mathematical. I mean if you asked them, do you consider yourself first and foremost a philosopher? Or I haven’t asked Eric or I haven’t asked all these people, what do you consider yourself first? But they certainly come to philosophy seminars, they give philosophy talks, and they certainly sound like philosophers. And they’re doing similar work in general relativity. They prove things about spacetime that are considered interesting facts. So you know, and of course, the dividing lines between quantum foundations and quantum information are also blurry. So I’ll tell you, this is an interesting story, okay? You’ve probably all heard about qubits, right? So a qubit is supposed to be a quantum bit. And usually the way this term is presented, people will say that it’s a mixture of quantum and bit, right? Bit, I think the term bit goes back to Claude Shannon. And this itself is a set of binary digits. You know, Claude Shannon introduced many ideas in information theory and communication theory in the 1940s, when he was at Bell Labs. And then the idea is that you have classical bits and you also have these modern quantum bits or qubits. But the name qubit is a very funny word, because if you look at it, it’s spelled Q U B I T. You’d be hard-pressed to think of many other words in English that are of the form Q U, and then there’s no other vowel, but just a consonant immediately following. Why is this spelling so funny? And I’m not saying I’m the first one to notice this funny spelling. In fact, there’s a very famous physicist, David Mermin, who’s also interested in quantum foundations, among other things. And he doesn’t like this spelling because he says it’s ungrammatical, like the spelling is totally non-standard. I think he likes to spell it Q hyphen bit, not QUBIT. So where did this spelling come from? This term was coined by Ben Schumacher at Kenyon College and Bill Wootters, who I mentioned before, at Williams College. The story is that Bill Wootters was visiting Kenyon College and that’s in Ohio. And they were both driving their cars to the airport in Columbus. And they were talking about how they needed a new scheme to talk about quantum information. This was in 1992, that’s 30 years ago, plus a bit. And Bill. So I got this information from one of Ben’s students, Mary Gerhardinger, who told me the story. Bill was in the car and said, wouldn’t it be funny to call these things qubits because there’s a unit of measurement in the Bible called a cubit. But in the Bible, it’s spelled cubit. It’s a unit of measurement. It’s like, I don’t know, the distance from your elbow to your fingertip. And if you read Genesis, right, you’ll hear God telling Noah to build the Ark and it’s supposed to be this many cubits long, and this many cubits high, right? And they say, but it starts with a C because the Bible is classical, you understand that? Like what’s more classical than the Bible? Let’s just replace the C with a Q and it’ll be a modern version of a cubit. That’s funny. And they both think it was hilarious. As you know, in Theories of Everything, we delve into some of the most ascendant concepts of reality ranging from theoretical physics and consciousness to artificial intelligence and emerging technologies. To stay abreast of the ever-evolving landscape, I find The Economist magazine a source of insightful analysis and in-depth reporting on the various subjects we explore here and beyond. The Economist’s commitment to rigorous journalism means that you get a clear picture of the most significant developments in the world, whether that be in the realm of scientific innovation or the shifting tectonic plates of global politics. The Economist provides comprehensive coverage that goes beyond the headlines. 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Ben Schumacher worked with John Wheeler, who, in addition to being a very great theoretical physicist and a wonderful teacher who had many, many famous students, Richard Feynman, one student, many students, Jacob Bekenstein, many very famous students, was also very philosophically curious. Hugh Everett of the many-worlds interpretation, which we hopefully will talk about, was also one of his students. And so he really enjoyed having these deep philosophical conversations. And he created a real atmosphere of philosophical inquiry in his research group. Wootters worked with John Wheeler. Does that count as a philosophical contribution? I mean Schumacher and Wootters weren’t at R1 universities. And they weren’t at major universities. They were both at liberal arts colleges, and they were interested in very foundational questions. I mean does this count as philosophy? It’s hard to say. But now I think you can go further than that. I mean, if you’re willing to go back and take ideas that came from philosophical thinking, but still prove to be very useful, there’s a lot, right? I mean you can, I mean if you’re just talking about quantum mechanics, and not even general relativity, you know, the notion of entanglement goes back to philosophical disagreements between people like Schrödinger and Einstein. The Einstein-Podolsky-Rosen paper that came out in 1935, and it’s probably the most cited paper for Einstein’s name, it’s a lengthy philosophical argument. They put their workplaces. They lay out a very detailed philosophical argument, which we could talk about. And you know, they make a metaphysical claim about quantum mechanics, a physical and metaphysical claim about whether quantum mechanics can be considered complete, even if it’s perfectly useful practically. Their work, you know, the EPR argument, the Einstein-Podolsky-Rosen paper inspired a lot of people. I’ll talk about who it inspired, but let me say that before I get to that, there’s a research paper written by the philosopher Grete Hermann. So Grete Hermann was a philosopher, and a student of Emmy Noether, who, as a mathematician, made huge contributions to physics and symmetries and conservation laws. Noether’s theorem is extremely important, arguably the most important theorem in physics. And so her student, Grete Hermann, is a philosopher, she’s a neo-Kantian, and she wrote a huge number of pieces of research about physics and metaphysics and about advanced quantum theory. And she wrote a research paper, we read it in my philosophy of quantum mechanics class, where she studies the nature of causality in quantum mechanics. And she lays out this thought experiment. It’s a beautiful thought experiment, and this paper was published in 1935, several months before the EPR paper was published. And it seems to have been widely read. And it’s likely that Einstein read this paper. And the thought experiment used in the EPR paper bears a strong resemblance to the thought experiment that’s in Grete Hermann’s paper. Okay, so you know, obvious and interesting things were going on in the 1930s. Then, of course, John Bell picks up the thread and publishes research in 1964, his famous paper on the no-go theorem, which is the first appearance of what we now call Bell’s theorem. And this paper is called “Einstein-Podolsky-Rosen Paradox.” That’s what he calls the paper. He takes the EPR paper and extends the argument to a statement about what he calls, what we now call hidden variable theories. You know, and you got further results that, you know, build on Bell’s theorem. You have the famous CHSH inequality, which came out in 1969. And that’s Clauser, Horne, Shimony, Holt, and it’s a somewhat more general version of Bell’s inequality. In the 90s, we’re now in the 90s. You have Greenberger, Horne, and Zeilinger, the GHZ paper. There’s a beautiful version of this argument written by David Mermin in the American Journal of Physics, which I can also send you links to. These are all beautiful papers to read. And you know, these papers all deal with entangled systems. And in particular, Bell’s paper and the GHZ paper deal with certain kinds of quantum states. The GHZ paper introduces these GHZ states. And GHZ states show up everywhere in atomic molecular optical physics today and in quantum information. I feel like every time somebody uses a GHZ state or uses, you know, Bell-violating states or things like that in order to do something in quantum cryptography or certify the randomness of quantum random number generators, they should be paying royalties to the field of philosophy of physics and quantum foundations. The no-signaling theorem is an important result that comes out of quantum foundations. That’s in the late 70s and early 80s I think. One version of the argument was written by the same people who gave us the GRW spontaneous collapse theory, right? And you know, as you know, and the no-signaling theorem is also a theorem that shows up everywhere. But I think, you know, I can give more examples. I mean there’s quantum teleportation, you know, in some early papers of David Deutsch that introduce some of the fundamental ideas that led to quantum computation. He was very clear in the papers about how what he’s trying to do in trying to imagine building a quantum computer confirms that many worlds is the correct interpretation of quantum mechanics, right? So he’s very much driven by interpretational philosophical questions. But I think my favorite example is decoherence. So whenever you propose a new way of thinking about quantum mechanics, people will often say, do we really need this? Doesn’t decoherence solve this problem? There’s a physical solution to this problem. We don’t need philosophy, right? But decoherence comes from philosophy, right? So—how? Well, there are some basic ideas that we can link to decoherence that go back to what happened with Bohr’s death in the 1920s. But the first serious and rigorous formulation of decoherence that I’ve been able to find shows up in chapter 22. So these are the final chapters of David Bohm’s book, Quantum Theory. This is 1951, he publishes this textbook. And this is before he introduces his pilot-wave theory. And you know, he’s a very philosophically curious person in addition to being a physicist. And in his book on quantum mechanics, he doesn’t just want to teach quantum mechanics. He also wants to deal with some of these outstanding questions about how the measurement process works. So in the later chapters of his book, he reviews the measurement process in as much detail as possible based on the axioms that were available, and the Dirac-von Neumann axioms, the axioms associated with Paul Dirac and John von Neumann from 1930 and 1932 respectively. And you know, he tries to formulate a measurement process. He has a system, a quantum system

