Audio Player
Starting at:
Jacob Barandes: There is No Wave Function
November 13, 2024
•
2:19:30
•
undefined
Audio:
Download MP3
⚠️ Timestamps are hidden: Some podcast MP3s have dynamically injected ads which can shift timestamps. Show timestamps for troubleshooting.
Transcript
Enhanced with Timestamps
321 sentences
22,446 words
Method: api-polled
Transcription time: 137m 50s
The Economist covers math, physics, philosophy, and AI in a manner that shows how different countries perceive developments and how they impact markets. They recently published a piece on China's new neutrino detector. They cover extending life via mitochondrial transplants, creating an entirely new field of medicine. But it's also not just science they analyze.
Culture, they analyze finance, economics, business, international affairs across every region. I'm particularly liking their new insider feature. It was just launched this month. It gives you, it gives me, a front row access to The Economist's internal editorial debates.
Where senior editors argue through the news with world leaders and policy makers in twice weekly long format shows. Basically an extremely high quality podcast. Whether it's scientific innovation or shifting global politics, The Economist provides comprehensive coverage beyond headlines. As a toe listener, you get a special discount. Head over to economist.com slash TOE to subscribe. That's economist.com slash TOE for your discount.
I didn't know it was impossible. So I brought these theories closer and closer together expecting that there would be a moment when I would need to make some kind of jump to get from one theory, classical physics, to the other theory, quantum physics. And the strangest thing happened. The two cliff faces merged. And there was just no chasm anymore.
Today I have a special treat. I traveled to Harvard University to meet in-person Jacob Barandes, the co-director of graduate studies in physics and someone making waves at the intersection of fundamental physics and philosophy. In his unassuming office, he's been working on a revolutionary framework that finally explains quantum mechanics.
His radical proposal suggests that there is no fundamental wave function, Hilbert spaces aren't real, and there's no mysterious quantum realm.
In this episode, we go in depth into the picture that resolves the measurement problem, eliminates the need for multiple worlds, and finally gives a clear view as to what's actually happening at nature's smallest scales. However, this clarity does come with a price. The question is, are physicists ready to accept a quantum mechanics without magic?
Professor Jacob Baroness, welcome to theories of everything. I've been following you for some time following you online in a non creepy manner and We were speaking off air about physics however You're also the co-director of the graduate studies here of physics and you have an interesting background as to how you Came into physics. So why don't we start off there? Why don't we start from the beginning? from the beginning my first
intellectual passion was for philosophy of mind. When I was five, I was sitting in one of those little assembly rooms they had in in schools, you know, like it was my elementary school. And one of the teachers was droning on about something I don't remember exactly what they were talking about. But I remember sitting on this soft carpet and there was a there was a piano with you know, the feet of the piano looked like lion's paws.
and i suddenly became aware of my existence in a very very explicit clear way and i was very confused and i tried to express my state of confusion to one of the other children sitting next to me and i failed miserably at being able to explain what i was feeling in the moment and so this left a sort of a mark on me
And from that moment, I was very interested in questions about, you know, what is the nature of our existence? What does it mean to be conscious? So philosophy of mind is really where things got started for me. But of course, I had no language with which to express any of these thoughts.
I like science documentaries. I grew up in New York City and my parents would take me to the Museum of Natural History in New York City, which is really a wonderful magical place and anyone who goes to New York City should really should really visited. It's amazing. So I got really interested in science. I got interested in math. And I just thought if you're interested in science and math and you're interested in foundational questions,
then that means you should go into physics, right? That's where I thought math and these foundational questions, it's where they come together. So I went, you know, through school. I got to high school. I took physics for the first time in an academic way in school. I loved it. It was my favorite class in high school. I still have all my old binders from from that time. It was the one class where I was actually excited to go and do the homework, which was great.
My teacher Doug Bartel was just phenomenal. He was just totally amazing. Around that time, I also started making trips back into New York City. We'd moved out of the city by that point, about an hour north. And so I would jump on the train and go in the city on the weekends.
And I would take science classes in the city. Columbia University has a program called the Science Honors Program. At the time it was run by Alan Blair, just an amazing human being who was a professor of physics there and also ran this special program, the Science Honors Program. And these were classes you could go to. There was no homework or grades or tests. You just show up on Saturday mornings and you would learn all kinds of amazing things. It was an amazing program.
And I would also work at the Museum of Natural History, so I started interning there when I was in high school. And I started working in the astrophysics department. I was not an expert in astrophysics in high school, but I was very curious about it. And I was doing a lot of computer programming at the time. And they were interested in having me work on some of the projects that they were doing. They were working on computer graphics visualizations of
of the galaxy. I worked on a project called the Digital Galaxy Project, if I remember the name correctly. And it was really my first opportunity to work with scientists. I really hadn't, I didn't know any scientists. We didn't have any scientists in my family. My father's a physician. But, you know, research scientists, I'd never met anybody like that. I didn't know academics or professors or anything like that. So this was, you know, these two experiences were very important for me.
And together with my physics class, you know, I decided I wanted to study science and maybe physics. But my love for philosophy of mind was still very strong. And so when I went to college, I decided I was going to try to study the brain. I loved computers. And so the idea was I would somehow find a way to bring together my interest in computers and neuroscience in some way. In order to go in that direction, I had to take some basic science classes, including
Physics, I had to take math classes and I really fell in love with these classes. I started taking biology in my sophomore year and I enjoyed it, but not as much. And I have immense respect for people who work in biology, but it just wasn't for me. Yeah. So for me, I just want to know if the reason was the same for you. For me, it's just there's a multiplicity of terms and I feel like it's more memorization than derivation.
Yeah, I do sometimes feel that way. I want to make very clear that I'm not a biologist and I don't want to make any presumptions about the way that biologists think about their subject. I know there's an inner logic to biology. Oh, I just mean at the first year level, at least from what I experienced, as you get older or as you get more seasoned in research,
I had that experience when I took the first semester of biology. It was microbiology and it was very logical. And then the second semester was anatomy and that was much more memorization and that I had the same experience that you're describing. It just wasn't really for me. But it was hard to convince myself that I should go into physics because there were all these very bright young people going into physics and going into mathematics. I was interested in the theoretical side, the mathematical side of physics and I just didn't feel like I was good enough to keep up with people.
But around sophomore year of college, you know, I had conversations with some really amazing people, some of my fellow college students. And basically, I decided, you know, it matters much more that I do what I'm excited about than, you know, to want to be the best at something. So I'm just going to I'm just going to do it anyway. And so I just started taking lots of physics and math classes. And it was fantastic. I had an amazing experience. And some of the philosophy courses we were required to take at the time just didn't really call to me.
There was a heavy emphasis on ancient Greek philosophy, on early modern philosophy. Now, I appreciated those subjects, but it wasn't as exciting to me as what I was doing in physics, at least at the time. Now, I should say that as the years went on and I began exploring other areas of philosophy that weren't part of the standard curriculum in college, analytic philosophy, philosophy of science, logic,
foundations of mathematics, philosophy of physics. My views on philosophy changed completely. But at the time, I didn't really get a chance to see much of that and I didn't see it growing up. And so I figured, okay, I'm going to throw my lot into physics. So I finished my undergraduate degree and then went on to graduate school. And I started a PhD actually here at Harvard in theoretical physics. And as I was progressing in that degree,
You know, I started to think back about some of these old philosophical questions that I had. I did my doctoral work in high-energy theoretical physics, and I think we did really meaningful work, but I was really much more excited about philosophical questions, and by the time I finished my PhD, I knew that was the direction I wanted to go in. So I continued on in the department,
I'm a lecturer here in the department and I also co-direct the graduate program as I think we talked about. So, you know, I mix teaching physics and research and advising students and it's been a really rewarding experience. The students here are amazing. They're idealistic and they're brilliant and they're deep and I've met really the most amazing people a person could ever ask to meet here.
I've met lifelong friends here. I mean, it's been just an incredible experience being here, and I've learned a lot. Much more, I think, than any of them have learned from me. But that's how someone who mainly works in philosophy, philosophy of physics, finds himself embedded in the physics department. So I have an associated faculty appointment with the philosophy department, and I take turns teaching classes in physics and also over there in philosophy. Yeah. But my research is primarily the intersection of philosophy and physics.
So what happened to the philosophy of mind?
I'm extremely interested in philosophy of mind, but I don't think that my distinct profile of strengths and weaknesses is optimized for working in philosophy of mind. So I read about it, I'm deeply interested in it, but I feel like I'm more well adapted to questions of the intersection of physics and philosophy, so that's where I've spent my time and my focus.
This episode is brought to you by State Farm. Listening to this podcast? Smart move. Being financially savvy? Smart move. Another smart move? Having State Farm help you create a competitive price when you choose to bundle home and auto. Bundling. Just another way to save with a personal price plan. Like a good neighbor, State Farm is there. Prices are based on rating plans that vary by state. Coverage options are selected by the customer. Availability, amount of discounts and savings, and eligibility vary by state.
Earlier, you said you didn't want to pursue something just to be the best at it. You want to follow your interests. But here you're saying, well, my interests still lie in philosophy of mine, but it's just not I'm not the sharpest tool in the shed when it comes to that. That's not my skill set. How do you reconcile those two? That's well put. Yeah. So, I mean, we all change as we grow and get older, right? Yeah. So I think for me, it was a matter of finding a balance. It's less important to me
And I talk with students about this also, right? It's less important what you want to be. It's less important about being big or famous or important. And to me, what's most important is doing work that's meaningful, that I feel like is meaningful, that a person feels like is meaningful, work that we feel is meaningful, but also we feel like we're making progress on. So it's not so much that
I'd like to get you to justify there is no wave function soon.
However, I want to know if there is a connection between the philosophy of mind and quantum mechanics first. Yes, this is a very interesting question. And actually, this will bring us to a very important paper that I'm hoping we could talk about from the early 1960s. It was a paper by Eugene Wigner. I believe the paper was called On the Mind-Body Question. I could have the title slightly wrong. But Wigner introduced a thought experiment that
The Thought Experiment
in Hugh Everett's extended thesis. Hugh Everett was a graduate student at Princeton, and was at Princeton at the same time, overlapped with Eugene Wigner. And Hugh Everett originated the Many Worlds Interpretation of Quantum Mechanics, and he wrote this very long thesis. It's 137 pages. I guess maybe that's not long in an absolute sense.
In 1956-1957, he ultimately didn't publish it. His advisor strongly pushed him to publish a shorter, different thesis. But you can find a copy of this extended thesis and he opens it up with the same thought experiment. So we know this thought experiment was introduced earlier than Wigner by at least
I guess seven years before Wigner's paper, something like that. But that wasn't published. Wigner's paper was published, and so it's most widely attributed to him. Wigner had this thought experiment that I'm going to talk about in a little more detail if you'd like, because I think it gives a good motivation for why one might think that there's a problem with the way that we formulate quantum mechanics at the level of its textbook axioms. So I'll come back to it. But I'll just say that this thought experiment
Apparently it was connected with Wigner's idea that somehow consciousness was related to collapse of wave functions and I think this creates a potential connection between philosophy of mind and quantum mechanics. But there are other connections. In the Many Worlds interpretation, the formulation of quantum mechanics that Hugh Everett introduced in the mid-50s,
One does run into some basic questions about consciousness and human identity in a universe in which a giant universal wave function is splintering into parallel realities, each of which contain copies of yourself. How do we make sense of this kind of a picture and make it connect with how we think about basic problems and philosophy of mind? I don't claim to have an answer to that question. It's an ongoing mystery, I think.
So there are, I think, some interesting connections between philosophy of mind and quantum mechanics. And I think my general attitude has been anytime you're unable to answer a question about quantum mechanics because you've connected it in some way to the philosophy of mind, and in particular to an unanswered and potentially unanswerable problem about the philosophy of mind, I get very worried. Okay, let's talk about the wave function because when we're speaking about the collapse of the wave function, the collapse of something,
What is this wave function and why do you believe that there is none? That's a great question. So let me say a little bit about some history. I think some history here might be helpful to ground things. But before I do the history, let me first answer your question. I'll give the short answer and then we'll talk a little bit of history because otherwise make it lots of weeds. There's this popular story about quantum mechanics that a lot of students coming into the fields have heard. The first
Primary object in quantum mechanics is the wave function. It's this mysterious undulating object. It's a little bit unusual. It's kind of like the electric fields sort of except that its values are complex value. They're complex numbers. They're like
ordinary real numbers plus a number times the square root of minus one. And somehow they're connected with probabilities in some way. And somehow the point of quantum mechanics is wave functions. They're the central player in the story. And how you think about quantum mechanics begins with how you think about wave functions, right? They're the protagonist of this story.
There are, I think, some good reasons to be a bit skeptical of that picture. And I don't think that there really is much, there would be much controversy about saying, I think, you know, when you learn about quantum mechanics and you begin to see that there's this much bigger picture, you know, you begin to see that the wave function in this sort of story is a little bit of an oversimplification. I think if you pressed someone who works in physics pretty far, they would admit actually this picture is a little bit
It's a little bit too quick, and there's a deeper picture beneath it. And so I think there's one view in what I'm saying here, your question, which is to take those concerns and take them to their logical conclusions, right? Ask ourselves, okay, what does this theory really consist of? Is it really about wave functions at all? And for that matter, are wave functions things that describe objects that are really out there in the world? And this is where one
lives in kind of a liminal space between physics and philosophy when you ask questions like that on the on one hand it's about physics it's about you know what's the right way to think about what's the way to formulate you know what may be our best most successful scientific theory certainly when it comes to numerical accuracy and precision you know and the other hand what's really out there what's out there in the world what exists right this is this word ontology that metaphysicians use ontology is is the study of what really exists
And ask, does the wave function describe something that physically exists? That's a question. To explain a little bit about how we've arrived here, I could say a little bit about the history, but let me just pause and ask, do you have follow-up questions about this? I want to make, you know, be careful to make sure we all have time to... Sure, sure. So when you say that there's the standard picture of the wave function, you said, okay, what people are taught is that there's the wave function, it's connected to complex numbers, and that it's also connected to probability somehow.
Is that the picture that you're referring to? Are you referring to the picture that the wave function represents something in physical space and is of something? So when I say that, what I mean is when people say the wave function, when physicists speak about the wave function, it's the wave function of something, the wave function of an electron, the wave function of a so-and-so. So what is precisely this picture that you're about to shatter? Yeah, so this is an excellent question. I think
The issue here is that it's a little of both. The wave function plays a functional role in quantum mechanics. That is, it does certain things for you in the theory.
There's this famous equation called the Schrödinger equation, which roughly says that when a system is left to itself, it's not being disturbed, it's not exchanging information with any other systems, then it has a wave function that changes with time in a smooth way. And this smooth process is described by a differential equation, which is roughly speaking an equation that just tells you what the wave function is at each infinitesimally next moment, given what it was at the
So we plug in initial wave function, we use the Schrodinger equation to figure out what the wave function will, how it will behave as time progresses, and then there are rules for taking the wave function and calculating predictions. So that's uncontroversial, and I certainly agree with that picture, that we should be using wave functions for that purpose.
But I think it's easy to let that picture, it's easy to let that picture lead one to think that wave functions are describing physical objects out in the world. And, you know, when I think students arrive in a quantum mechanics class for the first time, without having studied the theory, they may think that, okay, every particle has got some wave function, the wave functions are kind of like
They're kind of like waves in an empty space is kind of like the ocean and all the particles are kind of like small little waves moving around in the ocean. And that's actually not the picture that we get even from the textbook theory of quantum mechanics. In the textbook theory, a wave function is the assignment of a complex number to every possible configuration of your system.
If you're talking about a single particle, nothing else, then every possible configuration is every possible location the particle can be in. Each location is labeled by three numbers. It's x, y, and z coordinates, if you want. And so the wave function takes in those three coordinates and assigns it a complex number, and then we're supposed to do a mathematical operation of that complex number, and out comes a probability, or precisely a probability density, but a probability per unit volume that a measurement will find the particle at that spot.
