Why Physics Without Philosophy Is Deeply Broken Jacob Barandes

TITLE: Why Physics Without Philosophy Is Deeply Broken… | Jacob Barandes CHANNEL: Curt Jaimungal DATE: 2025-01-30 ---TRANSCRIPT--- There was no wave function, there was never  a superposition, there was never a need to   get anything to collapse. In this picture, some  observable quantities are reflecting things that   are really there. The people who gave us the  biggest revolutions in modern physics, quantum   theory and relativity, were all strongly connected  to philosophy. Physicists have grappled with   the seemingly outlandish implications of quantum  theory, that particles are purportedly in multiple   places simultaneously, and there’s a mysterious  wave function that collapses upon measurement,   and a framework that requires so-called imaginary  numbers, etc. I traveled to the oldest physics   laboratory in the United States to meet at Harvard  with theoretical physicist and philosopher Jacob   Barandes, who is the co-director of the graduate  studies department there, where we go into   technical depth into his innovative reformulation  of quantum theory for more fundamental mechanics,   called Indivisible Stochastic Processes. My  name is Curt Jaimungal, and this was part of   my three-day tour of Harvard, Tufts,  and MIT, where I recorded five podcasts,   one of them being with Jacob Barandes that  you’re seeing now, which was actually over   seven hours long, so we’re splitting it into two.  The others are with Mike Levin, Anna Ciaunica,   and Manolis Kellis. There’s also Professor  William Hahn, a computer scientist, and that   was filmed live at the MIT Media Lab. Subscribe  to get notified. Jacob’s breakthrough theory   raises new provocative questions such as, what  if quantum waves don’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  lovely to see you again. The last time we talked,   I enjoyed it tremendously. Yeah, me too. So  let’s talk about physical philosophy versus   the philosophy of physics. People have heard  about the philosophy of physics. What is physical   philosophy? Yeah, so my research has sort of  two sides. 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, it’s the use of  results and ideas and discoveries and theories   from physics to address traditional questions in  philosophy, in particular in metaphysics. So the   kinds of questions that we’re interested in here  are questions about space and time, the philosophy   of time, causation. There are very interesting  connections between physics and causation, some   of which we’ll hopefully have a chance to talk  about today. Also the philosophy of probability,   which is a very subtle and very complicated area.  And also the metaphysics of laws, which is a rich,   very interesting area of inquiry. And  so just thinking about what do our best   current physical theories bring to bear on these  traditional questions? How do they constrain what   we can say about those sorts of things? So  here’s a good example, a concrete example.   Philosophers, metaphysicians have been thinking  about the nature of time for a very, very   long time, right? You go back to Parmenides and  Heraclitus and people thinking about, you know,   is time something that flows? Is time something  that is just an illusion? And there’s this very   famous paper, which maybe you can link to because  it’s a beautiful paper and people should read it,   by McTaggart, a philosopher, about over 100  years ago on the nature of time. He introduces   this terminology, the A series, the B series,  the C series, these different ways of thinking   about time and how much structure it has, right?  The A series is this idea that events that take   place in time can be classified as past, present,  and future. But that seems to like distinguish   a notion of a presence, and is that really a  sensible notion? And then there’s the B series,   which has less structure. This just says that  events can only be classified in terms of earlier   or later. So there’s like a pairwise relationship  between them only, and there’s no distinguished   notion of a present. And the C series is even less  structure. It just says that there’s a sense of an   ordering of events, that given any three events,  we can say which takes place between the other   two, but without privileging a direction in time.  And, you know, he explores all of these ideas in   the essay. But right around the same time, Albert  Einstein was developing special relativity,   and special relativity has some pretty serious  implications for how we think about the nature   of time. In particular, although, you know, many  people have heard of phenomena like time dilation,   the idea that observers moving in different states  of motion will, you know, have different senses   in which time flows, like the rate at which time  flows for one observer may be different from the   rate at which time flows for another. And maybe  some people have heard of length contraction or   Lorentz contraction, that spatial distances in the  direction of the change of reference frame can be   distorted. Somewhat less known is the breakdown of  simultaneity, which is this 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, some collection of  events may be in what observer identifies as   their present moment. But to an observer in a  different frame of motion, their sense of the   present is like tilted. It’s like tilted a little  bit, so that things that the first observer would   have said were in the future are in the second  observer’s present, as are some things that might   have been in the first observer’s past. And this  feature of special relativity that simultaneity   is not an invariantly defined concept has profound  implications for how we think about the philosophy   of time. And these were explored by people like,  rather famously, the philosopher Hilary Putnam   in the 60s, who wrote a really beautiful paper,  which you should also link to because it’s just   very beautifully argued. And he makes the case for  what he calls four-dimensionalism, you might call   it eternalism, the idea that because different  observers will disagree on which events are in   their presence, if we just take the totality  of all the things that everybody thinks are in   their present, it’s basically all of space-time.  If you look at observers at different locations,   different frames of motion, and does that mean  that everything in space-time is just in some   sense there already? You know, the future is not a  thing that has yet to happen, the future is not a   thing that is unfolding, but our experience of the  flow of time is merely psychological. And special   relativity is actually telling us, in some very  strong sense, that we’re living in an eternalist   so-called block universe where everything is just  there. So this is a fantastic example of where the   things we’re learning from contemporary successful  physical theories, thoroughly empirically   established, like physical theories, bring to  bear some very important constraints on what   you might have thought were purely metaphysical  questions. So I call this general subject physical   philosophy. On the other hand, I also work  in what I would call philosophical physics,   and the name is supposed to resemble like…  Theoretical physics, mathematical physics,   computational physics, it’s a methodology for  doing physics, not philosophy. But rather than,   say, mathematical physics, where you’re doing  physics by stating axioms and proving theorems,   or theoretical physics, where you’re formulating  models and then calculating predictions within the   models and comparing them with experiments, or  computational physics, where you’re simulating   physical processes in a computer. And making  predictions that way. Philosophical physics   tries to make progress on physics using some  of the tools that you might traditionally have   associated with philosophy. So what are those  kinds of tools? Thought experiments, coming up   with counter-examples, sharpening definitions,  sharpening questions, right? Sometimes you’re   dealing with a problem in science, or physics  more specifically, where the questions are not yet   sharply formed enough that you could subject them  to experimental study. Sometimes you have to do   some work beforehand to sharpen those questions,  that’s the kind of thing that philosophers like to   do. Identifying implicit assumptions, hidden  assumptions, and that’s something we’ll be   talking about because some of my work is closely  connected with this idea of identifying implicit   assumptions. Assumptions that may get in the  way of making scientific progress. Subjecting   ideas to logical analysis, and also to what I  call rigorous scrutiny. Because in philosophy,   we’re not generally guided by empirical data or  observation. You might think that there’s just,   well, if you don’t have empirical data, what are  you doing? Well, you’re not without any tools at   all, right? So one of the things that philosophers  like to do is just be really, really careful in   how they talk about things and how they define  things. Being very careful with every step of   their logic, stating their premises as clearly  as possible so that if you find fault with their   arguments, you can identify where the problem  is. So just sharpening everything and subjecting   things to rigorous scrutiny. These are all tools  and techniques that come from philosophy, and I   call them philosophical physics. And this doesn’t  even include just taking ideas from philosophy,   like actual just picking up ideas from philosophy  and seeing if they have some use in physics. And   I think there’s a proud tradition of this kind  of work. I’ve talked to philosophers of science   who’ve told me that the greatest philosopher of  physics of the 20th century was Albert Einstein.   And when you look at especially Einstein’s  earlier work, what is he doing? He’s subjecting   definitions and ideas to rigorous scrutiny. I  mean, how much time did he spend trying to pin   down exactly what we mean by an inertial reference  frame? You might think inertial reference frames   are like the scenery of Newtonian physics. Like,  what could you really gain by spending a lot of   time really rigorously scrutinizing what is the  precise definition of an inertial reference frame   and scrutinizing when you know that you’re  actually in an inertial reference frame? But   think about how much mileage Einstein got out  of thinking about inertial reference frames,   which laws of physics should be the same in every  inertial reference frame, realizing that the speed   of light is one of these laws of physics that  should be the same in every inertial reference   frame. And then, you know, his greatest—what  he described as the greatest idea he ever had,   which is realizing that, you know, it’s impossible  to distinguish the local short-duration effects of   a gravitational field from being in a reference  frame that is in uniform acceleration. And that   realization is what, you know, eventually evolves  into the equivalence principle and leads him   into his theory of general relativity. He has  this idea in 1907, and he described it as the   happiest idea of his life. So—and, of course,  I’ll get into this more a little bit later,   but Einstein was thoroughly 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 really a strong tradition of   philosophical physics in history, and I’m  certainly not the only one who practices,   I think, this discipline, but I think there’s  really something to say about it. I think it   really does contribute something to how we can  make progress in physics, and so that’s the   other side, I think, of what I do. So what’s  the standard view of philosophy of physics or   philosophy in general from people who consider  themselves to be scientists or who actually   are practicing scientists? So, for instance,  when I was speaking to Neil deGrasse Tyson,   he was saying, well, philosophy, what has it  done? Give me, Curt, an example of something   that philosophy has contributed to modern-day  physics in the past 30 years. Sure, in the past,   thought experiments. That’s a lovely question. I  actually know Neil Tyson. We worked together when   I was in high school. This is some interesting  history. So 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 anyone who’s listening to this has never  been to the American Museum of Natural History,   you are missing out. It’s like going to a magical  fairyland for science, and it’s amazing. And I   got lucky when I was in high school to intern at  the museum. And there was a period of time when   I was working in the astronomy department, and I  worked with Neil Tyson. It was amazing. I mean,   he’s great. So, of course, I do very, very  politely disagree with that sentiment.   I’ll give you a couple of examples. So here are  some things that have come out of philosophical   thinking about physics, philosophy. I mean, the  lines are a little blurry here, because obviously,   if you’re doing philosophy that’s very  close to physics, one could accuse you of   just doing physics. But, okay, let me think of an  example. This one is from the 80s, okay? So 1982,   Zurich and Wouters, and then independently, an  absolutely, definitely philosopher of science,   Dennis Deeks, independently formulated what we now  call the no-cloning theorem. So no-cloning theorem   in quantum theory is a very simple, very beautiful  theorem. What it says is that if you’re given,   as traditionally formulated, a quantum state  in the form of a wave function or state vector,   just some object in Hilbert space that  describes, in a traditional sense,   the state of your quantum system, and you don’t  do any measurements on it. You’ve prepared it,   but you haven’t, like, measured the position or  whatever, you’re just, you’re leaving it pristine.   Is there a way to build some kind of apparatus  that can make another system be in exactly   the same quantum state? That is, can you, you  know, if your first system was, um… you know,   some simple quantum system and it’s in some  state, can you bring in a second quantum system   of the same kind and run both systems through some  kind of machine that will make the second system   be in the same quantum state as the first system  every time? Right, every time? And the answer is,   you can’t. If you set the machine up so that it  works some of the time, then all you have to do   is set up the first system in a superposition of  those possibilities, and what you’ll find is that   you cannot get the other system to be in the right  quantum state that is also the same superposition.   This is called the no-cloning theorem. And  the no-cloning theorem is useful. I mean,   people certainly, it shows up all over the place  in physics, it shows up in high-energy theory,   it shows up in all kinds of places. I guess that’s  1982. I mean, that’s a little bit outside the   boundary of the 30 years. What’s happened since  the 90s? And we’re not allowed to talk about your   work yet. Ah, yeah, we can’t talk about work yet.  I mean, that’s an interesting question. I mean,   from the point of view of like, so it’s a bit  difficult because, like I said, the boundaries   here are a little blurry. If you think about  people like Martin Lizord or Eric Uriel or J.B.   Manchek, these are people who work in foundations  of general relativity. And, you know, their work   is super mathematical. I mean, if you ask them,  do you consider yourself first and foremost a   philosopher? Or I haven’t asked Eric or I haven’t  asked all these people like, what do you first   think of yourself as? But they certainly come to  philosophy seminars, they give philosophy talks,   they certainly sound like philosophers. And  they’re doing like work on general relativity.   They’re proving things about space-time  that are interesting facts. So I, you know,   and then of course, the lines between quantum  foundations and quantum information are also very   blurry. So I’ll tell you, here’s an interesting  story, okay? You’ve all probably heard of qubits,   right, qubit, right? So a qubit is supposed to  be a quantum bit. And usually the way that we’re,   the term is introduced, people will say it’s  a portmanteau of quantum and bit, right? Bit,   I think the term bit goes back to Claude Shannon.  That itself is a portmanteau of binary digits. You   know, Claude Shannon introduced many of the ideas  in information theory and communication theory in   the 40s, back 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, it’s 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 a Q and a U and then there’s  no other vowel, just a constant right away. Why   that very funny spelling? And I’m not saying I’m  the first to notice this funny spelling. In fact,   there’s a very famous physicist, David Merman,  who also is interested in quantum foundations,   among other things. And he doesn’t like that  spelling because he says it’s grammatical, it’s   like the spelling is really very non-standard.  I think he likes to write it as Q hyphen bit and   not Q-U-B-I-T. So where did that spelling come  from? The term was coined by Ben Schumacher at   Kenyon College and Bill Wooters, who I mentioned  before, at Williams College. The story is that   Bill Wooters was visiting Kenyon College and this  was in Ohio. And they were both driving to the   airport in Columbus. And they were talking about  how they needed a new scheme for talking about   quantum information. This was in 1992, just  outside of the 30-year mark. I’m sorry, we’re   just a little over 30 years. And it was Bill. So  I got this information from one of Ben’s students,   Mary Gerhardinger, she told me the story. Bill  was in the car and he said, wouldn’t it be funny   if we called these things qubits because there’s  a unit of measure in the Bible called a qubit. But   in the Bible, it’s spelled C-U-B-I-T. It’s a unit  of measure. It’s like, I don’t know, a distance   from your elbow to the tip of your finger. And if  you read Genesis, right, you’ll hear God telling   Noah to build the ark and it’s supposed to be  this many qubits long and this many qubits tall,   right? And they’re like, but it starts with a  C because the Bible is classical, do you get   it? Like what’s more classical than the Bible?  Let’s just replace the C with a Q and it will   be a modern version of a qubit. That’s funny. And  they both thought it was hilarious. As you know,   on Theories of Everything, we delve into some  of the most reality-spiraling concepts from   theoretical physics and consciousness to AI and  emerging technologies. To stay informed in an   ever-evolving landscape, I see The Economist as  a wellspring of insightful analysis and in-depth   reporting on the various topics we explore here  and beyond. The Economist’s commitment to rigorous   journalism means you get a clear picture of the  world’s most significant developments, whether   it’s in scientific innovation or the shifting  tectonic plates of global politics. The Economist   provides comprehensive coverage that goes beyond  the headlines. What sets The Economist apart is   their ability to make complex issues accessible  and engaging, much like we strive to do in this   podcast. If you’re passionate about expanding your  knowledge and gaining a deeper understanding of   the forces that shape our world, then I highly  recommend subscribing to The Economist. It’s   an investment into intellectual growth, one  that you won’t regret. As a listener of TOE,   you get a special 20% off discount. Now you can  enjoy The Economist and all it has to offer for   less. Head over to their website www.economist.com  slash TOE, T-O-E, to get started. Thanks for   tuning in. And now, back to our explorations  of the mysteries of the universe. And they   both thought it was hilarious. And so the name  comes from this conversation that they had. And,   you know, Bill Wooters did a lot of work in  quantum foundations. Ben Schumacher worked   with John Wheeler, who, in addition to being a  very great theoretical physicist and a fantastic   mentor who had many, many famous students, Richard  Feynman, one of the students, so many students,   Jacob Bekenstein, many very famous students,  was also very philosophically curious. Hugh   Everett of the Many Worlds Interpretation, which  hopefully we’ll talk about, was also one of his   students. And so he really enjoyed having these  really deep philosophical conversations. And he   created a real atmosphere of philosophical inquiry  in his research group. Zurich worked with John   Wheeler. So does that count as a philosophical  contribution? I mean, Schumacher and Wooters   were not at R1 universities. They were not at  major universities. They were both at liberal   arts colleges, and they were interested in  very foundational questions. I mean, does   that count as philosophy? It’s kind of hard to  say. But now I guess you can go farther. I mean,   if you’re willing to go farther back and take  ideas that came out of philosophical thinking,   but that are still proving themselves to be  super useful, there’s a lot more, right? I mean,   you could, I mean, if you’re just talking about  quantum mechanics, not even general relativity,   you know, the notion of entanglement goes back  to philosophical disputes between, you know,   people like Schrodinger and Einstein. The  Einstein-Podolsky-Rosen paper from 1935,   maybe the most cited paper Einstein’s name  is on, is an extended philosophical argument.   