It must be measured. It’s in some superposition. It brings… like a physical measuring device, it designs everything systematically to be measured and the measuring device. It lets them interact. And it ends with this superposition. And then he argues that some of the probabilistic quantities that one might want to calculate, the averages that one might want to calculate, exhibit these very strange quantum effects, what are called interference effects. But once you continue the measurement sufficiently and the measuring device interacts strongly enough… and I don’t remember from the book whether it includes the environment or not. I have to remember exactly what he does there. But basically, when you involve sufficient degrees of freedom from the system, you get what he calls… the phrase he uses is destruction of interference in the process of measurements. That’s what he calls it. Destruction of interference in the process of measurement, and it’s decoherence. This is, as you know, a more encompassing version of the term decoherence. And that’s exactly what decoherence is. That’s why he wrote this book. He seems to have had conversations with Albert Einstein about this subject. This is 1951, 1952. Albert Einstein is still alive at that stage. And he had some conversations with Albert Einstein and Albert Einstein was dissatisfied with his approach. He says he should go work on it a little bit more. And he comes back and independently discovers some of the work that de Broglie had done in the late 1920s. De Broglie developed the very first kind of early pilot wave theories. Bohm independently redevelops these things. Eventually, he and de Broglie get in touch. Now we call these theories de Broglie-Bohm theory, or sometimes just Bohmian mechanics. And in this theory, you don’t just have the wave function that evolves in some high-dimensional space where the wave function lives, but the wave function also guides these particle-like things, the Bohmian particles, the Bohmian trajectories, Bohmian particles. And one obvious question you can ask is, well, if you have all these trajectories and you have a pilot wave, and Bell and Bohm in this particular research say that the pilot wave is real, and metaphysically real in the same way that the locations of the particles are. Then when you do something like the double slit experiment and you send a pilot wave through these two slits of the experiment, right, and it lands on the screen, why doesn’t the screen light up in all the places that the wave hits, right? So the wave diffracts, and you get these intensity peaks, these famous interference peaks in the wave function. The trajectory is guided to only one location. When you actually do the experiment, you see only one landing location. But the question is, well, but what about all the other empty waves, the empty shells, the parts of the wave function that land on the screen and don’t have particles in them? Why don’t they hit something and do something? And Bohm wrote two papers. It was a pair of papers. And in the second paper, he goes through the process of measurement. He goes through this example. And he basically uses the technique of decoherence to explain why we only see one landing location. So decoherence was developed in this book and then almost immediately used in a very applied sense to get the pilot wave theory off the ground and to implement it, to show that it was at least empirically adequate for non-relativistic systems with a finite number of particles. Then the thread was picked up again in the 1970s by Dieter Zeh, who did some extremely deep and important work in decoherence, and apparently suffered some career repercussions for working in such a philosophically foundational area. And then decades later, physicists, practical working physicists working with AMO systems, atomic molecular optical systems, physicists trying to implement real-world quantum computers, trying to implement unitary gates and run simple quantum computers. But even physicists in all the other areas, the physicists trying to understand the early cosmology of the universe, the physicists trying to understand condensed matter systems and materials. People are now worrying about decoherence all the time. You read papers, every paper talks about what the decoherence timescale is for this or that. Decoherence is now a major component of what we do in physics today. It happens all the time now. And again, I just want to say that maybe we should, we ought to pay some royalties to poor David Bohm, who was run out of the United States. He spent, you know, much of his career in Brazil and couldn’t come back to the United States. And Zeh who suffered some career repercussions. And there’s this attitude, oh, thinking about fundamental philosophical questions is a waste of time. How could it possibly be a waste of time given all the fruits it has borne? So, you know, what I want to say is, and this is just a general message to anyone who’s thinking about how best to contribute to the development of science. The field of philosophy of physics, the field, I would say, like the more philosophical side of quantum foundations, because there are also parts of quantum foundations that are much closer to like practical quantum information kinds of things. But it’s more the philosophical side of it, is a field that very few people have worked in, right? There are very few permanent academic positions dedicated to this kind of work. A lot of the people doing this work got their academic positions to do something else and then moved into this work. So there are very few people responsible for a lot of these results. There is very little research funding. So if you are one of the people watching this and wondering, where could funding make the biggest difference in physics? Should we allocate more funding to areas of physics that are already well-funded? Will an extra million dollars make a big difference in some of these fields? I can tell you that, like philosophy of physics, and the intersection of physics and philosophy, the more philosophical side of quantum foundations, and also the more philosophical side of foundations of general relativity and foundations of many other important, you know. Areas of physics, that’s where I think every dollar will go a very long way. So, you know, if you’re in the market for awarding professorships, this is a way to make a big impact in the field. Great. Speaking of foundations of quantum mechanics, is it inconsistent as it is in the book Quantum Theory? In 1932, the Mathematical Foundations of Quantum Mechanics. People partition the axioms in different ways. I’ll give a very quick discussion, you know. They say that in every quantum system, we associate some kind of vector space called a Hilbert space, which is a space of vectors that involves complex numbers. The elements of this vector space are called state vectors. Loosely, they can also be called wave functions. There’s some subtle difference in terminology around that. And these are supposed to, to some extent, represent the state of the quantum system. Generally, you have to use what are called density matrices, which are a little bit more complicated, but we’ll put that aside. And then the next axiom is that as time evolves, these quantum states, whether they’re state vectors or wave functions or density matrices, are supposed to evolve according to what’s called unitary time evolution. If it’s smooth and nice enough, it can be written as a differential equation, an equation that tells you moment by moment in a Markovian way what every successive state will give you given the present state. We call that differential equation, and when it’s wave functions, we call it the Schrödinger equation. If it’s density matrices, we call it the von Neumann equation. Then there are all these axioms for measurements. The things that are observable and that you can measure about the system are represented by operators or matrices, these self-adjoint things called self-adjoint operator matrices. These are the observable things from your theory. The possible outcomes that you can get when you measure one of them are called eigenvalues. It’s one of the eigenvalues of those operators. The probability that you’ll get that is given by this formula that takes the state, the quantum state of the system, and takes, you know, the projection operator, but a piece of that operator. If you put them together, this gives you the probability of getting that outcome when you do the measurements. And then once you’ve done the measurements, this quantum state of the system is projected or collapsed to reflect the outcome and ensures that you would get the same outcome if you measured it again immediately. These are the standard Dirac-von Neumann axioms, and people partition them in different ways. But I like to think of them as those five axioms, right? Hilbert spaces, unitary time evolution, observable things as self-adjoint operators, Born’s rule for probabilities of measurement outcomes, and then the collapse. There are problems with these axioms, not when dealing with microscopic systems, you know. Microscopic systems, things tend to work pretty well. And when people say that quantum mechanics works fantastically well, they mean microscopic systems. If you want to do a tabletop experiment, an atomic experiment or a laser experiment, you’re working with tabletop systems, microscopic systems, and the theory works fantastically well. It works wonderfully. If you are, you know, if you restrict yourself to these particular examples, what’s the problem? If you want to do a particle physics experiment, or a high energy physics experiment, you are, you know, building a giant particle accelerator, or talking about the Large Hadron Collider or something like that, you have beams of subatomic particles that fly together, and there’s debris that comes out, collect all the debris. These are all microscopic systems. Quantum mechanics gives beautiful predictions about these results. So you won’t see any inconsistencies in these kinds of systems, at least to the extent that the Dirac-von Neumann axioms give a self-consistent description of microscopic systems, which they seem to do. A perfectly empirically adequate description, the theory works fantastically well. So what’s the problem? Why would anybody have any problem? We talked before in our last conversation, and I talked about this thought experiment that was proposed, I think, originally by Hugh Everett in his long dissertation in 1956-1957 when he was a graduate student at Princeton working for John Wheeler. And not the one that he eventually published. He published a shorter version, but in the longer version, he opened it up with a thought experiment that is usually attributed to Eugene Wigner, who was also at Princeton. And we talked about how Wigner put this paper under the title “The Question of Mind and Body” in the early 1960s. But in this thought experiment, we imagine trying to do quantum mechanics with a system that’s not small. It’s not small. It’s not extremely cold. It’s not, you know, pure. The quantum system is something big enough to be a measuring device itself or even an observer. Again, this thought experiment is called the Wigner’s friend thought experiment. Wigner is on the outside of the box. The box is completely sealed. Wigner is one observer. Inside the box is Wigner’s friend. Wigner’s friend is also an observer, a large system, but completely sealed inside the box. And Wigner’s friend has done a measurement on a microscopic, superposed quantum system inside the box. And now we have a problem because we can describe the situation in two ways. We can treat Wigner’s friend, the person inside the sealed box, as something like an observer doing measurements, and then we’re supposed to use the measurement axioms and the collapse axiom. Or because the person is sealed in a box and there’s a second observer on the outside who hasn’t measured the box or its contents, perhaps we should treat the box and its contents as not subject to the collapse axiom. And now suddenly we have ambiguity in the middle of the theory. The Dirac-von Neumann axioms are simply ambiguous in these circumstances. They don’t pronounce a judgment on what you’re supposed to do. And when we last talked, I put up a whole list of possible things that you can do, each leading you down a different path, right, of how to resolve this problem. So this is simply an inconsistency. And I want to make it clear here, that there’s a difference between a theory being unintuitive or strange or quirky and a theory being inconsistent. Let me give you an analogy, a real-world analogy. You have a friend, and your friend is beloved and trustworthy and kind and always there for you, but your friend is quirky, okay? What do you do? What you do is you love your friend, because we all love quirky people. We’re all quirky to some extent. I’m quirky. We’re all quirky. We love quirky people. Quirky people are interesting. They’re interesting because they’re often surprising and creative and you never know what you’re going to get, and it’s always extremely interesting, even if sometimes, like, what they do is confusing. But that’s okay, right? They’re just quirky. We love quirky people, and we have quirky physical theories. Newtonian physics, you know, despite its fame, it’s Newtonian, it’s classical, when everything makes sense, there are lots of things about Newtonian physics that don’t bear much intuitive sense, right? You know, Newtonian physics says that a system, any moving body, will keep moving unless it’s acted upon by something. It doesn’t come to rest. That’s extremely unintuitive. We intuitively feel that things should come to rest. Aristotle thought that the natural state of all things was at rest, and in Newtonian physics, that’s not the case. You need an explanation for why something is at rest. But, you know, there are lots of other examples like this in Newtonian physics. We have all this intuition about how circular motion works. We have this intuition that when you, you know, swirl water in a bucket, that there’s a centrifugal force pulling it outwards. That’s intuitive, but that’s not really how things work. Gyroscopes are where all intuition breaks down, right? This is all in Newtonian physics. Newtonian physics is full of somewhat unintuitive things, and things get worse after that. I mean special relativity is extremely unintuitive. We talked about time dilation, the idea that time progresses differently for observers in different frames of motion. That what we call all simultaneous events, like, all happen now, and our notion of now is relative, and different people will disagree about which events are now and which events are in the future and the past. That’s extremely unintuitive. And don’t even get me started on general relativity. I love general relativity. I’ve taught general relativity here. So we have a graduate level course in general relativity, Physics 210. It’s one of my favorite courses to teach. I’ve been teaching it for over 10 years. I learn something new about general relativity every time. I’m always amazed. General relativity, that class, is like a quirky friend. Every time I teach it, it’s like you learn something completely new and amazing. And I was like, really? Does it really work that way? It really does. So, you know, general relativity is another example of a really unintuitive theory. I mean we always dedicate half an hour every time I teach the class just to talk about the weirdness of black holes. And this isn’t even when you start worrying about quantum effects. Just dealing with black holes as classical objects regularly. Black holes are unintuitive in many ways. And so I’ll just dedicate half an hour. I’ll open the floor, and I’ll ask the students to ask me any weird questions they have about black holes. Like, a student will ask, if I put my arm into a black hole, can I pull it out? Or, like, all these weird things that you can ask, like, what would it look like if you sent a person into a black hole? Could they come back? Like, all these weird questions you can ask. So general relativity is wonderful and extremely unintuitive. Jackson, Jackson level electromagnetism. So another course that I teach is Jackson level electromagnetism. There are lots of unintuitive things that happen in electromagnetism as well. So that doesn’t mean that we don’t have, like, we don’t have quirky theories, we do. I should say that all of these theories have places where they break down. The breakdown in a physical theory is called a singularity in the theory. Singularities aren’t necessarily geometric point-like things. They’re just places where your equations stop working. Electromagnetism has this famous divergence in the self-energy of point particles. General relativity is famous for its singularities. Everyone’s heard about the Big Bang singularity and black hole singularities and many other places where general relativity breaks down. Newtonian mechanics has weird singular behavior in certain kinds of systems. Yes, yes. There’s a famous paper written by the Shiites in the 1990s about a five-body system that exhibits singular behavior. Poincaré originally predicted that this could exist, I think, a century ago. So all these theories have places where they break down. And what do we do as philosophers, as scientists, as physicists, whatever? We look at these theories and say, well, the theories work in these systems. Sometimes they make very unintuitive claims or predictions, and that’s okay. We love weird and wonderful physics, as long as it’s consistent with itself. And there are certain places where the theory breaks down, and we’ll either need to replace the theory with something else if we’re lucky, and if we’re not lucky, maybe we won’t find a better theory to replace it, whatever. Quantum mechanics is kind of like that, right? There are systems where it works with microscopic systems, and quantum mechanics is nice and consistent with itself. We don’t run into these ambiguities or inconsistencies. It’s a little unintuitive in some of these situations, certainly. But when you run into something like the Wigner’s friend thought experiment, and other thought experiments that people have proposed over the years, now you’re not talking about unintuitive things. You’re talking about a singularity in the theory, you’re talking about an inconsistency, you’re talking about something where the theory is just broken. Nobody would say, well, the self-energy of the electromagnetic point particle is unintuitive. People might say, clearly this is something wrong and we have to fix it. And all I’m saying is that the same thing applies to quantum mechanics. There are systems where this thing works well, and there are other situations that we can extrapolate to where things seem like they break down. These situations involve extrapolating the theory from microscopic physics to macroscopic physics. I mean, we’re assuming that you can go from the Angstrom level, 10 to the minus 10 meters, that’s 10 billionths of a meter, all the way up to a one-meter scale, human-sized. To get the Wigner’s friend thought experiment, you have to have an extrapolation of the theory of that magnitude. Either you can do that extrapolation and you run into the Wigner’s friend problem, or you can’t, but if you can’t, well, then there must be some other place where the theory breaks down. In any case, there’s something wrong, and we just have to deal with it. And we have to confront this problem and manage it. But I’ll go one step further. It’s not just that the theory seems to have ambiguous places about what it predicts or where it’s inconsistent. The theory also only gives a very narrow kind of prediction, according to the Dirac-von Neumann axioms. So the Dirac-von Neumann axioms, and again, these are the axioms that you’ll read if you pick up Griffiths’ book on quantum mechanics or Shankar’s book on quantum mechanics or Sakurai’s book, all the standard textbooks, Townsend’s book on quantum mechanics, Gottfried’s book on quantum mechanics, Liboff. And the theory predicts measurement outcomes. It predicts what you’ll see on the readouts, on the dials, on the measurement devices, on the screens of the measurement devices, and it predicts the probability of seeing those readouts on the measurement devices. You can calculate averages in these theories, called expectation values, but these averages are by definition and by axiom statistically weighted averages of numerical measurement outcomes weighted by the probabilities of the measurement outcomes. We’re talking about a very narrow kind of phenomena, right? A very narrow class of phenomena. The Dirac-von Neumann formulation of quantum mechanics predicts measurements, what happens to measurements. It’s a very narrow slice, a very narrow class of phenomena. When we talked last time, we talked about how there are all sorts of other phenomena that seem to be going on around us. In the distant past, primordial gases coalesced in the early universe, today, birds look for food, people fall in love, all these things. There’s a lot of phenomena that seem to be going on, and they all fall, strictly speaking, outside the axiomatic scope of the Dirac-von Neumann axioms. What are we supposed to do about this? Either we say that the Dirac-von Neumann quantum mechanics simply doesn’t give a complete description of nature, which is kind of sad, and if that’s not the case, where are the outer boundaries? And now, there are some philosophers who advocate that view. Nancy Cartwright is a famous philosopher who said that maybe we have different theories in different domains, the universe is many-faceted, and it’s like different theories for different things. But it would certainly be an interesting intellectual exercise, and it would certainly be nice if we could expand quantum theory to describe more of the world. If we did that, now we have work to do. And we either have to show why all these other phenomena are actually measurements, even though there are no measuring devices or anything else. We have to somehow show that all these things are actually measurements, and therefore, in fact, fall within the axiomatic scope of the theory. And some people have proposed that. But the onus is on them to actually show it succeeds, and it’s not clear that it succeeds. Or we need to somehow expand the theory, change the axioms to encompass more of the world, and that’s part of what I’m interested in doing. Now, there are people who will say, wait a minute, decoherence. What about decoherence, right? I mean, surely, well, well. Philosophers, or at least physicists who have cared a lot about philosophy, have given us decoherence, but we haven’t done that yet. Doesn’t decoherence solve all these problems? Well, certainly Bohm didn’t think it would solve these problems. He introduced decoherence, and it was insufficient, and ultimately, he introduced his pilot wave theory in order to get an actual result. The reason why decoherence doesn’t do the job is that decoherence takes a wave function or a state vector, generally what’s called a density matrix, a density operator, and shows that under certain circumstances, when it evolves, interacts with an environment in the right direction in the right way, or interacts with a measuring device coupled to the environment in the right way, the density matrix will change in a certain way. It will become approximately what we call a diagonal matrix in a certain representation. We call this basis, and there will be some entries on this sort of diagonal of the matrix, and the other entries will be approximately zero. At this point, we’re supposed to say that the measurement has been done, and there’s an outcome. The problem is that there’s nothing in the dynamics, neither in the Schrödinger equation, nor in generalizations of the Schrödinger equation, nor the Lindblad equation, or the quantum channels that you use to describe that. There’s no known dynamics within ordinary quantum theory that picks out one outcome. You still need to apply Born’s rule to get a probability from this, and you still need to apply the projection postulate to pick out a single outcome. There’s nothing in the dynamics that will do that for you. From time to time, people have suggested that maybe there’s some sufficiently complicated standard quantum dynamics that, in fact, will make the system pick out a single outcome, but this is impossible because of the no-signaling theorem, the no-communication theorem that I mentioned before. The collapse to individual states appears phenomenologically to be a non-local process, and you can’t get a non-local process happening from what we call a local Hamiltonian, and this is guaranteed by the no-signaling theorem. There’s definitely something not working here, and pinning all this down, and not just waving your hand and saying, oh, decoherence, don’t ask me any more questions. Pinning this down is a worthwhile exercise. Subjected to rigorous scrutiny, this idea has already borne fruit and I think will continue to bear fruit in the future. In physics, artificial intelligence, consciousness, and philosophy, along with my personal musings, you’ll find it all in my Substack. Subscribers get first access to new episodes, new posts as well, behind-the-scenes insights, and the chance to be a part of a thriving community of like-minded inquirers. By joining, you’ll directly support my work and help keep these conversations at the forefront. So click the link that’s appearing on the screen here, hit “Subscribe”, and let’s continue pushing the boundaries of knowledge together. Thank you, and enjoy the show. Just FYI, if you’re listening, it’s curtjaimungal-dot-org. And I would argue that it will continue to bear fruit in the future. Now moving on, I’d like to talk about your approach, your indivisible random processes. Before that, well, and as people know, there are three sources. One is the previous interview we did with Jacob, which is appearing on the screen now. It’s over two hours long, and it’s very deep. Another source is that I have a Substack post where I cover my interpretation of Jacob’s theory. And obviously, the third is your papers directly. All three of these will be linked on the screen and in the description. Before that, I want to talk about the Wigner’s thought experiment, his friend. How it’s not just Schrödinger’s cat but the cat is replaced by a friend? You’re absolutely right. I mean, if you think of the cat as an observer, and the quantum system being observed is the radioactive atomic nucleus which is in…

A temporary superposition state of the decoherent and non-decoherent, it’s a friendly Wigner’s friend thought experiment. I mean, the origins of the Schrödinger’s cat thought experiment go back to discussions between Einstein and Schrödinger. Einstein had a somewhat less playful example involving gunpowder that could or could not explode. And Schrödinger, in this 1935 paper, replaced that with the famous cat. But Schrödinger doesn’t describe the cat as the observer. I think the real innovation is just a rethinking of the experiments. I think you can just as well think of the cat as a Wigner’s friend. If you think cats count as observers, which I do, and friends, cats are friends and observers, surely, then it’s really a matter of perspective, isn’t it? If you don’t think of the cat as an observer candidate, then you’re not doing a Wigner’s friend thought experiment. If you think the cat is just a legitimate observer like a person, even though it doesn’t have a PhD, then there are always obligatory jokes that go along with the Schrödinger’s cat experiment. You’re always supposed to say something like, but don’t call the humane society. I mean, I don’t know why people always, Scott Aaronson has some jokes about why people always make jokes about this, but yes, if you think of the cat as an observer, then it’s just a Wigner’s friend thought experiment.