So the wave function can be thought of as the assignment of a special complex number to every point in three-dimensional physical space where you do this operation. It's called mod-squaring. You do this operation, and then it tells you the probability, roughly speaking, with which a measurement will find a particle at that location. So it's very easy to think that a wave function is like a field, like the electric field in three-dimensional space. But if you have two particles instead of one,
the possibility space is much more complicated. We call this possibility space configuration space because each possible configuration of a two-particle system requires six numbers, not three. You need to know x, y, and z for the first particle and you need to know x, y, and z for the second particle. So the wave function assigns a complex number to a point in a six-dimensional
you need six numbers to specify its points. And that means a two particle wave function is a function we say whose domain is a six dimensional space. Six dimensional space is not physical three dimensional space. If you've got three particles, it's a nine dimensional space. If you've got 10 particles, it's a 30 dimensional space. And actually, our universe does not have a well defined number of particles at all.
Our leading physical model for the universe, at least for the non-gravitational parts of the universe, is the standard model, which is based on a set of models known as quantum field theories. And in quantum field theories, particles are emergent excitations of these sort of delocalized entities called quantum fields. And the number of particles can change from moment to moment. It's not always well-defined. So it's not even clear how to even think about
Okay, so,
You have a lecture about how Hilbert spaces are also not real. I'd like you to talk about that. Now, it's my understanding that you more precisely said Hilbert spaces are redundant in the same way that gauge symmetries are redundant or the gauge transformations are redundant. So at this point, if it's all right, let me do a little bit of history if it's OK. So where does quantum theory begin? Lightning like grand tour of quantum theory. There are these
actual physical objects called black bodies.
You know, a little hole is poked in them. I mean, you don't really poke a hole in them. It's more complicated. But this is I'm very much a theorist and my picture of experimental physics is it should be better. And I apologize in advance to anyone who's an experimentalist listening to me. But these were actual systems. People actually built these things. They were these chambers. They would heat them up.
And then they would have a little hole in the chamber through which they could actually see radiation coming out of them and they could put that radiation through experimental devices that could show them how intense the radiation was as a function of wavelength.
We all know that different wavelengths of light correspond to different colors in the visible range. And if you go outside the visible range, you have very long wavelengths that are infrared or microwave radiation or radio waves. And at the very short wavelengths, you've got X-rays and so forth, gamma rays going all the way out, ultraviolet X-rays, gamma rays going all the way out to very short wavelengths. And you could just ask yourself,
If I plot how strong the radiation is as a function of wavelength, what kind of pattern would I expect to see? And the pattern that was revealed in experiments was difficult to explain on first principles theoretical grounds. A very important physicist, Max Planck, in 1900 found a way
to generate a theoretical prediction of what this black body radiation curve should look like, and it agreed with experiments. But in order to get there, he had to kind of hack his formulas. He had introduced a fudge factor. He had to assume that radiation in this chamber could only occur in quantized amounts. That is, there were different wavelengths you could produce, but each wavelength could only be excited in discrete steps.
This led to the quantum hypothesis. This was his quantum hypothesis. And there was a sort of parameter that told you how big you wanted to make these steps. Today we would call it a regulator. And this parameter, we now call it h, little h. We call it Planck's constant. Planck introduced it. And I think at one point his idea was he wanted to
introduces an intermediate step in the calculation and once he calculated everything sends this clearly in his mind on physical parameter to zero but whenever he tried to send it to zero he would get the wrong results he realized this parameter was not zero it was very small it was today it has a value you know that's of order 10 to the negative 34 10 to the negative 33 in conventional units and he couldn't get rid of it
And so people had to accept that there was this basic discreteness in nature he couldn't explain. And then for the next 22, 23 years, the period from 1900 to 1922, 1923, physicists working on these questions were living in a time that today we call the old quantum theory, a paradigm we call the old quantum theory. The old quantum theory was based on a mixture of
physical pictures of particles moving around in space, in orbits, like in atoms, and then a collection of ad hoc formulas and rules that people didn't fully understand that seemed to capture some of the observations that were coming out of experiment. But it was a very murky time. There wasn't anything like an underlying theory from which this whole picture emerged. And the formulas weren't perfect. They didn't work exactly right.
In 1913, Niels Bohr proposed his famous model of the hydrogen atom. This is a model in which you've got the nucleus and for the hydrogen atom, it's just a proton, positively charged proton in the middle and an electron going around. And by making use of these sort of heuristic formulas that were characteristic of the time,
Bore argued that the electron could only be in certain definite orbits and when it transitioned between them its energy changed in discrete steps and whenever its energy changed it would either absorb or emit radiation in discrete amounts and with this he was able to account for the particular colors of radiation that we would see emitted from excited hydrogen atoms or that were absorbed by hydrogen atoms the so-called line spectra and we also found that other atoms had line spectra as well
Famously helium was discovered because we looked at the spectral lines from the Sun and after accounting for all the spectral lines we knew about there were still some more that we didn't account for and so people conjectured there was a new element they called the helium from Helios the Sun and eventually we found helium on Earth but it was first discovered in the Sun. So this was obviously a very important thing and Bohr ended up winning the Nobel Prize in 1922 for this Bohr model. But by around 1922, certainly at least by then, people were becoming very skeptical
because people couldn't take these clear pictures of particles moving in definite ways, particles interacting with fields like electric and magnetic field, which were well understood by this point. They couldn't take this world picture, this ontology, this picture of what was physically out there. They couldn't find laws that when combined with this picture gave you the right predictions.
that gave you an empirically adequate, empirical meaning subject to experiment, empirically adequate, a theory that was able to account for the things we were seeing and make predictions that were regularly confirmed. Niels Bohr gave a bunch of lectures in 1922. Heisenberg, Werner Heisenberg, attends one of these lectures, at least one of them.
And the story goes, and I'm not sure quite how much of the story is apocryphal or how much really happened, but the story goes that Heisenberg objected at one point
to this lecture. Heisenberg at this point was 20 years old, maybe 21. Niels Bohr was a Nobel Prize-winning physicist, widely regarded as the quantum whisperer, someone who just innately intuitively understood quantum mechanics in a way that no one else did. And here was Heisenberg challenging Bohr. People, I think, probably could have been expected to have thought that Bohr would be upset at this.
But the story goes that after the talk, Heisenberg took a long walk with Bohr, a many hours walk, and it had a huge impact on how Heisenberg thought about nature. The story, the legend goes that Bohr revealed to Heisenberg that, as Bohr put it, he was not convinced there were particles or orbits after all.
You start seeing comments by people like Sommerfeld. Arnold Sommerfeld was actually Heisenberg's doctoral advisor in Munich, where Heisenberg was, and then people like Wolfgang Pauli. Many of the people sort of at the foundations of this developing theory were increasingly skeptical that this world picture could survive.
And then in 1925, Heisenberg, who was visiting the premier institution in mathematics and theoretical physics at the time, Gerttingen, where people like David Hilbert were, Max Born was there, Felix Klein, your top, you know, mathematicians and physicists. Heisenberg was there visiting, he was visiting Max Born's group, Max Born and his student Pasquale Jordan.
And he was thinking about all these questions and he was very confused about all of it. There were all these new, more complicated formulas that people were writing down that were connecting energy levels and transitions and atoms to spectra. And he develops this very terrible case of hay fever. In the spring of 1925, he goes out to Heligoland, which is this island where the pollen levels are much lower. And he comes back with this
Totally bizarre draft of a paper And he gives this paper to Max Born and to Jordan and then he like goes on a vacation again He goes on some vacation. He's exhausted from all of his intellectual exertions and this paper begins with these incredibly These remarkable statements statements that a philosopher of science would immediately recognize as indicating some kind of paradigm shift Heisenberg says at the beginning
We shouldn't be thinking about orbits anymore or particles. We should rephrase our physics, our theories entirely in terms of quantities that can in principle be measured. And so he formulates this different way to think about quantum mechanics in terms of abstract objects that Max Born identifies as our matrices.
People who are listening to this may have heard of a matrix. Matrices and the subject that they belong to, linear algebra, that was not a standard part of the physics curriculum at this time. Heisenberg actually independently discovered matrices in this work and their mathematical operations.
And Born recognized what Heisenberg was doing, and then together they wrote a couple of papers in which they introduced this thing called matrix mechanics. In matrix mechanics, there's no picture anymore. There's no picture of atoms, of electrons, of particles going around atoms. There's just this abstract mathematical apparatus for predicting energy levels of things. Schrödinger comes along a few months later,
And through a series of theoretical arguments that I will not be able to do justice to here that connect with what's called Hamill and Jacobi theory, which is a beautiful area of classical physics, Heisenberg proposes a different way to think about quantum mechanics. He introduces his wave function. It's what shows up in these papers. Schrödinger introduces his wave function. This is in early 1926. In some papers, both in German and in English, he wrote in both.
I'm
he even says maybe this is what reality is maybe reality is some giant mechanical wave undulating in configuration space and some and through some mechanism that we don't fully understand this undulating wave in this high dimensional abstract space somehow projects facts down into three dimensional reality facts about where electrons are
He doesn't have the full picture here, but this is what he basically describes, and he's able to use this wave function as an indirect method for predicting energy levels. Max Born comes along very shortly thereafter and proposes that wave functions are not mechanical objects. They are mathematical tools.
The reason they're complex valued is because they're not really physical things. They're things that we operate on using these sort of mathematical operations to generate probabilities. The wave functions, when you take the complex numbers that they describe and you do this operation to them, what comes out is probabilities. The wave function should be understood as a mathematical mechanism for generating probabilities.
By 1928 Schrodinger is already recanting his view. He gives a lecture in 1928, his fourth lecture on wave mechanics, in which he says he used to think that wave functions were physical objects. He even presages in some ways the many worlds interpretation. He says they're an object where every single thing that the system could be doing is really playing out in this giant wave function. But he no longer thinks that.
He's accepted what seems to be the new idea. And then within the next couple of years, 1930, Paul Dirac writes a textbook in which he summarizes all of the quantum mechanics that was known at the time, and he sews together Schrodinger's wave functions with Heisenberg and Born and Jordan's matrix mechanics, and he realizes they're all part of this deeper reality. There's this mathematical construction
It's a kind of a space called the Hilbert space, which is kind of a vector space, but it's a vector space with complex numbers in it. And when you look at the vector space in one way, you see wave functions. If you look at the vector space in another way, you see matrices. You see what Heisenberg was doing. They're all parts of this mathematical structure called the Hilbert space. And then two years later,
John von Neumann, the great mathematician, he writes a book, Mathematical Foundations of Quantum Mechanics, in which he formalizes this theory in mathematical terms. And that's basically what we've had ever since. Today, when people refer to the Dirac von Neumann axioms, or the textbook axioms of quantum mechanics, they mean this prescription for generating predictions about what we'll see in experiments, empirical predictions. And
This framework is based on Hilbert spaces. Very roughly speaking, the first axiom says that every quantum system has this abstract space called a Hilbert space, which is not a configuration space, it's a different kind of a thing altogether, and that this state in some sense of a quantum system is represented by certain kinds of objects in this Hilbert space. State vectors, in the simplest case, are density operators, somewhat more complicatedly.
The second axiom is that when left to itself, the system evolves according to, roughly speaking, the Schrodinger equation, more generally unitary evolution.
And then there are three more axioms that talk about when a measurement is performed in the system, what you're likely to see. These are the so-called measurement axioms. And one of them is about what kind of mathematical objects represent the things we can measure. These are called observables. One of them is about how to generate probabilities of what you'll see when you do measurements. That's called the Born Rule. And then the final one is that after a measurement, the state vector of the quantum state collapses.
This is the way we introduce quantum mechanics to students in textbooks now. If you go to my shelf and look at any of the textbooks on quantum mechanics, they will present something like these five axioms. Different people will sort them differently. They may not say there's five. They may say there's four or six or some other number, but I like to carve them up as five, right? So we know we have these axioms. We know that they're very good at giving us a prescription for generating empirical predictions. But
What do they tell us about what's really going on in nature? Are they saying that the seat of reality really is some abstract Hilbert space, some vector space of possibly very high or infinite dimensions over the complex numbers, and that the universe is some object in this space trolling around according to some rule? There are some reasons to be skeptical of this. One is that we can reformulate the axioms of quantum theory in a very different language.
So people who work in various other areas of quantum physics, in mathematical physics, sometimes prefer to formulate quantum mechanics in terms of what are called c-star algebras. C-star algebras are not things you find on the beach. They're not that kind of c-star, but they're abstract sets of mathematical entities that codify
How systems evolve in quantum mechanics, how to generate measurement predictions in a way that doesn't start with Hilbert spaces. When you take that alternative point of view, you get a very general mathematical framework from which the Hilbert space picture can emerge in certain, well,
You can almost always pull out a Hilbert space picture in these stories. Sometimes you get a unique Hilbert space, sometimes you get a proliferation of different Hilbert spaces, and there's all kinds of deep questions about what that means. But when I began learning about the C-straw algebraic formulation of quantum mechanics, it opened my mind, as I think it does a lot of people, to the idea that maybe the Dirac-von Neumann axioms, the ones we hear about in the textbooks, phrased
primeval in terms of Hilbert spaces may not be the end of the story and Hilbert spaces may not be the most fundamental way to think about the structure of quantum mechanics. I think one can go much farther and maybe we'll talk a little bit about how one can go farther than that but once you already begin to see that there are mathematically equivalent ways to formulate quantum mechanics that don't start with Hilbert spaces it makes you become somewhat skeptical that the Hilbert space picture is fundamental and that the objects in the Hilbert space picture state vectors that
Well, what is it about the C-star approach that allows you to say that the Hilbert spaces that can come from the C-star approach implies that the Hilbert spaces are
So that's an excellent question. In the standard approach to quantum mechanics, the first of the three measurement axioms says that every observable thing you might want to look at is represented by a kind of a matrix, more technically a self-adjoint operator on the Hilbert space. It's just, it's kind of like
an abstract mathematical entity that you can add other such entities and multiply them together. It behaves kind of like a number, kind of like a variable X in algebra, but a little weirder, like they don't always commute with each other. They're kind of strange objects, but we have a mathematical set of tools to take these and generate empirical predictions. When you start with the textbook axioms, you begin with the Hilbert space, and then these operators are things that come out of the Hilbert space. In the c-straw algebra approach, you go the other way around.
You begin with an abstract specification of the observables, which are represented by these abstract mathematical symbols. And the symbols have all kinds of mathematical properties, rules for how you add them together, multiply them, just like I said, but they don't begin as objects that live in Hilbert spaces. They have their own existence, their identity. And there's even a funny way that people who work in this field sometimes talk about it. They'll say, are you a Hilbert space conservative?
Meaning you take the Hilbert space to be the starting point, or are you an algebraic imperialist? Do you take the algebraic objects to be the basic ingredients? When you start with these basic algebraic ingredients, they form a special kind of mathematical structure called a C star algebra. The C stands for closed, which just means that there's like no holes in the algebra. It's all filled in all the way. And the star just refers to the operation of, it's a complex conjugation, but on these objects, roughly speaking.
And there's some other properties you require these to have, but very rudimentary properties. And then what you can show is that there is a way to
to construct a Hilbert space out of these algebraic objects. And once you've done that, then they become the matrices or operators in the Hilbert space. But once you see this construction, it's called the Gelfand-Neymark-Siegel construction. It's a beautiful theorem. Once you see it done, you begin to wonder just how fundamental Hilbert spaces really are, especially because some of these sister algebras do not generate a unique Hilbert space.
And that's where the Hilbert space redundancy comes from. In a way, yeah. So, you know, for simple systems, if you've got one particle or three particles or 10 particles, it turns out you basically get a unique Hilbert space. So you really can think of either of them as being fundamental. But when you consider systems that have infinitely many moving parts,
so a system of so many particles that will model it as if it has infinitely many particles we do this in thermodynamics or a quantum field where there's like variables at every point in all of space for these kinds of systems you don't necessarily get a unique Hilbert space out and then there's this question of which is more fundamental and
Earlier we were talking about Heisenberg and how he started with observables and Schrodinger didn't.