They lay out their premises. They lay out  a very detailed philosophical argument,   which we can talk about. And, you know, they make  a metaphysical claim about quantum mechanics,   a physical and a metaphysical claim about whether  quantum mechanics could be considered complete,   even if it’s practically perfectly useful.  Their work, you know, the EPR argument,   the Einstein-Podolsky-Rosen paper inspired a  lot of people. I’ll get to who it inspired,   but let me just say that before I get to that,  there’s a paper by absolutely a philosopher,   Greta Hermann. So Greta Hermann was a philosopher,  a student of Emmy Noether, who, mathematician,   made major contributions to physics, symmetries  and conservation laws. Noether’s theorem is super   important, arguably the most important theorem  in physics. And so her student, Greta Hermann,   she’s a philosopher, she’s a neo-Kantian, and  she wrote a large number of papers on physics and   metaphysics and on the developing quantum theory.  And she wrote a paper, we read it in my philosophy   of quantum mechanics class, and it’s a paper in  which she is studying the nature of causation in   quantum mechanics. And she sets up this thought  experiment. It’s a beautiful thought experiment,   and the paper was published in 1935, several  months before the EPR paper. It was widely read,   apparently. It’s likely that Einstein read this  paper. And the thought experiment that’s used   in the EPR paper bears a strong resemblance  to the thought experiment that’s in Greta   Hermann’s paper. Okay, so, like, you know, clear,  interesting threads going on in the 1930s. Then,   of course, John Bell picks up the thread and  publishes a paper in 1964, his famous no-go   theorem paper, the first appearance of what we now  call Bell’s theorem. And that paper is called On   the Einstein-Podolsky-Rosen Paradox. That’s what  he calls the paper. He takes the EPR paper and   he extends the argument into a statement about  what he calls, what we now call hidden variables   theories. You know, and you’ve got further results  that, you know, build on Bell’s theorem. You have   the famous C-H-S-H inequality, which comes  in 1969. That’s Clauser, Horn, Shimony, Holt,   which is a somewhat more general version of the  Bell inequality in the 90s. So we’re in the 90s   now. You’ve got Greenberger, Horn, and Zeilinger,  the GHZ paper. There’s a beautiful version of this   argument by David Merman in 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 particular kinds of quantum states. The GHZ   paper introduces these GHZ states. And GHZ states  show up all over the place in atomic molecular   optical physics today and in quantum information.  I feel like every time someone uses a GHZ state or   uses, you know, Bell-violating states or things  like that in order to do something in quantum   cryptography or to certify the randomness  of a quantum random number generator,   they should have to pay 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. This   is in the late 70s and early 80s, I think. One  version of the argument is by the same people   who gave us the GRW spontaneous collapse  theory, right? And, you know, so, you know,   and the no-signaling theorem is also a theorem  that shows up all over the place. But I think,   you know, and I can make more examples. I mean,  there’s quantum teleportation, you know, in some   of David Deutsch’s early papers introducing some  of the basic ideas that led to quantum computing.   He is very explicit in the papers about how what  he’s trying to do in trying to imagine building   a quantum computer is confirm that many worlds is  the correct interpretation of quantum mechanics,   right? So he’s motivated by interpretational  philosophical questions to a substantial degree.   But I think probably my favorite example is  decoherence. So whenever you propose a new way to   think about quantum mechanics, people will often  say, do we really need this? Doesn’t decoherence   solve this problem? There’s a physics solution  to this problem. We don’t need philosophy,   do we? But decoherence comes out of philosophy,  right? So- How? Okay, so there are some rudiments   of ideas from, you know, that we might associate  with decoherence that go all the way back to like   Mott in the 1920s. But the first serious rigorous  formulation of decoherence that I have ever been   able to find shows up in chapter 22. So these  are the end chapters of David Bohm’s textbook,   Quantum Theory. This is 1951, he publishes this  textbook. It’s 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 wanna teach quantum mechanics. He also wants   to deal with some of these lingering questions  about how the measurement process is supposed   to work. So in the later chapters of his book,  he goes through the measurement process in as   much detail as he is able to based on the axioms  that were available, 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 that   is to be measured. It’s in some superposition.  He brings in… Like a physical measuring device,   he models the whole thing with a system  to be measured and the measuring device.   He lets them interact. He ends up with this  superposition. And then he argues that some   of the probabilistic quantities one might wanna  calculate, the averages one might wanna calculate,   they exhibit these very strange quantum effects,  these so-called interference effects. But once the   measurement proceeds far enough and the measuring  device interacts sufficiently strongly… And I   don’t remember in the book whether he includes the  environment or not. I’d have to remember exactly   what he does there. But basically, when enough  degrees of freedom from the system get involved,   you get what he calls… The phrasing he uses is  the destruction of interference in the process of   measurements. That’s what he calls it. The  destruction of interference in the process   of measurement, which is decoherence. That’s,  you know, a more extended version of the term   decoherence. And that’s exactly what decoherence  is. So he writes this book. He apparently has   conversations with Albert Einstein about it. This  is 1951, 1952. Albert Einstein is still alive at   that point. And he has some conversations  with Albert Einstein and Albert Einstein   is dissatisfied with his approach. Says he should  go work on it a little more. And he goes back and   he independently rediscovers some work that was  done by de Broglie in the late 1920s. De Broglie   had developed the first sort of early pilot  wave theories. Bohm independently redevelops   these. Eventually he and de Broglie connect.  Now we call these theories the de Broglie-Bohm   theory, or sometimes it’s just Bohmian mechanics.  And in this theory, you’ve got not just the wave   function evolving in some high dimensional space  where the wave functions live, but the wave   function is also guiding around these corpuscular  particle-like things, the Bohmian particles,   the Bohmian projectiles, the Bohmian corpuscles.  And one obvious question you could ask is, well,   if you have both these projectiles and you have  a pilot wave, and Bell and Bohm in these papers   specifically says that the pilot wave is real,  metaphysically real to the same extent that   the particle locations are. Then when you do  something like the double slit experiment and   you send a pilot wave through these two slits of  an experiment, right, and they land on a screen,   why doesn’t the screen light up in all the  places where the wave hits it, right? So the wave   diffracts, you get these intensity peaks, these  famous interference peaks in the wave function.   The projectile is guided to only one of the  locations. When you actually run the experiment,   you only see one landing site. But the question  is, well, but what about the other empty waves,   empty shells, the parts of the wave function that  land on the screen and don’t have a particle in   them? Why don’t they hit something and do  something? And Bohm wrote two papers. It   was a pair of papers. In the second paper,  he goes through the measurement process.   He goes through this example. And he basically  uses decoherence to explain why we only see one   landing site. So decoherence was developed  in this textbook and then put to use almost   immediately in a very applied sense to get his  pilot wave theory off the ground and to make it,   to show that it was empirically adequate at  least for nonrelativistic systems of finitely   many particles. The threat is then picked up  again in the 70s by Dieter Zeh, who did some   very deep and important work on decoherence,  apparently had some career repercussions for   working on such a philosophical foundational area.  And then decades later, physicists, practical   working physicists working with, you know,  AMO systems, atomic molecule optical systems,   physicists trying to implement real world quantum  computers, trying to implement unitary gates and   actually get simple quantum computers to work.  But even physicists in all kinds of other areas,   physicists trying to understand early universe  cosmology, physicists trying to understand systems   and condensed matter. People are now worrying  about decoherence all the time. You read papers,   every paper talks about what is the decoherence  timescale of this or that. Decoherence is now a   major component of what we do in physics today.  It’s happening all the time right now. And again,   I would just say that maybe we should, we  should pay some royalties to poor David Bohm,   who was run out of the United States. He like,  you know, spent a lot of his career in Brazil   and couldn’t get back to the United States. And  Zay, who suffered some career repercussions. And   there’s this attitude that, oh, thinking about  foundational philosophical questions is a waste   of time. How could it be a waste of time given all  of the fruit that it is, that it has produced? So,   you know, I, what I would 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 of, 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 type stuff. But  the sort of more like philosophical side of it,   this is an area that has had very few people work  on it, right? There are very few permanent tenure   track academic positions that are devoted to  this kind of work. A lot of the people who   are doing this work got their academic positions  to do something else and then transitioned into   this work. So there’s very few people responsible  for a lot of these results. There is very little   research funding. And so if you were the sort  of person watching this and wondering, like,   where would funding make the biggest difference in  physics? Should we devote more funding to already   very well-funded areas of physics? Would an  additional million dollars make a huge difference   to some of these areas? I can tell you that,  like, philosophy of physics, the intersection   of physics and philosophy, the more philosophical  side of quantum foundations, and also the more   philosophical side of the foundations of general  relativity and the foundations of, you know,   many other important areas of physics, that’s  where I think every dollar would go very far. So,   you know, if you’re in the market for endowing  professorships, like, that is a way to make a   huge impact on the field. Great. Speaking of  the foundations of quantum mechanics, are they   inconsistent as they stand in textbook quantum  theory? In 1932, mathematical foundations of   quantum mechanics. People divide the axioms up in  various ways. I’ll give a super quick, you know,   discussion. They say that to every quantum system,  we associate a kind of a vector space called   a Hilbert space, a space of vectors involving  complex numbers. The elements of this vector space   are called state vectors. Loosely speaking, they  can be also called wave functions. There’s some   terminological nuance around that. And these are  supposed to represent, in some sense, the state   of a quantum system. More generally, you have to  use what’s called a density operator, which is a   little more complicated, but we’ll put that aside.  And then the next axiom is that as time evolves,   these quantum states, whether state vectors or  wave functions or density matrices, are supposed   to evolve according to what’s called unitary time  evolution. If it’s sufficiently smooth and nice,   it can be written as a differential equation,  an equation that tells you moment to moment   in a Markovian way what each next state will be  given the present state. We call that differential   equation, when it’s for wave functions, we call  it the Schrodinger equation. If it’s density   operators, we call it the von Neumann equation.  And then there’s all these axioms of measurements.   The observable things that you could measure about  a system are represented by operators or matrices,   these self-adjoint things called self-adjoint  operators matrices. These are the observables   of your theory. The possible results you can  get when you measure one of them is called an   eigenvalue. It’s one of the eigenvalues of these  operators. The probability with which you’ll   get that is given by this formula that takes the  state, the quantum state of the system, and takes,   you know, we call it projection operator, but a  piece of this operator. You put them together,   it gives you the probability you’ll get that  result when you do the measurements. And then once   you’ve done the measurements, this quantum state  of the system is projected or collapses to reflect   the result and ensure that you’ll get the same  result if you measure it again right away. Those   are the traditional Dirac-Von Neumann axioms,  and people slice them up in different ways. But   I like to think of them as those five axioms,  right? Hilbert spaces, unitary time evolution,   observables as self-adjoint operators, the Born  rule for probabilities of measurement outcomes,   and then collapse. There are problems with  these axioms, not when dealing with, you know,   microscopic systems. Microscopic systems, things  tend to work out pretty well. And when people   say quantum mechanics works just great, 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, theory works great. Works  great. If you, you know, if you limit yourself   to these particular examples, what’s the problem?  If you want to do a particle physics experiment,   a high-energy physics experiment, you’re, you  know, building a giant particle accelerator,   you’re talking about the Large Hadron Collider  or something like that, you have beams of   subatomic particles that are flying together, and  there’s debris that comes out, you collect all   the debris. These are all microscopic systems.  Quantum mechanics makes beautiful predictions   about these results. So you’re not going to see  any discrepancies for these kinds of systems,   at least to the extent that the Dirac phenomenon  axioms give a self-consistent description for   microscopic systems, which they appear to do.  Perfectly empirically adequate description,   the theory works great. So what’s the problem? Why  does anyone have any issue? 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-form thesis  in 1956-57 when he was a graduate student at   Princeton working for John Wheeler. Not the one  he ultimately published. He published a shorter   version, but in the longer version, he opens it  up with a thought experiment that has since been   usually attributed to Eugene Wigner, who was also  at Princeton. And we talked about how Wigner had   this paper called On the Mind-Body Question in  the early 1960s. But in this thought experiment,   we imagine trying to do quantum mechanics with a  system that is not small. It is not small. It is   not ultra-cold. It is not, you know, pristine.  The quantum system is something big enough to   be a measuring device itself or even an observer.  So again, this thought experiment is called the   Wigner’s Friend Thought Experiment. Wigner is on  the outside of a box. The box is perfectly sealed.   Wigner is one observer. Inside the box is Wigner’s  friend. Wigner’s friend is also an observer, a big   system, but perfectly sealed inside the box.  And Wigner’s friend does a measurement on some   superposed microscopic 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 in the sealed box,   as a thing that is an observer, that does  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   is a second observer on the outside who has not  done a measurement on the box or the contents,   maybe we should treat the box and its contents as  not subject to the collapse axiom. And now all of   a sudden we have an ambiguity in the middle  of the theory. The Dirac phenomenon axioms   are simply ambiguous in this circumstance. They  don’t render a judgment of what you’re supposed   to do. And when we spoke last time, I laid out  a whole menu of possible things you could do,   and each of them leads you down a different  road, right, for how you would resolve this   problem. So this is just an inconsistency. And  I want to make clear here, there’s a difference   between a theory being unintuitive or exotic or  eccentric and a theory being inconsistent. Let me   give you an analogy, a real-world analogy.  You’ve got a friend, and your friend is   lovable and trustworthy and nice and always  there for you, but your friend is eccentric,   okay? What do you do? What you do is you love  your friend, because we all love eccentric   people. We’re all eccentric to some degree. I’m  eccentric. We’re all eccentric. We like eccentric   people. Eccentric people are interesting. They’re  interesting because they’re often surprising and   they’re creative and you never know what you’re  going to get, and it’s always very interesting,   even if it’s sometimes, like, confusing what they  do. But it’s okay, right? They’re just eccentric.   We like eccentric people, and we’ve got eccentric  physical theories. Newtonian physics, you know,   despite its reputation of being,  oh, it’s Newtonian, it’s classical,   it’s when everything made sense, there’s a lot  of stuff about Newtonian physics that doesn’t   make a lot of intuitive sense, right? You  know, Newtonian physics says that a system,   a body in motion will just stay in motion unless  it’s acted upon by something. It doesn’t come to   rest. That’s very unintuitive. We intuitively  feel like things should come to rest. Aristotle   believed that the natural state of all objects was  at rest, and in Newtonian physics, it’s just not.   You need an explanation for why a thing would  come to rest. But, you know, there are a lot of   other examples like this in Newtonian physics.  We have all this intuition about how circular   motion should work. We have this intuition that  when you’re, you know, moving water around in a   bucket that there’s a centrifugal force pulling  it in. That’s intuitive, but that’s, like,   not how it really works. Gyroscopes are where all  intuition breaks down, right? That’s all Newtonian   physics. Newtonian physics is filled with things  that are a little bit unintuitive, and things only   get worse from there. I mean, special relativity  is super unintuitive. We talked about time   dilation, the idea that the time, like, progresses  differently for observers in different frames of   motion. That what we call all the events that are  simultaneous, like, they’re all happening now,   our notion of now is relative, and the different  people will disagree on which events are now and   which events are in the future and the past.  