I think part of the reason why people want to separate these two is that in some versions of the Wigner’s friend thought experiment, you’re supposed to be able to ask a Wigner’s friend a question, like slip in a little note and ask questions. And if you ask the wrong kind of questions, you’ll cause a collapse. And if you ask the right kind of questions, you won’t cause a collapse. And you can’t do that with a cat. Cats don’t talk. At least all the cats I’ve ever met in my life don’t talk. So there are some situations where we’d like to have a conscious, sapient observer that can communicate. But overall, they’re very similar thought experiments. Okay, now, before we move directly on, we’ll get to some audience questions that people raised in the comments and then also on Twitter threads and so on about the previous podcast. Okay, I mentioned Putnam earlier, and this is the everettian, because you can slice it at any moment of now. So if there are multiple moments of now, are all the moments of now existing? Okay, what are the counterarguments to that? It's tough or rough Putnam's argument about four-dimensionality or everettianism is a tough argument to refute. But there have been attempts. And I would recommend people watching this read some of these papers because they are, you know, beautifully written by extremely smart and amazing people.

So again, just to rehearse this argument, if you think of space, for our purposes, just like the horizontal line, and time as the vertical line, you can visualize the whole spacetime as, like thinking of graph paper with the horizontal axis being space, the three dimensions of space are somehow projected down into one dimension, and then a vertical dimension, right? The idea is that what an observer calls now might be a horizontal line in this picture, all the moments at all points in space which all happen at the same vertical time coordinate, all the same time coordinate now. And what special relativity suggests is that if you’re in motion, that slice is tilted a little bit. It looks like it’s no longer perfectly horizontal relative to the first slice. And thus, things that are further in the future relative to one observer are in the present of the second observer and so on. One way I like to think about this is the pancake model of spacetime. So imagine a stack of pancakes. Each pancake is supposed to be the whole of space, the whole spatial universe at one moment of time, okay? And think about this in a pre-relativistic way, like the Newtonian notion that there’s just a well-defined notion of what is all of space at each moment of time, you get a stack of pancakes. And let’s say one of the pancakes is the hot pancake. The hot pancake is the now pancake. It’s the pancake that’s happening now. And somehow the hot pancake is increasing in some way, right? And that’s the passage of time. You run into some very profound questions like how fast are the pancakes moving? They are moving at a rate of one second per second. Does one second per second make sense? If you divide a second by a second, isn’t that just a unit? What are we talking about? Okay, but let’s put all that aside for a second. Just imagine there’s some notion of “now moving,” this kind of metaphysical present-tense idea that the present exists, it’s a well-defined thing, and it’s somehow increasing forward. What special relativity seems to suggest is that observers in different states of motion will slice the stack of pancakes diagonally a little bit. And so for an observer who’s moving somewhere, you know, it doesn’t even have to be at super high speed, because if you’re talking about the whole universe, even slow motion will eventually produce a clear contradiction. But, you know, the slices are now tilted. And if you’re slicing the stack of pancakes with a slight tilt, how can there be a hot pancake anymore? The two observers don’t even agree on whether the slices are horizontal slices or slightly diagonal slices. How can there be a fixed metaphysical notion that one of them at a particular slice is in fact the hot pancake? So you can see why this is considered a tough argument to refute. But there have been attempts. So Brad Skow at MIT has a book that includes a particular perspective on this. I encourage people to take a look at that approach. Another approach is by Jan Anis Mail, she’s at Johns Hopkins University, a philosopher of physics, philosopher of science. She has a book called How Physics Makes Us Free. And she has a very interesting argument about how to overcome this problem. I won’t be able to do justice to the argument here, but I recommend people read the book because she’s a wonderful writer, and I think people would find reading this book interesting. There’s a recent paper by David Willis at Princeton. He’s a metaphysician who does some work in philosophy of science as well at Princeton. And he has an argument, you know, regardless of the special relativistic argument, he says, you know, maybe we can’t, maybe that’s a tough argument to deal with, but at least instead of trying to refute that negative argument, the argument against presentism, maybe there are good arguments for presentism. We should focus on those. And his argument in that paper is that many of our fundamental laws of physics seem to be Markovian. And Markovian laws are by definition laws that take a notion of the present state and tell you about the later states without really worrying about anything in the past. And he says, you know, why should the laws be Markovian if we live in an everettian universe? If we live in a four-dimensional everettian world where the whole block is just as it is, why do our laws only care about the present state? There wouldn’t be an explanation for that. But if the present actually exists and the past doesn’t exist, that would give an explanation for why our laws only care about the present. Unfortunately, as I’m sure you and the people who are watching you, you know, have some problems with this argument because the fundamental goal of formulating quantum mechanics which we’ll talk about is that in fact the laws may not be fundamentally Markovian at all. And if they weren’t Markovian, then suddenly this argument may not work so well.

Yes. What I understand, and we’ll get to it, is that your laws of evolution depend on the past. It’s not as if they depend on the future. Right. So in the everettian case, when they say, why do we privilege the present? And then you say, well, in your case, you don’t, but you also don’t privilege the future. You actually privilege the past. So you still don’t get an everettian block. So that’s a subtlety, isn’t it? The fundamental laws of physics that we know today, to a very good approximation, have a property called time-reversal invariance or time symmetry. Newtonian mechanics, famously, if you run a system in a particular process, you know, in a particular process, then somebody runs a reverse version of, you watch a video of it and somebody rewinds and plays it at normal speed and you watch everything happen in reverse. Although it might seem strange or improbable, it doesn’t seem like there’s any violation of Newtonian physics in what you see. You know, the famous example, a teacup falling off the table, shattering. There, you can also make all the pieces have the right initial conditions such that they have some appropriate initial velocities to bounce back together. And they perfectly land together. And they reclose themselves and form the teacup. And the teacup has the right kinetic energy to bounce off and land on the table. It seems improbable, but it doesn’t actually violate any of the laws of Newtonian physics. And this works pretty well until you get to the standard model. There are some systems involving kaons in the standard model that exhibit a slight violation of time-reversal invariance. Technically, it’s CP invariance, but the symmetry where you swap particles and antiparticles is called C symmetry. The symmetry where you do parity or spatial reflection and everything is called parity symmetry. And then there’s time reversal. And the standard model, our best theory for fundamental particle physics which relies on quantum field theory, has this property that it’s exactly CPT invariant. If you take any process in the standard model and you do particle swap goes to antiparticle and vice versa and parity transformation and reverse time, everything remains the same. And there are some systems that violate CP symmetry. And then by CPT invariance, this means they violate T or time-reversal symmetry. But those are rare processes. It’s not clear that they have anything to do with the macroscopic distinction between future and past that we tend to see. There’s some speculation about this, but nobody has a strong argument that these two are closely related. So the idea of a physical theory that we’re talking about that privileges the past somehow, but not the future in an everettian universe seems a little bit strange. I should immediately say that the decoherent histories formulation doesn’t fundamentally privilege the past or the future. You can also formulate a quantum system that runs in the other direction. There’s nothing, not, the theory doesn’t specifically determine that, it’s just that when you actually think about a particular such system, it would be a system where the past plays a different role than the future, but you can also think of the system where the future plays a different role than the past. We call it not a fundamental breaking of time-reversal invariance, but a spontaneous breaking of time-reversal invariance. Not a breaking in the sense that fundamentally, like it’s in the nature about choosing the future versus the past, but just in a particular instantiation, in a particular situation, nature has to choose a particular direction in each instantiation and one over the other. Like Newton’s laws of mechanics are fundamentally rotationally invariant, but you’re not rotationally invariant. Your atoms formed in a particular shape, and whatever shape they formed it determines a direction in space. So you spontaneously break rotational invariance, even though the laws of Newtonian physics are rotationally invariant. The laws of quantum mechanics, according to this decoherent histories approach, are fundamentally time-reversal invariant, but for a particular model, they typically privilege one direction of time over the other. I should have said that there’s another way to save, at least I can think of, another way to save the idea of the flow of time, the forward direction to time. That is to say, well, special relativity is a very good theory, but we live in an expanding universe. We live in a spacetime that seems to go back to some sort of big bang hypersurface, and some initial big bang everywhere. And the distances between things grow over time in a particular way. It turns out that in these kinds, we call it cosmology. So cosmology is the subject of studying the universe, but a particular model like a spacetime model that solves Einstein’s field equations on the level of the whole universe is called cosmology. And in cosmology, we seem to live in approximately what’s called the Einstein-de Sitter cosmology described by the FLRW model. In this model, there’s actually a preferred slicing of spacetime, right? All you have to do is take every point in the universe and ask how long ago was the big bang from that point and take all the points that date back to 13.78 billion years ago since the big bang, and they form a hypersurface. And if you do that, you actually get some sort of preferred slicing of the universe. And you might go on to say that this seems contradictory to special relativity. Well, but general relativity is not special relativity. General relativity is a different theory. And in general relativity, different spacetimes globally, like on the scale of the whole spacetime, can spontaneously break the slicing symmetry, which is called Lorentz symmetry. Because there’s a preferred big bang hypersurface, there’s a preferred foliation or slicing of spacetime into slices of now. And so the history of the universe, the way that the instance of the big bang was created, seems to have picked the preferred way to slice the universe. And then you can say, well, okay, so that’s the fundamental idea of time. Time really flows from slice to slice. And sure, if you zoom in really close like a planet or a star or some very local things, things will look like special relativity. You don’t notice the full shape of the cosmology and all the different frames of reference look similar and all the slices look like they’re on the same footing. But on a global cosmological level, there’s actually a preferred way to slice things. And time really does flow from slice to slice in a fundamental sense in that picture. But this leads to some other profound questions. Is the geometry of our cosmology a fundamental fact? Or is it just a contingent fact? Could the universe have formed in many other ways? And it just happened to form in this particular way with this preferred slicing. And if it’s contingent, if the universe could have formed in many ways or could have been everettian, but it just happened to form in this particular way, can you say metaphysically that time flows fundamentally based on what was a contingent fact about the universe? Like, if you think the flow of time is a fundamental feature of reality, should it depend on accidents of history? I didn’t mean the pun, but you get my point, right? So just to close the loop, that’s like one of the other ways people have thought about maybe recovering the idea of the flow of time. Okay, sorry, that was a lot, but yes.