And now you're talking about taking those observables seriously and forming an algebra of just them called the C star algebra. But then you also said that you can take representations of the observables which become matrices. Yeah. And Heisenberg was dealing with the matrices. Exactly. OK. Yeah. Your picture is exactly correct. So now this isn't what I'm working on right now. But when you begin to realize that you can reformulate the rules of quantum quantum theory in a different way, it kind of opens your mind up to other possibilities. I want to know what your mind has been opened up to. Yeah.
Where is your mind these days on quantum time? That's an excellent question. So let me go back to Wigner's thought experiment again, because I think this is a good hook for where I end up and where I think a lot of people end up. So what was this thought experiment about? In a way, I mean, it's a thought experiment that a lot of people in physics and certainly philosophy of physics are familiar with.
It's a real good workhorse in quantum foundations, but I think there's still a lot of lessons to learn from it. And people have extended this experiment in lots of different, there's the so-called extended Wigner's Friends scenarios that a lot of people are working on, but I think the original version of it is actually really, really nice. And like I said, phrased all the way back in 1956 in Hugh Everett's original thesis. But it's a very simple question. The axioms say
that we have a Hilbert space and we represent the state of the system as some object this Hilbert space.
Questions we can ask observables are represented by these symbols. We can generate probabilities and then after a measurement, we collapse. Why do we collapse? What's the purpose of collapse? Collapse is to ensure robustness of measurement results. After you do the measurement, you're guaranteed to get the same result again. That's what collapse accomplishes. It ensures that once you've gotten a definite result, if you measure right again before you've given the system any chance to evolve further, you're guaranteed with almost 100% probability to get the same result.
Now, the problem of course is that, well, what is a measurement? What kinds of physical processes count as measurements? One view is, we don't need to worry about this. One view is, all scientific theories are ultimately instrumentalist enterprises, meaning that they exist solely to allow us to connect
Preparations, setups of measurements to predictions of measurement outcomes or measurement results. That's all a scientific theory is meant to do. Doing anything else, painting pictures of reality is all just there for color. It's like a fable. It's not necessary. It's philosophy. It's metaphysics. It's not important for physics to do that. And the theory does that. The theory says that we do a measurement. Here's what comes out.
The theory is doing what it's supposed to do. What more could you ask of it? The theory says when we do a measurement, we do this thing, we run this prescription, we collapse the state of the quantum state of the system, and then we proceed. It all works just fine. What's your problem? The Vigner's Friend Thought experiment considers two observers. One is Vigner in the outside world, enjoying a nice sunny day, maybe a nice beautiful autumn day like today. And Vigner's friend,
who is inside a perfectly sealed box. Now, people may wonder in quantum mechanics, can you really seal anything in a box? Can't things tunnel out? Well, particles can tunnel out of certain kinds of enclosures, but if you make the box thick enough, impenetrable enough, in some highly idealized sense, then you can keep everything inside the box, at least for the duration of the experiment.
Wigner's friend is inside this box along with some quantum system, some system that is in a superposition of two possibilities, a particle that is spin up and blended with spin down in some superposition, let's say. Wigner's friend engages in some interaction that you might call a measurement on this superposed quantum system inside this box. Wigner, on the outside of the sealed box, does not do a measurement, does not in any way learn what has happened.
Now we've got two observers and now we have a question. Do we activate the collapse postulate or do we not activate the collapse postulate? We have two observers. We have to now take a stand. We have to say whether we activate it or not. And there are only a few possibilities. One possibility is, yes, we activate it. We activate this measurement axiom. The quantum state of the system collapses. Even though Wigner on the outside has not seen anything, it just collapses.
For everybody, it just collapses. But now we have a question. Wigner's on the outside, why should Wigner think it collapsed? Because Wigner's friend did a measurement? But how do we know that the thing Wigner's friend did qualified as a measurement? Wigner's friend is just some physical system in the box. If Wigner's friend were replaced with an electron,
that somehow interacted with the other particle. We wouldn't have called that a measurement. If Ignor's friend is replaced with a water bear, you know, tardigrade, one of those microscopic, very resilient organisms that are very hard to see with their naked eye, would that have done a measurement? Like now we just have a physics question. At what point do we cross the line into yes measurement or no not measurement? Now, there's this thing called decoherence.
that one often hears in these sorts of discussions. Oh, when a big system interacts with the quantum system, there's this thing called decoherence. Decoherence changes the quantum state of the system being observed. But decoherence does not collapse anything. It doesn't single out one result.
And you can actually show that there's no way to take the non-collapse axioms of quantum theory and get a definite result out, to get one result singled out from all the others. So the question is, what do we do here? In principle, we need to supply a rigorous definition of what kinds of processes are measurements and what kind are not, and this is called the measurement problem. We don't have such a rigorous definition, and we haven't for a hundred years.
Maybe one day someone will come along and say this is what a measurement is and this is not what a measurement is but at this point we don't have that statement. And without it we just have this ambiguity. This is the famous measurement problem. That's one possibility. The next possibility is to say there is a definite outcome of the experiment but somehow it happens without a collapse. Or collapse is perspective based, perspectival. Wigner's friend sees the collapse but Wigner on the outside doesn't. But if you take that
That horn of this dilemma, trilemma, quadrilemma, you take this path, then what you're saying is that Wigner on the outside has some quantum state he uses to describe the system, and this quantum state is incomplete. It doesn't know the definite result that happened in the experiment. And if you're accepting that the wave function is incomplete, you're accepting that there are additional or hidden variables beyond the wave function.
which again is not consistent with the textbook formulation of quantum theory, at least according to the usual axioms. The third possibility is you replace measurement with something else, some kind of dynamical process by which things just naturally collapse when they're big enough, and there's a whole collection of approaches to quantum foundations called dynamical stochastic collapse approaches that do this. The wave function or quantum state is this thing and for individual particles it persists a very long time
before collapsing but you put enough particles together if any one of them collapses the whole thing comes crashing down and this explains why very big objects naturally collapse very quickly that's option three those approaches are very interesting some of them have been tested experimentally they involve a lot of you know new parameters and you have to guess equations and we don't really have a well-motivated way to understand which ones to use the fourth possibility is that there just isn't
An outcome. No one gets a definite measurement. Either there is no outcome at all, which doesn't really seem to make sense, or all the outcomes happen in some sense. And this is what Hugh Everett argued in his thesis when he considered this problem. There's no collapse, we get rid of the collapse axiom, and Wigner's friend splits into two parallel copies, each of whom sees a different outcome. One sees spin up, one sees spin down, and these are inside the box. Wigner on the outside,
also doesn't register a definite outcome if the box opens up, then Wigner sees the definite outcome and Wigner splits into two copies. And the universe kind of unzips as the copies propagate and branches or the wave function of the universe splinters into multiple possibilities. This is the many worlds interpretation and it's an ongoing source of dispute. There are a lot of questions about how to make sense of basic questions about identity and philosophy of mind in a universe like that.
It's not clear how to make sense of probability in the universe like that. There's ongoing debates about how to make that work. That's basically what we're left with. That's what this vigorous and thought experiment leaves you with. You have to make a decision. I guess there's a fifth possibility, which is just quantum mechanics is wrong. But until we have good reason to think it's just wrong, we probably have to operate under the assumption that we need to make the theory work better.
So this, I think, is a good motivation for taking seriously that there's something wrong with the axioms of quantum mechanics. We need to do something about them. It's not just that they're instrumentalist, but they're either ambiguous or incomplete or inconsistent in some way, and we need to fix them. Where does that leave me and where do I come in? One way to understand what I'm trying to do is going back to 1922, just when people were ready to abandon the old pictures of
Particles and fields and actual things out there doing things behaving. And just as people were about to give up on finding laws, acting on those ingredients that would give you an empirically adequate theory. Maybe it's premature to give up. Maybe we need to think a little more generally about what form laws can take. So by 1922, people already understood that you could have laws that were chancy.
Chancy probabilistic laws that didn't tell you in a definite deterministic way what was going to happen. But laws that simply told you probabilistically what would happen. We knew about these Einstein certainly knew about these kinds of models. One of his great papers 1905 was on Brownian motion. This helped provide solid evidence for the existence of atoms even allowed you to figure out how big the atoms were.
And this is a model based on what's called a stochastic process, stochastic from the Greek word stochasticos, which means to aim or guess. These are models where the laws predict probabilistic behavior. So people knew about these things. Markov had introduced the Markov matrix by the early knots 1906 or something like that.
So these ideas were in the air and people were thinking about, well, quantum mechanics behaves in an unpredictable way. Maybe that unpredictability could be captured in probabilistic laws, but people couldn't come up with the right set of probabilistic laws at the time. Over the years, people did try to come back to this question. In fact, in Hugh Everett's thesis, he talks about an effort by a physicist named Fritz Bopp
that replaced the usual quantum-mechanical formalism with probabilistic laws, with particles moving around according to probabilistic laws. And Everett actually said this was a promising direction. He wasn't going to study it in his thesis, but this was worth paying attention to. Several other people worked on these proposals, Imre Fenyes in like the 1950s, most famously Edward Nelson in the 1960s. But the models were very complicated.
To get the same predictions that you get from the textbook theory of quantum mechanics, you had to, this is the one political thing I'll say, gerrymander, you had to gerrymander, I mean this in metaphorically the same sense, you had to gerrymander the laws. You had to start with what we knew was supposed to be predicted and then work backward and design these incredibly complicated stochastic laws in order to get the same predictions. So it just felt very unmotivated.
The spirit was a very interesting spirit. Let's just have particles bouncing around or fields, whatever, evolving without a Hilbert space, without wave functions. Let's just directly give them rules that are probabilistic. And in such a way that those probabilities agree with the probabilities we see for measurement outcomes in our experiments. But getting the idea to work was hard. It wasn't clear that we had the right kinds of laws to do it.
And the laws to make them work even in the simplest cases required a lot of fine tuning and gerrymandering. And when you look at, for example, Nelson's stochastic mechanics, you know, his laws are super complicated. And you actually have to first find the wave function from the Schrodinger equation, then you plug it into these laws and laws involve rates that go forward and incredibly complicated.
There were rival approaches. So, Louis Dubois introduced a pilot wave theory in the 1920s that was independently discovered by David Bohm and these theories were based originally on hidden variables, particles that were piloted around by the wave function in some sense. When you try to extend these models beyond systems of non-relativistic particles but to like relativistic systems and fields,
It gets very complicated and you end up having to deduce probabilities and stochastic laws again. So there seems to be this understanding that ultimately to describe most kinds of quantum systems will need something like laws that are inherently probabilistic. But none of the probabilistic laws that people knew about seemed to work well. They either didn't work or required so much fine tuning that they just seemed unmotivated. In 2022, I was trying to teach
a class and I had a problem. We were getting to the point in the class where I was trying to introduce a little bit of quantum mechanics and I was trying to decide how to do it and I taught this class a few times. Which class? It's called Introduction to Theoretical Physics. It's Physics 19 here at Harvard and we cover a lot of topics in the foundations of theoretical physics in this class.
Throughout the class, we're introducing some concepts from quantum mechanics, but this is the sort of toward the end of the class and I'm trying to give them a nice self-contained preview of quantum mechanics. But these are students who are mostly very new to physics. Many of them are just beginning to learn college level mathematics. So I can't start by talking about Hilbert spaces or C star algebras or the GNS theorem or any of those things. I need to find a more
Friendly way to get into quantum mechanics and every year I would just tear apart my curriculum and try again I was never satisfied with how I was doing it Sometimes I would say maybe we'll just start with wave functions and sometimes I would say maybe we should start with matrices and some I just I couldn't come up with a way that I wanted to do it and in the fall of 2022
I remembered back to a couple of projects I'd worked on as an undergraduate and even in graduate school where I needed to use the theory of stochastic processes in order to, you know, in undergrad, it was like a special extra homework set assignment for a linear algebra class in grad school actually used it for simulations. And, you know, the theory of Markov chains and stochastic processes, it bears some very vague resemblances to quantum mechanics.
It's got probabilistic laws. You represent the probabilities for a system with a vector. Evolution in time is represented with matrices. Now they're all a little bit different. The probabilities don't involve complex numbers. The matrices are what are called stochastic matrices.
But there are these like resemblances. And so I sat down and I thought to myself, maybe I can find some way to bring these two theories together. The theory of stochastic processes on the one hand, and the theory of quantum mechanics on the other hand. I had this sort of image in my mind of like walking along the edge of a chasm. On one side,
You had sort of the classical world, classical stochastic processes, probabilistic processes. On the other side, you had quantum mechanics and there was this huge gulf between them. And I was looking for a place where maybe the cliffs came closer together and where it was easier to hop across from one to the other. So I began modifying the mathematics of the theory of stochastic processes and quantum mechanics to try to bring these two pictures closer and closer together.
I was doing this without really knowing very much about this earlier work that had been done, the work of Bopp and Fenyes and Nelson. If I'd read all those papers, I would have given up because I would have decided it was impossible. But sometimes you can only do something if you don't know it's impossible. I did know it was impossible.
I brought these theories closer and closer together, expecting that there would be a moment when I would need to make some kind of jump to get from one theory, classical physics, to the other theory, quantum physics. And the strangest thing happened. The two cliff faces merged. And there was just no chasm anymore. For those who are familiar with second order phase transitions in statistical mechanics, it was like I had reached a point of a second order phase transition. On one side, you have the
You know, two phases of some substance like water, right? And then you go past a point and the phases merge and there's only one super phase, right? There's no distinction between like liquid and gas anymore, right? So, and I didn't understand what had happened. I was very confused. So I began looking in literature to see if other people had done what I had done and no one had done what I had done. No one had, I guess, thought it was worthwhile to try to do this thing that I was doing.
But I began to read some literature on stochastic processes and Nelson's work and I was confused why had they not succeeded when this seemed to work. And it was about October of 2022. I know because I went to the office of one of my colleagues, the great Logan McCarty, who directs science education here at Harvard. He's a quantum chemist. He knows quantum mechanics backward and forward. And I went and I talked to him and I went to his, he had a whiteboard and I
I began writing out everything I was doing because that point I'd realized that the secret sauce, the thing that made this work was I had implicitly given up an assumption I didn't even know that I was supposed to make or that anyone had made. When people model stochastic processes, they usually assume that the process is a Markov process. Named after Markov, like Markov, the Russian mathematician who introduced Markov matrices. A Markov process is a process where
If you want
And the generalizations of Brownian motion, Wiener processes, and many of the familiar processes that we have heard of, random walks, Poisson processes, these are all Markov processes. Nelson's work, a Markov process, they're all memoryless processes. Now, I was vaguely aware that there existed a subject called non-Markovian stochastic processes. And I went and I looked in textbooks to see if anyone had done what I was doing.
And usually at the end of the textbook, the textbook would say something like, and that's it for the theory of stochastic processes. There is a larger subject called the theory of non-Markovian stochastic processes, but this is too complicated. It is beyond the scope of this book. So it was very hard to find any books on non-Markovian processes. And I went into the literature and I discovered some people were trying to develop tools for handling non-Markovian processes. There's some that can be turned into Markov processes with a change of variables. They become what are called hidden Markov processes.
And some of them if they're just sufficiently non Markovian are just super hard to deal with and so it just feels like the wild west there's just this discipline going beyond the mark of approximation that a lot of people didn't really. You know felt a little uncomfortable exploring it wasn't clear how much we needed them i mean mark of chains are really good at modeling the world around us to really need to spend so much time worrying about non markovian processes.
And what I realized was that I had inadvertently introduced a kind of a non-Markovian process without realizing it. As I plumbed this more, I discovered that what I was working with wasn't even a non-Markovian process in the most familiar sense. It was an entirely, it was a more general kind of a process that first shows up in the research literature in 2006. It's called an indivisible process.
Indivisible processes are in some ways the most general kinds of rules, dynamical laws, generally probabilistic, that fail to have that Markov property. They're more general than what we usually think of as non-Markovian processes. I guess there's more than one way to be non-Markovian and people had a very particular idea of what they meant by non-Markovian. This is like even more non-Markovian than a non-Markovian process.