That’s very unintuitive. And don’t even get me   started about general relativity. I love general  relativity. I have taught general relativity   here. So we have a graduate-level course in  general relativity, Physics 210. It’s, like,   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 surprised. General relativity, that class,   is like an eccentric friend. Every time I teach  it, it’s like you learn something totally new and   surprising. And you’re like, really? It really  works this way? It really does. So, you know,   general relativity is another example of a theory  that is just really, really deeply unintuitive.   I mean, we always set aside, like, a half hour  every time I teach the class just to talk about   the weirdness of black holes. And this is just not  even, like, when you start worrying about quantum   effects. Just, like, regular treating black holes  as classical objects. Black holes are really   unintuitive in a lot of ways. And so I’ll just  set aside half an hour. I’ll just open the floor,   and I’ll just ask students to ask me whatever  weird questions they have about black holes.   Like, a student will be like, if I stick my  arm in a black hole, can I pull it out? Or,   like, all these weird things you could ask,  like, what does it look like if I send someone   to a black hole? Can they ever come? Like, all  these, like, weird questions you could ask. So,   generosity is super, super unintuitive. Jackson,  Jackson level electromagnetism. So one other   course I teach is Jackson level electromagnetism.  There are a lot of very unintuitive things that   happen in electromagnetism also. So it’s not that  we don’t have, like, we don’t have theories that   are eccentric, we do. I should say that all  of these theories do have places where they   break down. The breakdown in a physical theory  is called, well, a singularity in a theory.   Singularities aren’t necessarily geometric  point-like things. They’re just places where   your equations stop working. Electromagnetism  has this famous divergence of the self-energy   of point particles. Generalitivity famously  has singularities. Everyone’s heard of the   singularities of the Big Bang and black holes and  various other places where generalitivity breaks   down. Newtonian mechanics has weird singular  behavior in certain kinds of systems. Yep, yep.   There’s a famous paper by Shia in the 1990s on a  five-body system that exhibits singular behavior.   It was originally predicted that this could  exist by Poincaré, I think, a century earlier.   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 we go, okay, the theories   work in these regimes. Sometimes they make very  unintuitive claims or predictions, and we’re okay   with that. We like weird, cool physics, as long  as it’s self-consistent. And there are certain   places in which the theory breaks down, and we’ll  need to either replace the theory with something   else if we’re lucky, if we’re unlucky, maybe we  won’t find a better theory that will replace it,   whatever. Quantum mechanics is kind of like that,  right? There are regimes in which you’re working   with microscopic systems, and quantum mechanics  is nice and self-consistent. We don’t run into   these ambiguities or inconsistencies. It’s a  little unintuitive in some of these situations,   sure. But when you confront something like  the Wigner’s Friend thought experiment,   and other thought experiments people have proposed  over the years, now you’re talking not about   things being unintuitive. 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. No one would say,   well, the self-energy of a point particle  electromagnetism is just unintuitive. People   would say, this is clearly something wrong that  we need to fix. And all I’m saying is the same   thing is true of quantum mechanics. There are  regimes in which it works well, and there are   other situations that we can extrapolate it to  where things seem to break down. These situations   do entail an extrapolation of the theory from  microscopic physics to macroscopic physics. I   mean, we’re assuming you can go from the level  of an angstrom, 10 to the negative 10 meters,   that’s 10 billionths of a meter, all the way up to  a one meter scale, the size of a human. To get the   Wigner’s Friend thought experiment, you have to  have an extrapolation of the theory to that size.   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   event, something goes wrong, and we just have to  deal with that. We have to confront that problem   and manage it. But I would go a step farther  than that. It’s not just that the theory seems to   have places where it’s ambiguous about what it’s  predicting or where it’s inconsistent. The theory   also only makes a very narrow kind of prediction,  according to the Dirac-Von Ohmen axioms. So the   Dirac-Von Ohmen axioms, and again, these are  the axioms you’ll read if you pick up Griffith’s   textbook on quantum mechanics or Shankar’s  textbook on quantum mechanics or Sakurai’s, all   the standard textbooks, Townsend’s book on quantum  mechanics, Gottfried’s book on quantum mechanics,   Leboff. The theory predicts measurement outcomes.  It predicts what you’ll see on the readings,   on the dials, on the gauges, on the displays of  measuring devices, and it predicts the probability   with which you will see those readings on  measuring devices. You can compute averages   in these theories, they’re called expectation  values, but those averages are definitionally,   axiomatically, statistically weighted averages  of numerical measurement results weighted   by measurement outcome probabilities. We’re  talking about a very narrow kind of phenomenon,   right? A very narrow category of phenomena.  The Dirac-Von Ohmen formulation of quantum   mechanics predicts measurements, what happens  with measurements. It’s a very narrow slice,   a very narrow category of phenomena. When we  spoke last time, we talked about how there are   all other kinds of phenomena that seem to  be happening around us. In the deep past,   primordial gases mixing in the early universe,  today, birds foraging, people falling in love,   all that stuff. There’s lots of phenomena  that seem to be taking place that all lie,   strictly speaking, outside the axiomatic ambit  of the Dirac-Von Ohmen axioms. What are we to   do with this? We either say that Dirac-Von Ohmen  quantum mechanics simply is not giving a complete   description of nature, which is kind of sad, and  if it’s not, where is the outer boundary? Now,   there are some philosophers who defend this point  of view. Nancy Cartwright is a famous philosopher   who has argued that maybe we just have different  theories in different domains, the universe is   many dappled, they’re just like different theories  for different things. But it would certainly be an   interesting intellectual exercise, and it would  certainly be nice if we could extend quantum   theory to describe more of the world. If we do  that, now we have a job to do. We either have   to explain why all these other phenomena are, in  fact, measurements, despite the lack of measuring   devices or whatever. We have to somehow show that  all of these things are, in fact, measurements,   and therefore, in fact, lie within the axiomatic  ambit of theory. Some people have proposed that.   But the onus is on them to show that it really  works, and it’s not clear that it does. Or we   need to somehow extend the theory, change the  axioms in order 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 second,   decoherence. What about decoherence, right?  I mean, sure, okay, fine. The philosophers,   or at least physicists who cared a lot about  philosophy, they gave us decoherence, but we   haven’t now. Doesn’t decoherence solve all these  problems? Well, Bohm certainly didn’t think it   solved these problems. He introduced decoherence,  and it was insufficient, and ultimately,   he introduced his pilot wave corpuscular  theory in order to actually get a result.   The reason decoherence doesn’t do the job is  decoherence takes a wave function or state vector,   more generally what’s called the density matrix, a  density operator, and it shows that under certain   circumstances, when it’s evolving, interacting  with an environment in the right way, or   interacting with a measuring device that’s coupled  to an environment in the right way, the density   matrix will change in a certain way. It’ll become  approximately what we call a diagonal matrix in a   certain representation. We call this a basis, and  there’ll be some entries on the sort of diagonal   of the matrix, and the other entries will be  approximately zero. At this point, we’re supposed   to say the measurement’s been done, and there’s  an outcome. The problem is there is nothing in the   dynamics, not in the Schrodinger equation, not in  the generalizations of the Schrodinger equation,   not the Lindblad equation, or the quantum channels  that you use to describe this. There’s no known   dynamics within normal quantum theory that singles  out one of the outcomes. You still need to apply   the Born rule to get a probability out of this,  and you still need to apply a projection postulate   to single out one outcome. There’s nothing in  the dynamics that will do that for you. From   time to time, people have proposed that maybe  there’s some sufficiently complicated standard   textbook quantum dynamics that will, in fact,  cause the system to single out one outcome, but   this is impossible because of the no communication  theorem, the no signaling theorem that I mentioned   before. Collapsing down to individual states  looks superficially like 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 that’s just not working here,   and pinning all this down, not just  hand-waving and saying, oh, decoherence,   don’t ask me any more questions. Pinning this  down is a worthwhile exercise. Subjecting this   problem to rigorous scrutiny may bear fruit.  It has borne fruit already, and I would argue   it will continue to bear fruit going forward.  into physics, AI, consciousness, philosophy,   along with my personal reflections, you’ll find it  all on my sub stack. 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 pilgrimers.  By joining, you’ll directly be supporting my   work and helping keep these conversations at the  cutting edge. So click the link on screen here,   hit subscribe, and let’s keep pushing the  boundaries of knowledge together. Thank you,   and enjoy the show. Just so you know, if you’re  listening, it’s c-u-r-t-j-a-i-m-u-n-g-a-l-dot-org.   And I would argue it will continue to bear  fruit going forward. Now going forward,   I’d like to talk about your approach, your  indivisible stochastic processes. Prior to that,   okay, and just so people know, there are three  sources. One is the previous interview that we’ve   had with Jacob, and that’s on screen right now.  It’s over two hours long, and it’s quite in depth.   Another source is, I have a sub stack post where  I cover my interpretation of Jacob’s theory. And   then the third is obviously your papers directly.  All three of these will be linked on screen and   in the description. Prior to that, I want to talk  about Wigner’s thought experiment, his friend. How   is that not just Schrodinger’s cat, but replacing  the cat with a friend? You’re completely right. I   mean, if you think of the cat as an observer,  and the quantum system being observed is the   radioactive atomic nucleus that is momentarily  in a superposition of decayed and not decayed,   it is Wigner’s friend thought experiment. When, I  mean, the origins of the Schrodinger’s cat thought   experiment go back to discussions between Einstein  and Schrodinger. Einstein had a somewhat less   playful example involving gunpowder that could  either go off or not go off. And Schrodinger,   in this 1935 paper, replaces this with the famous  cat. But Schrodinger doesn’t describe the cat as   an observer. I think the real innovation is  just rethinking the experiments. You could,   I think, absolutely think of the cat as Wigner’s  friend. If you think that cats count as observers,   which I do, and friends, cats are friends  and observers, absolutely, then it really,   it’s more a question of perspective, right? If you  don’t think of the cat as a candidate observer,   then you’re not doing the Wigner’s friend thought  experiment. If you think of the cat as just as   legitimate observer as a person, despite not  having a PhD, there’s always obligatory jokes   that go with the Schrodinger’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 like some joke about why is it people always  make jokes about this, but yes, if you think of   the cat as an observer, then it is just the  Wigner’s friend thought experiment. I think   part of the reason why people like to separate  these two is in some versions of the Wigner’s   friend thought experiment, you’re supposed to  be able to ask a question to Wigner’s friend,   like slide a little note in and ask questions.  And if you ask the wrong kind of question,   you’ll cause a collapse. And if you ask the right  kind of a question, you don’t get a collapse. And   you can’t do that with a cat. Cats don’t talk.  At least all the cats I’ve ever met don’t talk.   So there are some situations in which actually we  do like it to be a sentient and sapient observer   who can communicate. But broadly speaking, they  are very similar thought experiments. Okay, now,   just before we move on, and we’re going to get  to some of the audience questions that people   have asked both in the comments and then also  on Twitter threads and so on about the previous   podcast. Okay, you mentioned Putnam earlier, and  then it’s this eternalism, because you can slice   up any moment of now. So if there are multiple  moments of now, then is it just that every   single moment of now exists? Okay, what are the  counter arguments to that? It’s tough. The Putnam   argument for four-dimensionalism or eternalism is,  it’s a tough argument to refute. But there have   been attempts. And I would recommend that people  watching this read some of these papers because,   you know, they’re beautifully written by  very smart, amazing people. So again, just   to rehearse this argument, if you think of space,  for our purposes, just as like a horizontal line,   and time as a vertical line, you can visualize all  of space-time as like a, like think of graph paper   with like the horizontal axis is space, all three  dimensions of space somehow like 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 that are all   happening at the same vertical time coordinate,  all the same time coordinates now. And what   special relativity suggests is that if you’re  in a state of motion, then that slice is tilted   a little bit. It’s like not quite horizontal  anymore relative to the first slice. And so things   that are further in the future compared with one  observer are in the present of the second observer   and so forth. One way I like to think about this  is the pancake model of space-time. So imagine a   stack of pancakes. Each pancake is supposed to  be all of space, the whole spatial universe at   one moment in time, okay? And think of this in  the pre-relativistic idea, like the Newtonian   conception that there’s just a well-defined notion  of what is all of space at every moment in 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 is  what’s happening right now. And somehow the   hot pancake is somehow incrementing, right? And  this is the passage of time. Now you run into   some very deep questions like how quickly are the  pancakes moving? They’re moving at one second per   second. Does one second per second make sense?  If you divide a second by a second, isn’t that   just unitless? What are we talking about? Okay,  but let’s put all that aside for a second. Just   imagine that there is some notion of a moving  now, this sort of metaphysically presentist   idea that the present exists, it’s a well-defined  thing, and it is somehow incrementing forward.   What special activity seems to suggest is that  observers in different states of motion will slice   the stack of pancakes slightly diagonally. And so  to an observer who is moving at some, you know,   it doesn’t even have to be super fast, because  if you’re talking about the whole universe,   even slow motion will actually, you know,  ultimately produce a clear discrepancy. But,   you know, the slices are now tilted. And if you’re  cutting the stack of pancakes at 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 could there be a metaphysically   invariant notion that one of them in one  particular slicing is in fact the hot pancake?   So you can see why this is like a very difficult  argument to refute. But there have been attempts.   So Brad Scout MIT has a book with a particular  perspective on this. I encourage people to take   a look at this approach. Another approach is Jean  Annis Mayle, who is at Johns Hopkins University,   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 you might get around this problem. I’m not   going to be able to do justice to the argument  here, but I would recommend people read the book   because she’s a fantastic writer, and I think  people will find it very interesting to read this   book. There’s a paper from not long ago by David  Wheelies at Princeton. He’s a metaphysician who   does some work in philosophy of science also at  Princeton. And he has an argument that, you know,   putting aside the special advisory argument,  he’s like, you know, maybe we can’t, maybe it’s   a difficult argument to deal with, but at least  rather than try to refute that negative argument,   an 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 appear to   be Markovian. And Markovian laws are by definition  laws that take a notion of a present state and   tell you the later states without really worrying  about anything in the past. And he’s like,   you know, why should the laws be Markovian if  we’re living in an eternalist universe? If we live   in an eternalist four-dimensional universe where  the whole block is just like there, why would our   laws only care about the present state? There’d be  no explanation for this. But if only the present   really 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 people who are watching will, you know,   surmise, I have some issues with this argument  because the whole point of the formulation of   quantum mechanics we’re going to talk about is  that actually the laws may not fundamentally be   Markovian at all. And if they’re not Markovian,  then all of a sudden that argument doesn’t maybe   work so well. Yeah. It’s my understanding, and  we’re going to get to it, that your evolution laws   depend on the past. It’s not as if they depend  on the future. Right. So in the eternalist state,   when they’re saying that, why would we privilege  the present? And then you’re saying, well,   in yours, you’re not, but you’re also not  privileging the future. You actually are   privileging the past. So you still don’t take an  eternalist block. So this is, this is a subtlety,   right? The fundamental laws of physics that we  know about today, to a very good approximation,   have a feature called time-reversal invariance  or time symmetry. Newtonian mechanics, famously,   if you run a system in one particular,  you know, in some particular process,   and then someone plays a reverse version of the,  you watch a video of it and someone’s rewinding   and they’re winding at normal speed and you watch  the whole thing happen in reverse. Although it may   look weird or unlikely, there doesn’t appear  to be any violation of Newtonian physics in   what you’re seeing. You know, so famous example, a  teacup falls off the table, shatters. There is a,   you could also have all the pieces have just the  right initial conditions so that they have some   initial velocity that’s just right to bounce them  together. And they just land perfectly together.   And they re-seal together and form the teacup.  And the teacup has just the right kinetic energy   that it bounces off and lands on the table. Like  it’s unlikely, but doesn’t actually violate any of   the laws of Newtonian physics. And this works  out 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   in which you replace particles and antiparticles  is called C-symmetry. The symmetry in which you   do a parity or spatial reflection and everything  is called parity symmetry. And then there’s time   reversal. And the standard model, our best theory  of fundamental particle physics that’s based on   quantum field theory has this feature that it is  exactly CPT invariance. If you take any process   in the standard model and do a combined particle  goes to antiparticle vice versa and parity and   time reversal transformation, everything stays the  same. And there are some systems that violate CP   symmetry. And then by the CPT invariance, that  means they violate T or time reversal symmetry.   