Okay, in short, before we close that loop, I mentioned that in GR you can spontaneously break Lorentz symmetry. What’s the difference between breaking a symmetry and spontaneously breaking a symmetry? Well, if you take a theory and the fundamental equations that formulate the laws of that theory simply fail to have a particular symmetry. And by symmetry here I mean transformation that will have a particular symmetry. So if you take a theory and the fundamental equations that formulate the laws of that theory simply fail to have a particular symmetry. Maybe for particular kinds of theories, there are particular kinds of laws that leave the laws unchanged. For this particular theory, they don’t leave the laws unchanged. So let me give an example. Let’s suppose the universe is described by Newtonian physics near the surface of the Earth, and that’s the whole universe. In fact, there is no Earth. The universe is infinitely large, and it’s like the surface of the Earth forever, right? The surface of the Earth continues in every direction forever. There’s the Earth, and it will never end. You can go as far as you want, and it doesn’t wrap around on itself. It goes on forever, right? There are no planets or anything like that. The whole universe is just life near an infinitely large surface. Right. That’s all there ever is. And that’s fundamentally all there is. It’s not an accident of history. That’s just how the universe is. It’s fundamentally that its existence is just this infinite Earth that continues forever. When gravity points down, and that’s a law of nature, a completely fundamental law of nature that gravity points down, this is a theory that fundamentally breaks three-dimensional rotational invariance. The fundamental laws of this theory involve that there’s a force called gravity that points in a particular direction, and if you take any system in this universe and rotate it in a way that’s not parallel to the Earth, the laws look different now, right?? Things fall down now. And theoretically, the laws are not invariant under this transformation. We call that an explicit breaking of rotational symmetry. I see. Right. So I think I’m confused terminologically, because breaking seems to me as if it existed before, and now it’s broken. So breaking in this case just means it failed to have it to begin with. That’s right. It failed to have it from the beginning. That’s the better way to say it. I think the reason for the terminology is that these are often symmetries that were present in earlier theories, and then maybe in a deeper theory, the symmetry disappears. So we say that like kaons violate time-reversal symmetry, right? We call it a violation or breaking because before we discovered these particles, we thought it was a symmetry, and it’s broken by the kaons, right? So I think that’s maybe one way to think about it, or maybe we have a lot of theories where some symmetries are approximately true, but they’re not exactly true. And then we can think of some specific things in the theory that violate it, whereas they’re not generally violated. That’s perfectly fair. But Sventi Hensprig’s example would be like the actual Earth, right? The actual Earth is not an infinite plane, it’s a sphere in space. And when you’re on Earth, you feel like gravity points in a particular direction, but that’s just an accident of having the Earth there. If you could delete the Earth, and we’re floating in space, you would suddenly have full access to the way. There wouldn’t be a notion of up or down, or left, like left or right is actually subtle because it’s parity invariance, which is a different thing. But I mean there’s no preferred direction in space if the Earth weren’t there. The existence of the Earth, by accident, that’s just how this particular corner of the universe was created, not on the level of the fundamental laws of physics changing. But the existence of the Earth there and our living on Earth makes us think that the symmetry that’s fundamentally there, rotational invariance, full three-dimensional rotational invariance, is not actually there. It’s hidden from us. Some people say that spontaneous hiding of symmetry is a better term than spontaneous breaking of symmetry. But yes, this just points to this distinction between, am I actually saying that there’s a particular symmetry that’s not present in the fundamental statement of the theory, or is it hidden or missing because of the way a particular system instantiated the theory? Well, I didn’t know that, for example, when you were talking about the molecules that make you up, the molecules have some rotational invariance. But fortunately, you don’t have that rotational invariance. I do have rotational invariance. As far as we can tell. But that formation wasn’t spontaneous, so the person watching or listening is thinking, well, Jacob’s formation took some time. Jacob didn’t do— Spontaneous is a technical term, yes. Okay, because I thought spontaneous symmetry breaking had to do with, you have a potential well, and then you go to the minimum of it, and you produce some ghost bosons. And I thought it was only for that case. I didn’t realize that there was a time when the symmetry was broken. You call it spontaneously broken. When it’s broken by the way a particular system forms or a particular solution of the theory. So that’s another way to think about spontaneous symmetry breaking. There’s a puzzle called Shape by Shape. It’s very small, it’s a square. It’s a delightful little puzzle. You have these yellow shapes and these orange shapes. And you have a picture that you’re supposed to create. And you take all the shapes and you put them in the square. And you try to fit them all in the square. And they have to fit perfectly in the square without any gaps. And they have to replicate the picture that you see. It’s like a yellow background with an orange shape in the middle, and you have to replicate that. And the setup of this game is mirror symmetric. It’s a square, and the playing field is a perfectly mirror-symmetric square. And although some of the pieces are what we call chiral. Chiral means that they’re handed. The pieces seem like they’re a left-handed piece or a right-handed piece. It turns out they’re not really chiral because you can just flip them. You can flip them and then you discover the fact that, yes. But whichever particular way you flip them, it picks out what seems like one direction. So, and there’s like an equal number of pieces. Everything about the setup of this game is mirror symmetric. You can put the board down, and put all the pieces down, and put them in a way where you look at the picture, and you just flip the thing upside down and it’ll look exactly the same. And you can also have the picture that you’re trying to capture. And this picture that you’re trying to capture is also mirror symmetric, right? When you look at the picture, it looks perfectly symmetric. So you say, okay, I should be able to take mirror-symmetric puzzle pieces and create a mirror-symmetric picture. And I should be able to do that by putting the pieces in a mirror-symmetric configuration. And it turns out that in some cases, you can’t. In some cases all the solutions to this problem, even though the problem, the laws of this system are mirror symmetric, none of the solutions are mirror symmetric. Once you solve it, you discover that the solutions are always asymmetric. There are different pieces on one side versus the other, and there’s no symmetric and mirror-symmetric solution. We can say that this is a system that exhibits spontaneous symmetry breaking. The fundamental equations and laws are symmetric, but all the possible ways to solve it are not. Now, you can also have systems, maybe there’s a puzzle that can be solved in a symmetric way, and it can also be solved in a nonsymmetric way. We still call the nonsymmetric solutions, but they still solve the puzzle, and we still call them spontaneously broken solutions. So this is a phenomenon that occurs everywhere. Another example is that one of my colleagues here, Cameron Fava, a professor of high-energy theoretical physics, works in string theory. I think he has a beautiful book called Puzzles to Solve the Universe. It’s connected to a course that he teaches here. And he has this puzzle that he really likes. It’s this puzzle where you have four cities located on the corners of a square. And the question is how can you connect them with roads? So you can go from any city to any other city, driving on the roads, using the least possible amount of road or pavement. This problem is perfectly rotationally symmetric. It’s a square, right? It’s stated in a way that doesn’t privilege any direction. And you can always rotate the square any way you want, it looks the same. So you might think the solution would be, I don’t know, an X. But an X doesn’t do it, an X works because you can create an X and then you can go to the middle of the X and you can get to any city. It turns out that Xs use a lot of pavement. The solutions that minimize the amount of pavement used are like double Ys solutions. And there’s one that goes horizontally and one that goes vertically. And this minimizes the amount of pavement and both of these violate the symmetry of the problem. So this is spontaneous symmetry breaking and we see it everywhere. If you’ve ever wondered, how can the universe seem so asymmetric, given that the fundamental laws of physics seem like they have a lot of symmetries? The fundamental laws of physics don’t seem to privilege direction. And to a very good approximation, they don’t seem to privilege left-handedness versus right-handedness. They don’t seem to privilege the direction of time. And yet, the universe seems totally asymmetric. This is basically just a large collection of examples of spontaneous symmetry breaking. You can have a fundamental system where the laws or equations are fundamentally invariant under a set of symmetries. But when you write down the solutions to it, every molecular configuration is a solution to the standard model. Many of them simply fail to have all the symmetries of the fundamental theory. Okay, we’ve kept the audience on the edge of their seats for a long time now. So tell the audience and myself again, summarizing the last podcast on what decoherent histories are. And feel free to connect it to Bohmian mechanics, because people already know what Bohmian mechanics is, you’ve covered it, feel free to do that as a bridge. Sounds great, yes. So the higher-level version of this is, there’s this joke about how the TV show “Seinfeld” is a show about nothing. This is a theory about something. It’s a theory about phenomena that occur. So again, we had this problem in von Neumann’s formulation of quantum mechanics, which is the textbook formulation. The only class of phenomena we’re talking about is this narrow class of results