These processes first showed up when people were trying to understand the kinds of dynamical rules that describe Hilbert space objects. So not what I had in mind. They were already in the Hilbert space picture trying to describe how objects in the Hilbert space picture could evolve in time. And for them, an indivisible process was just a law that could tell you how your process would evolve from one time to another, but couldn't be divided up into smaller times.
So you have a law that tells you how to get from zero to the final time, but the theory just doesn't give you laws for the intermediate times. That's it. That's the indivisibility. Certainly not laws that can be iterated and concatenated into a bigger, bigger law. And if you think about it, this is certainly more general than divisible laws. I mean, because there's this bigger category where we don't have some of the properties we might want a lot of have divisibility. Newtonian mechanics is divisible.
You evolve a system from an initial time to some intermediate time, and then you can stop, look at the system state right now, and then if you want, you can use Newton's laws to tell you what will happen next, nice and divisible. The Maxwell equations that describe the evolution of electric-magnetic fields are divisible, and quantum mechanics, as usually formulated in terms of the Schrodinger equation, beautifully divisible. The Schrodinger equation tells you how the quantum state will evolve, and you can evolve it however far you want, and then read off the quantum state in some way, and then predict where it will go next.
Is another way of saying divisibility as a continuous time parameter? That's a good question, not necessarily, because you could imagine an indivisible process where you're allowed to go from the initial time to any time you want, so time is smooth, but once you pick one of those times, you don't have a law that will tell you how to get from that time to later times.
So time is not necessarily discrete here. It's an excellent question. But what you lack is the ability to break time up into smaller intervals. Yeah. So we just don't have much experience with these kinds of laws until this paper comes out in 2006. It's called Dividing Quantum Channels by Ignacio Chirac and Michael Wolff. Ultimately, it was published in 2008 in Communications and Mathematical Physics. And people play around with these. You know, the paper gets a lot of citations. It's not until 2021
that a couple of folks introduced the idea of a classical process that could be indivisible, like just a process where the system has some configuration and it's changing, it's behaving in some probabilistic way, but the way it's behaving probabilistically is indivisible. That shows up in a figure on like page 15 of this beautiful review article
by Mills and Modi where they mention the idea that you could have a process like this. I didn't know it existed. I came up with the term indivisible independently because I didn't want to use irreducible, which is used in so many ways in physics. I didn't want to use
I basically just was looking for a word that would give you evoke the right idea. And it turned out they use the exact same terminology. So this was a year before I did it. They did not connect it to quantum mechanics. They were just mentioning always the possibility you could in theory have a classical process with probabilistic behavior where the laws are not rich enough. They're too sparse. They won't tell you how to go from any time to any other time. You can only evolve from certain times to other times. The process in general doesn't divide.
What I had inadvertently done was discovered these indivisible stochastic processes and shown that there was just a change of mathematical representation that would take such a system with classical like configurations, could be a system of particles, could be a system of fields, whatever we're trying to model. And if it has indivisible stochastic laws, then through this mathematical representation, this correspondence,
You get a Hilbert space picture. Super interesting. Yeah. And all the weirdnesses of the Hilbert space picture, superposition of states, interference effects, these are all related to what are called coherences, phases, right? They're all the all the connect all these things are connected to, to, you know, superposition interference and coherences. These could be understood now.
They could be given a meaning. So in textbook quantum theory, these things don't have meanings. They're just pieces of mathematics that show up in the formalism. We don't understand what they mean. We know that interference shows up in experiments. We know that these things called phases or coherences or superpositions, we see these show up in all over the place, but they don't directly have like a physical meaning. We don't know what they represent and what they really mean. What I was able to show is
that in going from this very physically concrete picture of objects of a clear ontology probabilistically evolving in this indivisible way in going from that picture to a picture with a nice Schrodinger equation where the evolution is divisible it's a nice differential equation very familiar mathematics in going to that picture that looks divisible you have to give something up that indivisibility doesn't disappear
It becomes all those weird phases, interference effects and coherences. That's how they manifest in this picture. It's like there's no free lunch. If you want a picture that's mathematically convenient and simpler, a picture where you can evolve a system any amount of time you want, pause, re-evolve, a nice divisible dynamical picture, you have to pay the price. And the price is that all that indivisibility becomes these weird phases. In some very loose sense,
If you want to think roughly speaking of these individual processes as being like processes with memory, all those interferences and faces, those are the memory encoded in this strange way. And that's the picture. That's fantastic. Yeah. So in this picture, there's no fundamental role for a wave function. I mean, you just have objects bouncing around, according to laws that are more general than laws of Newtonian mechanics, or even the laws of a Markov process.
And if you want to model a measurement, you just model another system that interacts with your first system, give the whole thing a nice simple set of stochastic, indivisible stochastic dynamics. And what you'll find is that the measuring device will stochastically evolve into one of its final readout configurations with exactly the correct probability that we would expect from the Born Rule. But there's no wave function, there's no collapsing,
It's just some big stochastic process happening. Experience a membership that backs your business journey with American Express Business Platinum. When you pay with membership rewards points for all or part of an eligible flight booked with a qualifying airline through Amex Travel, you can get 35% of those points back, up to 1 million points back per calendar year. American Express Business Platinum. There's nothing like it.
Terms apply. Learn more at americanexpress.com business-platinum. So what's doing the choosing of what interval to make that time? He said that you can choose any interval but then you can't choose a sub interval. Right, this is an excellent question. So
In order to get an indivisible stochastic process started, you need a time at which you can begin, right? And then the process tells you probabilistically where the system will end up at really any smooth choice of later time. But is there just one special time where things can get started? The answer is no. What you can show is that when you have a system interacting with some larger system, so not left to itself,
interacting with some larger system. What you find is that if this larger system is exchanging information with your original system, as would happen if you've got a measuring device reading out the configuration of your system, then when it does this, you just let the stochastic process tell you what happens. There's no axiom here. You let it evolve and what you discover is that you get a division event. The evolution divides at that moment, seen from the point of view of the smaller system.
And now there's a new time at which the evolution breaks and you can start now again from that new time. So in an individual stochastic process, it's not that there are no times where you can divide. There are times at which you can break up the evolution, but the times aren't given to you at the beginning. They're not fundamental. They arise from mutual interactions between systems.
Now when you ask what does this look like from the Hilbert space point of view, in the standard textbook quantum mechanical picture, the Hilbert space point of view, what are those division events look like? They look just like decoherence. So decoherence again is when a big system interacts with maybe a smaller system, the environment comes in interacts with the system exchanges information, and we get these changes to the quantum state of the other system changes that don't single out one answer, but do change it in some way.
Those changes kill off the coherence effects. They kill off interference effects. From the point of view of the indivisible stochastic process, they just look like the generation of a new moment, a new division event, an event where the evolution can be started again. And this happens in the end of measurements. And this is a physical process in this picture. And it coincides with what you would call a measurement. But it's generated by the laws of this picture themselves.
Okay, I'm confused. So division events, is that just another relabeling of what a measurement is? Good question. So in a way, sort of, if you give me a second system that I model explicitly, so let me phrase it a different way. In the textbook axioms of quantum theory, measuring devices are treated as outside the formalism, right? They're not
They're kind of in the background. They're kind of like the person behind the curtain, right? We do a measurement and we just sort of change the quantum state of the system being measured, but we don't usually explicitly put the measuring device into the description itself. If you try to do that, if you try to put the measuring device into the description, what you find after a measurement is
that the measuring device and its possible readout configurations become entangled with the possible configurations of the system being measured. There's this entanglement that happens. And the question is, well, then what? Now they're entangled, what do I do? What you're supposed to do is collapse down to one of those entangled branches. That's the collapse. Now, if there's a bigger environment that comes in, and the bigger environment looks at the measuring device,
Then it gets entangled with the measuring device and there's this operation, this sort of formal operation where you can kind of ignore the environment and you see that there's a suppression of all the interference effects but still no singling out of one outcome. You have to at some point pull the fifth axiom, activate it and collapse down to one thing at some point. In this indivisible picture, you can bring in that measuring device, you bring it in,
you let the overall system of all stochastically and what you find is that and bring in an environment the environment comes and you can treat them all as actual systems none of them are are outside the formalism they're all modeled as systems in the formalism when you find is you let the systems of all the system being measured and the measuring device probabilistically evolved toward the configurations that we would expect from the you collapse axiom
And because of the environment, you can show that the measuring device and the subject system, they experience a division event at almost exactly the moment of the interaction that we would call a measurement. And this division event means that you can now restart the laws and start them from this moment. This division event is not postulated. It's not an axiom. It's something that just shows up from the usual rules of probability theory.
when you actually model the systems explicitly. So in a way it is a measurement, but it doesn't require a conscious being, it doesn't require a human. Any system that has a robustly large number of moving parts, we call them degrees of freedom, in contact with a nice big environment with a big number of degrees of freedom,
will to an extremely high level of precision, produce measurement results that probabilistically coincide with what we would expect from textbook quantum theory, and will generate a moment at which the stochastic dynamics of the system being measured in the measuring device can be restarted and have their own dynamics. So
So yes, in a way it's a measurement, but it lets us get inside the measurement. It lets us see the measurement actually happen, and it gives us a way to understand why measurements do this thing, rather than merely positing that they collapse wave functions. So do you require three different systems to be stated? So the environment, the measurer, and the measured? Yes, that's right. And we require that in standard quantum measurement theory anyway, in the usual textbook theory. The environment as well?
The environment is needed, yeah. Yep. Because the usual argument is that the environment is what generates the decoherence of the measuring device and the system being measured. But when you say the environment, I mean, in any realistic measuring device, you have, you know, the part of the measuring device that's actually directly engaged in the measurement, but then you have the rest of the measuring device. I mean, it's a big object, it's in a box, it's got dials, it's got other experimental things on it. I'm sorry, this is me not being a very good experimentalist again.
So you firstly describe the environment, the measure, and the measured classically, and then you do your version of a quantizing procedure? Yeah, so you model them classically in the sense that they have classical-like configurations. The measuring device
is some system, some physical object that can be in different possible configurations. Among those we include at some level of coarse graining. We include, you know, the system is empty, it doesn't yet show a reading, the system shows spin up on the dial, the system shows spin down on the dial, you know, like, but these are concrete configurations made of particular configurations of the constituent atoms, whatever you want. So
That is to say that their configurations their ontology their physical existence is visualized in a roughly classical way. The quantum part is that the laws they satisfy are not deterministic differential equations like Newton's law or Newton's laws or electric or the Maxwell's laws of electromagnetism.
The laws we give them are these indivisible stochastic laws, which we don't usually see in classical systems. The claim is that when you give these systems these more general kinds of laws, that's enough to make them behave like quantum systems. So what is it that's jittering around or being random here? Good question. So all these systems have configurations, and these configurations are evolving according to stochastic laws.
That is to say that the configurations are changing with time in a probabilistic way. Now, why are they changing in a probabilistic way? I don't know. These are the axioms, right? At some point you have a physical theory you have to propose some axioms. I mean, there's a
What a posture in how we think about basic questions in philosophy called foundationalism. You have to begin with something. The standard textbook version of quantum theory, which works fantastically well, and I'm certainly not making any claims that any of the predictions it makes are wrong. They're all spot on. Those axioms are axioms and they're very strange. We posit Gilbert spaces and
state vectors or density operators and the Schrodinger equation and self-adjoint operators and all the collapse postulate and we postulate them because with these axioms we get the right predictions empirically. This picture I'm presenting has axioms too. The axioms are simpler. Every system just has a set of possible configurations, classical-like configurations and the laws are these indivisible stochastic laws.
That's it. Um, now, if you want to ask why the laws are into the fantastic, I don't know. The best I could say is that when we try to explain things, there is a case to be made that you want to start with the least constrained possibilities, the most general possibilities, and then argue that in some circumstances, you get more constrained possibilities.
Indivisible
To me, it makes sense that you would begin with the most general kind of law and then you would explain why in certain special circumstances we would expect to see a Markov process, why in certain circumstances we would expect to see deterministic second-order differential equation kind of a law.
You know, that's the job of understanding the quantum classical transition, understanding the so-called classical limit. How do we get from the laws of quantum mechanics to laws that look like Newtonian mechanical laws or that look like classical Markov processes and those arguments carry through just as well in this picture.
We don't start with deterministic laws. We don't start with a Markov chain or anything like that. We start with these much more general laws. And then by adapting the usual arguments people usually make in trying to get to the classical limit, the classical regime, we see why in certain circumstances we get big classical looking systems whose laws look deterministic or at least look like their Markov probabilistic laws. And to me, that's the right direction of explanation. You start with the more general, the least constrained kinds of laws and you move to the more constrained ones.
So I guess I would say it's not that I feel like I need to explain why particles or objects behave probabilistically. Probabilistic behavior is the default. It's what happens if we don't have a good reason to think the laws need to be deterministic. And then the goal is to show why in some circumstances we get predictably deterministic behavior. But the truth is I don't have a deeper explanation for why we expect the particles to be jiggling around probabilistically.
That's what it means to have an indivisible stochastic law, really stochastic law in general. And your probabilities, are they classical probabilities or are they quantum amplitudes? It's a great question. They're classical probabilities and that's kind of key. So this underlying picture, the claim that every quantum system in its beating heart is really
some system with configurations. If it's a particle, we're talking about where the particle could be. If it's a field, we're talking about what are the different intensities the field could have in space. If it's a system of abstract bits, like in a computer, it's some configuration of zeros and ones. This is what I mean when I say a classical-like ontology or a classic-like configuration space. And the probabilistic laws are assigning
ordinary probabilities to these things. They're saying that the system begins in some configuration and then the indivisible stochastic law takes the form of laws that probabilistically tell you where it will end up. And those are just ordinary probabilities. They're real numbers between zero and one. They sum to one. There are no complex numbers at all in this picture at this point. But if you want to describe the same process in a more mathematically convenient way, I mean, indivisible processes are really
So instead, we use this mathematical change of representation to the Hilbert space picture. We translate all of the ingredients in this underlying process into this Hilbert space picture. In the Hilbert space picture, we have nice differential equation type laws, the Schrodinger equation. We've got complex numbers that show up. And then the probabilities that you have in the indivisible stochastic theory become what we call mod squares of
complex numbers. The complex numbers that you mod square to get probabilities are called amplitudes. So it's only in going to the Hilbert space picture that we have the need for amplitudes. And the amplitudes do all kinds of funny things. They interfere with each other. If you want to write down a process where a system could go one way or the other, you're supposed to consider all the possibilities and then add all the amplitudes together and there's interference, right? But that's all happening in this sort of mathematical representation, this Hilbert space side. And the claim is that's not telling you what's physically happening in the system.
That's just very convenient mathematics. And again, makes all the right predictions, right? The idea here is you get back the usual textbook axioms of quantum theory, but now you understand where they come from. And now they're not inconsistent anymore because at a fundamental level, there's no special role of the observer. There's no special rule for measurements. All the processes that we think of in quantum mechanics are just ordinary processes. They just look weird and exotic when you see them on the Hilbert space side.
Have you encountered any resistance from people who like their quantum mechanics mystical? Yes. Explain. Well, I mean, quantum mechanics is so exciting. Actually, let me rephrase that. Not that they like their quantum mechanics mystical. Have you encountered any resistance from people who like their quantum mechanics mystified? Mystified.
Yeah, they like it shaken not stirred, right? I mean, a little bit. Yeah, I think it's so there's a sense in which this picture is deflationary. It deflates. It takes exotic statements. Oh, the cat is alive and it's dead. And it deflates them and says, actually, it's really one or the other. And
We merely represent it mathematically with a state that looks like it's a superposition of live and dead, because it gives us divisible evolution we can use. It's easier to study mathematically, but it's not the reality. It deflates that, yeah. Just to be clear, deflationary is the philosopher's term for saying there's nothing to see here, folks. Just calm down. Yeah, it's basically that. It just like sucking the air out of a balloon, right? It brings it down to Earth, which is basically what this does. It makes quantum mechanics, I think, in some ways much more boring.
And, you know, as I was working on this, I kind of felt that because when young people go into physics and they begin learning about quantum mechanics, it's super exciting to think that you can be able to understand what's going on when the cat, Schrodinger's cat, is alive and dead and particles can go through both holes in the interference experiment at once and it interferes with itself and everything is entangled with everything else. And maybe when we think about things, humans are special, we collapse things.