But there are rare processes. It’s not clear that  they have anything to do with the macroscopic   distinction of future and past that we tend to  see. There are some, you know, conjectures about   this, but no one has a firm argument that these  two things are closely related. So the idea of   a physical theory like we’re talking about that  somehow privileges the past, but not the future in   an eternalist universe seems a little bit odd. I  should say right off the bat that the indivisible   stochastic formulation does not fundamentally  privilege the past or the future. You could   just as well formulate a quantum system that’s  going the other way. There’s nothing, it’s not,   the theory doesn’t specifically, it’s just that  like when you actually consider a particular like   system, it’ll be a system in which the past plays  a different role from the future, but you could   also consider a system which the future plays  a different role from the past. It’s, 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 nature’s about picking   out future versus past, but just that in a  given instantiation, in a given situation,   nature has to pick one particular direction in  each instantiation and depicts one over the other.   Like the laws of Newtonian mechanics fundamentally  are rotation invariant, but you are not rotation   invariant. Your atoms formed in a particular  shape and whatever shape they formed picked out   a direction in space. So you spontaneously break  rotation invariance, even though fundamentally   like the laws of Newtonian physics are rotation  invariant. The laws of quantum physics,   according to this indivisible stochastic approach  are fundamentally time reversal invariant, but   for a given model, they will typically favor one  direction of time over the other. I should have   said there is one other way to save, at least I  can think of, one other way to save the idea of a   flow of time, a directness to time. And this is to  say, well, okay, special relativity is a very good   theory, but we’re living in an expanding universe.  We’re living in a space time that appears to go   back to some kind of big bang hypersurface, some  initial big bang everywhere. And distances between   objects are growing with time in some particular  way. It turns out that in these kinds of, we call   them cosmologies. So cosmology is the subject of  the study of the universe, but a particular like   space time model that solves Einstein’s field  equations at the level of the whole universe   is called a cosmology. And in the cosmology, we  seem to be living in approximately what’s called   Einstein-De Sitter cosmology described by the  FLRW model. In this model, there is in fact a   preferred slicing of space, right? You just take  every point in the universe and ask like how long   ago was the big bang from that point and take all  the points that are all 13.78 billion years since   the big bang, and they form a hypersurface. And if  you just do that, you actually get kind of like a   preferred slicing of the universe. And you might  go, that seems to contradict special relativity.   Well, but general relativity is not special  relativity. General relativity is a different   theory. And in general relativity, different space  times can globally, like at the scale of the whole   space time, spontaneously break the symmetry of  the slicings, the so-called Lorentz symmetry.   Because there’s a preferred big bang hypersurface,  there’s a preferred foliation or slicing of space   time into slices of now. And so just the history  of the universe, the way that it happened to be   instantiated for the bang appears to have picked  out a preferred way to slice the universe.   And then you could say, okay, well then that  really is the fundamental notion of time. Time   is really flowing from one such surface to the  next. And sure, if you zoom in really close to   like a planet or a star or some very localized  thing, things look like special relativity. You   don’t notice the whole shape of the cosmology  and all the different reference frames look the   same and all the slicings look like they’re in the  same footing. But on a global cosmological scale,   there in fact is a preferred way to slice things.  And time really flows from one slice to the other   in some fundamental sense in that picture. But  this leads to some other really deep questions.   Is the geometry of our cosmology a fundamental  fact? Or is it merely a contingency? Could the   universe have formed in lots of other ways? And  it just happened that it formed in this particular   way with this preferred slicing. And if it was  contingent, if the universe could have formed   in lots of ways or could have been eternal, but  happened to form in this particular way, can you   metaphysically say that time flows in  some fundamental sense based on what was   a contingent fact about the universe? Like if  you think the flow of time is some fundamental   feature of reality, should depend on accidents of  history? No pun intended, but you get my point,   right? So just to close the circle, that’s  like one other way people have thought about   maybe restoring a notion of a flow of time. Okay,  sorry, that was a lot, but yeah. Okay, briefly,   before we close that circle, you mentioned  that in GR you can spontaneously break Lorentz   symmetry. What’s the difference between breaking  a symmetry and spontaneously breaking a symmetry?   Okay, so if you take a theory and the basic  equations that formulate laws of that theory   simply fail to have a certain symmetry. And by  a symmetry here, I mean a transformation that   would have a certain symmetry. So if you take  a theory and the basic equations that formulate   laws of that theory simply fail to have a certain  symmetry. Maybe for certain kinds of theories,   certain kind of laws leave the laws  unchanged. For this particular theory,   they do not leave the laws unchanged. So let me  give an example. Let’s suppose that the universe   is described by the Newtonian physics near Earth’s  surface, and that is the whole universe. There is,   in fact, no Earth. The universe is infinitely  big, and it is like Earth’s surface forever,   right? Earth’s surface just goes on in every  direction forever. There is the ground, and   it never ends. You can go as far as you want, and  it doesn’t wrap around. It just goes on forever,   right? There’s no planets or anything like  that. The whole universe is just life near   an infinitely big surface. Okay. That’s all that  there ever is. And that’s fundamentally all that   there is. It’s not an accident of history. That’s  just how the universe is. It was fundamentally,   its existence is just this infinite ground that  goes 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  rotation invariance. The basic laws of this theory   include 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 is not parallel to the ground, the laws look   different now, right? Things fall sideways now.  The theory, the laws are not invariant under this   transformation. We would call that an explicit  breaking of rotation symmetry. I see. Okay. So   I guess terminologically I’m confused because  breaking to me seems like it was there before,   and then now it’s broken. So breaking in this  instance just means it fails to have it to   begin with. That’s right. It fails to have it to  begin with. That’s the better way to say it. I   guess the terminology is because these are often  symmetries that were there in earlier theories,   and then maybe in a deeper theory, the  symmetry is gone. So we say that like the   kaons violate time reversal symmetry, right? We  call it a violation or a breaking because before   we discovered these particles, we thought it was  a symmetry, and it’s broken by kaons, right? So   I think maybe that’s one way to think about it, or  maybe it’s that we have a lot of theories in which   certain symmetries are approximately true, but  they’re not exactly true. And then we can think   of certain particular things in the theory that  violate it, whereas broadly speaking, it’s not   violated. That’s entirely fair. But the example  of Svante Hinsbryg would be like the actual Earth,   right? The actual Earth is not an infinite  surface, it’s a sphere in space. And when you’re   on the Earth, you do feel like gravity is pointing  in a particular direction, but this is just an   accident of Earth being there. If you could delete  the Earth, and we’re just floating in space, then   suddenly you would have full access to the road.  There’d be no notion of up or down, or left, like   the 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 Earth isn’t there. Earth’s presence, by an   accident of just that’s the way this particular  corner of the universe was instantiated,   not at the level of fundamentally changing laws  of physics. But Earth being there and us living   on the Earth makes us think that a symmetry  that is fundamentally there, rotation variance,   full three-dimensional rotation variance, is  in fact not there. It’s hidden from us. Some   people say spontaneous symmetry hiding is a better  term than spontaneous symmetry breaking. But yeah,   so this just points to this distinction between,  am I really saying a certain symmetry is not there   in the fundamental statement of the theory,  or is it just hidden or missing because of the   way that a particular system has instantiated the  theory? Okay, so I didn’t know that, for instance,   when you were talking about molecules to form you,  and the molecules have some rotational invariance.   But you don’t, thankfully, have that rotational  invariance. I have rotational invariance. As far   as we can tell. But that forming of you was  not spontaneous, so the person who’s watching   or listening is thinking, well, it took quite  some time to form Jacob. Jacob didn’t- The word   spontaneous is a term of art, yeah. Okay, because  I thought spontaneous symmetry breaking had to do   with, you have a potential well, and then you  get to the minimum of it, and you produce some   ghost-home bosons. And I thought it was just for  that case. I didn’t realize it was any time that   a symmetry was broken. You call it spontaneously  broken. When it’s broken by the way a particular   system happens to form or a particular solution  to the theory. So here’s another way to think   about spontaneous symmetry breaking. There is a  puzzle called shape by shape. It’s this little,   it’s a square. It’s a delightful little puzzle.  You’ve got these yellow shapes and these orange   shapes. And you have a picture you’re supposed to  create. And you take all the shapes and you put   them into the square. And you try to fit them all  in the square. And they have to fit exactly in the   square with no gaps. And they have to replicate  the picture 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, the playing field  is a square which is perfectly mirror symmetric.   And although some of the pieces are what we call  chiral. Chiral means that they’re handed. There’s   like, the pieces look like a left-handed piece  or right-handed piece. It turns out they’re not   really chiral cuz you can just flip them over.  You can flip them over and then you discover the   fact that, yeah. But in any particular way that  they’re flipped, they pick 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 lay out the board,  lay out all the pieces, lay them out in a way   that you look at a picture and you just flip the  thing over and it looks exactly the same. And you   can even have a picture you’re trying to make.  And this picture you’re trying to make is also   mirror symmetric, right? You look at the picture,  it’s some totally symmetric looking figure. And so   you’re like, okay, I should be able to take my  symmetric puzzle pieces and create a symmetric   picture. And I should be able to do it by putting  the pieces into a configuration that is mirror   symmetric. And it turns out, in some cases, you  can’t. In some cases, all the solutions to this   problem, despite the fact that the problem,  the laws of this system are mirror symmetric,   none of its solutions are mirror symmetric. Once  you’ve solved it, you discover that the solutions   are always lopsided. There’s like different pieces  on one side versus the other, and there’s no   solution that is balanced and symmetric. We would  say this is a system that entails spontaneous   symmetry breaking. The equations, the fundamental  laws are symmetric, but all the possible ways   to solve it are not. Now, you could also have  systems, maybe there’s a puzzle in which it can   be solved in a symmetric way, and it can also be  solved in a non-symmetric way. We would still call   the solutions that are not symmetric, but still  solve the puzzle, we’d still call them spontaneous   breaking solutions. So this is a phenomenon  that happens all over the place. There’s another   example that one of my colleagues here, Cameron  Vafa, a professor of high energy theoretical   physics, works in string theory. He has a lovely  book called Puzzles to Solve the Universe,   I think. It’s connected to a seminar course he  teaches here. And he has this puzzle he really   likes. It’s this puzzle where you’ve got four  cities that are on the corners of a square.   And the question is, how can you connect them with  roads? So you can get from any one city to any   other city, driving on roads, using the minimum  amount of road length or pavement possible. This   problem is completely rotation symmetric. It’s a  square, right? It was stated in a way that didn’t   privilege any direction. And you can always rotate  the square any way you want, it looks the same. So   you might think that the solution is gonna be,  I don’t know, an X. But an X doesn’t, an X works   because you can make 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 too much pavement. The  solutions that minimize the amount of pavement   used are these kind of like double Y solutions.  And there’s one that goes horizontally and one   that goes vertically. And these minimize the  amount of pavement and they both violate the   symmetry of the problem. So this is spontaneous  symmetry breaking and we see it all over the   place. If you’ve ever wondered, how can the  universe look so asymmetric, given that the   fundamental laws of physics appear to have so many  symmetries? The fundamental laws of physics don’t   seem to privilege direction. To a very good  approximation, they don’t seem to privilege   handedness, left versus right handedness. They  don’t seem to privilege the direction of time.   And yet, the universe looks so asymmetric. This  is basically all just a huge set of examples   of spontaneous symmetry breaking. You can have a  fundamental system where the laws or the equations   are fundamentally invariant under a bunch of  symmetries. But when you actually write down the   solutions to them, every molecular configuration  is a solution to the standard model. Many of   them simply fail to have all the symmetries of  the underlying theory. Okay, so we’ve made the   audience titillated too long now. So tell the  audience and myself again, a recapitulation of   last podcast about what indivisible stochastic  processes are. And if you feel like relating it   to Bohmian mechanics, because people already know  what Bohmian mechanics are, you’ve covered it,   then feel free to do so as a bridge. Sounds  great, yeah. So the top line version of this is,   there’s this joke about the television show  Seinfeld being a show about nothing. This   is a theory about something. It’s a theory about  phenomena happening. So again, we had this problem   in the Drach von Neumann formulation of quantum  mechanics, the textbook formulation. And the only   category of phenomena we’re talking about is this  narrow category of measurement outcomes. Whereas   we have this much bigger category of phenomena  that’s gonna be happening all over the place.   I call this the category problem. It’s distinct  from the famous measurement problem of quantum   mechanics. So it’d be nice to have a theory  in which stuff is just happening. Now, this is   not the only approach that does this. And later  on, I’ll talk about pilot wave theory, Bohmian   mechanics, the Everettian or many-worlds approach,  spontaneous collapse approaches. There are other   reformulations of quantum mechanics in which  phenomena are happening. And they all, in various   ways, address this category problem that is not  adequately addressed by the standard theory. So   one way to think about this is, this is yet one  more way to actually have phenomena happening. In   a broad sense, beyond merely the narrow category  of measurement outcomes. Another way to think   about this is, it’s a way to make the world safe  for good old-fashioned probability theory. So   when we do quantum mechanics according to the  Hilbert space, Drach von Neumann formulation,   we have these very exotic mathematical entities.  These vectors are density operators, and Hilbert   spaces, and Born rule, and it’s all very, it feels  very different from ordinary probability theory.   Probabilities do show up, but there are many  things that you just can’t do using probability   theory. You have to use this much more ornate,  esoteric apparatus, this formal apparatus in this   sort of Hilbert space language. In this approach,  we restore our ability to do quantum mechanics   using good old-fashioned probability theory.  That’s one other way to think about what we’re   trying to accomplish with all of this. So, but let  me actually go one step deeper before I lay out   how it works. Another way to think about this is,  there are two long-running prevailing assumptions   about what physical theories are supposed to be  like. One assumption is that laws of a theory   should be Markovian. Laws of a theory should take  some notion of a present physical state, and then   tell you what happens next. If your theory is time  reversible, the laws are time reversible, then it   should also be able to tell you what would happen  previously, at least in principle. Another of the   two assumptions is that there’s an all or nothing  deal when it comes to observables. The things we   can observe about a theory are either all there,  they’re all, when we measure some observable, we   are passively revealing some existing feature or  property of our system. In which case, we should   be able to describe these things with any kind  of probability distribution we want, including   joint probabilities, where we can say what’s  the probability that this observable has this   pre-existing value, and that observable has that  pre-existing value, and that observable, and we   can put a probability distribution on all of  these things in some simple way. And if we can’t,   then we just give up. If we can’t, then it’s  all out the window, can’t do it. There are   good reasons to think that we can’t do this in  quantum mechanics. There’s a famous no-go theorem,   originally proved by Bell, but because of the way  that it was published, the first version that came   into print, I think, was by Kochen and Specker in  the 1960s. It’s called the Kochen-Specker no-go   theorem. And the Kochen-Specker theorem basically  says that there are some quantum systems in which   this is impossible. There’s some systems in which  you cannot assume all observable things have prior   values that you are merely passively revealing.  And there’s a beautiful way to explain it,   a very simple version, much simpler than the  original version. It’s due to Asher Perez in   the 1990s. Imagine you’re playing a weird version  of tic-tac-TOE. This is a very strange version of   tic-tac-TOE. Here’s how it’s gonna work. You know  tic-tac-TOE, this we call it in America. I know   it’s called like crosses and O’s or whatever in  different places. But tic-tac-TOE, you’ve got a   grid, it’s got nine empty squares. We’re not gonna  play it the normal way, we’re gonna play it the   following way. I am going to close my eyes and I’m  going to imagine an arrangement of O’s and X’s on   this board. I’m gonna close my eyes and I’m gonna  tell you, I promise you, I can visualize, I see   it, I see a bunch of O’s and X’s. It’s in my head.  Believe me, I really know what it is. And what   you’re gonna do is you’re gonna call out a single  row or a single column. That’s it. And if your   row or column that 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, then we’re done, you lose that   round. We can play again, but then I have to come  up with a new board. It’s a super simple game. So   the way that the game would 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’m gonna go to, first person,   you pick a row or column. The person says, 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’m gonna 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, I come up  with a new board, 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. First row,  it’s always an even number of X’s. Second row,   third row, always an even number of X’s.  