Measurement. While we have a much larger class of phenomena that will happen everywhere. I call this the class problem. It is different from the famous measurement problem in quantum mechanics. So it would be nice to have a theory where things just happen. Now, that is not the only approach that does that. And then I will talk about pilot wave theory, Bohmian mechanics, Everett's approach or many worlds, and the spontaneous collapse approach. There are other reformulations of quantum mechanics where phenomena happen. And all of them, in different ways, address this class problem that standard theory hasn't adequately addressed. So, one way to think about this is that this is another way for phenomena to actually happen. In a broad sense, it goes beyond just the narrow class of measurement outcomes. There's another way to think about this, which is that it's a way to make the world safe for good old probability theory. So when we do quantum mechanics according to Hilbert space, and the Dirac von Neumann formulation, we have these very strange mathematical entities. These vectors are density operators, and Hilbert spaces, and Born's rule, all very different, and look completely unlike ordinary probability theory. Probabilities do appear, but there are many things you cannot do using probability theory. You have to use this ornate, confined to a certain class, this formal apparatus in this kind of Hilbert space language. In this approach, we regain our ability to do quantum mechanics using good old probability theory. That's another way of thinking about what we're trying to achieve with all of this. So, but let me delve a little bit deeper before I explain how this works. There's another way to think about this, which is that there are two long-standing assumptions about what physical theories are supposed to look like. One assumption is that the laws of the theory should be Markovian. The laws of the theory should take some idea of the current physical state, and then tell you what will happen next. If your theory is time-reversible, and the laws are reversible, you should also be able to tell you what would have happened previously, at least in principle. One other assumption is that there's an all-or-nothing deal when it comes to things that can be observed. The things we can observe about the theory are either all there, or all there, and when we measure some observable, we are passively revealing some features or properties that are already present in our system. In this case, we should be able to describe these things by any kind of probability distribution we want, including joint probabilities, where we can say what is the probability that this observable has this pre-existing value, and that this observable has that pre-existing value, which are observable, and we can put a probability distribution on all of these things in a straightforward way. And if we can't, then we just give up. If we can't, then everything is out the window, we can't do it. There are good reasons to believe that we can't do that in quantum mechanics. There's the famous "no-go" theorem, originally proven by Bell, but because of the way it was published, I think the first version that appeared in print was by Kochen and Specker in the 1960s. And this theorem is called the Kochen-Specker no-go theorem. And the Kochen-Specker theorem basically says that there are some quantum systems where this is impossible. There are some systems where you cannot assume that all observables have pre-existing values that are only passively revealed. And there's a beautiful way to explain this, a very simple version, much simpler than the original version. It's due to Asher Peres in the 1990s. Imagine you play a weird version of tic-tac-TOE. This is a very strange version of tic-tac-TOE. And here's how it will work. You know tic-tac-toe, that's what we call it in America. I know it's called like crosses and O's or something else in different places. But tic-tac-toe, you have a grid, with nine empty squares. We won't play it the normal way, we will play it in the following way. I will close my eyes and I will imagine an arrangement of O's and X's on this board. I'll close my eyes and I'll tell you, I promise, I can imagine, I see it, I see a set of O's and X's. It's in my head. Trust me, I really know what it is. And what you will do is you will call out one row or one column. That's it. And if the row or column you call out has an odd number of X's, you win. If it has an even number of X's, you lose. And you only get one try. If you guess and you fail, that means we're done, and you lose that round. We can play again, but then I have to come up with a new board. It's a very simple game. So the way the game will work, and when I teach my philosophy of quantum mechanics class, we do this, we do this example. I say, I've got the board, okay, and I'll go, from the first-person perspective, pick a row or a column. The person says, the second row, and I write X O X. Sorry, even number of X's, you lose. We erase it. I say, I'm coming up with a new board. The second person says, I'll pick the second row again. And this time, the second row is O O O. Sorry, even number of X's, zero in this case, you lose. And I erase it, and I come up with a new board, and the next person goes. And they keep trying different rows and columns. And what they discover is that every time they pick a row, they always get an even number of X's. The first row, always has an even number of X's. The second row, the third row, always an even number of X's. When they pick the columns, the first column always has an even number of X's. The second column, always has an even number of X's. But the third one always has an odd number of X's every time. And so what they learn is that they will just keep picking the last column and they will always win. Just keep picking the last column and they'll always win. But then they say, well, wait a second, that doesn't make sense. If you really thought of this board in your head, you say you thought of a board in your head where every row has an even number of X's. The first two columns also have an even number of X's, but the third column has an odd number of X's. That's impossible. It can't even be even plus even plus even if all the rows in my head have an even number of X's. As if they couldn't just be a static picture in your head. Right. There can't be a static picture in my head that has all rows with an even number of X's. And the first two columns have an even number, and the third column has an odd number; because row plus row plus row will be even. Column plus column will be odd. This is clearly incompatible. You must be creating the results only when we ask for them. You can't actually have a pre-existing board in your mind. And I go, you win. You're right. But there are quantum systems with this feature, with nine observables, nine observables, with the feature that the rows all have an even number and the first two columns have an even number, but the last one has an odd number. And you look at the system and you discover that it's impossible for this system to know beforehand what it will reveal. And the act of measurement must be creating the outcomes, at least in some cases. So the hard way of reading that is to say, well, if some outcomes are a result of the measurement process and not just passively revealing a pre-existing situation, then simply there are no pre-existing outcomes. All or nothing. Either they're all there or they're not there. And that's also something I would like to back away from. So again, Markovianity in the laws, this assumption that the laws should be things like differential equations that take the current state and give you subsequent states. And second, there's the all-or-nothing relationship. Either all the things you can observe are there, waiting to be seen, or joint probability distributions can be assigned to them as needed, or they're just not there at all. There's nothing there. And these are two things that are challenged in this approach. These two things have been dropped, the Markovianity and this assumption. In this picture, the fundamental laws of nature are not Markovian and some observable quantities reflect things that already exist and others are emergent effects of the interaction between the measuring apparatus and the system being measured. And this is one way in which the theory is very similar to Bohmian mechanics. People have known for a very long time that in Bohmian mechanics, some things you observe, like where your particles are, reveal pre-existing facts about the matter. Bell gave a word for things that were already there. And he didn't call them observables, he called them beables. It's the way the system can be, as being beable rather than being observable. Some people read it and they think it's actionable, but it's actually actionable. Whereas other things you can observe don't really reflect something that was there and are just emergent features of the story. I call these unbeables instead of unobservables. To an outside measuring apparatus, they look just as real as a beable, but what you are really seeing in the measuring apparatus is this kind of emergent pattern. It doesn't really reflect something fundamentally existing. Bohmian mechanics does this. In Bohmian mechanics, the positions of particles are beables. You measure them and you really see where the particles were. But when you measure the momentum of your particle, the momentum that you actually see in your experiment is not literally the pre-existing momentum. It's this kind of emergent effect of the interaction with the system. There's a paper, you can look it up in the archive. It's called Naïve Realism about beables. It's from 1996. And it's written by Domer, Dürr, Goldstein, and Zanghì. It's specifically about this thing, which is that the belief that every adjacent factor in quantum mechanics textbooks, direct quantum mechanics can relate it to what's observable is a discovery of something pre-existing in the system is actually, in their words, very naïve. You can really have some things existing and some things not existing, and that's perfectly fine. It's not a serious problem. I'll come back to this point in a little bit because some questions that we received from people were about basis dependence and in this picture, can you really measure everything? The answer is that you can. It's just that some will be beables and some will be unbeables. Okay, so we're going to give up these two things. There's a saying. I can't quite pinpoint who said it. Some people attribute it to John Wheeler, again, that if you can explain quantum mechanics, you should be able to say it in one sentence. I don't know if Wheeler was the one who originally said this. People can source this. But here in one sentence. In the ontological formulation of quantum mechanics, every system has an actual configuration belonging to a list of possible configurations that we call the configuration space. I have to put a and. And there's a comma and a and. It's still one sentence. And the dynamics, and the dynamical rules, and the laws by which the configuration changes with time are characterized by a set of discrete directed conditional probabilities that generally fail to be time divisible. That's the whole picture. And in principle, you can get everything from that one sentence. Everything now is just mathematics. So there's no more. There's no more. That's it. That's the picture. Now let's talk about like what. So, if you want to talk in terms of Occam's razor in this way, we'll come back to Occam's razor in a little bit, please. But just saying this is very simple intuitively. There's no statement about Hilbert space or anything else. Everything is formulated in terms of things that we know and are familiar with, and actually existing configurations. Configurations that depend on the system. If you want to model a system of particles, you can use particle configurations. If you want to use fields, you can use field configurations. If you want to use any discrete registers in qubits, you know, memory register, you will use them, whatever you want to use, discrete, continuous, whatever you want. And then the laws themselves are formulated as probabilistic statements, but they are classical probabilities. They're ordinary classical probabilities. Classical is maybe too strong a word because maybe you might require that the probabilities of classical time evolution be Markovian. I don't think so, I think it's a little bit detrimental to say that they should be that way, but they're certainly just ordinary probabilities. They're not these strange Hilbert space things. There are complex numbers in them. They're just regular probabilities. They sum to one. They do the things that probabilities are supposed to do. That's the picture. And then in the first research papers, the paper is called the quantum random correspondence, it's in the archive, it's now just a bunch of mathematical mappings. It takes this picture and does this kind of mathematical transformation and you end up with the same story, but formulated in Hilbert space language with time evolution operators and state vectors and density operators and adjacencies. This picture is just a different mathematical formulation of this ontological picture. And there's a beautiful analogy that can be found here between these ontological systems, these ontological random systems and that have this very strange Hilbert space formulation which has complex numbers. And it's got all these strange symmetries. It's got basis invariance. You have all these different bases you can use. There's a beautiful correspondence between this correspondence, that quantum random correspondence and what's called the Hamiltonian formulation of classical physics. And it's interesting that Newtonian systems, classical Newtonian systems, are not quite Markovian, right? Think about it, right? You can't predict how the particle will behave knowing only its position. You actually have to know its position and you have to know its previous position infinitesimally close by. You actually need two pieces of information. Now, we don't usually formulate it that way because it's a little cumbersome to talk about where it is now and where it was infinitesimally before, like dT, you know, d like infinitesimal calculus, d infinitesimally before. That's kind of cumbersome to do. So instead what we do is we subtract the two and divide by dT and we call that the velocity. But it's the same information. If you want to numerically simulate a Newtonian system and you want to discretize time to do that, you have to specify where it is now, and where it was a moment before, and you can plug that into a discrete version of Newton's second law force equals mass times acceleration and you can predict the behavior of the system. So, even Newtonian physics is somewhat non-Markovian. But we do tricks. We don't like it to be non-Markovian. So what we do is we replace the two positions at infinitesimally close-by times with position and what's called the instantaneous velocity, which is kind of this trick so we can treat these two things as existing at the same time. And now we've made the formalism look Markovian. Now we have a state at initial time consisting of the coordinates, so-called coordinates, the position, and the velocity. But we need to double the variables now. We've increased the number of variables in order to formulate this thing as a Markovian system. And this is an old thing that you can do in stochastic processes. In the theory of stochastic processes, if you think about a system that is somewhat non-Markovian, it's not quite as non-Markovian as these ontological processes we're talking about, but it's a system where you need to know the current state and maybe just one previous state or maybe two previous states to know how the system will evolve. You can take these systems and you can treat them as if they were Markovian simply by increasing what you mean by the state space. I see. Like you're tripling the state space, so you can now treat these three things as if they're all in one slice, and then you're now turning it into a Markovian system. And then there's this idea that you can take any non-Markovian system and make it Markovian just at the expense of making the state space large enough. Just like in Newtonian mechanics, we take what was just coordinates and we double it to become coordinates and velocities. And now we have something that looks like a Markovian description. This doesn't work for an ontological system. When systems are sufficiently non-Markovian, you can't do that. And I think this has been a bit of tunnel vision. People think, well, you can always do this. So what's the interesting thing about non-Markovian systems? But if the system is sufficiently non-Markovian, this trick will fail and you will actually have something completely different. But what you can do then is reformulate the Hamiltonian system in what's called the Hamiltonian formulation. In the Hamiltonian formulation, we reformulate what we were talking about, the state space, the states, the positions and velocities in terms of what are called canonical coordinates, which are kind of a generalization of the notion of position, and canonical momenta, which generalize the idea of velocity. And then we call the state space the phase space. Obviously, the term goes back to Boltzmann, because he was thinking about the phase of a pendulum or something like that, in some oscillatory system. Where is it in its motion, in its cycle? What stage is it in? This idea is much more general than that. We call this phase space. And in phase space, we have these variables, Q variables, which are like generalizations of position, and P variables, which are like generalizations of velocity, so-called canonical momenta. And in terms of the Qs and Ps, we can reformulate Newton's laws as first-order differential equations, which basically just means Markovian. You specify Q and P, and then you uniquely get the next Q and P at all subsequent moments of time. And this makes the system look like a beautiful Markovian system, where position and momentum are now completely on equal footing. Differential geometry talks about this, where we are now working on what's called the cotangent bundle of the configuration manifold, but it's not necessary to understand theoretically what's going on here. But what's interesting about this Hamiltonian formulation is that it looks weird. It's got all these enhanced symmetries. For example, now that we've put the coordinates, Qs, which generalize the idea of position again, and Ps, which generalize momentum, we've put them on this kind of very similar footing, and entered into the theory in this very fair way. We can now make changes of variables where we can take Q and replace it with P, and P and replace it with minus Q. And by doing that, you can take a harmonic oscillator with a mass and a spring constant and get a new harmonic oscillator where the mass of the new harmonic oscillator is the inverse of the old spring constant, and the new spring constant is the inverse of the old mass of the oscillator, but you can also do much stranger transformations. These changes of variables, which are carefully designed to keep the equations, the laws look very similar, are called canonical transformations. And there's a beautiful relationship between these changes of variables in your phase space and the unitary transformations in Hilbert spaces. There's actually a beautiful mathematical relationship between them. This helped inspire Dirac to come up with his formulation of quantum mechanics, which is kind of an analogy between these two things. And this analogy can be made stronger through a series of research papers. There was a paper by Franco Strocchi in the 1960s titled Complex coordinates for quantum mechanics, I believe, and then a paper in 1985 by André Heslot. And this paper, I can't remember the name of the journal, but it's from 1985, where they made this analogy much more rigorous. They showed that any quantum system in Hilbert space language can be rewritten in a way that looks exactly like a classical Hamiltonian system of a bunch of coupled harmonic oscillators. It's this beautiful framework, I call it the Strocchi-Heslot formulation, and I think there's like a YouTube video of a talk I gave about it. If people want to see the details, we can link that. People can see how this works. So the relationship between this freedom to do all these strange changes of variables that mix up what you mean by Qs and what you mean by Ps, you can create a new Q plus P and a new P, and mix them up in all these strange ways that makes the underlying picture extremely obscure. Once we do that, it'll be kind of hard to remember what our original system was. There's a close relationship between that enhanced set of symmetries and the unitary transformations in quantum mechanics. You also see the emergence of complex structure and complex numbers in the Hamiltonian formulation. There's a beautiful way you can take Qs and Ps and write Qs as Q plus the square root of minus one, the imaginary unit times P, up to some dimensional factors. You have to get the units right. But basically you can define a complex variable and rewrite the whole picture in complex coordinates, and this simplifies the mathematics in a very beautiful way. And this makes the analogy with quantum mechanics much tighter. For those viewers who know Poisson brackets, if you reformulate the Poisson brackets in terms of this kind of complex representation, this makes canonical quantization look much cleaner. So we have this stunning analogy. You start with a non-Markovian system, in this case just second-order non-Markovian Newtonian mechanics, which depends on coordinates and previous time coordinates. And we can reformulate it into a beautiful Markovian one, this phase-space based Hamiltonian formalism with all these enhanced symmetries and even complex structures, and we can do really powerful things. And these complex formulations can be used to solve all kinds of difficult problems in ways that are hard to implement in Newtonian mechanics. It even led to a wave-like picture called the Hamilton-Jacobi formulation, which led to Schrödinger's discovery of wave mechanics. And there's this complete analogy where you can take a non-Markovian ontological random system, which is also non-Markovian, and much more probabilistically non-Markovian, which is the system I just described to you, which I presented, and make this change in the mathematical representation, and you get the Hilbert space picture, which also looks very strange, and also has a very obscure kind of picture of the physical world, and also has all these enhanced symmetries, and these unitary transformations, and also sees the emergence of complex numbers. And the analogy is actually very close between these two pictures. And again, this change of representation into the Hilbert space picture is called the quantum random correspondence. But now we can do all kinds of things that we couldn't do before, okay? One example, why is the dynamical equation of quantum mechanics Markovian? It's Markovian because you see while you're doing this change of representation, you see how we took something non-Markovian and wrote it as a Markovian kind of evolution at the expense of introducing all these strange new components. The phases, and the off-diagonal entries, and the density matrices, and interference effects, and superposition, all these components are the price you pay by trying to represent what is essentially not a Markovian system, a perfectly non-Markovian system, as a Markovian system. It's the price you pay. We talked before about, are these memory effects? Memory is not quite the right metaphor for ontological stochastic processes. Traditional non-Markovian processes require specifying kind of arbitrarily conditioned conditional probabilities over many previous times. This is very complicated and has lots of structure and contains lots of information. And you can legitimately ask, where is that information stored? The ontological process is actually much simpler. It doesn't require specifying all those higher-order non-Markovian probabilities. It's much less. All you're supplied with are first-order conditional probabilities that are non-sequential and non-divisible and non-Markovian. So there's actually less information and less memory, much less memory, than there is in a traditionally declared non-Markovian process. So there's no question about where the memory is stored. It's not that there's memory per se. The evolution of the system doesn't just depend on the present state. So memory is not quite the right word for it, but there's a kind of memory-like thing. And that's what's encoded in all those coherences and superposition interferences, which otherwise have nothing, in the traditional textbook formulation, they're just mathematics that produce experimental implications when we do experiments. But we don't have a meaning that we can attach to them. And here we can attach meaning. Where are the tools of taking what is ultimately not a Markovian process and forcing it to be in the Markovian formalism? But we can go further than that, right? So we can explain why the equations look Markovian. We can explain what the interference terms and phases and coherences and superpositions are. We can explain what those things are. We can also explain why the law of evolution is linear. For a closed quantum system, a system that's not participating in the exchange of information with its larger environment, the evolution is given by a linear equation, the Schrödinger equation if the system evolves smoothly enough with time, or in general, unitary evolution. This is linear. And the question is,