It says that at some level quantum systems might, if this all works out right, might just be kind of prosaic. There's no wave function in Hilbert space, there's just objects, atoms, chairs, whatever, and they're just evolving just in an indeterministic way, a very indeterministic way.
Well, still probabilistic. We can still assign probabilities to things, because you could imagine laws that are so badly indeterministic that we can't even assign probabilities to them, but we can at least assign probabilities to them, but then a lot of the magic is gone, right? There's no special world for humans. In some sense, I mean, what is it? The history of science has pushed humans farther and farther out of the center of the story. You know, first we were the center of the universe, then we weren't.
Then maybe we were the center of all observations and quantum mechanics and this takes us out of that altogether. There's nothing particularly special about human observation or the human mind. And I guess with AI development, we might soon not even be the smartest people on the planet, the smartest organisms or entities on the planet. So I don't know. I mean, I can only speak for myself. I have felt a little sad to think that there's a way to think about quantum mechanics where there's no wave function.
Nothing is splintering into multiple realities. So there's a way to take Newtonian physics and introduce kinetic energy, which is an energy associated with things moving and potential energy, which is an energy associated with configurations of things.
And you take these two quantities, they're a bit more abstract than like particles and forces and stuff, but you can imagine kinetic energy and potential energy. And you subtract them from each other, which is kind of a weird thing to do. Usually, we think that the total energy is the sum of these things. You can subtract them, and then you can integrate this thing over time. And you get a mathematical construction called an action, the action functional. We're actually covering this in my class right now. The thing you're integrating, kinetic minus potential energy, is called the Lagrangian. At least in the simplest cases, it's kinetic minus potential energy.
And you can use this to encode the laws of your system. You can use this to describe how the system will behave. But you could ask, what is the action? Like, is it a physical object?
You can make the action evolve in time. You get what's called Hamilton's principle function. It obeys a partial differential equation, and I didn't mention it, but this is the beginning of Hamilton-Jacobi theory, and it was by studying the time-evolving action, the Hamilton's principle function, and its differential equation that led Schrodinger to discover the Schrodinger equation. It was a beautiful extrapolation from the partial differential equation satisfied by this action. So this action as a function of time or Hamilton's principle function
is a lot like the wave function of quantum mechanics, so much so, like I said, that it inspired Schrodinger to develop the wave function. In some sense, Schrodinger's wave function was like an exponentiated version of this Hamilton's principle function. So you could ask, what is the meaning of Hamilton's principle function? Is there an object out in the world evolving according to this partial differential equation, the Hamilton-Jacobi equation, the equation satisfied by this principle function, this integrated kinetic minus potential energy?
I think most physicists would say no. They would say that it's just a mathematical convenience. It's an appurtenance of the theory. We can use it to generate predictions. We can use it to make predictions. And that's wonderful. It's beautiful mathematics. But there is no object in physical reality it's describing. And what I'm saying is the wave function is basically just like that. It's in the same conceptual or metaphysical category as Hamilton principle functions.
Sure, it's in the mathematics, it's convenient, but there is no physical object that it is describing. And because there's no physical object, there's nothing branching, there's nothing splintering into branches. So you would never even think that there could be many worlds or anything like that. There's just nothing in the ontology of the picture as I've presented it that would play the role of branching realities. So things like many worlds don't even get off the ground in this picture.
I think that's kind of what I mean when I say that there's no wave function. I mean it in that somewhat precise sense. I don't mean that we shouldn't use wave functions in the mathematics or use them to make predictions, but we should be a little more modest in how we talk about them. Have you spoken to Sean Carroll about this? That's an interesting question. Not yet.
But at some point we'll chat, hopefully. Yeah. I say it's an interesting question because I have not done a lot of traveling in the last year or so, so our paths really haven't crossed. But I'd love to have a chat about it at some point. Well, any Everettians or many worlds, people? A little bit. A little bit. But I think, you know, you talked about mysticism, you talked about how people like their physics. The truth is that people get really good at doing physics in a certain way.
And we develop intuitions. When you learn to play an instrument, learn to play the piano, right? You learn to play chess. You learn gourmet cooking. And you do this over many years. And if you've got the right combination of motivation and talent and skill and the right environment and the right mentors, the right combination of all these factors, you end up becoming very proficient at it.
And you can do wonderful things. You can play beautiful pieces of music. You can make just fantastic cuisine. You can become a grandmaster in chess. And if someone comes along and says, I think you should do this differently, you should go back to the to the starting board, you should sit on the piano bench like this, and you should hold your hands like this, or you should play chess. And the pieces should start off in a different position. And we should change all the rules, right? The chess pieces should move differently.
You're going to render a person back to square one. And you could imagine why someone probably wouldn't want to do that. And it's not for any negative reason. It's just that they've optimized themselves to do really good work, right? And to ask them to go back to the drawing board and start again is a huge ask.
And so I would basically say anyone who's been doing quantum mechanics in a certain way their whole career, who's developed all kinds of intuition, they just have a good feeling for what to do with wave functions and stuff, you know, I could imagine someone, you know, in that position, being reluctant to want to go back and rethink all the foundations from the beginning, especially if most of their career, what they've heard is the foundations are fine. Quantum mechanics is just a device for generating predictions. Why should I go back and even think about any of this stuff? So I don't think that
I certainly am not critical about any of that attitude, but what I have certainly found is that people who are newer to physics, students, tend to be much more interested in talking about a project like this. But there are absolutely exceptions among professors as well. I'm going to have some wonderful colleagues who've been incredibly receptive and open-minded and we've talked about this project a lot and I've gotten a lot of really good input from people.
You know, but so I think it's a combination of intuition building and also what calls us to do quantum mechanics. I mean, quantum mechanics is such an exotic theory and to think that you're going to spend your time imagining the world is some wave function.
Or state vector or some abstract object living in a high dimensional configuration space or in somewhat modern sense in a high dimensional Hilbert space. Hilbert spaces are beautiful. The mathematics is incredibly elegant and it has a certain kind of spiciness to it. But complex numbers floating around. We don't know why, you know, at least the way we usually talk about it. I can imagine being romanced by that. I was. I feel like that's what brought me into quantum mechanics.
So I can definitely see why some people would like to keep that. And I think among all people who take that romantic view about quantum mechanics, I don't think anyone takes a more romantic view than Everettians, people who work in the many worlds interpretation, because their picture of the world isn't just exotic. It's profound, right? The idea that
Every time a quantum event takes place, the universe splits into, in the cartoon picture it's like two or three branches, but in the sort of more sophisticated, more fine-grained version of the Everett approach, it's an uncountable profusion of branches. I mean, it's mind-blowing and amazing and it forces you to confront some very deep questions in metaphysics, in philosophy of mind. It's just so rich with inquiry
I can imagine people working in that field would like to hang on to it. So I'll give you two examples, because I can relate to this to being inveterate and obstinate. So when I was learning about the categorification of quantum mechanics, and I'm reading papers like, okay, here's another way you can think of quantum theory as a daggers symmetric monoidal category. And I'm looking at him thinking, okay, but but so what? I still have that so what but I think a part of it is that I'm used to doing quantum mechanics.
Windows XP
Couple years ago, Windows XP on his computer because he's familiar with Windows XP and wants to use DOS and can't run QBasic on Windows 10 without some emulator or virtual machine. So my dad is like what you're classifying as the or what you're characterizing as some people who are used to quantum mechanics in the old way, at least when it just comes from not their dislike of it for being deflationary, but their dislike of it from being different.
Now the question could be, well, Jacob, what does it provide me? What does your approach give? Why should I learn it? You've just said that it seems like regular quantum mechanics. Okay, cool. Perhaps to you, it's a more beautiful version. Maybe to someone else, it's more convoluted. But whatever, what does it give you? What's the upshot? It's a great question. So the first upshot is it patches up the axioms. The axioms had this ambiguity or inconsistency or incompleteness to them.
They had this mystery about what a measurement is that seems to play a role in the axioms but isn't defined by the axioms. And you run into problematic thought experiments like Wigner's Friend experiment. And the Wigner's Friend thought experiment is, it's not exactly the same thing as the problem of black hole information loss by any stretch, but there are some resemblances, right? There's this big problem in quantum gravity, black holes appear to radiate according to work going back to Stephen Hawking.
um and there's this tension between evaporation of black holes quantum mechanically and unitary or schrodinger evolution which is information conserving in some quantum mechanical sense and the fact that black holes supposedly can't allow information to escape there's this tension between all of these things um that's the kind of tension we're seeing with thought experiments like the vigner's friend thought experiment and it's not like the black hole evaporation problem is more accessible experimentally
I mean, to go out and actually do experiments on black hole evaporation, you'd have to set up 10,000 identically prepared black holes, which we don't have to do, wait many times the age of the universe for all of them to evaporate, ensure they all evaporate inside of a completely sealed chamber with perfect detection mechanisms to collect all the Hawking radiation that comes out, with sensitivity enough that we can detect, you know, incredibly tiny, tiny entanglement effects, right? And then subject all the data to a level of analysis that we think may be computationally impractical.
I mean this is not a practical problem at least as far as we know yet that could change but as far as we know it's not a practical problem yet this is considered a serious area of research whereas the inconsistencies in quantum mechanics are not considered as serious for some reason I don't quite understand there's some sociology there what I would tell quantum physicists is one advantage this approach is that it it resolves some of those inconsistencies which is itself may be a good thing
It does it in a way that doesn't require that we model only one kind of quantum system. One of the disadvantages of like Bohm's pilot wave theory is it works really well for very simple kinds of systems consisting of finitely many fixed numbers of non relativistic particles but has resisted being neatly generalized beyond that. So it's nice to have a model that's a little more model independent and simpler than the Bohmian approach.
And it doesn't run into many of the confounding metaphysical mysteries that one has to deal with with Everettian quantum mechanics. You know, we're not making zillions of copies of us in this picture. So it provides, I would argue, one, and maybe at this point, maybe the only attractive, in my opinion, way to resolve these inconsistencies with quantum mechanics, although your mileage may vary, and I don't want to speak for everybody by any stretch,
That to me is already something. The second thing is it provides a picture. Quantum mechanics, when I teach quantum mechanics to students, they're expecting me to talk about waves moving in 3D space. And when I show them the axioms, a lot of them are very disappointed. They're like, but where's the picture? And isn't it like there's an electron and it emits a photon? And I'm like, well, the textbook axioms don't really talk about an electron here emitting a photon there. According to the axioms, that's just added for color. We draw pictures of electrons emitting photons just
Just to help tell the story, but none of this is actually legitimated by the axioms of quantum mechanics. There is just also the problem that there are a lot of phenomena out happening in the world that aren't measurements. You know, when early gases are mixing in the primordial universe, when stars far away are colliding, when, you know, a piece of aluminum sits on the surface of Mars and doesn't collapse under its own weight, when birds forage, when humans fall in love,
These don't appear to be measurements, and yet the axioms of quantum theory only make predictions about measurement outcomes, probabilities of measurement outcomes, and averages of measurement outcomes weighted by measurement outcome probabilities, and that's it.
That's a very narrow category phenomena. How do we get from that narrow category phenomena to the wider category of all the other things that we think are happening in nature? Or are we just going to say that our talk of all those other things of birds foraging and early gases mixing is just for color, is just storytelling? So this allows quantum mechanics to be a theory of all the much larger category phenomena rather than just this narrow category of measurements. I call this the category problem of textbook quantum theory.
But ultimately, I think physicists are going to be interested in applications, practical applications. Or you'd hope. Well, we would hope, but yeah. But in my experience, physicists, they want to know, what can we do with this? I think there's some things you could do with this. One is, indivisible stochastic processes, at least classical indivisible stochastic processes, are currently three years old.
This is an area of dynamical systems theory that is completely unexplored. It's like opening up a sketch pad that's full and turning the page and finding like a totally blank new page. How often does that happen in mathematics or science that you turn a page and you open the door to some completely new area of inquiry? I don't know a lot about the mathematics of indivisible stochastic processes because nobody does yet.
I think that's just interesting. I think it would be very interesting for people to think about these kinds of systems and work out their properties. It may be that the best way to study an indivisible plastic system is to write down a Hilbert space for it and basically do quantum mechanics. Just like sometimes the easiest way to study Newtonian system is to write down Lagrangian for it and do Lagrangian mechanics. But it may be that we can understand things about these systems on their own merits.
It may be that when you don't start from a Hilbert space but instead start with these different axioms, you can point to new ways to generalize quantum mechanics that would have been impossible to imagine before. If you're starting with a Hilbert space, that limits your imagination about what else you can do. If instead you don't start with a Hilbert space, you start with a more general kind of probabilistic system like I was talking about in this picture, this indivisible stochastic process.
Maybe there are deformations you can do to the assumptions, changes you can make to it to generalize these systems in ways that do not give you a Hilbert space. You could generalize these systems and get something else that doesn't give you a Hilbert space and that you never could have gotten to if you'd started from Hilbert spaces. And maybe we need a generalization like this in order to make progress on foundational questions in say quantum gravity. So I think that's another potential area of use. And then another area is
If there's this correspondence between Hilbert space representations of quantum systems and classical looking probabilistic systems, especially beyond the Markov approximation, this might suggest that there are efficient ways to simulate non-Markovian classical stochastic systems using quantum computers. So one open question is, if we had a quantum computer today,
What would we use it for? There are already a number of known algorithms. There's no proof that the algorithms are stronger than what you could ever do with a classical system, but it's widely believed that many of the things you could do with these quantum algorithms are far more efficient than you could ever do with classical algorithms. But it's not like every question you'd want to do in a classical computer can be done more efficiently or more quickly in a quantum computer. So figuring out what are the kinds of things
That a quantum computer would help us do more efficiently is a really open question. And when you set up a correspondence between quantum systems and a large class of stochastic systems, you open the door that there are some problems that may be difficult to simulate classically that are easier to simulate quantum mechanically. I don't quite know what those are yet. That's an area of research that I'm working on right now.
But I'm talking to people who work in the theory of quantum simulations of classical stochastic processes. And we're trying to determine maybe there are ways to use this correspondence to provide more efficient ways to simulate these systems and provide a new application for quantum computers. So now there's also the possibility that in some circumstances, indivisible stochastic systems might actually behave differently from quantum systems, at least textbook quantum systems.
There are maybe slightly different predictions for a Wigner's Friend thought experiment. Unfortunately, doing the Wigner's Friend thought experiment is probably out of our experimental capacity for the next thousand years. Who knows? But there are some cases in which you want to model the quantum system and you need to throw in additional assumptions in order to actually make predictions, assumptions that go beyond the textbook axioms.
For example, if you want to model a very, very complicated quantum system, you may have to add certain additional axioms about, you know, what are typical initial states for the system? What kind of typical evolution would we expect? These go beyond the textbook axioms, and it's possible that when you start with different axioms, you would actually modify some of those assumptions. And so for some classes of very complicated quantum system, it's possible you could get slightly different predictions. But these are all highly conjectural claims. A lot more work needs to be done to determine if or when any of these could pan out. So I want to be very clear
We're only the very beginning here, but even to have this correspondence at all, I think opens up a lot of doors and there's nothing more exciting to me in science or philosophy than having open doors. Well, this is certainly cutting edge. My cutting edge is in it's been developed in the past couple of years and also it may have wide application soon and may actually be on the right track.
Does it provide any insight into QFT, which depends on a Fox space, which depends on Hilbert spaces? Yeah, so it's an excellent question. So quantum field theories are situated within the axioms of textbook quantum mechanics. So those axioms, I mentioned Hilbert spaces and showed all that stuff. Quantum field is a particular kind of a system that lives within the framework defined by those axioms. What makes quantum fields
Well, there's many things that make them complicated. One thing that makes them complicated is they have infinitely many moving parts. Unlike a system of, like, five particles, they have infinitely many moving parts. We see that these are systems with infinitely many degrees of freedom. And this causes all kinds of mathematical complications. When working with a quantum field theory, like regular, everyday physicists using quantum field theories today, often you have to regulate the theory. I mentioned Planck introducing Planck's constant to regulate.