When they pick columns, the first column,   always an even number of X’s. The second column,  always an even number of X’s. But the third always   has an odd number of X’s every time. And so what  they learn is they’ll just keep picking the last   column and they always win. Just keep picking the  last column and they always win. But then they go,   well, wait a second, this doesn’t make sense. If  you’ve really thought of this board in your head,   then you’re saying that you’ve 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. This is impossible. It can’t  be because even plus even plus even is even   if all the rows secretly in my head have an even  number of X’s. Like it can’t be just an image in   your head that’s static. Right. There can’t be  a static image in my head in which all the rows   have an even number of X’s. And the first two  columns have an even number, the third has an   odd number because row plus row plus row would  be even. Column plus column would be odd. That’s   clearly incompatible. You must be creating the  results only when we ask about them. You can’t   already have a preexisting 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  go, there’s no way this system could already   know beforehand what it was going to reveal.  The measurement process must bring about, at   least in some cases, the results. So the hard way  to read this is to say, well, if some results are   the result of the measurement process and don’t  merely passively reveal a preexisting situation,   then there’s simply no preexisting results.  It’s all or nothing. They’re either all there or   they’re not there. That is also something I would  push back on. So again, Markovianity in the laws,   this assumption that laws should be things like  differential equations that take the present state   and give you later states. And second, there’s  this all or nothing relationship. Either all   the things you could observe are there, waiting  to be seen, can be assigned joint probability   distributions as needed, or they’re just like not  there. There’s just nothing there. And these are   two things that are challenged in this approach.  Both of these things are dropped, the Markovianity   and this assumption. In this picture, the  fundamental laws of nature are not Markovian and   some observable quantities are reflecting things  that are really there and others are emergent   effects of the interaction between the measuring  device and the system being measured. This is one   way in which the theory is actually quite 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,   are revealing preexisting facts of the matter.  Bell gave a word for things that were really   out there. He called them not observables, but  beables. It’s the way that the system can be,   like beable instead of observable. Some  people read it and think it’s beable,   but it’s actually beable. Whereas other things  you could observe are not really reflecting a   thing that was there and they’re just emergent  features of the story. I call these emergibles   instead of beables. To an external measuring  device, they look just as real as a beable, but   really what you’re seeing in the measuring device  is this sort of emergent pattern. It’s not really   reflecting something that’s fundamentally there.  Bohmian mechanics does this. In Bohmian mechanics,   the positions of particles are beables. You  measure them and you’re really seeing where the   particles were. But when you measure the momentum  of your particle, the momentum you actually see in   your experiment is not literally the preexisting  momentum. It’s this sort of emergent effect of   the interaction with the system. There’s a paper,  you can look up on the archive. It’s called Naive   Realism About Operators. It’s from 1996. It was  written by Daumer, Durer, Goldstein, and Zanghi.   It’s specifically about this thing, that to think  that every self-adjoint operator that in textbook   quantum mechanics, direct quantum mechanics would  associate with observable is revealing something   that preexists in the system is actually, as they  put it, too naive. You can really have some things   that are there and some things that are not there  and it’s totally fine. It’s not a serious problem.   I’ll come back to this point a little bit later  because some of the questions that we’ve gotten   from people have been about basis dependence  and in this picture, can you really measure   everything? The answer is you can. It’s just that  some of them are going to be beables and some of   them are going to be emergibles. Okay, so we drop  those two things. There’s an old saying. I can’t   quite pin down who said it. Some people attribute  it to John Wheeler, again, that if you could   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 it is in one sentence. In   the indivisible formulation of quantum mechanics,  every system has an actual configuration belonging   to some menu of possible configurations we call  the configuration space. I do have to put an and   in. And there’s a comma and an and. It’s still one  sentence. And the dynamics, the dynamical rules,   the laws by which the configuration changes with  time is characterized by a sparse set of directed   conditional probabilities that generically fail  to be divisible in time. That’s the whole picture.   And in principle, you can get everything out  of that one sentence. Everything is now just   mathematics. So there’s no more ands. There’s no  more ands. That’s it. That’s the picture. Let’s   now let’s talk about like what. So if you want  to talk in terms of Occam’s razor like this is,   you know, we’ll come back to Occam’s razor in  a little bit, please. But but just to say like   this is this is like axiomatically pretty  simple. There’s no statement about Hilbert   space or whatever. Everything is phrased in  terms of things we know and are familiar with,   configurations that physically are. Which  configurations depend on the system. If you want   to model a system of particles, you use particle  configurations. If you want to use fields,   you use field configurations. If you want to use  whatever discrete registers in a qubit, you know,   memory register, you’d use those, whatever it is  you want to use, discrete, continuous, whatever   you want. And then the the laws themselves are  phrased as probabilistic statements, but they’re   classical probabilities. They’re classical  ordinary probabilities. Classical is maybe   too strong a word because maybe you might demand  that classical time evolving probabilities must be   Markovian. I don’t, I think it’s it’s a little bit  prejudicial to say that they have to be that way,   but certainly they’re just normal probabilities.  They’re not weird 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. So that’s  the picture. And then in the first of the papers,   the paper called the stochastic quantum  correspondence, which is on the archive,   it’s now just a set of mathematical mappings.  You take this picture and you just do these   sort of mathematical transformations  and you end up with the same story,   but formulated in this Hilbert space language with  time evolution operators and state vectors and   density operators and self-adjoint. This picture  is just like a different mathematical phrasing   of this indivisible picture. And there’s a lovely  analogy to be found here between these indivisible   systems, these indivisible stochastic systems that  have this Hilbert space formulation that’s very   exotic and has complex numbers in it. And it’s  got all these weird symmetries. It’s got basis   invariance. You have all these different bases  you can use. There’s a beautiful correspondence   between that connection, that stochastic  quantum correspondence and the so-called   Hamiltonian formulation of classical physics. So  Newtonian systems, classical Newtonian systems,   interestingly, are not quite Markovian, right?  Think about it, right? You can’t predict how a   particle will behave knowing only its position.  You actually have to know its position and you   have to know its infinitesimally earlier position.  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 is infinitesimally before,  like DT, you know, D like infinite calculus,   infinitesimal D before. That’s kind of  cumbersome to do. So instead what we do is   we subtract the two and divide by DT and call that  a velocity. But it’s the same information. If you   want to like numerically simulate a Newtonian  system and you like discretize time to do it,   you would specify where it is now, where it was a  moment ago, and you’d plug this into a discretized   version of Newton’s second law of force equals  mass times acceleration and you would predict the   behavior of the system. So even Newtonian physics  is a little bit non-Markovian. But we do tricks.   We don’t like having it be non-Markovian. So  what we do is we replace the two positions   at the two infinitesimally adjacent times with a  position and a so-called instantaneous velocity,   which is kind of this trick so that we can  treat these two things as both being at the   same time. And now we’ve made the formalism look  Markovian. Now we have a state at the initial time   that consists of both the coordinate, so-called  coordinate, the position and the velocity. But we   need twice the variables now. We’ve increased the  number of variables in order to phrase this thing   as a Markovian system. And this is an old thing  you could do with in stochastic processes. In   theory of stochastic processes, if you consider  a system that is a little bit non-Markovian,   so not extremely non-Markovian like these  indivisible processes we’re talking about,   but a system in which you need to know the present  state and maybe just one earlier state or maybe   two earlier states to then figure out how the  system will evolve. You could take these systems   and you can treat them like they’re Markovian  by just increasing what you mean by the state   space. I see. Like you triple the state space so  that now you can just treat these three things as   if they’re all on one slice and now you turn it  to a Markovian system. And so there’s this lore   that you can take any non-Markovian system and  make it Markovian just at the cost of making the   state space big enough. Just like in Newtonian  mechanics, we take what was just coordinates and   we double it to be coordinates and velocities.  And now we have what looks like a Markovian   description. This doesn’t work for an indivisible  system. When systems are sufficiently extremely   non-Markovian, you can’t do this. And I think this  was a little bit of tunnel vision. People thought,   well, you can always do this. So what’s so  interesting about very non-Markovian systems?   But if the system is non-Markovian enough, this  trick doesn’t work and you actually have something   that’s really non-trivially different. But then  what you can do is reformulate the Hamiltonian   system in what’s called the Hamiltonian  formulation. In the Hamiltonian formulation,   we rephrase what we were talking about, the  state space, the states, the positions and   velocities in terms of what are called canonical  coordinates, which kind of generalize the notion   of the position, and the canonical momenta,  which generalize the idea of a velocity. And   then we call the state space a phase space. The  terminology apparently goes back to Boltzmann,   because he was thinking in terms of the phase of a  pendulum or something like that, some oscillatory   system. Where is it in its motion, in its cycle?  What phase is it in? This idea is much more   general than that. We call this a phase space.  And in a phase space, we’ve got these variables,   the Q variables, which are like the generalization  of position, and the P variables, which are like   the generalizations of velocity, the 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 the Q and the P, and  then you uniquely get what the next Q and P are   at all subsequent moments in time. So this makes  the system look like it’s beautifully Markovian,   position and momentum are now on a perfectly  equal footing. The differential geometry speak   for this is we’re now working on what’s called the  cotangent bundle of the configuration manifold,   but it’s not necessary to conceptually understand  what’s going on here. But what’s interesting about   this Hamiltonian formulation is it looks weird.  It has all these enhanced symmetries. For example,   now that we’ve put the coordinates, the Qs,  which again generalize the notion of position,   and the Ps, which generalize momentum, we’ve put  them on this sort of very similar footing, and   they enter into the theory in this very equitable  way. We can now do changes of variables where   we can take Q and replace it with P, and P and  replace it with negative Q. And in so doing, you   could 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 reciprocal of the spring constant of the old,   and the new spring constant is the reciprocal of  the mass of the old, but you could also do much   more bizarre transformations. These changes  of variables, which are carefully designed   to keep the equations, the laws looking very  similar, are called canonical transformations.   And there is a beautiful connection between  these changes of variables of your phase space   and basis transformations in Hilbert spaces.  There’s actually a beautiful mathematical   relationship between them. It helped inspire Dirac  to introduce his formulation of quantum mechanics,   this sort of analogy between these two things.  And the analogy can be made even stronger through   a series of papers. There was a paper by Franco  Strocci in the 1960s called Complex Coordinates   for Quantum Mechanics, I think, and then a  paper in 1985 by Andrei Heslot. And that paper,   I can’t remember the name of the paper, but  it’s from 1985, where they make this analogy   much tighter. They show that any quantum system in  Hilbert space language can be rewritten in a way   that looks just like a classical Hamiltonian  system for a system of coupled harmonic   oscillators. It’s this beautiful framework,  I call it the Strocci-Heslot formulation,   and I think there’s like a YouTube video of a talk  I gave on it. If people want to see the details,   we can link to that. People can see how it works.  So the connection between this freedom to do all   these weird changes of variables that mix up what  you mean by the Qs and what you mean by the Ps,   you could make a new Q be Q plus P and a new  P, mix them up in all these bizarre ways that   make the fundamental picture very murky. Once  we’ve done this, it’s sort of hard to remember   what our original system even was. There’s a close  connection between that enhanced set of symmetries   and the basis rotations in quantum mechanics.  You also see the emergence of complex structure,   complex numbers in the Hamiltonian formulation.  There’s a beautiful way you could take the Qs and   the Ps and write the Qs as Q plus square root of  minus one, the imaginary unit times P, up to some   engineering dimensions. You have to get the units  right. But basically you can define a complex   variable and rewrite the whole picture in complex  coordinates, and it simplifies the mathematics in   a very beautiful way. And this brings the analogy  out with quantum mechanics even tighter. For those   viewers who know about Poisson brackets, if you  rephrase Poisson brackets in terms of these sort   of complex representations, it makes canonical  quantization look even more like clean. So   we have this incredible similarity. You start  with a non-Markovian system, in this case just   second-order non-Markovian Newtonian mechanics,  depends on coordinates and the previous time   coordinate. And we can reformulate it as a  Markovian-looking, beautiful, this Hamiltonian   phase-based 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 difficult  to do in Newtonian mechanics. They even lead   to a wave-like picture called the Hamilton-Jacobi  formulation, which led to Schrodinger discovering   wave mechanics. And there’s this complete analogy  where you could take an indivisible stochastic   system, which is also a non-Markovian system,  much more non-Markovian and probabilistic, the   system I just described to you, that I laid out,  and do this change of mathematical representation,   and you get a Hilbert space picture, which also  is very exotic-looking, and also has a very murky   sort of physical world picture, and also has all  these enhanced symmetries, these basis rotations,   and also sees the emergence of complex numbers.  The analogy is actually very close between   these two pictures. And again, that change of  representation to the Hilbert space picture is   called the stochastic quantum correspondence.  But now we can do all kinds of things that we   couldn’t do before, okay? So one example, why  is the dynamical equation of quantum mechanics   Markovian? It’s Markovian because you can just see  as you do this change of representation, you can   see how we took a non-Markovian thing and wrote  it as a Markovian kind of evolution at the cost   of introducing all of these weird new ingredients.  The phases, the off-diagonal entries, the density   matrices, interference effects, superposition,  all of these ingredients are the cost that you   incur by trying to represent what is fundamentally  not a Markovian system, an extremely non-Markovian   system, as a Markovian system. They’re the  prices you pay. We talked before about, like,   are these memory effects? Memory is not quite  the right metaphor for indivisible stochastic   processes. Traditional non-Markovian processes  require that you specify sort of conditional   probabilities conditioned in arbitrarily many  previous times. That’s very complicated and   has a lot of structure and contains a lot of  information. And you can legitimately ask, where   is that information being stored? An indivisible  process is actually much simpler. It doesn’t   entail the specification of all those higher  order non-Markovian probabilities. It’s much   sparser. All you’re supplied with are first order  conditional probabilities that don’t concatenate,   that can’t be divided, that aren’t Markovian. So  there’s actually less information and less memory,   much less memory, than is in a traditionally  stated non-Markovian process. So there’s no   question about where is the memory being stored.  It’s not that there’s memory per se. It’s that   the system’s evolution doesn’t depend only on the  present state. So memory is not quite the right   word for it, but there’s a kind of memory-ish  kind of thing. And that’s what’s being encoded   in all of those coherences and superpositions  interference, which otherwise don’t have any,   in the traditional textbook formulation, they’re  just math that produce empirical implications when   we do experiments. But we don’t have a meaning  that we can attach to them. Here, we can attach   a meaning. Where are the artifacts of taking  what is ultimately not a Markovian process and   forcing it to be in a Markovian formalism? But  we can go beyond that, right? So we can explain   why the equations look Markovian. We can explain  what the interference terms are and the phases   and the coherences and the superpositions. We can  explain what those things are. We can also explain   why the evolution law is linear. For a closed  quantum system, a system that is not engaging in   information exchange with its larger environment,  the evolution is given by a linear equation,   the Schrodinger equation if the system is  sufficiently smoothly evolving in time,   or more generally, unitary evolution.  These are linear. And the question is,   where does that linearity come from? It’s just an  axiom according to the textbook Dirac von Neumann   axioms. But in the indivisible approach, it just  comes right out of the change of representation.   It comes out of the fact that ordinary probability  has a linear law. If you’re given initial   probabilities, and you want to compute final  probabilities, and you’re using the conditional   probabilities that are given to you in laws, 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’s various terms for it, law of  total probability. But it’s a linear relationship,   and that linear relationship becomes the linearity  of time evolution of quantum mechanics, which,   so now that has an explanation too. And you might  go, well, what about unitarity? I mean, I didn’t   start my indivisible process, how did it know to  become unitary? It turns out that there’s a class   of indivisible processes called, they’re based on  what’s called a unistochastic transition matrix.   