Where does this linearity come from? It’s just an axiom, according to the Dirac-von Neumann textbook axioms. But in the non-demolition approach, it comes directly from the change of representation. It comes from the fact that ordinary probability has a linear law. If you are given prior probabilities, and you want to compute posterior probabilities, and you’re using conditional probabilities given to you in the laws, then the relationship between the early probabilities and the later probabilities is a linear law. It’s given by what’s called Bayesian marginalization, I mean there are different terms for it, the law of total probability. But it’s a linear relationship, and that linear relationship becomes the linear time evolution of quantum mechanics, which, now, has an interpretation as well. And you might say, well, what about unitarity? I mean I didn’t start my non-demolition process, how did I know it becomes unitary? It turns out that there’s a class of non-demolition processes called, they’re built upon what’s called a non-homogeneous stochastic matrix. The term non-homogeneous goes back to a lecture in the late eighties, but the idea actually goes back further, it’s a much older term. So Robert Thompson introduced the term non-homogeneous, but the original term was orthostochastic, and that was introduced by Alfred Horn, a mathematician in the fifties. And he wasn’t studying stochastic processes, he was just studying the analytic properties, the purely mathematical analytic properties of stochastic matrices. And he pointed out that there’s a certain kind of stochastic matrix, these are the kinds of matrices that appear in stochastic theories. These matrices are matrices with non-negative entries, they’re square, and they have non-negative entries, and the sum of their columns equals one. But there’s a particular subclass of them that he called “orthostochastic,” today we call them “orthostochastic,” which have very beautiful and interesting analytic properties. From the point of view of a pure mathematician, they have very remarkable properties. The idea of building a physical stochastic process using these matrices which contain all the conditional probabilities, is a new idea. I mean this wasn’t an idea that people had proposed. So you can just say, the particular kind of non-demolition processes that I’m interested in are the non-homogeneous ones, and these are precisely the processes that when you run them through the quantum-stochastic correspondence, on the other side you end up with unitary evolution. Now you might say, this is somewhat unsatisfactory because it doesn’t explain why the evolution is unitary. You had to assume a special kind of stochastic process, a non-demolition process that was non-homogeneous. The technical definition is that a unitary process is a process where all the conditional probabilities are related in a very simple way to the entries of the unitary matrix. This makes it seem a little bit canned. But there’s a theorem that was proven in the first paper, the quantum stochastic correspondence paper, that even if you don’t start with a non-homogeneous stochastic process, even if you start with a completely boring and ordinary and generic non-demolition stochastic process, you change the representation to a Hilbert space picture, you can always write that process as what’s called a quantum channel. A quantum channel is also known as a completely positive trace-preserving linear map. And this has been well-studied in the quantum information literature. It’s not obvious that you can do this. But you can. It’s simple, yes. The mapping from non-demolition stochastic processes to a Hilbert space picture can be represented by a quantum channel, or is it a quantum channel? So you start with the non-demolition stochastic process, it’s a probabilistic process, it just says that given where the system is now, this is the probability that it will be there later. You run it through the quantum-stochastic correspondence, you now have density matrices and state vectors, and all these things appear. And now the time evolution is implemented by what’s called the time evolution operator that takes your current state and gives you your later state. In general, this time evolution operator is not unitary, unless your original process was non-homogeneous. In general, if it wasn’t non-homogeneous originally, the time evolution operator will not be non-homogeneous. But it turns out that you can still write it as a quantum channel. This time evolution operator that appears on the other side looks kind of strange, but it turns out that it can be written as something well-studied called a quantum channel. And quantum channels can be turned into unitary evolution by yet another change of representation. Borrowing a theorem from the fifties, the Steinspring dilation theorem, by increasing the dimensions of your Hilbert space in a controlled way, for those who are interested, it goes from an n-dimensional Hilbert space to an n-cubed dimensional Hilbert space at most, which corresponds to adding one or two extra degrees of freedom. You can implement the evolution as a unitary evolution anyway. And this is really cool because it means that even if you don’t start with a special kind of non-demolition element, you start with a completely generic non-demolition stochastic process, all you say is give the configuration of the system here, and here’s the probability distribution for where it will be later. When you run it through the quantum-stochastic correspondence you get a Hilbert space picture, oh no, it’s a Hilbert space picture and I see lots of things, but the evolution is not given by a unitary operator, it’s not given by the Schrödinger equation, that’s not great. It turns out that with a simple change of representation, a one-second change of representation, you can implement the evolution in a unitary way through what’s called a Hilbert space dilation. And this gives, finally, an explanation of where unitarity comes from, where that axiom that time evolution should be unitary comes from, from this set of transformations. So it’s really nice to be able to explain the source of these things. And now I can get to a question that some people raised in the comments. It seems like we started with this non-demolition stochastic process, and we ended up on this other side, and it seems like a special basis for Hilbert space, right? So a Hilbert space is a vector space, and all the objects, and state vectors are vectors, and people may know that a vector is a mathematical object. The simplest versions of vectors are arrows, let’s take an arrow, an arrow pointing in some direction in space with some direction and some length. And if you draw a coordinate system, imagine an arrow on graph paper, right? An arrow on graph paper, there’s an x-axis and a y-axis, and you can ask, how far do I have to go along the x-axis and how far do I have to go along the y-axis to get from the bottom of the arrow to the top of the arrow? And the distance along the x-axis and the distance along the y-axis are called the components of the vector. It has the x component and this y component, those are the components of the vector. But if I change my axes, if I want to rotate them a little bit, without changing the arrow, the arrow is the same but the axes are tilted, well, I have different distances now. I have a new distance, the original x distance and the original y distance, the two new distances. So one vector has different component representations depending on the basis that you use. And Hilbert spaces in quantum mechanics have this feature. In quantum mechanics, different bases are associated with different kinds of things that you might want to measure. For example, if the vector points exactly along a particular axis, that means that if you measure that observable, you will definitely get that outcome, and you will definitely not get other outcomes. But if you measure a different observable, which has tilted axes, the vector no longer points exactly along that direction anymore. It has some components along one axis and some components along another axis. And Born’s rule tells you how to take these components and compute probabilities. And so what we discover is that even if something has a definite outcome for one observable because the arrow points exactly along one axis, a different observable with different axes will give probabilistic outcomes. And if you change your arrow in some way so that it points along one of those axes, then the first observable will no longer have a definite outcome and this is just the uncertainty principle. That for certain pairs of observables when you know one with certainty, when measurements are guaranteed to give a definite outcome for one with certainty, measurements cannot be guaranteed to give definite outcomes for the others with certainty. And this is connected to the ability to change bases. You might ask, is this basis dependence preserved, this basis independence that I can take a vector and write it in any basis I want? But the answer is very similar to Hamiltonian mechanics. We start with a physical system with a definite position and momentum that have a clear meaning. It’s the momentum, as in some systems, where it’s the mass times the velocity. It’s like a clear definition of momentum. We formulate it in this Hamiltonian phase space picture. But then we can do all these weird canonical transformations where we can change variables and change what we mean by q and change what we mean by p. And suddenly, it’s not clear what the new q means, and what the new p means. And you might say, well, Newtonian mechanics must be wrong because Newtonian mechanics didn’t have this independence. Newtonian mechanics picked out particular q and p. But Hamiltonian mechanics treats them all as if they’re symmetric. There’s this symmetry under changing your definition of q and p. This might just mean that Newtonian mechanics is wrong because it doesn’t respect the canonical transformation. And this is very similar to what’s happening here. It’s true that you start with a particular system on the non-demolition stochastic side of the picture. The system has configurations. These configurations correspond to a particular basis on the Hilbert space side. Once you’re in the Hilbert space side, you now have the freedom to change your basis as you like. But because the theory is mathematical, it’s just a theory. You can go from one picture to the other. And this Hilbert space picture is a mathematical representation of the first picture. Just as in classical Hamiltonian mechanics, you have the freedom to make these basis transformations. They are perfectly available. The only question you might ask now is, well, but can I measure other observables? The ones that were associated with the configurations are the ones that will be very easy to represent on the Hilbert space side. They correspond to what we call diagonal operators. What about all the other observables? The ones that are not diagonal? The ones that don’t commute with the first set? That correspond to these other bases, right? And those can be measured too. What happens with those? And the answer is that it’s like in Bohmian mechanics. If you prepare your system and couple it to a measuring apparatus, and the measuring apparatus can measure one of the eigenstates, one of the ones that correspond exactly to the original configurations, it will passively reveal what the system already had as that feature. But if you change your measuring apparatus, just pick up a quantum textbook, and look at measurement, like how measurements are formulated in terms of unitary transformations. And just change your measuring apparatus, and now it’s going to measure a different property, measure one of the off-diagonal ones. You run the same process exactly. The measuring apparatus will randomly end up in one of its measurement outcomes with the correct probability given by Born’s rule. It just comes out of the formalism. But the thing that is being measured is not a pre-existing property of the system. It’s really measuring like an emergent pattern of the interplay of the system itself and the measuring apparatus that’s measuring it. In some properties, you passively reveal what was already there. Those correspond to this special basis. And the properties that don’t correspond to the special basis can still be measured, and they will still produce outcomes on the measuring apparatuses. And the measuring apparatuses will still end up in their correct readout configurations with the correct probabilities. As far as the measuring apparatus is concerned, it has measured something real just as much as for the diagonalizable ones. But what’s really being measured is one of these emergent patterns, these off-diagonal things. And so, from the point of view of the outside world, the off-diagonalizable things are on a par with the diagonalizable things. Together, the diagonalizable things and the off-diagonalizable things collectively form a complete set, and we call it a non-commutative algebra of observables for the quantum system. So this deals with the issue of basis dependence. And this isn’t new. So, there’s another way to formulate quantum mechanics and that’s path integral formulation. So people may be familiar that there’s this kind of Hilbert space formulation and there’s another formulation whereby you probabilistically predict where the system will end up, and you’re supposed to somehow start with the initial configuration and write down every possible path that the system could take. All the paths, the ones that don’t violate the laws of classical physics, assign to each of them a particular numerical factor. Add all the factors together where this is called a very difficult integral, the functional integral. And you get a complex number, and when you square it, and you do this particular operation on it, you get a probability. And you can reformulate quantum mechanics, at least at the level of making its predictions in this way. This path integral formulation goes back to Paul Dirac in a 1932 paper. I didn’t know that. And Paul Dirac was the first one to introduce it. Along the way you want to divide the time interval into small pieces and introduce complete sets. It’s a beautiful, beautiful paper. He was trying to understand what the role of the Lagrangian is. So, before 1932, people formulated quantum mechanics in the language of Hamiltonians, in the language of Hamilton-Jacobi theory. And Dirac was very curious. He wanted to know does the Lagrangian formulation appear in quantum mechanics as well? And he found a very beautiful way to do that using this kind of functional integrals. But Dirac was content to just write everything down, like state everything formally, and not turn it into a machine to calculate things. And ten years later, Richard Feynman picked it up when he was a PhD student. And this was like in 1942, when he was a PhD student at Princeton University, and also a student of John Wheeler again. And he turned Dirac’s formalism into an actual recipe for calculating things. And a few years later, he ended up publishing a review article talking in detail. And we can post all this on the YouTube video if you want, or people can see all these papers. And a few years later, he wrote a review article about all this. And he says at the beginning, there’s nothing I can do so far with this that cannot be done by ordinary methods. You can imagine somebody saying, well, what’s the point? If it’s just making the same predictions as ordinary quantum mechanics and you cannot do anything with functional integrals or path integrals that you couldn’t do with the previous methods, what’s the point? And by the way, it also picks out the basis. Because to do path integral formulation, you have to pick a basis. For example, when you do path integrals for particles, typically what you do is you pick positions. You can pick what’s called the position basis and do everything with positions. You can’t typically do path integrals in other bases, but you can. But any particular choice of how you formulate the path integral picks out one basis. So you could say this is basis dependent. You could say it doesn’t do anything we couldn’t already do. It’s a strange picture, and it’s been around for a long time. And eventually people discover that there are some calculations that were very difficult to do in the traditional way. Today, if you want to formulate a non-Abelian gauge theory, like Yang-Mills theory, like QCD. You probably wouldn’t want to do that using the canonical Hilbert space approach. You probably want to do it using the functional path integral approach. In the end, it took many years, I mean from 1932 until when people really needed this for decades until people realize that there are some things that we can now do much more easily with this new formalism. So of course, this gives me hope that formulating quantum mechanics in a new way, not the Hilbert space way, not the path integral way, a new way. Even if it’s not clear that it does anything you can’t do another way, even if there are no obvious immediate applications as a kind of things that might be 10 or 15, who knows? Feynman himself said that any good theorist should know a bunch of different ways of doing the same thing. Because when you formulate a theory in several different ways, you discover different knobs you can turn, and different things you can do that maybe it was hard to imagine doing in one formulation, and it was easier to imagine doing in another formulation. So, yes, this raises this kind of question about independence. We can get to some of the other comments and questions that people raised, but let me stop here and ask if you have any questions before we continue. So let’s see if I understand this correctly and I can simplify it. So Markovian, let’s understand what Markovian means. And that means that your system looks at the present state and you can determine the next state. Okay. When we say present state, we tend to think, oh, Newtonian mechanics is Markovian because you say, well, let’s specify the position and maybe the mass and then also the velocity now. But then you say, well, what is velocity? It’s actually the position from some infinitely small time ago. So you can introduce a new variable called velocity, or you can just think of the present time and what it was like in the past, making it non-Markovian because it’s no longer just the present now. I think this is equivalent to the Newtonian equation, the Newtonian formulation. But in what we learned from the Newtonian formulation, it introduced something new. So you’re saying, look, in this analogous way, we can draw an analogy here where there are these non-demolition stochastic processes, these little guys working here. What exactly are they? I’ll ask you about that next, but they work here and they’re stochastic. What about all of these? You’re saying they correspond to quantum mechanics, how? Quantum mechanics is linearity, unitarity, superposition, interference. Are you suggesting that when we take this non-Markovian and make it Markovian, as in the Newtonian case, we introduce something new, that we introduce something new that corresponds to linearity and superposition and interference etc? Yes. Yes. And the complex structure and the ability to change bases and all these things, are all perfectly correct. That’s perfectly correct. Okay. Okay. So the question the audience is asking now is how do you deal with interference experiments? Also, we can get to them in order, if you want Bill, what do you say about Bell’s inequality and what exactly are the elements in this framework, this formulation? Let me start with interference experiments. Let’s start there. So the simplest answer to this question is that if there is a mathematical isomorphism or representation that takes you from a non-demolition stochastic process to this Hilbert space picture, and let me say quickly, the mapping is not one-to-one. It’s many-to-many. A particular non-demolition stochastic process may have many Hilbert space representations and a Hilbert space representation can represent many different non-demolition stochastic processes, but this is not new. The same relationship holds for Newtonian systems and the Hamiltonian formulation. One Newtonian system can have several different Hamiltonian formulations and one Hamiltonian formulation can represent many different Newtonian systems. So this isn’t like something new. Okay. But the important point is that these non-demolition systems have this representation in this kind of Hilbert space picture, and the representation is just mathematics. I mean any Hilbert space picture can be regarded as a consistent non-demolition stochastic system, and vice versa. So any predictions you make using the Hilbert space picture will be preserved. Although the interpretation will be different. So let’s take the double slit experiment, and this will actually be useful because I think one of the questions that somebody raised was, can I give a helloworld example? You know, computer programming, the simplest program you read is something that prints hello world. What is the simplest example I can give? I’ll give you a simple example. Let’s think about the double slit experiment, and we’ll make it extremely simple, where we’ll coarse-grain it. That’s the term of art. We’ll coarse-grain it to simplify it. So instead of the particle being able to be like anywhere, we’ll simplify the description so that we only talk about the particle being in the top part of the chamber or the bottom part of the chamber, only top and bottom. Okay? We’ll put the particle in a qubit, in a quantum state system, okay? It’s a two-state system. Top chamber, bottom chamber. The particle is top chamber, bottom chamber, and then in, and we’ll imagine something like moving it forward and so on, just make it extremely simple. We move the particle forward, and it encounters a wall, and the wall has a top slit and a bottom slit, right? As walls do. As walls do, well, not all walls have top slits and bottom slits. This particular wall has a top slit and a bottom slit. And then behind the wall, there’s a display screen, a detection screen, a screen where the particle can land. And we’ll coarse-grain it, where the particle can land in the top part or the bottom part of the screen. So this system is simple enough that it actually encompasses many systems that you might deal with in the field of quantum information. Mach-Zehnder interferometers, there were some questions about Mach-Zehnder interferometers and the Elitzer-Vaidman bomb-testing example. All these experiments rely on a very similar kind of highly simplified version of the double slit experiment. Now, I won’t be able to do the calculations on the fly. But when I teach my course on the philosophy of quantum mechanics, I do the calculations and I get a good writeup. And if you want, I can send you a draft of it. It’s not printed on paper yet, but I can send you the draft and show you all the steps. But even this example, right, because we, you know, we fill in all the details now using the traditional textbook approach. You basically prepare it and then you measure the end and you don’t really talk about what happens existentially and physically in between. I mean you write down like the wave equation, and you think in terms of waves. But of course, the moment you go beyond one particle to 10 or 20, which is now the wave function is living in a 20-dimensional space, this doesn’t have any intuitive meaning. We do it very differently. We actually like to follow the particle and write down the probabilities, and write down everything. And what you do when you do this is every time you do the experiment, one particle goes through, the particle lands in the top chamber, or the top part of the detection screen or the bottom part. And you did this experiment many times. In every round of the experiment, the particle lands in only one place, either the top or the bottom part. For many, many, many repetitions of the experiment, you build a histogram, and you build like a distribution of landing locations. And what you find is that these landing locations look exactly like the distribution that you would get if there were wave interference in the problem. But there’s no wave in the problem. There’s actually no wave in the problem and the interference is an artifact. Of non-demolition. Why? How can that be, so there’s a limit to what we can say about the analogy, because non-demolition processes are inherently really non-intuitive. Physical theories can be non-intuitive. That’s the thing about physical theories. But in this simple case, at least, we can shed some light on the source of interference in this extremely simple example. And why there’s no interference when we do it as with the Newtonian system. In the Newtonian system where you’re like throwing stones at the wall, one after another, you don’t get this distribution, this pattern in the many landing locations. Why? One way to understand it is that if you’re throwing stones and they’re thrown either deterministically or if we want to, let’s make it probabilistic. The way you would say it is you would say, well, okay, I throw the stone. It reaches the wall which has holes in it. It either goes to the top hole or the bottom hole. Let’s suppose it goes to the top hole. Now that we know it’s in the top hole, let’s start there and then use the laws of Newtonian mechanics to figure out where it’s going. If it went to the bottom hole, let’s start there and use the laws of Newtonian mechanics to figure out where it’s going. But notice what I did there, I split the evolution. I assumed that the Newtonian, that the laws given to you in the system are of the form where you can take the system at the intermediate location, at the holes. And Newtonian mechanics gives you the laws for what will happen next. And when you do that, you won’t get any interference, you’ll get the classical pattern. In the non-demolition formulation, you’re not given those laws. The dynamical laws that describe where this particle is going do not have the property that they do when it reaches the middle wall and goes through it. I mean the particle at any instant is in only one place. Whether it’s in the top hole or in the bottom hole, that’s still true. But once it gets there, you can’t say, well, let’s assume it’s in the top hole. Let’s redo the evolution and then the theory doesn’t give you a law for that. There’s simply no dynamical description for starting from the holes and then seeing what comes next.