The regulators we use temporarily make many of these infinite things finite so we can do the calculation and then what we do is we try to send the regulator to infinity and usually we can do that, then it goes away and we believe we have a good solid prediction that doesn't depend on the regulator. Unlike Planck's constant, the regulator goes away and we believe that we have a robust result that holds in the continuum infinite limit.
And there's a whole beautiful intricate story called renormalization and effective field theory. That's all about how to do that in a mathematically consistent way, reasonably consistent way, and generate good predictions. I'm not going to have time to go into all of that. But at the end of the day, right, this is still just a quantum system, a very complicated quantum system. And to the extent that you can generate the axioms
For any quantum system, you can generate them for quantum fields starting from an indivisible stochastic process. According to this picture, a quantum field is a collection of entities delocalized, spread out in space with configurations, and these configurations evolve in this indivisibly stochastic way that can be modeled in Hilbert space language.
In a sense, it's just like any other kind of a system, you are still going to run into the same mathematical complications, maybe new ones, from the fact that we have infinitely many and you have to do mathematical tricks to make these things tractable. But yeah, so the answer is quantum fields fit into this framework, but it's inherently going to be very complicated because quantum fields are super complicated.
And do you reproduce the exact postulates of quantum mechanics or do you have some deviations that there's an experimental way of testing whether the stochastic approach is the more underlying correct one? It's a good question. So at the level of the correspondence, there's just a mapping that takes you from the ingredients of the invisible stochastic theory into the corresponding Hilbert space description of its quantum Hilbert space representation.
There are in principle deviations because collapse doesn't fundamentally happen in this picture. However, the deviations are going to be pretty much the same as for any no-collapse formulation of quantum mechanics. So, Bohmian mechanics, the pilot wave theory of de Broglie and Bohm with particles being guided around by wave functions, Everettian quantum mechanics, you know, the many-worlds interpretation, these are all no-collapse interpretations. Collapse is not fundamentally happening. There's no collapse axiom.
And so you're going to get tiny discrepancies in the predictions of these theories as compared with textbook quantum theory. And I can make this super explicit. Go back to Wigner's friend. According to textbook quantum theory, Wigner's friend on the inside does a measurement, collapses the quantum system inside the box. That system is collapsed. It's collapsed for everybody. It's collapsed for Wigner's friend in the box. It's collapsed for Wigner outside the box. It's just collapsed. In a no-collapse approach, like many worlds or Bohmian mechanics or my approach,
There isn't really a collapse that's happened. And what this means is that the wave function Wigner is using on the outside, the quantum state, is a non-collapsed quantum state. It contains those superposition interference phase effects that have not been erased. They haven't been erased because there's not been a collapse. So in principle, Wigner on the outside, with a sufficiently powerful measurement apparatus, could detect
those small discrepancies, which would be discrepant from textbook quantum mechanics, but detecting them would be extremely hard. So there's a paper from a few years ago that Scott Aronson and Lenny Suskind and I believe one other author published in which they prove what people call the quantum necromancy theorem, which is just to say that
If you could, if Wigner could design an experimental apparatus sophisticated and sensitive enough to detect those tiny little discrepancies between the no collapse interpretation and textbook quantum theory, then that apparatus with some relatively simple modifications could take a long dead cat and bring it back to life.
Which we usually regard as a thermodynamically impossible feat, right? That's why they call it necromancy, like magically bringing the dead back to life. It would be akin to unscrambling an egg, right? Like taking a scrambled egg and turning it back into the original egg. I mean, this is beyond really any technological capacity we could imagine. So, yes, it makes somewhat different predictions.
But only as far as other no collapse interpretations make those same slightly discrepant predictions. And fortunately, those discrepant predictions are so minuscule that they would be extremely hard to measure. Easier to measure probably than the black hole information problem could be measured. But kind of the same level of like extremely tiny suppressed effects.
Hola, Miami! When's the last time you've been in Burlington? We've updated, organized, and added fresh fashion. See for yourself Friday, November 14th to Sunday, November 16th at our Big Deal event. You can enter for a chance to win free Wawa gas for a year, plus more surprises in your Burlington. Miami, that means so many ways and days to save. Burlington. Deals. Brands. Wow! No purchase necessary. Visit bigdealevent.com for more details.
Okay, before we end, I want to know what is a particle in your view? Also, is your view called an interpretation? Is it a theory? Is it a correspondence? What would you call it? Why don't we settle that right now? I don't have a good answer to that question. I think you could call it whatever you want. One could think of it as a physical theory. It has variables and ingredients in it and those ingredients have laws.
So it's a physical theory. It's a physical theory that makes the same predictions as textbook quantum theory in all realistic scenarios, as far as I know. You can think of it as an interpretation of quantum theory in the sense that if you start with the formalism of quantum mechanics and ask, how do we interpret the things? What do the things mean? This provides a platform for actually talking about what's really out there in nature possibly. I should say it's not a unique picture.
A given quantum system may represent many different indivisible stochastic processes, just like a Lagrangian or better yet a Hamiltonian formulation of classical physics can describe many different Newtonian systems. There's not a one-to-one relationship between these pictures. You could think of it as a formulation because it's a new mathematical framework. I think what you couldn't call it is a prescription, a recipe, because
It's more than just a list of steps to follow. It's more than just an algorithm the way the textbook axioms of quantum theory are just an algorithm to follow. It actually tells the story of things happening. So I don't know if that answers your question, but did you want to follow up on that or do you want me to talk about particles? Yeah. What's a particle? What's a particle? So classically, a course of particle is a point-like entity characterized by a mass of some kind, could be zero mass,
I guess it's a tachyon, it could have some weird imaginary mass. It's characterized by spatial degrees of freedom, meaning it has a location in some notion of physical space, usually XYZ coordinates when I think of it that way. It will generally have something like different locations, different moments in time, which we can think of as being like a trajectory. And
You know, if it's a truly point-like particle, then it has no internal structure. It has no volume. Nonetheless, it can carry certain other quantities. It can have other attributes like electric charge, which are related to how it interacts with fields and other kinds of particles. It can have an intrinsic form of angular momentum. So just as
You can have kinetic energy, but kinetic energy can kind of be frozen in and become kind of rest energy like an internal energy of a particle. Angular momentum is a kind of emotional kind of momentum, a kind of rotating momentum, but you could also have a frozen in kind that's called intrinsic spin. Particles can carry that intrinsic spin that can be converted into other forms of angular momentum just like rest mass can be converted into other forms of energy. So these are what a particle is. It's a thing with this collection of possible properties. In
Quantum mechanics, at least since Wigner's work on representation theory, particles have been understood as the simplest kinds of quantum systems that have a well-defined nature or behavior under space-time transformations. So if you ask what's the simplest kind of quantum system with a Hilbert space that is as small as possible, doesn't include anything extraneous,
But for which, when we move around in space or turn around or change inertial reference frame, change frame of motion, we just get a new element of the same Hilbert space. We don't get something new, but it's like minimal, it's irreducible. Then you have a math problem. What are the irreducible unitary, which just means they're represented by, you know, certain kinds of operators in the Hilbert space,
representation of the space-time symmetry group, the Poincare group, the abstract representation of moving around in space, changing frame of motion, rotating. And that's a math problem, you can classify it, and what you find is there are distinct kinds of Hilbert spaces with these properties, and they are characterized by mass, and by spin, and by charges, and they have motional degrees of freedom, and so forth. That's usually how we think about particles in quantum mechanics.
And that's all we can say in quantum mechanics, because all we've got are Hilbert spaces in the textbook formulation, if you're going to describe a system of particles, you just got a Hilbert space. And so all we can do is talk about what that Hilbert space, what a structure is, and its structure for particle is related to these transformations of spacetime. In the picture I'm proposing particles go back to the classic like picture, a particle is a point like object in space.
in three dimensional physical space, if we think that physical space is three dimensional, with various properties or dispositions interacting with other particles.
Yeah, that is when you interact with a particle, it may be disposed to give you certain results on your measuring device, is all I mean. So if you measure its position, you'll read off what its position is, but if you measure some more complicated feature, then what you get on the measuring device will be some more complicated result of the interaction with the particle. So it has a disposition to produce certain kinds of
In metaphysical speak we would say that certain properties are categorical. They just explicitly exist as they are and others are dispositional. That is you look at them and what you're seeing is really like how the particle will be disposed to show you what it's going to do. But at the end of the day particles are much more like they are the classical picture. Just point like entities with some properties with different positions through time. So that's all particle is according to this picture.
And I should say that I'm not saying that particles are the fundamental ontology of nature. I don't know what the fundamental ontology is. But so far in your theory, what is the fundamental ontology? We go back to the old classical way of doing things that if you want to model a given system, you propose a certain ontology for it.
You have to say what you think the configurations are. If you want to model particles, it's going to be arrangements of particles. If you want to model fields, it's going to be, you know, delocalized field intensities distributed throughout space. If you want to model strings, if you want to model bits on a computer register, you pick the right ontology for the right kind of a system and then you model it. It's possible there is some truly fundamental ontology of all of nature. I don't know what that is. I think to some people, especially people working in Everettian quantum theory,
The idea that the fundamental ontology is state vectors or wave functions in a Hilbert space is very appealing. It would mean we already know what the fundamental grounding of all of reality is. A Hilbert space. There's some Hilbert space and there's an object or objects in a Hilbert space and that is the fundamental ontology of everything. I'm not saying that. Hilbert spaces are not fundamental in this picture. We go back to really having to be kind of metaphysically humble.
We know about some systems. Some systems appear to be particles, some appear to be fields. Maybe particles are emergent from fields and we don't need particles as a separate category. Maybe fields are fundamental, maybe they're not. I think it's premature to try to guess at what the fundamental ontology is just yet. And in this picture, you don't have to. You just pick whatever ontology you need for the model you want to talk about. Particles, fields, registers on a computer, and then you proceed from there. Maybe one day we'll discover that there is one model
With one ontology from which we can get all the other models. That would be a very exciting day, but I don't think that we can guess what that is today. And I don't think that we can just take that to be Hilbert spaces and be done. I think that's premature. There's so much more I want to talk to you about. We didn't talk about causation either. And there's a whole other, you know, connection to causation.
Reichenbach's Common Cause Principle.
It was wonderful to see you in person. I've been following you for again, following politely, diplomatically. You understand for quite some time now. And why don't we end? I know you're about to rush off to see your students. Why don't we end with your advice to students? Oh, actually to your advice to students who are watching and researchers who are watching. Um,
I'll just use my standby advice, which I think has been really helpful to me. And people have told this to me and maybe I'll share this. We all come at the work we do with a distinct profile of strengths and weaknesses, like I just said. Every person is, you know, our particular set of strengths and weaknesses is like a point in a very high dimensional configuration space or parameter space. So we're not rankable.
You can't order people. We're not an ordered set. It's very easy for students going into science to think that they lie on a linear ranking system. There are people who are better or smarter than they are. And if they're not as smart as those people, they can't make contributions. They can't do good work. And in my experience, having worked with so many students over the years, but also having read a lot of history, history of science, we discover is that it really is true that we all
We're all points in some very high dimensional parameter space. We're not rankable. And figuring out how your unique profile of strengths and weaknesses can be brought to bear to make progress on work that you find meaningful. Figuring how to do that is part of what it is to go into an area of scholarly work and grow and learn and develop. So I would say don't worry too much about where you think you fall.
Interdisciplinarity is wonderful. We should have more focus and spend more money on the places where disciplines
intersect. I work at the intersection of physics and math and philosophy, and I guess now, you know, statistics, like, you know, dynamical system, there's so many different, different fields that sort of meet where I'm currently working. And I think this is not novel to say, but I think some of the most exciting work happening in
scholarship generally and certainly in science or philosophy in particular is happening at interdisciplinary boundaries. So I would say that maybe not for the researchers, but for the people who pay researchers. Yeah, spending a little more time thinking about how to promote work at the boundaries of disciplines where there's real cross pollination between disciplines, I think would bear a lot of fruit for progress in all of our work.
I agree. Last night, one of the reasons I'm here in addition to see you was at MIT, there was an event by Addie right here yesterday last night called Echolopto, which was about neuroscience, cognition, biology, physics, language. Yeah, it was a combination of basically every sort of major field in STEM and the arts where they intersect and can be used to create something that's actually useful. But you have to be rigorous about it. You can't just
So that was fun. Anyhow, thank you. It's been a pleasure. And I know that you're itching to get going. And I appreciate that your students have been kept waiting for this. This is wonderful. I appreciate your time. Thank you for inviting me. This is wonderful. I really appreciate the invitation and all the work you've been doing on this amazing podcast series. It's it's amazing work talking to the public and and talking to, you know, people who are working in all these different fields about their work and
Clarifying complicated topics for everybody I think is amazing work. Thank you. And next time the interview we'll do will be more technical. We may even use the blackboard. We'll see. We'll see. Anyway, it was a delight. Thank you so much for the invitation. Thank you.
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 Kurt, you've spoken to so many people in the fields of theoretical physics, philosophy, and consciousness. What are your thoughts?
Also, thank you to our partner, The Economist.
Firstly, thank you for watching, thank you for listening. If you haven't subscribed or clicked that like button, now is the time to do so. Why? Because each subscribe, each like helps YouTube push this content to more people like yourself, plus it helps out Kurt directly, aka me. I also found out last year that external links count plenty toward the algorithm,
which means that 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 gained from rewatching lectures and podcasts. I also read in the comments that, hey, toll listeners also gain from replaying. So how about instead you re-listen on those platforms like iTunes, Spotify, Google Podcasts, which
If you
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.
Think Verizon, the best 5G network is expensive? Think again. Bring in your AT&T or T-Mobile bill to a Verizon store today and we'll give you a better deal.
Jokes aside, Verizon has the most ways to save on phones and plans where everyone in the family can choose their own plan and save. So bring in your bill to your local Miami Verizon store today and we'll give you a better deal.
▶ View Full JSON Data (Word-Level Timestamps)
{
"source": "transcribe.metaboat.io",
"workspace_id": "AXs1igz",
"job_seq": 4054,
"audio_duration_seconds": 8270.18,
"completed_at": "2025-11-30T22:56:58Z",
"segments": [
{
"end_time": 20.896,
"index": 0,
"start_time": 0.009,
"text": " The Economist covers math, physics, philosophy, and AI in a manner that shows how different countries perceive developments and how they impact markets. They recently published a piece on China's new neutrino detector. They cover extending life via mitochondrial transplants, creating an entirely new field of medicine. But it's also not just science they analyze."
},
{
"end_time": 36.067,
"index": 1,
"start_time": 20.896,
"text": " Culture, they analyze finance, economics, business, international affairs across every region. I'm particularly liking their new insider feature. It was just launched this month. It gives you, it gives me, a front row access to The Economist's internal editorial debates."
},
{
"end_time": 64.531,
"index": 2,
"start_time": 36.34,
"text": " Where senior editors argue through the news with world leaders and policy makers in twice weekly long format shows. Basically an extremely high quality podcast. Whether it's scientific innovation or shifting global politics, The Economist provides comprehensive coverage beyond headlines. As a toe listener, you get a special discount. Head over to economist.com slash TOE to subscribe. That's economist.com slash TOE for your discount."
},
{
"end_time": 85.998,
"index": 3,
"start_time": 66.203,
"text": " I didn't know it was impossible. So I brought these theories closer and closer together expecting that there would be a moment when I would need to make some kind of jump to get from one theory, classical physics, to the other theory, quantum physics. And the strangest thing happened. The two cliff faces merged. And there was just no chasm anymore."
},
{
"end_time": 110.077,
"index": 4,
"start_time": 88.37,
"text": " Today I have a special treat. I traveled to Harvard University to meet in-person Jacob Barandes, the co-director of graduate studies in physics and someone making waves at the intersection of fundamental physics and philosophy. In his unassuming office, he's been working on a revolutionary framework that finally explains quantum mechanics."