The term unistochastic goes back to a lecture  in like the late 1980s, but the idea actually   goes back, it’s a much older term. So Robert  Thompson introduced the term unistochastic,   but the original term was orthostochastic, and it  was introduced by Alfred Horn, a mathematician in   the 1950s. And he wasn’t studying stochastic  processes, he was just studying the analytic   properties, the pure math analytic properties  of stochastic matrices. And he noted there was   a particular kind of stochastic matrix, the kinds  of matrices that show up in stochastic theories.   These matrices are matrices with non-negative  entries, they’re square, they have non-negative   entries, and their columns all sum to one. But  there’s a particular subclass of them that he   called orthostochastic, today we would call  them unistochastic, that have very beautiful,   interesting analytic properties. From  the standpoint of a pure mathematician,   they have very neat properties. The idea of  building a physical stochastic process using   these as the matrices that contain all of your  conditional probabilities, that is new. I mean,   that wasn’t an idea that people had proposed.  So you could just say, the particular kind   of indivisible processes I’m interested in are  unistochastic processes, and these are exactly   the processes that when you run them through the  stochastic quantum correspondence, on the other   side you end up with unitary evolution. Now  you might go, that’s a little dissatisfying   because that doesn’t explain why evolution is  unitary. You had to assume a particularly special   kind of stochastic process, of an indivisible  process that it was unistochastic. The technical   definition is unistochastic process is a process  where all the conditional probabilities are   related in a very simple way to the entries of  unitary matrix. That makes it seem a little bit   too canned. But there’s a theorem that’s proved  in the first of the papers, the stochastic quantum   correspondence paper, that even if you don’t start  with a unistochastic process, even if you start   with just a completely boring, ordinary, generic,  indivisible stochastic process, you do the change   of representation to the Hilbert space picture,  you can always write that process as what’s called   a quantum channel. A quantum channel is also known  as a linear, completely positive, trace-preserving   map. These are well-studied in the quantum  information literature. It’s not obvious that you   can do this. But you can. It’s a simple, yeah. The  mapping from the indivisible stochastic processes   to the Hilbert space picture can be represented by  a quantum channel, or is a quantum channel? So you   start with your indivisible stochastic process,  which is a probabilistic, it just says given where   the system is now, this is the probability it’ll  be there later. You run it through the stochastic   quantum correspondence, you now have density  matrices and state vectors, all this stuff show   up. And the time evolution is now carried out  by what’s called a 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  unistochastic. In general, if it’s not originally   unistochastic, then the time evolution operator  will not be unistochastic. But it turns out you   can still write it as a quantum channel. This time  evolution operator that shows up on the other side   looks kind of weird, but it turns out it can be  written as this very well-studied thing called   a quantum channel. And quantum channels can be  turned into unitary evolution by another change of   representation. Borrowing a theorem by Steinspring  in the 50s, the Steinspring dilation theorem,   by increasing the dimension of your Hilbert space  in a bounded way, for those who care, it’s going   from an n-dimensional Hilbert space to an n-cubed  dimensional Hilbert space at the most, which   corresponds to adding one or two extra degrees  of freedom. You can implement the evolution as   unitary evolution anyway. And this is really cool  because it means that even if you didn’t start   with a special kind of indivisible, you start with  a totally generic indivisible stochastic process,   all it’s saying is given the configuration of the  system here, here’s the probability distribution   of where it will be later. When you run it  through the stochastic quantum correspondence,   get a Hilbert space picture, you go, oh no, it’s  a Hilbert space picture and I see a lot of stuff,   but the evolution is not given by a unitary  operator, it’s not given by the Schrodinger   equation, that’s not great. It turns out with a  simple change of representation, one second change   of representation, you can implement the evolution  in a unitary way by what’s called the dilation of   the Hilbert space. And this gives, finally,  an explanation of where unitarity comes from,   where that axiom that the time evolution  should be unitary, it emerges from this   set of transformations. So it’s really nice to be  able to explain where these things come from. And   now I can get to a question that came up from a  couple of people in the comments. It seems like we   started with this indivisible stochastic process,  we end up on this other side, and it kind of seems   like one basis for the Hilbert space is special,  right? So a Hilbert space is a vector space, all   of the objects, the 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 a graph paper, right? An arrow  on graph paper, there’s an x-axis and a y-axis,   and you can ask, how far do we have to go  along the x-axis and how far along do we   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’s got this x component and this  y component, those are the components of the   vector. But if I change my axes, if I like turn  them a little bit, without changing the arrow,   the arrow’s the same but the axes have tilted,  well then I have different distances now. I have   a new distance, the x prime distance and the y  prime distance, the new distances. So a single   vector has different component representations  depending which basis you use. And the Hilbert   spaces of quantum mechanics have this feature.  In quantum mechanics, the different bases are   associated with different kinds of things you  might want to measure. So for example, if your   vector is pointing exactly along a certain axis,  it means that if you measure that observable,   you’re definitely going to get that result and  definitely no other results. But if you measure   a different observable, one whose axes are tilted,  now your vector is not pointing exactly along that   direction anymore. It’s got some component along  one axis and some component along another. And the   Born rule tells you how to take those components  and compute probabilities. And so what we discover   is that even if one observable has a definite  result because the arrow is pointing exactly along   one axis, a different observable with different  axes will give probabilistic results. And if you   somehow change your arrow so it’s pointing along  one of those axes, now the first observable will   not have a definite result and this is just the  uncertainty principle. That for certain pairs of   observables when you know one with certainty,  when measurements are guaranteed to yield a   definite result for one of them with certainty,  measurements are not guaranteed to yield definite   results for the others with certainty. This is  related to the ability to change bases. You may   wonder, 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 a  lot like in Hamiltonian mechanics. We start with   a physical system with an actual position and a  particular momentum that has a clear meaning. It’s   the momentum, it’s like for some systems it’s mass  times 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 all of a sudden it’s  not clear what the new q means, what the new p   means. And you might go, well, Newtonian mechanics  must be wrong because Newtonian mechanics didn’t   have this independence. Newtonian mechanics  picked out a particular q and p. But Hamiltonian   mechanics treats them all like they’re the  same. There’s this symmetry under changing your   definition of q and p. This may just mean that  Newtonian mechanics is wrong because it doesn’t   have canonical transformation dependence. That’s  very analogous to what’s going on here. It’s true   that you start with a particular system in the  indivisible stochastic side of the picture. The   system has configurations. Those configurations  correspond to a particular basis on the Hilbert   space side. Once you’re on the Hilbert space  side, now you have the freedom to change your   basis however you want. But because the theory is  mathematic, it’s just a theorem. You can go from   one picture to the other. And this Hilbert space  picture is mathematically a representation of the   first picture. Just like in Hamiltonian classical  mechanics, you have the freedom to do these basis   transformations. They’re totally available. The  one lingering question you might ask now is,   well, but can I measure other observable? The  ones that were tied to the configurations are   ones that will be very simple 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? Those can also be measured. What’s going  on with those? And the answer is it’s just like in   Bohmian mechanics. If you set your system up and  couple it to a measuring device, and the measuring   device could measure one of the beables, one of  the ones that tightly corresponds to the original   configurations, it will passively reveal what the  system had as that feature. But if you change your   measuring device, just pick up a quantum textbook,  look at measurement, like how they formulate   measurements in terms of unitary transformations.  And just change your measuring device, now it’s   gonna measure a different property, measure one  of the emergibles. You run the exact same process.   The measuring device will stochastically end up in  one of its measurement outcomes with the correct   probability given by the Born rule. It just comes  out of the formalism. But the thing it’s measuring   is not a fundamental feature of the system. It’s  measuring really like an emergent pattern of the   mutual dynamics of the system itself and the  measuring device measuring it. Some properties,   you’re passively revealing what was already  there. Those correspond to that special basis.   And properties that don’t correspond to the  special basis can still be measured, and they’ll   still produce results on measuring devices. And  the measuring devices will still stochastically   end up in their correct readout configurations  with the correct probabilities. And as far as   the measuring device is concerned, it has measured  something just as real as for a beable. But what   it’s really measured is one of these emergent  patterns, these emergibles. And so from the   point of view of the outside world, the emergibles  are on the same footing as the beables. Together,   the beables and the emergibles collectively form  the full, we call it a non-commutative algebra of   observables for the quantum system. So this deals  with this question of basis dependence. And this   isn’t new. So another way to formulate quantum  mechanics is the path integral formulation. So   people may be familiar that there’s this sort of  Hilbert space formulation and there’s this other   formulation in which to predict probabilistically  where the system will end up, you’re supposed   to somehow start with initial configuration and  write down every candidate trajectory the system   could have. All the trajectories, ones that  do not satisfy the classical laws of physics,   assign each of them a special numerical factor.  Add all the factors together as this very tricky   integration called a functional integral. And get  a complex number out that when you mod square it,   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. Paul Dirac was the   first to introduce it. All the way down to like  you slice up the time interval into little bits   and you introduce complete sets. It’s a beautiful,  beautiful paper. He was trying to understand what   is the role of the Lagrangian. So before 1932,  people had formulated quantum mechanics in the   language of Hamiltonians, in the language of  Hamilton-Jacobi theory. And Dirac was just very   curious. He wanted to know, does the Lagrangian  formulation show up in quantum mechanics also?   And he found this very beautiful way to do it  using these sort of functional integrals. But   Dirac was just content to write it all out, like  formally state everything, and not turn it into a   machine for calculating things. Ten years later,  Richard Feynman picked it up while he was a PhD   student. And this was like in 1942, he was a PhD  student at Princeton, also again a student of John   Wheeler. And he turned Dirac’s formalism into an  actual recipe for calculating things. And then a   few years later, he ended up publishing a review  article, talking in detail. And we can post all of   these to the YouTube video if you want, or people  can see all these papers. So a few years later,   he wrote a review article about all of this. And  he says at the beginning, there’s nothing so far   that I can do with this that cannot be done with  ordinary methods. You can imagine someone saying,   well, then what good is it? If it only makes the  same predictions as ordinary quantum mechanics and   you can’t do anything with functional integrals or  path integrals that you couldn’t do with earlier   methods, what use is it? And by the way, it also  picks out a basis. Because to do the path integral   formulation, you have to pick a basis. For  example, when you do path integrals for particles,   usually what you do is you pick positions.  You pick what’s called a position basis and   do everything with positions. You don’t usually  do the path integral in other bases, you can.   But any particular choice of how you form a path  integral picks out one basis. So you could say,   this is basis dependent. You could say it doesn’t  do anything that we couldn’t already do. It’s a   weird picture, and it was for a long time. And  then eventually people discover there were some   calculations that were just too hard to do in  the traditional approach. Today, if you want   to formulate a non-Abelian gauge theory, like a  Yang-Mills theory, like QCD. You’re probably not   going to want to do it using the canonical Hilbert  space approach. You’re probably going to want to   do it with the functional path integral approach.  Eventually, and it took many years, I mean from   1932 until when people really needed these decades  for people to realize there were some things that   now we can 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 doesn’t obviously do  anything that you couldn’t do otherwise,   even if there aren’t any obvious immediate  applications as the sort of thing that may be   10, 15, who knows? Feynman himself said that any  good theorist should know a bunch of different   ways to do the same thing. Because when you  formulate a theory in multiple different ways, you   discover different knobs you can turn, different  things you can do that might have been harder to   imagine doing in one formulation that are easier  to imagine doing in another formulation. So yeah,   so that gets this sort of basis independence  question. We can get to some of the other   comments and questions people have had, but let  me pause there and ask if you have questions   before we go on. So let’s see if I understand this  correctly and I can simplify this. So Markovian,   let’s understand what Markovian means. This means  your system, you look at the present state and you   can determine the next state. Okay. When we  say the present state, we tend to think, oh,   Newtonian mechanics is Markovian because you say,  well, let’s specify the position and then maybe   the mass and then the velocity as well now. But  then you’re saying, well, what is the velocity?   It’s actually the position just an infinitesimal  time ago. So you could introduce a new variable   called velocity, or you could just think of  what the time is now and what the time was ago,   making it non-Markovian because it’s now no  longer the present. This is equivalent, I believe,   it’s equivalent to Newtonian, the Newtonian  formulation. But in what we’re taught as the   Newtonian formulation, you’ve introduced something  new. So you’re saying that, look, in that similar   manner, we can make an analogy here where  there’s these indivisible stochastic processes,   these little guys operating around here. What  exactly are they? I’m going to ask you about that   afterward, but they’re operating 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 we make   it Markovian, that just as in the Newtonian  case, we introduce something new, that we’re   introducing something new and those correspond  to linearity, superposition, interference,   and so on? Yeah. Yeah. And complex structure and  the ability to change bases and all this stuff,   they all, it’s exactly right. It’s exactly right.  Okay. Okay. So now the question that the audience   has or had is how do you deal with interference  experiments? Also, we can get to it in order,   if you like, Bell, what does it say about the  Bell’s inequality and what are the beables   exactly in this framework, this formulation? Let  me start with the interference experiment ones.   Let’s start there. So the simplest answer to that  question is if there’s a mathematical duality or   representation that takes you from an indivisible  stochastic process to this Hilbert space picture,   and let me just quickly say, the mapping  is not one-to-one. It’s many-to-many. A   given indivisible stochastic process may have many  Hilbert space representations and a given Hilbert   space representation can represent many different  indivisible stochastic processes, but this is not   new. The same relationship holds for Newtonian  systems and Hamiltonian formulation. A single   Newtonian system can have multiple different  Hamiltonian formulations and a single Hamiltonian   formulation can represent many different Newtonian  systems. So this is not like a new thing. Okay.   But the point is that these indivisible systems do  have this representation in this sort of Hilbert   space picture, and the representation is just  math. I mean, every Hilbert space picture can   be regarded as an indivisible stochastic system  in disguise and vice versa. So any predictions   you make with a Hilbert space picture are going  to be preserved. The explanation though is going   to be different. So let’s take the double slit  experiment, and this is actually going to be   helpful because I think one question someone had  was, can I give a hello world example? You know,   computer programming, the simplest program you  read is something that just prints hello world.   What’s the simplest example I can give? I’ll give  you a simple example. Let’s consider a double slit   experiment, and we’ll make it so simple, we’re  going to coarse grain it. That’s the term of   art. We’re going to coarse grain it to simplify  it. So instead of the particle being able to   be just like anywhere, we’re going to coarse grain  the description so that we’re only talking about   is the particle in the upper part of the chamber  or the lower part of the chamber, just upper and   lower. Okay? We’re going to put the particle  into a qubit, into a two quantum state system,   okay? It’s a two state system. Upper chamber,  lower chamber. The particle is upper chamber,   lower chamber, it then in a, and we’ll just  imagine something is like sliding it forward   and just some like, just keep it super simple.  