That. It wasn't provided to the laws. That is, the indivisible law that describes the entire experiment from beginning to end is more general. There is simply a more general class of these indivisible laws that fail to possess the property of divisibility at the holes. If we demand that the laws be divisible at the holes, then we single out a subclass of indivisible processes. Because you can only imagine, let me not think about the most general indivisible process. Let's think about indivisible processes where you are given the laws from the beginning to the wall, and you also have new laws that go from the wall to the screen. If you restrict yourself to only those indivisible processes, you will see almost no interference. A little will remain because there is still some indivisibility, but it will mostly disappear. But if you don't restrict yourself to those special cases, you will generally see interference. So the failure of Markovianity at the holes, the inability to restart the evolution and lay down the laws for what comes next during the holes in your hand. The failure to possess that means you can have kinds of laws that would lead to interference.

Now, there are modifications to this experiment. For example, what if you looked to see which hole the particle goes through? And we can implement that quite simply by adding another two-state, two-configuration system near the holes. Let's say I have a second tiny particle, a second tiny device with two configurations. And all it does is it remains in its initial off state, if the particle goes to the upper hole. If the particle goes to the lower hole, it turns on, okay? That's all it does, it only does those two things. You can design this very precisely, and put it in there. You actually want to give this thing deterministic laws. You want it to deterministically possess the property that when the particle goes to the upper hole, it always stays off. And when it goes to the lower hole, it always turns on. You can implement that with a very easy set of equations, and give it this deterministic behavior. Now when you evolve the system, the interference disappears. You can just, I mean, restart the indivisible process and you'll see there is no more interference anymore. The really nice thing, and this is actually a beautiful example of this, is if you get rid of the information that was in that little detector particle, that particle that was detecting it. Or if the detector particle communicates with the outside world and that information now becomes unrecoverable and inaccessible to us. And what we can do is classically marginalize.

So marginalization is when you have a joint probability distribution. It's the probability of like two things. And we sum over one of the variables to drop it from our awareness. This is a standard step in ordinary probability theory. When you do that for the time evolution process, the time evolution process of the original particle suddenly has a split event, a split that's now available at the walls. And so what was an indivisible process now becomes divisible at the walls, thanks to the detector particle that we marginalized over. And that gives another way of seeing the recoverability of divisibility now at the walls and gives another way of understanding why the interference effects disappear. But there are some things that can be said about this. Number one, this split event is related to decoherence. I mean, the process by which we marginalize is just, in the language of random, what we call in Hilbert space language, decoherence. If you look at the density matrices, you'll see that the split event that appears at the level of Hilbert space corresponds to the disappearance of the off-diagonal trees. That's what happens in decoherence. But the important thing here is that there is no wave function here. The particle always had one location as it moved through the apparatus. There is no superposition. There's nothing to collapse. So if the question is, isn't the split event just a collapse? Well, no, there was no wave function. The particle wasn't superposed between the upper and lower parts of the room. There was nothing to collapse at all. The split event is what you can say on the random side of the correspondence, and what's decoherence on the other side. But since there was never any superposition, there's now no need to single out one outcome or collapse anything or highlight anything. So the measurement problem, this fundamental fact is that in the textbook formulation, when you bring in a measuring apparatus, it becomes entangled, and you get a superposition, and now you have all these superposed probabilities. And then somehow, if there's a measuring apparatus somewhere in the superposition, we're supposed to somehow collapse it, but why and what is the magical property of measuring apparatuses that make things collapse? That's the measurement problem. That fails to happen in this picture. There's never any need to collapse anything. So I would say this is the simplest Hello World example, and has a side effect of also explaining what happens in the double-slit experiment and the interference that happens there.

So is the split event your version of what's traditionally viewed as collapse? And are split events what happen upon integrating over the marginal probability? That's right. So you marginalize over whatever your system's configuration read, and then your system now has what looks like divisible, stochastic dynamics. And this certainly plays a functional role in the theory analogous to what decoherence and then collapse plays in Hilbert axioms, in Dirac-von Neumann. And certainly if you were going to tell this story in the language that Hilbert relies on, you would use decoherence and collapse to explain what's happening in the Hilbert-based picture. But now we've grounded those seemingly ad hoc and very mysterious axioms, through a very boring random process where there's no wave function to collapse. And when measurement happens, in this case, just the reading of a small part of the detector, there's just classical marginalization that causes the indivisible dynamics to have an event where you can split. It's divisible for moments, then the inference goes away. So I want to bring up something you just mentioned, which brings us back to earlier in the conversation. So you said, in the Newtonian picture, when you throw a ball, there are two slits, two holes. And then you observe that it goes over the top, you say, okay, let's start the evolution from here or the bottom, it went from there. And you said, well, that doesn't apply in the quantum case or in the indivisible case because you can't split. And what was interesting to me is that you said, observe that such and such. And what you said, which is the observation that you said, you can now look at it. In other words, you can split your time. I was thinking, well, I didn't, while I was following you, I didn't notice I was making this assumption. And earlier in the conversation, you said what philosophers train on a lot is noticing implicit assumptions.

Yes. So this, although this, although it's not, well, let me read about Hegel because Hegel will tell me about physics. It's not that in and of itself, although that may be the case. I'm sure there's some inspiration that can be taken there. It's also the thinking that Hegel had or the thinking that philosophers have that you can apply. Yes, I mean it's important to know that philosophy is a huge field, right? And there's ancient Greek philosophy. There are all sorts of philosophies associated with different regions of the world historically. And in the Western tradition, so to speak, there's early modern philosophy. And then you develop this kind of weird split between continental philosophy and analytic philosophy. And then where does philosophy of science fit in? Philosophy of science is probably closer to analytic philosophy in many ways. There's some debate about whether it's part of analytic philosophy or not. But a lot of the toolkits that one uses in philosophical physics come from the analytic tradition in philosophy. That's the part of philosophy that's associated with logic and metaphysics and philosophy of mind, and to some extent, depending on how you phrase things, philosophy of science. So Hegel is much more associated with the continental tradition in philosophy. And I think there's been less interaction between the continental traditions and physics. I think a lot of people who've maybe been exposed to some philosophy, maybe not a lot, when they think about how useful philosophy is to physics, I think they often think of parts of philosophy that aren't closely connected to mathematical physics and physics. Excuse me, how would Fear and Trembling impact that F equals MA? Right, but I think a lot of those people would say, Bohr and Russell. Well, of course, it's good to say Bohr and Russell about physics. He wrote a book about relativity, he's a mathematician. But he was an analytic philosopher. He was like one of the leading analytic philosophers, right? Quine, and also the early people who developed quantum physics, the early people who developed quantum mechanics were deeply involved. In Wittgenstein, I mean there's a beautiful interview. And I would also recommend to lick. It's from the seventies by Pete and Buckley who were interviewing for CBC. It's an interview with Werner Heisenberg towards the end of his life. It's a fantastic interview. I mean, it's amazing to hear him talk, and actually hear his voice and hear him describe the early days of quantum theory and all the people he met. And he spends a lot of time talking about philosophy. He talks about his friendship with Wittgenstein. He talks about how confused he was by the message, and he's not unique. I mean, he wrote a book called Physics and Philosophy. And the book is full of Kantian metaphysics, and that's where he put this chapter, it's from 1958, where he presents the Copenhagen interpretation, where he tries to formulate it. We'll talk a little bit about that. And he's arguing with Schrödinger and Einstein. And they're all arguing about who's right, like who represents Kantian philosophy correctly. And you had neo-Kantians like Greta Hermann. We talked about Greta Hermann. And all these people were talking, and they were all connected. So there was an incredible amount of cross-pollination between analytic philosophers in the early 20th century and physicists. The physicists themselves were fully trained in philosophy. I mean there's another paper you should link to. This is a paper by Don Howard. It's a research paper in Physics Today from 2005. It's called Albert Einstein as a Philosopher of Science. And it's all about how much philosophy Einstein did. He read Kant's three critiques when he was sixteen. And—that takes sixteen years. I mean, that's what he did, right? He was very interested in philosophy. When he went to university, there were mandatory courses in philosophy of science. Whether at university or after he left university, he ran a philosophy of science reading group. He was deeply immersed in Spinoza. He was very inspired by Ernst Mach. He even wrote an obituary for Ernst Mach where he talks about the importance of epistemology. And he says, the most capable students, the ones who are most independent of thought, are the ones who took epistemology seriously. As in, this is 1916 when Mach died. And he was a huge fan of Schopenhauer as well. And so was Schrödinger. Schrödinger's cat paper has sections that have words like epistemology, as in physics paper. And Bohr was a philosopher. I mean they were all like… And I find this kind of striking because there's this attitude today like, who needs philosophy? But the people who gave us the biggest revolutions in modern physics, quantum theory and relativity, were either deeply, strongly connected to philosophers, or were interacting with philosophers, or were philosophers, or at least were fully trained in philosophy. If you're trying to make new breakthroughs in physics, shouldn't you take that as an example? Now, look, I understand that there are a lot of philosophers who haven't been trained in physics. And sometimes people who aren't trained in physics say things that aren't very helpful to physics. But the answer to that is very simple. We need people who are fully trained in physics and fully trained in philosophy so that they don't say nonsense. So they make meaningful contributions and help bring these two disciplines together. Because I think that would enrich the soil, so to speak. I mean a huge part of modern physics has its roots in ideas that were generated during that amazing formative period in the first half of the 20th century, the first half of the 20th century. And we're facing a lot of very deep problems today. Like Einstein, I think in a research paper, I think it's mentioned in Howard's paper, in 1936, Einstein wrote a paper called Physics and Reality, where he talks about how we live in a time in 1936, when there was a lot there was a lot that we didn't understand about nature, and there are a lot of deep questions that we have. And that's exactly the time when you need philosophy. You need to be deeply immersed in philosophy and think very philosophically about things carefully and rigorously using all these toolkits that I called philosophical physics, you know, to avoid falling prey to slogans, to avoid falling prey to groupthink, to be able to have independence. Of mind. And one of the most famous things Einstein wrote about philosophy is a letter he wrote to a philosopher of science named Robert Thornton in 1944, where he said that when he meets many scientists of his time, he feels like he's meeting someone who's seen a lot of trees, but never seen a forest. And that a full training in philosophy gives people a kind of independence of mind that distinguishes them, you know, a mere artisan from a true seeker of truth. I think that's very reasonable. And from my own experience, having taught courses here for a long time, the students who were more philosophically curious, many of whom took philosophy courses, higher-level philosophy courses, often became the strongest physicists. They were very careful about how they phrased things. They knew the difference between deductive arguments and inductive arguments and those that weren't. So this is a thing that happens a lot, okay? So on the one hand, if you have premises that are rigorous and credible and you follow them in a strictly mathematically logical way to arrive at conclusions, you have a deductive argument, and you have mathematical proof. We love that. Science often doesn't take that form. Sometimes theorems in science are proved, but more often we present inductive arguments. We start with credible premises. We call them evidence. And then we use arguments that are more or less rigorous. They may not be able to be perfectly rigorous. And we arrive at a conclusion that's stronger than the premises in the strict sense of the word. Something that's not strictly entailed by the premise, but is strongly supported by the premise. We assign some credibility or probability to the evidence. We say, I'm pretty sure my conclusions are right, given the logical premises, which have great credibility and accuracy and reliability, and are logical. That's an inductive argument. And a lot of science is inductive arguments. And then what we do is we take the conclusions and they're usually like a theory or prediction and we go out and we measure them and we get confirmation and we feel that we're stronger that we've done a good job. But there are many arguments in some areas of physics that are neither deductive nor inductive, where the premises themselves are wild guesses. And you take those wild guesses and then you present arguments that are themselves largely conjectural. And you arrive at conclusions that are guesses on top of guesses on top of guesses. And I don't even know what to do with something like that. I don't know how to follow those arguments. And I don't really think that someone who's well-trained in philosophy would find those kinds of arguments very credible. And I especially think at a time when our experimental data are very limited in some areas of physics. And we're trying very hard to be very careful in our thinking. That's exactly the time when you want that kind of meticulous scrutiny that you get from training in philosophy. Again, this is a second call to anybody who wants to make a big impact on physics, I think in terms of cost-benefit ratio, you know, supporting people who do this kind of work, I think would be especially important. Okay, so you said independence of thought is what philosophy trains you to have precision of thought as well. So Scott Aaronson is someone we've brought up before for the two we've brought up. And Will Han is here too, you can't see him, but he's behind the cameras, a professor at Florida Atlantic University, helped organize this event called MindFest. And Scott Aaronson was there. So Scott Aaronson said, well, he didn't say this. But the implicit meaning was that most physicists, most scientists think that philosophers are just engaged in this unspecified, unfalsifiable, incoherent nonsense. And he was saying when he was speaking, he never had to be as precise in his talk as if he were around a philosopher.