},
{
"end_time": 125.623,
"index": 5,
"start_time": 110.503,
"text": " His radical proposal suggests that there is no fundamental wave function, Hilbert spaces aren't real, and there's no mysterious quantum realm."
},
{
"end_time": 151.527,
"index": 6,
"start_time": 125.623,
"text": " In this episode, we go in depth into the picture that resolves the measurement problem, eliminates the need for multiple worlds, and finally gives a clear view as to what's actually happening at nature's smallest scales. However, this clarity does come with a price. The question is, are physicists ready to accept a quantum mechanics without magic?"
},
{
"end_time": 182.756,
"index": 7,
"start_time": 153.114,
"text": " Professor Jacob Baroness, welcome to theories of everything. I've been following you for some time following you online in a non creepy manner and We were speaking off air about physics however You're also the co-director of the graduate studies here of physics and you have an interesting background as to how you Came into physics. So why don't we start off there? Why don't we start from the beginning? from the beginning my first"
},
{
"end_time": 212.159,
"index": 8,
"start_time": 183.933,
"text": " intellectual passion was for philosophy of mind. When I was five, I was sitting in one of those little assembly rooms they had in in schools, you know, like it was my elementary school. And one of the teachers was droning on about something I don't remember exactly what they were talking about. But I remember sitting on this soft carpet and there was a there was a piano with you know, the feet of the piano looked like lion's paws."
},
{
"end_time": 237.005,
"index": 9,
"start_time": 212.773,
"text": " and i suddenly became aware of my existence in a very very explicit clear way and i was very confused and i tried to express my state of confusion to one of the other children sitting next to me and i failed miserably at being able to explain what i was feeling in the moment and so this left a sort of a mark on me"
},
{
"end_time": 255.708,
"index": 10,
"start_time": 237.619,
"text": " And from that moment, I was very interested in questions about, you know, what is the nature of our existence? What does it mean to be conscious? So philosophy of mind is really where things got started for me. But of course, I had no language with which to express any of these thoughts."
},
{
"end_time": 282.875,
"index": 11,
"start_time": 256.527,
"text": " I like science documentaries. I grew up in New York City and my parents would take me to the Museum of Natural History in New York City, which is really a wonderful magical place and anyone who goes to New York City should really should really visited. It's amazing. So I got really interested in science. I got interested in math. And I just thought if you're interested in science and math and you're interested in foundational questions,"
},
{
"end_time": 309.753,
"index": 12,
"start_time": 283.558,
"text": " then that means you should go into physics, right? That's where I thought math and these foundational questions, it's where they come together. So I went, you know, through school. I got to high school. I took physics for the first time in an academic way in school. I loved it. It was my favorite class in high school. I still have all my old binders from from that time. It was the one class where I was actually excited to go and do the homework, which was great."
},
{
"end_time": 331.101,
"index": 13,
"start_time": 310.247,
"text": " My teacher Doug Bartel was just phenomenal. He was just totally amazing. Around that time, I also started making trips back into New York City. We'd moved out of the city by that point, about an hour north. And so I would jump on the train and go in the city on the weekends."
},
{
"end_time": 357.193,
"index": 14,
"start_time": 331.766,
"text": " And I would take science classes in the city. Columbia University has a program called the Science Honors Program. At the time it was run by Alan Blair, just an amazing human being who was a professor of physics there and also ran this special program, the Science Honors Program. And these were classes you could go to. There was no homework or grades or tests. You just show up on Saturday mornings and you would learn all kinds of amazing things. It was an amazing program."
},
{
"end_time": 386.63,
"index": 15,
"start_time": 357.739,
"text": " And I would also work at the Museum of Natural History, so I started interning there when I was in high school. And I started working in the astrophysics department. I was not an expert in astrophysics in high school, but I was very curious about it. And I was doing a lot of computer programming at the time. And they were interested in having me work on some of the projects that they were doing. They were working on computer graphics visualizations of"
},
{
"end_time": 414.787,
"index": 16,
"start_time": 386.869,
"text": " of the galaxy. I worked on a project called the Digital Galaxy Project, if I remember the name correctly. And it was really my first opportunity to work with scientists. I really hadn't, I didn't know any scientists. We didn't have any scientists in my family. My father's a physician. But, you know, research scientists, I'd never met anybody like that. I didn't know academics or professors or anything like that. So this was, you know, these two experiences were very important for me."
},
{
"end_time": 443.865,
"index": 17,
"start_time": 415.196,
"text": " And together with my physics class, you know, I decided I wanted to study science and maybe physics. But my love for philosophy of mind was still very strong. And so when I went to college, I decided I was going to try to study the brain. I loved computers. And so the idea was I would somehow find a way to bring together my interest in computers and neuroscience in some way. In order to go in that direction, I had to take some basic science classes, including"
},
{
"end_time": 469.94,
"index": 18,
"start_time": 444.241,
"text": " Physics, I had to take math classes and I really fell in love with these classes. I started taking biology in my sophomore year and I enjoyed it, but not as much. And I have immense respect for people who work in biology, but it just wasn't for me. Yeah. So for me, I just want to know if the reason was the same for you. For me, it's just there's a multiplicity of terms and I feel like it's more memorization than derivation."
},
{
"end_time": 492.312,
"index": 19,
"start_time": 470.879,
"text": " Yeah, I do sometimes feel that way. I want to make very clear that I'm not a biologist and I don't want to make any presumptions about the way that biologists think about their subject. I know there's an inner logic to biology. Oh, I just mean at the first year level, at least from what I experienced, as you get older or as you get more seasoned in research,"
},
{
"end_time": 522.705,
"index": 20,
"start_time": 492.756,
"text": " I had that experience when I took the first semester of biology. It was microbiology and it was very logical. And then the second semester was anatomy and that was much more memorization and that I had the same experience that you're describing. It just wasn't really for me. But it was hard to convince myself that I should go into physics because there were all these very bright young people going into physics and going into mathematics. I was interested in the theoretical side, the mathematical side of physics and I just didn't feel like I was good enough to keep up with people."
},
{
"end_time": 552.381,
"index": 21,
"start_time": 523.114,
"text": " But around sophomore year of college, you know, I had conversations with some really amazing people, some of my fellow college students. And basically, I decided, you know, it matters much more that I do what I'm excited about than, you know, to want to be the best at something. So I'm just going to I'm just going to do it anyway. And so I just started taking lots of physics and math classes. And it was fantastic. I had an amazing experience. And some of the philosophy courses we were required to take at the time just didn't really call to me."
},
{
"end_time": 580.452,
"index": 22,
"start_time": 552.824,
"text": " There was a heavy emphasis on ancient Greek philosophy, on early modern philosophy. Now, I appreciated those subjects, but it wasn't as exciting to me as what I was doing in physics, at least at the time. Now, I should say that as the years went on and I began exploring other areas of philosophy that weren't part of the standard curriculum in college, analytic philosophy, philosophy of science, logic,"
},
{
"end_time": 607.534,
"index": 23,
"start_time": 580.981,
"text": " foundations of mathematics, philosophy of physics. My views on philosophy changed completely. But at the time, I didn't really get a chance to see much of that and I didn't see it growing up. And so I figured, okay, I'm going to throw my lot into physics. So I finished my undergraduate degree and then went on to graduate school. And I started a PhD actually here at Harvard in theoretical physics. And as I was progressing in that degree,"
},
{
"end_time": 633.2,
"index": 24,
"start_time": 608.148,
"text": " You know, I started to think back about some of these old philosophical questions that I had. I did my doctoral work in high-energy theoretical physics, and I think we did really meaningful work, but I was really much more excited about philosophical questions, and by the time I finished my PhD, I knew that was the direction I wanted to go in. So I continued on in the department,"
},
{
"end_time": 662.637,
"index": 25,
"start_time": 633.797,
"text": " I'm a lecturer here in the department and I also co-direct the graduate program as I think we talked about. So, you know, I mix teaching physics and research and advising students and it's been a really rewarding experience. The students here are amazing. They're idealistic and they're brilliant and they're deep and I've met really the most amazing people a person could ever ask to meet here."
},
{
"end_time": 691.578,
"index": 26,
"start_time": 663.08,
"text": " I've met lifelong friends here. I mean, it's been just an incredible experience being here, and I've learned a lot. Much more, I think, than any of them have learned from me. But that's how someone who mainly works in philosophy, philosophy of physics, finds himself embedded in the physics department. So I have an associated faculty appointment with the philosophy department, and I take turns teaching classes in physics and also over there in philosophy. Yeah. But my research is primarily the intersection of philosophy and physics."
},
{
"end_time": 711.032,
"index": 27,
"start_time": 692.039,
"text": " So what happened to the philosophy of mind?"
},
{
"end_time": 728.916,
"index": 28,
"start_time": 711.578,
"text": " I'm extremely interested in philosophy of mind, but I don't think that my distinct profile of strengths and weaknesses is optimized for working in philosophy of mind. So I read about it, I'm deeply interested in it, but I feel like I'm more well adapted to questions of the intersection of physics and philosophy, so that's where I've spent my time and my focus."
},
{
"end_time": 758.353,
"index": 29,
"start_time": 729.616,
"text": " This episode is brought to you by State Farm. Listening to this podcast? Smart move. Being financially savvy? Smart move. Another smart move? Having State Farm help you create a competitive price when you choose to bundle home and auto. Bundling. Just another way to save with a personal price plan. Like a good neighbor, State Farm is there. Prices are based on rating plans that vary by state. Coverage options are selected by the customer. Availability, amount of discounts and savings, and eligibility vary by state."
},
{
"end_time": 787.329,
"index": 30,
"start_time": 759.377,
"text": " Earlier, you said you didn't want to pursue something just to be the best at it. You want to follow your interests. But here you're saying, well, my interests still lie in philosophy of mine, but it's just not I'm not the sharpest tool in the shed when it comes to that. That's not my skill set. How do you reconcile those two? That's well put. Yeah. So, I mean, we all change as we grow and get older, right? Yeah. So I think for me, it was a matter of finding a balance. It's less important to me"
},
{
"end_time": 815.009,
"index": 31,
"start_time": 787.705,
"text": " And I talk with students about this also, right? It's less important what you want to be. It's less important about being big or famous or important. And to me, what's most important is doing work that's meaningful, that I feel like is meaningful, that a person feels like is meaningful, work that we feel is meaningful, but also we feel like we're making progress on. So it's not so much that"
},
{
"end_time": 845.145,
"index": 32,
"start_time": 815.845,
"text": " I'd like to get you to justify there is no wave function soon."
},
{
"end_time": 875.094,
"index": 33,
"start_time": 846.391,
"text": " However, I want to know if there is a connection between the philosophy of mind and quantum mechanics first. Yes, this is a very interesting question. And actually, this will bring us to a very important paper that I'm hoping we could talk about from the early 1960s. It was a paper by Eugene Wigner. I believe the paper was called On the Mind-Body Question. I could have the title slightly wrong. But Wigner introduced a thought experiment that"
},
{
"end_time": 892.193,
"index": 34,
"start_time": 876.084,
"text": " The Thought Experiment"
},
{
"end_time": 915.026,
"index": 35,
"start_time": 892.807,
"text": " in Hugh Everett's extended thesis. Hugh Everett was a graduate student at Princeton, and was at Princeton at the same time, overlapped with Eugene Wigner. And Hugh Everett originated the Many Worlds Interpretation of Quantum Mechanics, and he wrote this very long thesis. It's 137 pages. I guess maybe that's not long in an absolute sense."
},
{
"end_time": 937.961,
"index": 36,
"start_time": 915.691,
"text": " In 1956-1957, he ultimately didn't publish it. His advisor strongly pushed him to publish a shorter, different thesis. But you can find a copy of this extended thesis and he opens it up with the same thought experiment. So we know this thought experiment was introduced earlier than Wigner by at least"
},
{
"end_time": 962.961,
"index": 37,
"start_time": 938.183,
"text": " I guess seven years before Wigner's paper, something like that. But that wasn't published. Wigner's paper was published, and so it's most widely attributed to him. Wigner had this thought experiment that I'm going to talk about in a little more detail if you'd like, because I think it gives a good motivation for why one might think that there's a problem with the way that we formulate quantum mechanics at the level of its textbook axioms. So I'll come back to it. But I'll just say that this thought experiment"
},
{
"end_time": 987.551,
"index": 38,
"start_time": 964.292,
"text": " Apparently it was connected with Wigner's idea that somehow consciousness was related to collapse of wave functions and I think this creates a potential connection between philosophy of mind and quantum mechanics. But there are other connections. In the Many Worlds interpretation, the formulation of quantum mechanics that Hugh Everett introduced in the mid-50s,"
},
{
"end_time": 1016.596,
"index": 39,
"start_time": 988.148,
"text": " One does run into some basic questions about consciousness and human identity in a universe in which a giant universal wave function is splintering into parallel realities, each of which contain copies of yourself. How do we make sense of this kind of a picture and make it connect with how we think about basic problems and philosophy of mind? I don't claim to have an answer to that question. It's an ongoing mystery, I think."
},
{
"end_time": 1045.947,
"index": 40,
"start_time": 1017.363,
"text": " So there are, I think, some interesting connections between philosophy of mind and quantum mechanics. And I think my general attitude has been anytime you're unable to answer a question about quantum mechanics because you've connected it in some way to the philosophy of mind, and in particular to an unanswered and potentially unanswerable problem about the philosophy of mind, I get very worried. Okay, let's talk about the wave function because when we're speaking about the collapse of the wave function, the collapse of something,"
},
{
"end_time": 1075.282,
"index": 41,
"start_time": 1046.596,
"text": " What is this wave function and why do you believe that there is none? That's a great question. So let me say a little bit about some history. I think some history here might be helpful to ground things. But before I do the history, let me first answer your question. I'll give the short answer and then we'll talk a little bit of history because otherwise make it lots of weeds. There's this popular story about quantum mechanics that a lot of students coming into the fields have heard. The first"
},
{
"end_time": 1096.92,
"index": 42,
"start_time": 1076.34,
"text": " Primary object in quantum mechanics is the wave function. It's this mysterious undulating object. It's a little bit unusual. It's kind of like the electric fields sort of except that its values are complex value. They're complex numbers. They're like"
},
{
"end_time": 1123.848,
"index": 43,
"start_time": 1097.671,
"text": " ordinary real numbers plus a number times the square root of minus one. And somehow they're connected with probabilities in some way. And somehow the point of quantum mechanics is wave functions. They're the central player in the story. And how you think about quantum mechanics begins with how you think about wave functions, right? They're the protagonist of this story."
},
{
"end_time": 1154.445,
"index": 44,
"start_time": 1126.237,
"text": " There are, I think, some good reasons to be a bit skeptical of that picture. And I don't think that there really is much, there would be much controversy about saying, I think, you know, when you learn about quantum mechanics and you begin to see that there's this much bigger picture, you know, you begin to see that the wave function in this sort of story is a little bit of an oversimplification. I think if you pressed someone who works in physics pretty far, they would admit actually this picture is a little bit"
},
{
"end_time": 1182.398,
"index": 45,
"start_time": 1154.906,
"text": " It's a little bit too quick, and there's a deeper picture beneath it. And so I think there's one view in what I'm saying here, your question, which is to take those concerns and take them to their logical conclusions, right? Ask ourselves, okay, what does this theory really consist of? Is it really about wave functions at all? And for that matter, are wave functions things that describe objects that are really out there in the world? And this is where one"
},
{
"end_time": 1209.582,
"index": 46,
"start_time": 1183.234,
"text": " lives in kind of a liminal space between physics and philosophy when you ask questions like that on the on one hand it's about physics it's about you know what's the right way to think about what's the way to formulate you know what may be our best most successful scientific theory certainly when it comes to numerical accuracy and precision you know and the other hand what's really out there what's out there in the world what exists right this is this word ontology that metaphysicians use ontology is is the study of what really exists"
},
{
"end_time": 1239.735,
"index": 47,
"start_time": 1210.111,
"text": " And ask, does the wave function describe something that physically exists? That's a question. To explain a little bit about how we've arrived here, I could say a little bit about the history, but let me just pause and ask, do you have follow-up questions about this? I want to make, you know, be careful to make sure we all have time to... Sure, sure. So when you say that there's the standard picture of the wave function, you said, okay, what people are taught is that there's the wave function, it's connected to complex numbers, and that it's also connected to probability somehow."