We’re sliding the particle forward, it encounters   a wall, and the wall’s got an upper hole and  a lower hole, right? As walls do. As walls,   well, not all walls have upper holes and lower  holes. This particular wall is an upper hole and   a lower hole. And then beyond the wall, there is  a projection, a detection screen, a screen where   the particle can land. And we’re going to coarse  grain that, the particle can land in the upper   part or the lower part of the screen. So this  system is sufficiently simple that it actually   encompasses many systems you might deal with in  quantum information. Mach-Zehnder interferometers,   there were some questions about Mach-Zehnder  interferometers and the Elitzer-Vaidman bomb   tester example. These are all based on a very  similar kind of very simplified coarse grained   version of the double slit experiment. Now, I’m  not going to be able to do the calculations in the   air. But when I teach my class on philosophy  of quantum mechanics, I do go through the   calculations and I’ve got a nice write up. And if  you want, I can send you a draft of it. It’s not   in paper yet, but I can send you the draft and  show you all the steps. But even this example,   right, because, you know, we’re filling in all the  details now in the traditional textbook approach.   You basically set it up and then you measure  the end and you don’t really talk about what’s   going on ontologically, physically in between. I  mean, you, you write down like a wave equation,   you think in terms of waves. But of course, the  moment you go beyond one particle to 10 or 20,   something the wave picture is now in a  20 dimensional space, it doesn’t make any   intuitive sense. We’re doing it very differently.  We’re actually going to like follow the particle   and like write down the probabilities, write  everything down. And what you do when you do this   is every time you run the experiment, one particle  going through the particle lands in the upper   chamber, upper part of the detection screen or the  lower part. And you do this experiment many times.   Every run of the experiment, the particle lands in  just one spot, either the upper part or the lower   part. For many, many, many repetitions of the  experiment, you build up a histogram, you build   up like a distribution of landing sites. And what  you find is those landing sites look just like   the distribution you would have gotten if there  had been 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 the indivisibility. Why? How can we,  so there’s a limit to how much we can say about   like, because indivisible processes are by their  nature really unintuitive. Physical theories can   be unintuitive. That’s the thing about physical  theories. But in this simple case, at least,   we can actually shed some light on where the  interference is coming from in this very simple   example. And why there isn’t interference when  we do this like with a Newtonian system. In a   Newtonian system where you’re just like throwing  rocks at the wall, one at a time, you don’t, over   many landing sites, get this distribution, this  pattern. Why? One way to understand it is that   if you’re throwing the rocks and they’re being  thrown either deterministically or if we want to   even like let it be probabilistically. The way you  would say it is you would say, okay, well, I throw   the rock. It gets to the wall with the holes in  it. Either it goes to the upper hole or the lower   hole. Let’s suppose it goes to the upper hole. Now  that we know it’s at the upper hole, let’s start   there and then use the laws of Newtonian mechanics  to figure out where it goes. If it goes to the   lower hole, let’s start there and use the laws of  Newtonian mechanics to figure out where it goes.   But notice what I did there, I divided up the  evolution. I assumed that Newtonian, that the   laws given to you in the system are of the form  that you can take the system at the intermediate   location, at the holes. And Newtonian mechanics  gives you the laws for what happens next. And when   you do that, you get no interference, you get the  standard pattern. In the indivisible formulation,   you’re not given those laws. The dynamical  laws that describe where this particle is   going do not have the feature that when they  get to the middle wall and go through. I mean,   the particle at any moment is only in one place.  It’s either in the upper hole or the lower hole,   still true. But once it’s there, you can’t say,  all right, let’s suppose it’s in the upper hole.   Let’s restart the evolution and then the theory  doesn’t give you a law for that. There’s simply   no dynamical description for starting at the holes  and then seeing what comes next. It’s not supplied   to the laws. That is, the indivisible law that  describes the entire experiment from beginning   to end is more general. There’s simply a more  general class of such indivisible laws that   fail to have this divisibility property at the  holes. If we demand that the laws be divisible   at the holes, we’re singling out a subclass of  indivisible processes. Cuz you could just imagine,   let me not consider the most general indivisible  process. Let’s consider just indivisible processes   where you’re 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 limit yourself  to just those indivisible processes, you will   see almost no interference. There’ll be a little  bit left cuz there’s still some indivisibility,   but it will mostly be gone. But if you don’t  limit yourself to those special cases, you   will in general see interference. So the failure  of Markovianity at the holes, the inability to   restart the evolution and have in your hands the  laws for what comes next during the holes. The   failure to have that means that you can have the  kinds of laws that will lead to interference. Now,   there are modifications to this experiment. For  example, what if you look to see what hole the   particle goes through? And we can implement  this very simply by adding another two-state,   two-configuration system near the holes. Suppose  I’ve got a little second particle, little second   device with two configurations. And all it does  is it stays off in its initial off configuration,   if the particle goes to the upper hole.  If the particle goes to the lower hole,   it switches it on, okay? That’s all it does,  it just does these two things. You can model   this very neatly, you put it in. You actually  wanna give this thing deterministic laws. You   want this to deterministically have 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 changes to on. You can implement   that with a pretty easy set of equations, give  it that deterministic behavior. Now when you   evolve the system, the interference goes away. You  can just, I mean, you just rerun the indivisible   process and you’ll see that there’s just no  interference anymore. What’s really nice,   and this is actually a really nice example  of this, is if you throw away the information   that was in that little detector particle, the one  that was detecting it. Or if the detector particle   communicates with the outside world and  that information is now irretrievable and   it’s not accessible to us. And what we can do is  classically marginalize. So marginalization is   when you have a joint probability distribution.  It’s probability for like two things. And we sum   over one of the variables to drop it out of our  awareness. This is a standard move in ordinary   probability theory. When you do that for the time  evolving process, the time evolving process for   the original particle suddenly has a division  event, a division that is now available at the   walls. And so what was an indivisible process  is now divisible at the walls, thanks to the   detector particle that we have marginalized out.  And this is another way to see that divisibility   is now restored at the walls and gives another  way to understand why the interference effects go   away. But there are a couple things to say about  this. Number one, this division event is related   to decoherence. I mean, the process by which  we marginalize is just in stochastic language,   which in Hilbert space language we would call  decoherence. If you look at density matrices,   you’ll see that the division event seen at the  level of Hilbert space corresponds to off-diagonal   trees disappearing. That’s what happens in  decoherence. But the crucial thing here is there   was no wave function here. The particle always  had one location as it was moving through the   apparatus. There’s no superposition. There’s  nothing to collapse. So if the question is,   isn’t a division event just collapse? Well, no,  there was no wave function. The particle was   not superposed between being in the upper and  lower parts of the chamber. Nothing ever had   to collapse. The division event is what you would  say on the stochastic side of the correspondence,   what decoherence is on the other side. But because  there was never a superposition, there’s no need   to now single out one outcome or collapse anything  or project anything. So the measurement problem,   this basic fact that in the textbook formulation,  you bring in a measuring device, it becomes   entangled, you get a superposition, now you have  all these superposed possibilities. And then   somehow if somewhere in the superposition there is  a measuring device, we’re supposed to collapse it   somehow, but why and what magical property of  measuring devices makes things collapse? This   is the measurement problem. It just fails to  happen in this picture. There’s never a need   to get anything to collapse. So I would say that’s  the simplest Hello World example, and has the side   effect of also explaining what’s going on in the  double slit experiment and what interference is   happening here. So is the division event your  version of what traditionally is thought of as   collapse? And are division events just what occurs  when you integrate out over marginal probability?   That’s right. So you marginalize over whatever  has read out the configuration of your system,   and then your system now has what looks like  divisible stochastic dynamics. And this certainly   plays a functional role in the theory that is  analogous to what decoherence and then collapse   plays in Hilbert’s, in the Dirac-Van Leeuwen  axioms. And certainly if you’re going to write   this story in Hilbert’s based language, you would  use decoherence and collapse to explain what’s   going on in Hilbert’s based picture. But now we  have underwritten those weird axioms that seem   very ad hoc and mysterious, with a very boring  stochastic process where there is no wave function   to collapse. And when the measurement happens, in  this case, just the readout from a little detector   bit, there’s just a classical marginalization that  causes the indivisible dynamics to have an event   when you can divide. It’s momentarily divisible,  and then the inference goes away. So I want to   bring up something that you just mentioned, which  harkens back to earlier in the conversation. So   you said, in the Newtonian picture, you throw a  ball and there are two slits, two holes. And then   you notice that it goes over the top one, you say,  okay, let’s just start the evolution from here or   the bottom one, you go from there. And you said,  well, this doesn’t apply in the quantum case or in   the indivisible case because you can’t divide.  And what was interesting to me was you said,   notice that so-and-so. And what you said, which is  notice that you said, hey, you can look at it now.   So in other words, you can divide your time. I was  thinking, okay, I didn’t, as I was following you   along, I didn’t notice that I was making that  assumption. And earlier in the conversation,   you said, what philosophers are extremely trained  in is noticing implicit assumptions. Yes. So this,   even though this is, even though it’s not, well,  let me read about Hegel because Hegel will inform   my physics. It’s not that per se, even though 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. Yeah, I mean, it’s  important to know that philosophy is a huge   discipline, right? And there’s ancient Greek  philosophy. There are all kinds of philosophies   associated with different areas of the world  historically. And in the Western tradition,   so to speak, there’s early modern philosophy.  And then you develop this sort of weird divide   between the continental philosophy and analytic  philosophy. And then where does philosophy of   science fit in? Philosophy of science is probably  closer to analytic philosophy in a lot of ways.   There’s some dispute over exactly whether it’s a  part of analytic philosophy or not. But a lot of   the tool sets that one uses in philosophical  physics do seem to come from the analytic   tradition in philosophy. This is the part of  philosophy associated with logic and metaphysics   and philosophy of mind, and to some degree,  depending on how you phrase things, philosophy   of science. So Hegel is sort of more associated  with the continental tradition in philosophy.   And there’s just been, I think, less interaction  between the continental tradition and physics. I   think what a lot of people who maybe have had  some exposure to philosophy, maybe not a lot,   when they think about how useful philosophy  is to physics, I think they’re often thinking   about the parts of philosophy that are not super  connected to math and physics. Sorry, how is fear   and trembling gonna have the implication about  F equals MA? Right, but I think a lot of those   people would say, Bursch and Russell. Well, of  course, Bursch and Russell is a good thing to   say about physics. He wrote a book on relativity,  and he’s a mathematician. But he was an analytic   philosopher. He was like one of the towering  analytic philosophers, right? Quine, and so   the early people who developed quantum physics,  and the early people who developed quantum   mechanics were deeply enmeshed. In Wittgenstein,  I mean, there’s a beautiful interview. I would   also recommend licking it. It’s from the 1970s  by Pete and Buckley who were doing an interview   with the CBC. It’s an interview with Werner  Heisenberg toward the end of his life. It’s a   fantastic interview. I mean, it’s amazing to  hear him talking and actually hear his voice   and hear him describing 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 Tractatus, and  he’s not unique. I mean, he wrote a book called   Physics and Philosophy. And the book is filled  with Kantian metaphysics, and that’s the book   where he has this chapter, it’s from 1958, where  he introduces the Copenhagen Interpretation, where   he tries to formulate it. We’ll talk a little  bit about that. And he’s arguing with Schrodinger   and Einstein. And they’re all arguing over who’s  the proper, like who’s more correctly representing   Kantian philosophy. And you had neo-Kantians like  Greta Hermann. We talked about Greta Hermann. And   all these people were talking, and they were  all connected with. So there was an incredible   amount of cross-pollination between the  analytic philosophers of the early 20th   century and physicists. Physicists themselves  were thoroughly trained in philosophy. I mean,   there’s another paper you should link to.  This is a paper by Don Howard. It’s a paper   in Physics Today from 2005. It’s called Albert  Einstein as a Philosopher of Science. And it’s   all about just how much philosophy Einstein  was doing. He’d read Kant’s Three Critiques   by age 16. Wow. And- That takes 16 years. I mean,  it’s what he did, right? He was super interested   in philosophy. When he went to university, there  were mandatory courses in philosophy of science.   Both at the university and then after he left  university, he ran a philosophy of science reading   club. He was deeply immersed in Spinoza. He was  very inspired by Ernst Mach. He even wrote an   obituary for Ernst Mach in which he talks about  the importance of epistemology. He says, the   ablest students, the ones who are most independent  of thought, are the ones who took epistemology the   most seriously. Like he’s, this is 1916 when Mach  died. And he was a huge fan of Schopenhauer also.   And so was Schrodinger. Schrodinger cat paper has  sections with words like epistemology in them,   like in a physics paper. And Bohr was philosopher.  I mean, they were all like… And I find this kind   of striking because there’s this attitude today  that like, who needs philosophy? But the people   who gave us the biggest revolutions in modern  physics, quantum theory and relativity, were all   either deep, strongly connected to philosophers,  or they were interacting with philosophers,   or they were philosophers, or they were at least  very thoroughly trained in philosophy. If you were   trying to create new breakthroughs in physics,  wouldn’t you take that as an example? Now, look,   I understand that there are a lot of philosophers  who are not trained in physics. And people who are   not trained in physics sometimes say things  that are not very helpful for physics. But   the answer to this is very simple. We need  people who are thoroughly trained in physics   and thoroughly trained in philosophy so that they  don’t say nonsense things. So they actually make   meaningful contributions and help bring these  two disciplines together. Because I think that   would fertilize the soil, so to speak. I mean, so  much of modern physics has its roots in ideas that   were generated during that incredibly formative  period in the early half of the 20th century,   the first half of the 20th century. And we’re  facing a lot of very deep problems today. You   know, Einstein, I think in a paper, I think  it’s mentioned in the Howard paper, in 1936,   Einstein wrote a paper called Physics and Reality,  which he talked about how we’re living in a time   in 1936, when there’s so much we don’t understand  about nature, and there’s so many deep questions   we have. And this is exactly the time you need  philosophy. You need to be steep in philosophy and   think very philosophically about things carefully  and rigorously using all these tools that I   called philosophical physics, you know, to avoid  falling prey to slogans, to avoid falling prey to   groupthink, to being able to have an independence  of mind. One of the most famous things that   Einstein wrote about philosophy is a letter he  wrote to a philosopher of science named Robert   Thornton in 1944, in which he said that when  he meets many scientists of his time, he feels   like he’s meeting someone who’s seen many trees,  but has never seen a forest. And that a thorough   training in philosophy gives people the kind of  independence of mind that distinguishes, you know,   a mere artisan from a real pursuer of truth. I  think that makes a lot of sense. And in my own   experience, having taught courses here for a long  time, the students who were most philosophically   curious, many of whom took philosophy  courses, upper level philosophy courses,   often made the strongest physicists. They were  very careful in how they formulated things. They   knew the difference between deductive argument and  an inductive argument and one that was neither. So   here’s the thing that happens frequently, okay? So  on the one hand, if you’ve got rigorous, credible   premises and you follow them in a rigorous logical  mathematical way to conclusions, you’ve got a   deductive argument, you’ve got a math proof. We  like this. Science often doesn’t take that form.   Sometimes you prove theorems in science, but a  lot of the time we’re making inductive arguments.   We start with credible premises. We call it the  evidence. And then we use arguments that are more   or less rigorous. They can’t be maybe perfectly  rigorous. And we arrive at a conclusion that is   strictly speaking stronger than the premises.  Something that is not necessarily entailed by   the premises, but is strongly supported by the  premises. We assign some evidentiary credence   or probability. We say, I’m this certain that  my conclusions are true, given the premises,   which are very credible and rigorous and reliable  and my reasoning. That’s an inductive argument.   