Yes, philosophy seminars. So maybe there are many people watching this seminar who haven't been to a philosophy seminar before. Maybe many people watching haven't been to a physics seminar. That's fine. I mean people come to this. I mean, you have new people, maybe they're students, and maybe they're, you know, in high school, maybe pre-high school, I don't know. Or maybe they've just entered into different fields. Or maybe they're not in academia. And that's all, that's all great. I mean we're all contributing in some way to the world, we hope. But there are many people who've maybe been to physics seminars and don't know what philosophy seminars are like. And I'll tell you, when you go to a philosophy seminar, especially in philosophy of science or philosophy of physics or analytic philosophy, the level of precision in your language, I mean, you have to be so, and so the way they usually work is, so physics seminars usually work this way. There's a speaker who talks for 45 minutes, maybe an hour, depending on the length of the seminar. Often people interrupt in the middle of the seminar. They'll just ask questions, they're just kind of interrupting in the middle. And the person who's maybe not very seasoned, who's giving the talk, might get thrown off track. And that can sometimes lead to problems, but hopefully everybody is respectful and the questions, if any, are brief. And then at the end of the seminar, they all thank the speaker, and they clap, and they thank the speaker. And then they say, okay, we have five minutes for questions, any questions? And you know, most people don't, I mean they can't, I mean there's no time to ask a substantive question. A lot of people are very nervous because they say, oh, maybe there's a higher-up here, a professor who wants to ask a question and I don't want to intrude. Or if there's only time for one question, I don't want to ask a question that will be a bad question. So people are often very nervous about asking questions and there's not really a good substantive dialogue. In philosophy seminars, what often happens is that you'll speak for half an hour or 45 minutes, sometimes it goes for an hour, and then there's a break. People go and they take five minutes, get refreshments, and then they come back, and then there's an hour of discussion, right? And often the discussion is the most interesting part of the seminar, right? And because there's about an hour, everybody asks questions, students ask questions, because nobody's afraid to ask the only question. Nobody's afraid to look bad because there will be 10 other questions after theirs. And people can really have a substantive discussion and dialogue. That's fantastic. And I actually love the culture of these seminars because it's very welcoming. Often they'll say that students should go first because they really want to prioritize students asking questions. But I'll tell you your expectations for precision of your language are high, right? If you say something that's not very carefully phrased, people will immediately say, I'm sorry, that's too vague. And you like to clarify that. So I think there's this attitude, and I think some, you know, I can't say there are many scientists who are aware of this, but I think some who think that philosophers just make things up and we're very vague, and we're just kind of that, but, if you've been to a philosophy seminar, it's quite the opposite because you don't have the ability to rely on experimental data. You can't just say, well, you don't need to explain that. Just look at the data. You rely very heavily on the strength of your logical reasoning. And I think that can influence how we do physics more than we currently do. I don't know if you've seen some of the lectures in TOE. I hope I'll bring some of that to it. So like Yang Hui, he was following along and saying, I love this because Curt, usually I have 45 minutes, but here I have two hours. And so you can ask me questions and we can get to all of it. Plus questions. Well, I know you're sitting there waiting to catch me when I say something that's not sharp and rigorous enough. And that's it. And that reminds me a lot of the philosophy seminars I go to, and that's really nice. And look, there are many things I think your program does right. I mean you're bringing interesting ideas to the public from all directions. You're inspiring, but I think you also represent a model of the kind of dialogue that I think we need more of in academia, and in science and philosophy, generally, and holding people accountable, extending like the discussion, really getting to the questions, really getting to the deep parts of people's thoughts, not letting people get away with slogans, you know, and physics is a lot of slogans that people just hear, and they hear a very prominent person say it, and then they repeat it. Right. I mean, like you're dismantling that. And this isn't like a public service announcement. Because I know there are a lot of people watching who haven't become scientists yet, or maybe haven't become scientists yet, maybe that's not the direction they want to go. And maybe this is just advice, right? Obviously watching your podcast series is a great step. That's great. But, you know, people will sometimes say, well, you know, you can't really contribute to science or philosophy, whatever, until you do the required training, you need to go to a university program. You need to read the books. You need to take the courses. You need to get grades on them. You need to take the exams. You need to really love learning all these techniques. You have to learn how to do it in physics. And that means learning Newtonian mechanics, and learning electromagnetism, and learning thermodynamics, and learning quantum mechanics, depending on which direction you're going. And you might learn astronomy, or biophysics, or computational physics, or high energy, or whatever you're going to learn. But as you really do all that, solve all the problem sets, learn everything, and take the time. It's a long process of rigorous training for a year. And if you want to make contributions at the research level, you'll most likely have to do some kind of graduate work like a PhD program. And a lot of people don't know by the way that PhD programs, at least in the US in science, are funded. You don't pay to go to graduate school to get a PhD. It's important to know that when I wanted to learn science, I thought that you had to pay to go to a PhD program. And I thought that was significant, but you actually get paid to go to a PhD program in science. It's important for people to know. And a lot of people look at that and think it's insurmountable. They're like, but I have an idea. I have a great idea. I just want to call up a physicist and tell them my idea and have them work on it. And I would just say do you really need to do the training first. Because there's so much you have to learn. It's like Picasso was a fantastic artist, but he had to master the traditional techniques before he could break them. And I know a lot of people will say, but if I learn all the techniques and spend all those years learning all this, first, I'll become like everybody else. When I internalize the same conventional wisdom and all the slogans, that's a risk. So what I would say to people is, if you want to embark on this journey, it's an amazing journey. I mean learning physics has been incredible. If you love physics and you spend years learning it, it's the most wonderful thing you can imagine. You just have to work a little bit so that you don't become steeped in some kind of calcified conventional wisdom. So while you're learning it, you just have to remind yourself every once in a while. Of your original ideas. Of your original ideas. Certainly. Sometimes you find that the ideas will keep working. Sometimes you'll find that they don't work. That's fine. But you also, every time you learn to do a technique, learn how to calculate something, learn how to

Calculating the eigenvalues of a one-dimensional quantum mechanical system, or learning how to calculate the scattering amplitude in quantum field theory, or whatever. Do you want to separate the learning methodologies, like how can I calculate something? How do I do something? How do I design something? From the ideology? Because people will say, okay, you said you calculated that, and what that means is that what happens in nature is, and this is the moment where you want to be like, whoa, wait a minute. Wait a minute. I'm following the calculations, they're empirical, whatever, but you've now transcended this particular methodology, and now you're making an objective statement about metaphysics, about something out there. And that requires some careful scrutiny. That's where you need a little bit of skepticism. And I think keeping your foot in that sort of skeptical camp, as you go through, is the best way to do it. But that's exactly what it means to be a good philosopher. For example, a good philosopher will see statements, sometimes very provocative statements, sometimes very ambitious statements, maybe overly ambitious statements from any quarter, could be from a scientist, and say, hold on a second. Wait a second. Not so fast. Let's make sure that this induction you're making here is really rigorous and really logical. And I'll give you an example. So this is a concrete example. This is all kind of abstract. Let me bring it down to earth. This is a slightly sensitive topic. One of my favorites, like one of my heroes in physics is David Griffiths. Many people in physics have read David Griffiths' books. David Griffiths is legendary, and I think the world is like that. I learned physics from his books. I learned particle physics for the first time from his book, Introduction to Elementary Particles. Quantum mechanics, I learned from his book, Quantum Mechanics. Electromagnetism, I learned from his book, Electromagnetism. He's rightfully earned this kind of legendary figure status in physics. He's had a bigger impact on physics than almost anybody else. And I love his writing most of the time, but he has a kind of tone sometimes when he writes that's very dismissive. Sometimes he will dismiss things. And because he's, in fact, kind of honest, he will often have a footnote where he'll say, I'm being very strong. I shouldn't be dismissing this. Really, it's like this. But a lot of people don't read the footnotes or get confused by them. And I'll give you a very concrete example. In his book on quantum mechanics, he says at the beginning, and many students have read this, he says that there are three ways of thinking about quantum mechanics. There's a realist way of thinking about quantum mechanics, which is just to say that before we make a measurement, the thing that we're measuring already exists. Now, we've already talked about how that's not, it's not accurate enough of a presentation. There's the realist viewpoint. The thing that we're about to measure already existed. And the second is the orthodox view, which is that the thing that we're measuring didn't exist. There weren't pre-existing properties. The thing that we were measuring didn't exist before we measured it. Particles aren't anywhere until we measure them. Then the third possibility is the agnostic position. I won't try to answer. He says, these are the three positions. And this, this is really like steamrollering, there are a lot of nuances to this discussion. Then he says, for a while, they were proponents of these three views. And not so long ago, but that means 1964, which is actually quite a long time ago, a guy named John Bell came along and proved a theorem. And the theorem ruled out the agnostic position as a possibility and turned it into an empirical question of whether the realist position is correct or the orthodox position. And experiments have now confirmed the correctness of the orthodox position. And that's it. He just says, that's it. And then you like to read the footnote and the footnote, he says, well, that's a very strong statement. There are actually other theories, you know, but the words he uses tend to be cumbersome and unconvincing, but never mind. This particular phrasing is kind of funny because I worked on a project two years ago, about whether magnetic forces can do work on particles. It turns out that this is possible if the particles have an intrinsic magnetic dipole moment. And Griffiths and I updated the fifth edition of his electromagnetism book and included a footnote pointing to this paper. I have a footnote, but he says theories like what I wrote, he says they tend to be cumbersome and unconvincing, but never mind. He uses the exact same language for this stuff as he does for all these other people in quantum mechanics. And because these I think the other formulations of quantum mechanics are good and people should work on them. They're telling us something. I think now I feel like I'm a good company, right? We'll get back to some of that magnetic dipole stuff, maybe a little later. Now, the curious thing about this is that at the end of Griffiths' book, he has something beautiful afterwards. It's the last chapter. It's chapter 12, where he reviews Bell, and he reviews Bell's theorem in detail, which you don't usually find in introductory quantum mechanics books. And he has a good and loving treatment of Bell's 1964 theorem. It's the older version of Bell's theorem. He says a few slightly dodgy things there, but his treatment is actually really, really good. Okay, he mentioned some of these other approaches, but it seems as if at the end of the book, not many students see this part of the book. And I worry that students who read this book will take the things he says in the main text, not the footnotes, not the qualifications, not the other things that have happened later. And they will just repeat them. They'll just say, okay, you were wrong. Realism is wrong. David Griffiths said that the orthodox approach is the only approach, and there's no point in pursuing this any further. And any further attempts to pursue anything else are just pursuing cumbersome and unconvincing theories, but never mind. That's the thing that a newcomer to physics should look out for. You see that such statements now become really metaphysical statements, and you have to be like, okay, wait a minute. That doesn't quite follow the methodologies that we're doing. And I think somebody who writes a textbook, or teaches physics, should be as clear and as careful as possible when they stop presenting something calculational and methodological and model-building, and they've now moved into this is how nature is as a result. We've learned that there's no fact of the matter about anything we measure, that particles don't have anything before they're measured, that there's no way of fixing quantum mechanics, and that these statements are not supported by what we have. And I think people who are interested in doing serious study in physics should know early on to be aware of these kinds of statements. I think that would be the advice that I would share. Jacob, it's been a pleasure. Three hours, and we haven't even gotten halfway. Yeah, Curt, it turns out that when you want to reformulate a fundamental theory in physics, it takes time. It doesn't all happen at once. Well, it takes chunks of time. Chunks of time, they're indivisible, but we seem to have a good chunk coming up. Okay, great. Okay, we're now going to do the chunk event, which means you'll get the second part of this conversation, which is the third time I've spoken with Jacob overall. The first time I spoke to Jacob was on screen, the second time here, and the third part will come out in two weeks from now, and what we'll talk about is Bell experiments or Bell inequalities. We'll get to the other questions that people asked. People had questions about entanglement, people had questions about causality in this approach, and there were also questions about how this approach relates to problems in statistical mechanics and some other interpretations and formulations of quantum mechanics. Right. And also wave-particle duality. Right. What does that mean in this approach and also traditionally? Right. Well, see you next time. Yes. Definitely subscribe and make sure you watch part two where we talk about what are the misconceptions about wave-particle duality. And also, what are the challenges of applying indivisible random processes to quantum field theory? Is gravity actually quantum? What about random general relativity? What about misconceptions about non-locality and Bell's theorem? Jacob also gives a fresh perspective on entanglement without wave function collapse and talks about the difficulty of defining causality at the fundamental level. We also talk about the philosophy of probability and what the origin of probability is in statistical mechanics. And of course, Jacob has his critiques of the many-worlds interpretation, then gets into open questions and future research in indivisible random processes. You do not want to miss this. It's a banger episode. Subscribe to get notified. New update! A substack has started. 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