And a lot of science is inductive arguments. And  then what we do is we take the conclusions and   usually they’re like a theory or a prediction and  we go out and measure them and we get confirmation   and we feel stronger that we’ve done a good  job. But there are a lot of arguments in some   areas of physics that are neither deductive or  inductive, where the premises are themselves wild   speculations. And you take these wild speculations  and then you make arguments that are themselves   wildly speculative. And you arrive at conclusions  that are speculations on top of speculations   on top of speculations. And I just don’t even know  what to do with something like that. I don’t know   how to follow those arguments. And I really don’t  think that someone who’s like thoroughly trained   in philosophy is going to find those sorts of  arguments very credible. And I think especially   at a time when in certain areas of physics, we  are very limited in our experimental data. And   we’re trying very hard to be very careful in  our reasoning. This is exactly the time when   you want the kind of rigorous scrutinizing that  you get from a training in philosophy. So again,   this is like a second appeal for anyone 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 particularly important. Okay, so you said  independence of thought is what philosophy trains   you to to have also precision of thought. So Scott  Aaronson is someone that we brought up earlier for   the two brought up. And Will Hahn here, also,  you can’t see him, but he’s behind the cameras,   professor at Florida Atlantic University, helped  put on this event called MindFest. And Scott   Aaronson was there. And Scott Aaronson said, Okay,  well, he didn’t say this. But the implication was   that most physicists, most scientists think of  philosophers as just engaging in this ill-defined,   unfalsifiable nonsense that’s incoherent. And he  was saying when he was speaking, he never had to   be so precise in his speech as he was around a  philosopher. Yeah, philosophy seminars. So there   are many people maybe who are watching who’ve  never been to a philosophy seminar before. Maybe   many people watching haven’t been to a physics  seminar. That’s okay. I mean, people come to   this. I mean, you’ve got people who are brand new,  maybe they’re, they’re students, maybe they’re,   you know, in secondary school, maybe earlier than  secondary school, I don’t know. Or maybe they just   got 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, hopefully. But there are many people   who maybe have been to physics seminars and  don’t know what a philosophy seminar is like.   And I will 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 the way they usually work is, so  physics seminars usually work like this. There’s   a speaker who talks for 45 minutes, maybe an hour,  depends on the length of the seminar. People often   interrupt like the middle of the seminar. They’ll  just make questions, they just sort of interrupt   in the middle. And someone who’s maybe not very  practiced, who’s giving the talk may get derailed.   And this can sometimes lead to problems, but  hopefully everyone’s respectful and the questions,   if there are any, are kept brief. And then at  the very end of the seminar, they all thank the   speaker, they clap, they thank the speaker. And  then they say, all right, we’ve got five minutes   for questions, any questions? And, you know, most  people don’t, I mean, they can’t, I mean, there’s   just no time to really ask a substantive question.  A lot of people feel very nervous because they’re   like, oh, maybe there’s a more senior person here,  a professor who wants to ask a question and I   don’t want to interfere. Or if there’s only going  to be like time for one question, I don’t want   to ask a question that’s going to be like a bad  question. So people like often feel very nervous   about asking questions and there isn’t really a  good substantive dialogue. In philosophy seminars,   what often happens is you’ll have a talk, half  hour, 45 minutes, sometimes they go an hour,   then there’s a break. People go and they  take five minutes, they get refreshments,   they come back, and then there’s like an hour of  discussion, right? And the discussion is often   the most interesting part of the seminar, right?  And because there’s like an hour, everybody asks   questions, the students ask questions, because  no one is afraid they’re asking the one question.   No one’s afraid they’re going to look bad because  there’s going to be 10 more questions after their   question. And people can really have a substantive  discussion and dialogue. So that’s great. And I   actually really like the culture of these seminars  because they’re very welcoming. A lot of times   they’ll say that students get to go first because  they really want to prioritize students asking   questions. But I will tell you, the expectation  of the precision of your language is high, right?   If you say something that is not very carefully  stated, people will immediately say, I’m sorry,   that’s too vague. And you like precisify that. So  I think there’s this attitude, I think among some,   you know, some, I wouldn’t say there’s a lot  of scientists who are very familiar with this,   but I think some who think that philosophers  are just making stuff up and we’re very,   very vague and we’re just sort of, but, but if  you’ve been to a philosophy seminar, it’s quite   the opposite because you don’t have the ability  to rely on empirical data. You can’t just say,   well, I don’t need to explain it. Just look  at the data. You rely on the strength of your   logical reasoning in a very significant  way. And I think that could be brought   to bear in how we do physics more than we  currently do it. I don’t know if you saw   some of the lectures on TOE. I hope to bring  some of that to it. So like with Yang Hui, he,   he was going on and he’s like, I like this because  Curt, normally 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  whenever I say something that’s not sufficiently   sharp and rigorous. And that’s it. So this reminds  me a lot more of the philosophy seminars that I go   to, and that’s really nice. And look, there  are many things I think that your program is   doing right. I mean, you’re informing audiences  of, of interesting ideas from all directions.   You’re inspiring, but I think you’re also modeling  a kind of dialogue that I think we need more of in   academia, in science and philosophy, generally  speaking, holding people accountable, having   extended like discussion, really getting to the,  the questions, really getting to the deep parts of   people’s ideas, not letting people get away with  slogans, you know, and physics is a lot of slogans   that people just, they hear someone very prominent  say, and then they just repeat it. Right. I mean,   like really like you’re taking this apart. And  this is just not like a general public service   announcement. Cause I know there are a lot of  people who are watching who are not scientists   yet, or maybe ever, maybe this is just not the  direction they want to pursue. And maybe this is   like just some advice, right? Obviously watching  your podcast series is a great move. That’s   great. But, you know, people will sometimes  tell folks, well, you know, you really can’t   contribute to science or philosophy, whatever,  until you’ve done the requisite training,   you need to do an undergraduate program. You need  to read books. You need to take coursework. You   need to get graded on them. You need to do exams.  You need to, to like actually learn all these   techniques. You need to learn how to do this in  physics. It means learning Newtonian mechanics,   learning electromagnetism learning thermodynamics,  learning quantum mechanics, depending on what   direction you go. And you may learn astronomy  or, or biophysics or computational physics or   high energy or whatever it is that you will learn.  But like really do all of that, do all the problem   sets, learn everything, take the time. This is  a year’s long process of rigorous training. 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 many people  don’t know that by the way, that PhD programs,   at least the United States in the sciences are  funded. You don’t pay to go to graduate school   for a PhD. It’s important to know that when I was  like learning about science, I thought you had to   pay to do a PhD program. And I thought that was  important, but you actually get paid to be in a   PhD program in the sciences. It’s important for  people to know. And a lot of people look at that   and they think it’s insurmountable. They’re like,  but I have an idea. I have a great idea. I just   want to contact a physicist and tell them my idea  and have them work on it. And I’ll just say is   you really, really need to do the training first.  Cause there’s just so much you have to learn. It’s   like Picasso was this amazing artist, but he had  to master traditional techniques before he could   go and break them. And I know a lot of people  will say, but if I learn all the techniques and I,   I spent all the years learning all of this, one,  I just become like everybody else. When I imbibe   all the same conventional wisdom and all the  slogans, that is a risk. So what I would tell   people, if you want to embark on this, on this  journey, and it is an amazing journey. I mean,   learning physics has been, it’s like, it’s, it’s  incredible. If you love physics and you spend   years learning it, it’s the most incredible thing  you could imagine. You do have to work a little   bit not to get absorbed into sort 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. Sure. Sometimes you discover that the ideas  will continue to work. Sometimes you’ll discover   that they don’t work. That’s fine. But you also  just, every time you learn to do a technique,   you learn how to calculate something, you learn  how to calculate the energy eigenvalues of a   one-dimensional quantum mechanical system, or you  learn how to calculate scattering amplitudes in   a quantum field theory or whatever. You want to  separate out the methodologies learning, like, how   do I calculate something? How do I do something?  How do I model something? From the ideology.   Because people will say, they’ll say, well,  you said you calculate it, and what this   means is that what’s going on in nature is,  and that’s the moment you want to be like,   whoa, hang on a second. Hang on a second. I  follow the calculation, it’s empiric, whatever,   but you’ve now transcended this particular  methodology, and now you’re making a substantive   statement about metaphysics, about something  that’s out there. That requires some rigorous   scrutiny. That’s where you require a little bit of  skepticism. And maintaining a foot in that sort of   skeptical sphere, as you go through, I think is  the best way to do it. But that’s just what it is   to be a good philosopher. Like, a good philosopher  will see statements, sometimes very provocative,   sometimes very ambitious statements, maybe  overambitious statements from any quarter,   could be from a scientist, and say, hang on a  second. Wait a second. Not so fast. Let’s make   sure that this extrapolation that you’re making  here is really rigorous and really makes sense.   And I’ll give you an example. So here’s a concrete  example. This is all very sort of abstract. Let me   bring it down to earth. This is a little bit of a  sensitive topic. Okay. One of my favorite, like,   one of my idols in physics is David Griffiths.  Many people in physics have read David Griffiths’   books. David Griffiths is legendary, and I  think the world of him. I learned physics from   his books. I learned particle physics the first  time from his book, Introduction to Elementary   Particles. Quantum Mechanics, I learned from  his Quantum Mechanics book. Electromagnetism,   I learned from his electromagnetism book. He has  rightly earned a status of this sort of legendary   figure in physics. He’s had a bigger impact  on physics than almost anybody. And I like   his writing for the most part, but he does have  a kind of tone sometimes when he writes that’s   very dismissive. He’ll sometimes just dismiss  things. And because he’s so, like, actually kind   of honest, he’ll often have a footnote where  he’ll say, I’m being too strong. I shouldn’t   dismiss this. Really, it’s like this. But a lot  of people don’t read the footnotes or they get   confused about them. And I’ll give you a very  concrete example. In his Quantum Mechanics book,   he says in the beginning, and so many students  have read this, he says there are three ways   to think about quantum mechanics. There’s the  realist way to think about quantum mechanics,   which is just to say that before we do a  measurement, the thing we’re measuring just   exists. Now, we’ve already talked about  how that’s really of not, that’s like a,   it’s not really a nuanced enough view. There’s the  realist view. The thing we’re about to measure was   already there. The second is the orthodox view,  which is the thing we’re measuring wasn’t there.   There was no preexisting property. The thing we  were measuring didn’t exist before we measured   it. Particles are nowhere until we measure them.  And then the third possibility is the agnostic   position. I’m not going to try to answer. He  says, these are the three positions. And this,   this really like steamrolls, a lot of nuance in  this discussion. And then he says, for a while,   they were partisans of all three of these views.  And then not long ago, but that means 1964,   which is actually a long time ago, a guy named  John Bell came along and proved a theorem. And   the theorem eliminated the agnostic position as  being possible and turn it into an experimental   question whether the realist position was true  or the orthodox position. Experiments have now   confirmed that the orthodox position is correct.  And that’s it. He just says, that’s it. And then   you like read the footnote and the footnote, he’s  like, well, that’s too strong a statement. There   are actually other theories that, you know,  but they’re the words he uses is they tend   to be cumbersome and implausible, but nevermind.  That particular phrasing is kind of funny because   I worked on a project a couple of years ago,  um, on whether magnetic forces could do work   on particles. It turns out they can if particles  have intrinsic magnetic dipole moments. And I,   and Griffiths updated the fifth edition of his  book on electromagnetism and included a footnote   mentioning this paper. So I have a footnote, but  he says theories like the thing I wrote down, he   says they tend to be cumbersome and implausible,  but nevermind. He uses exactly the same language   for these things as he does for all these other  persons of quantum mechanics. And given that these   other formulations of quantum mechanics, I think  are good and people should work on them. They do   tell us something. I think now I feel like I’m  a good company, right? We’ll come back to some   of that magnetic dipole stuff, um, maybe a little  bit later. Now, what’s, what’s strange about this   is that at the end of Griffiths’ book, he has  a beautiful afterward. It’s the final chapter.   It’s a chapter 12, where he goes through the  Bell, he goes through Bell’s theorem in detail,   which is not a thing you commonly find in  introductory quantum mechanics books. And he has a   lovingly good treatment of Bell’s 1964 theorem.  It’s the earliest version of Bell’s theorem.   He does say a couple of things that are a  little bit dodgy there, but his treatment   is actually really very good. Um, and he does  make mention to some of these other approaches,   but it’s like at the end of the book, a lot of  students don’t see that part of the book. And   I just worry that students reading this book will  take the things he says in the main text, not the   footnotes, not the, the qualifications, not the  other stuff that happened later. And they’ll just   repeat them. They’ll just say, oh, well, I was  wrong. Realism is wrong. David Griffiths has said   that the orthodox approach is the only approach,  and there’s no point in pursuing this further.   And any other attempts to pursue anything else  are just pursuing theories that are cumbersome   and implausible, but never mind. That’s the kind  of thing that someone who’s new in physics needs   to be on the lookout for. You see statements like  that that are really now metaphysical statements,   and you need to be like, well, hang on a second.  That doesn’t quite follow from the methodologies   that we’re doing. And I think it behooves someone  writing a textbook, someone teaching physics,   to be as clear and careful as they can be about  when they’ve stopped presenting something that’s   calculational, methodological, model development,  and they’ve now moved into this is the way nature   is as a result. We’ve learned that there is no  fact of the matter about anything we’re measuring,   that particles don’t have anything before they’re  measured, that there’s no way to fix quantum   mechanics, that these are statements that are not  supported by what we have. And I think people who   are interested in doing a serious study in physics  should know at the beginning to be on the lookout   for those kinds of statements. I think that  would be the piece of advice I would share.   Jacob, it’s been a pleasure. Three hours,  and we’re not even halfway through. Yes,   Curt, it turns out when you want to reformulate a  foundational theory in physics, it takes time. It   doesn’t happen all at once. Well, it takes chunks  of time. Chunks of time, and it’s indivisible,   but it looks like we have a good division event  coming up. Okay, great. Okay, so we’re going to   take a division event now, which means that you’ll  get part two of this conversation, which is the   third time that I’m speaking to Jacob in total.  The first time I’ve spoken to Jacob is on screen,   the second time is right here, the third part  will come out in a couple weeks from now,   and what we’ll talk about are the Bell experiments  or the Bell inequalities. We’re going to get to   other questions people had. People had questions  about entanglements, people had questions about   causation in this approach, and there were also  questions about what relationship this approach   has to problems in statistical mechanics and to  some of the other interpretations and formulations   of quantum mechanics. Right. Also, wave-particle  duality. Right. What does that mean in this   approach and also just traditionally? Right. Okay,  see you next time. Yep. Definitely subscribe and   ensure that you watch part two as we talk about  what are the misconceptions of the wave-particle   duality. Also, what are challenges of applying  indivisible stochastic processes to quantum field   theory? Is gravity indeed quantum? What about  stochastic general relativity? What about the   misinterpretations of non-locality and Bell’s  theorem? Jacob also gives a new perspective on   entanglement without wave-function collapse and  talks about the difficulty in defining causation   at a 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 and then goes over open questions  and future research in indivisible stochastic   processes. You do not want to miss this. It’s a  banger episode. Subscribe to get notified. New   update! Started a sub-stack. Writings on there  are currently about language and ill-defined   concepts as well as some other mathematical  details. Much more being written there. This   is content that isn’t anywhere else. It’s not on  Theories of Everything. It’s not on Patreon. Also,   full transcripts will be placed there at some  point in the future. Several people ask me,   Hey Curt, you’ve spoken to so many people in  the fields of theoretical physics, philosophy,   and consciousness. What are your thoughts? While  I remain impartial in interviews, this sub-stack   is a way to peer into my present deliberations  on these topics. Also, thank you to our partner,   The Economist. Whenever you share on Twitter,  say on Facebook, or even on Reddit, etc.,   it shows YouTube, Hey, people are talking about  this content outside of YouTube, which in turn   greatly aids the distribution on YouTube. Thirdly,  there’s a remarkably active Discord and subreddit   for Theories of Everything, where people explicate  TOEs, they disagree respectfully about theories,   and build, as a community, our own TOE. Links  to both are in the description. Fourthly,   you should know this podcast is on iTunes, it’s  on Spotify, it’s on all of the audio platforms.   All you have to do is type in Theories of  Everything and you’ll find it. Personally,   I gain from re-watching lectures and podcasts. I  also read in the comments that, hey, TOE listeners   also gain from replaying. So how about instead you  re-listen on those platforms like iTunes, Spotify,   Google Podcasts, whichever podcast catcher  you use. And finally, if you’d like to support   more conversations like this, more content like  this, then do consider visiting patreon.com slash   CURTJAIMUNGAL and donating with whatever you like.  There’s also PayPal, there’s also crypto, there’s   also just joining on YouTube. Again, keep in mind,  it’s support from the sponsors and you that allow   me to work on TOE full-time. You also get early  access to ad-free episodes, whether it’s audio   or video. It’s audio in the case of Patreon, video  in the case of YouTube. For instance, this episode   that you’re listening to right now was released  a few days earlier. Every dollar helps far more   than you think. Either way, your viewership  is generosity enough. Thank you so much.