},
{
"end_time": 1267.517,
"index": 48,
"start_time": 1240.742,
"text": " Is that the picture that you're referring to? Are you referring to the picture that the wave function represents something in physical space and is of something? So when I say that, what I mean is when people say the wave function, when physicists speak about the wave function, it's the wave function of something, the wave function of an electron, the wave function of a so-and-so. So what is precisely this picture that you're about to shatter? Yeah, so this is an excellent question. I think"
},
{
"end_time": 1285.64,
"index": 49,
"start_time": 1268.353,
"text": " The issue here is that it's a little of both. The wave function plays a functional role in quantum mechanics. That is, it does certain things for you in the theory."
},
{
"end_time": 1315.981,
"index": 50,
"start_time": 1285.998,
"text": " There's this famous equation called the Schrödinger equation, which roughly says that when a system is left to itself, it's not being disturbed, it's not exchanging information with any other systems, then it has a wave function that changes with time in a smooth way. And this smooth process is described by a differential equation, which is roughly speaking an equation that just tells you what the wave function is at each infinitesimally next moment, given what it was at the"
},
{
"end_time": 1341.203,
"index": 51,
"start_time": 1315.981,
"text": " So we plug in initial wave function, we use the Schrodinger equation to figure out what the wave function will, how it will behave as time progresses, and then there are rules for taking the wave function and calculating predictions. So that's uncontroversial, and I certainly agree with that picture, that we should be using wave functions for that purpose."
},
{
"end_time": 1365.043,
"index": 52,
"start_time": 1341.783,
"text": " But I think it's easy to let that picture, it's easy to let that picture lead one to think that wave functions are describing physical objects out in the world. And, you know, when I think students arrive in a quantum mechanics class for the first time, without having studied the theory, they may think that, okay, every particle has got some wave function, the wave functions are kind of like"
},
{
"end_time": 1392.602,
"index": 53,
"start_time": 1365.759,
"text": " They're kind of like waves in an empty space is kind of like the ocean and all the particles are kind of like small little waves moving around in the ocean. And that's actually not the picture that we get even from the textbook theory of quantum mechanics. In the textbook theory, a wave function is the assignment of a complex number to every possible configuration of your system."
},
{
"end_time": 1422.125,
"index": 54,
"start_time": 1393.609,
"text": " If you're talking about a single particle, nothing else, then every possible configuration is every possible location the particle can be in. Each location is labeled by three numbers. It's x, y, and z coordinates, if you want. And so the wave function takes in those three coordinates and assigns it a complex number, and then we're supposed to do a mathematical operation of that complex number, and out comes a probability, or precisely a probability density, but a probability per unit volume that a measurement will find the particle at that spot."
},
{
"end_time": 1448.422,
"index": 55,
"start_time": 1422.602,
"text": " So the wave function can be thought of as the assignment of a special complex number to every point in three-dimensional physical space where you do this operation. It's called mod-squaring. You do this operation, and then it tells you the probability, roughly speaking, with which a measurement will find a particle at that location. So it's very easy to think that a wave function is like a field, like the electric field in three-dimensional space. But if you have two particles instead of one,"
},
{
"end_time": 1471.681,
"index": 56,
"start_time": 1448.814,
"text": " the possibility space is much more complicated. We call this possibility space configuration space because each possible configuration of a two-particle system requires six numbers, not three. You need to know x, y, and z for the first particle and you need to know x, y, and z for the second particle. So the wave function assigns a complex number to a point in a six-dimensional"
},
{
"end_time": 1498.012,
"index": 57,
"start_time": 1473.831,
"text": " you need six numbers to specify its points. And that means a two particle wave function is a function we say whose domain is a six dimensional space. Six dimensional space is not physical three dimensional space. If you've got three particles, it's a nine dimensional space. If you've got 10 particles, it's a 30 dimensional space. And actually, our universe does not have a well defined number of particles at all."
},
{
"end_time": 1528.268,
"index": 58,
"start_time": 1498.473,
"text": " Our leading physical model for the universe, at least for the non-gravitational parts of the universe, is the standard model, which is based on a set of models known as quantum field theories. And in quantum field theories, particles are emergent excitations of these sort of delocalized entities called quantum fields. And the number of particles can change from moment to moment. It's not always well-defined. So it's not even clear how to even think about"
},
{
"end_time": 1557.449,
"index": 59,
"start_time": 1528.746,
"text": " Okay, so,"
},
{
"end_time": 1586.561,
"index": 60,
"start_time": 1558.302,
"text": " You have a lecture about how Hilbert spaces are also not real. I'd like you to talk about that. Now, it's my understanding that you more precisely said Hilbert spaces are redundant in the same way that gauge symmetries are redundant or the gauge transformations are redundant. So at this point, if it's all right, let me do a little bit of history if it's OK. So where does quantum theory begin? Lightning like grand tour of quantum theory. There are these"
},
{
"end_time": 1597.244,
"index": 61,
"start_time": 1586.903,
"text": " actual physical objects called black bodies."
},
{
"end_time": 1618.336,
"index": 62,
"start_time": 1597.995,
"text": " You know, a little hole is poked in them. I mean, you don't really poke a hole in them. It's more complicated. But this is I'm very much a theorist and my picture of experimental physics is it should be better. And I apologize in advance to anyone who's an experimentalist listening to me. But these were actual systems. People actually built these things. They were these chambers. They would heat them up."
},
{
"end_time": 1635.196,
"index": 63,
"start_time": 1618.336,
"text": " And then they would have a little hole in the chamber through which they could actually see radiation coming out of them and they could put that radiation through experimental devices that could show them how intense the radiation was as a function of wavelength."
},
{
"end_time": 1663.592,
"index": 64,
"start_time": 1635.674,
"text": " We all know that different wavelengths of light correspond to different colors in the visible range. And if you go outside the visible range, you have very long wavelengths that are infrared or microwave radiation or radio waves. And at the very short wavelengths, you've got X-rays and so forth, gamma rays going all the way out, ultraviolet X-rays, gamma rays going all the way out to very short wavelengths. And you could just ask yourself,"
},
{
"end_time": 1686.8,
"index": 65,
"start_time": 1664.206,
"text": " If I plot how strong the radiation is as a function of wavelength, what kind of pattern would I expect to see? And the pattern that was revealed in experiments was difficult to explain on first principles theoretical grounds. A very important physicist, Max Planck, in 1900 found a way"
},
{
"end_time": 1716.544,
"index": 66,
"start_time": 1687.09,
"text": " to generate a theoretical prediction of what this black body radiation curve should look like, and it agreed with experiments. But in order to get there, he had to kind of hack his formulas. He had introduced a fudge factor. He had to assume that radiation in this chamber could only occur in quantized amounts. That is, there were different wavelengths you could produce, but each wavelength could only be excited in discrete steps."
},
{
"end_time": 1739.889,
"index": 67,
"start_time": 1717.21,
"text": " This led to the quantum hypothesis. This was his quantum hypothesis. And there was a sort of parameter that told you how big you wanted to make these steps. Today we would call it a regulator. And this parameter, we now call it h, little h. We call it Planck's constant. Planck introduced it. And I think at one point his idea was he wanted to"
},
{
"end_time": 1768.166,
"index": 68,
"start_time": 1740.742,
"text": " introduces an intermediate step in the calculation and once he calculated everything sends this clearly in his mind on physical parameter to zero but whenever he tried to send it to zero he would get the wrong results he realized this parameter was not zero it was very small it was today it has a value you know that's of order 10 to the negative 34 10 to the negative 33 in conventional units and he couldn't get rid of it"
},
{
"end_time": 1796.493,
"index": 69,
"start_time": 1768.746,
"text": " And so people had to accept that there was this basic discreteness in nature he couldn't explain. And then for the next 22, 23 years, the period from 1900 to 1922, 1923, physicists working on these questions were living in a time that today we call the old quantum theory, a paradigm we call the old quantum theory. The old quantum theory was based on a mixture of"
},
{
"end_time": 1825.862,
"index": 70,
"start_time": 1796.869,
"text": " physical pictures of particles moving around in space, in orbits, like in atoms, and then a collection of ad hoc formulas and rules that people didn't fully understand that seemed to capture some of the observations that were coming out of experiment. But it was a very murky time. There wasn't anything like an underlying theory from which this whole picture emerged. And the formulas weren't perfect. They didn't work exactly right."
},
{
"end_time": 1847.108,
"index": 71,
"start_time": 1826.493,
"text": " In 1913, Niels Bohr proposed his famous model of the hydrogen atom. This is a model in which you've got the nucleus and for the hydrogen atom, it's just a proton, positively charged proton in the middle and an electron going around. And by making use of these sort of heuristic formulas that were characteristic of the time,"
},
{
"end_time": 1876.971,
"index": 72,
"start_time": 1847.432,
"text": " Bore argued that the electron could only be in certain definite orbits and when it transitioned between them its energy changed in discrete steps and whenever its energy changed it would either absorb or emit radiation in discrete amounts and with this he was able to account for the particular colors of radiation that we would see emitted from excited hydrogen atoms or that were absorbed by hydrogen atoms the so-called line spectra and we also found that other atoms had line spectra as well"
},
{
"end_time": 1906.937,
"index": 73,
"start_time": 1877.415,
"text": " Famously helium was discovered because we looked at the spectral lines from the Sun and after accounting for all the spectral lines we knew about there were still some more that we didn't account for and so people conjectured there was a new element they called the helium from Helios the Sun and eventually we found helium on Earth but it was first discovered in the Sun. So this was obviously a very important thing and Bohr ended up winning the Nobel Prize in 1922 for this Bohr model. But by around 1922, certainly at least by then, people were becoming very skeptical"
},
{
"end_time": 1932.21,
"index": 74,
"start_time": 1907.688,
"text": " because people couldn't take these clear pictures of particles moving in definite ways, particles interacting with fields like electric and magnetic field, which were well understood by this point. They couldn't take this world picture, this ontology, this picture of what was physically out there. They couldn't find laws that when combined with this picture gave you the right predictions."
},
{
"end_time": 1959.548,
"index": 75,
"start_time": 1932.722,
"text": " that gave you an empirically adequate, empirical meaning subject to experiment, empirically adequate, a theory that was able to account for the things we were seeing and make predictions that were regularly confirmed. Niels Bohr gave a bunch of lectures in 1922. Heisenberg, Werner Heisenberg, attends one of these lectures, at least one of them."
},
{
"end_time": 1967.858,
"index": 76,
"start_time": 1960.196,
"text": " And the story goes, and I'm not sure quite how much of the story is apocryphal or how much really happened, but the story goes that Heisenberg objected at one point"
},
{
"end_time": 1992.159,
"index": 77,
"start_time": 1968.404,
"text": " to this lecture. Heisenberg at this point was 20 years old, maybe 21. Niels Bohr was a Nobel Prize-winning physicist, widely regarded as the quantum whisperer, someone who just innately intuitively understood quantum mechanics in a way that no one else did. And here was Heisenberg challenging Bohr. People, I think, probably could have been expected to have thought that Bohr would be upset at this."
},
{
"end_time": 2013.592,
"index": 78,
"start_time": 1992.688,
"text": " But the story goes that after the talk, Heisenberg took a long walk with Bohr, a many hours walk, and it had a huge impact on how Heisenberg thought about nature. The story, the legend goes that Bohr revealed to Heisenberg that, as Bohr put it, he was not convinced there were particles or orbits after all."
},
{
"end_time": 2035.418,
"index": 79,
"start_time": 2014.821,
"text": " You start seeing comments by people like Sommerfeld. Arnold Sommerfeld was actually Heisenberg's doctoral advisor in Munich, where Heisenberg was, and then people like Wolfgang Pauli. Many of the people sort of at the foundations of this developing theory were increasingly skeptical that this world picture could survive."
},
{
"end_time": 2061.664,
"index": 80,
"start_time": 2035.896,
"text": " And then in 1925, Heisenberg, who was visiting the premier institution in mathematics and theoretical physics at the time, Gerttingen, where people like David Hilbert were, Max Born was there, Felix Klein, your top, you know, mathematicians and physicists. Heisenberg was there visiting, he was visiting Max Born's group, Max Born and his student Pasquale Jordan."
},
{
"end_time": 2089.735,
"index": 81,
"start_time": 2062.432,
"text": " And he was thinking about all these questions and he was very confused about all of it. There were all these new, more complicated formulas that people were writing down that were connecting energy levels and transitions and atoms to spectra. And he develops this very terrible case of hay fever. In the spring of 1925, he goes out to Heligoland, which is this island where the pollen levels are much lower. And he comes back with this"
},
{
"end_time": 2120.401,
"index": 82,
"start_time": 2090.742,
"text": " Totally bizarre draft of a paper And he gives this paper to Max Born and to Jordan and then he like goes on a vacation again He goes on some vacation. He's exhausted from all of his intellectual exertions and this paper begins with these incredibly These remarkable statements statements that a philosopher of science would immediately recognize as indicating some kind of paradigm shift Heisenberg says at the beginning"
},
{
"end_time": 2146.971,
"index": 83,
"start_time": 2121.698,
"text": " We shouldn't be thinking about orbits anymore or particles. We should rephrase our physics, our theories entirely in terms of quantities that can in principle be measured. And so he formulates this different way to think about quantum mechanics in terms of abstract objects that Max Born identifies as our matrices."
},
{
"end_time": 2167.688,
"index": 84,
"start_time": 2147.585,
"text": " People who are listening to this may have heard of a matrix. Matrices and the subject that they belong to, linear algebra, that was not a standard part of the physics curriculum at this time. Heisenberg actually independently discovered matrices in this work and their mathematical operations."
},
{
"end_time": 2191.988,
"index": 85,
"start_time": 2168.592,
"text": " And Born recognized what Heisenberg was doing, and then together they wrote a couple of papers in which they introduced this thing called matrix mechanics. In matrix mechanics, there's no picture anymore. There's no picture of atoms, of electrons, of particles going around atoms. There's just this abstract mathematical apparatus for predicting energy levels of things. Schrödinger comes along a few months later,"
},
{
"end_time": 2217.995,
"index": 86,
"start_time": 2193.012,
"text": " And through a series of theoretical arguments that I will not be able to do justice to here that connect with what's called Hamill and Jacobi theory, which is a beautiful area of classical physics, Heisenberg proposes a different way to think about quantum mechanics. He introduces his wave function. It's what shows up in these papers. Schrödinger introduces his wave function. This is in early 1926. In some papers, both in German and in English, he wrote in both."
},
{
"end_time": 2239.94,
"index": 87,
"start_time": 2218.422,
"text": " I'm"
},
{
"end_time": 2262.108,
"index": 88,
"start_time": 2240.486,
"text": " he even says maybe this is what reality is maybe reality is some giant mechanical wave undulating in configuration space and some and through some mechanism that we don't fully understand this undulating wave in this high dimensional abstract space somehow projects facts down into three dimensional reality facts about where electrons are"
},
{
"end_time": 2282.21,
"index": 89,
"start_time": 2262.705,
"text": " He doesn't have the full picture here, but this is what he basically describes, and he's able to use this wave function as an indirect method for predicting energy levels. Max Born comes along very shortly thereafter and proposes that wave functions are not mechanical objects. They are mathematical tools."
},
{
"end_time": 2304.002,
"index": 90,
"start_time": 2282.705,
"text": " The reason they're complex valued is because they're not really physical things. They're things that we operate on using these sort of mathematical operations to generate probabilities. The wave functions, when you take the complex numbers that they describe and you do this operation to them, what comes out is probabilities. The wave function should be understood as a mathematical mechanism for generating probabilities."
},
{
"end_time": 2326.032,
"index": 91,
"start_time": 2304.497,
"text": " By 1928 Schrodinger is already recanting his view. He gives a lecture in 1928, his fourth lecture on wave mechanics, in which he says he used to think that wave functions were physical objects. He even presages in some ways the many worlds interpretation. He says they're an object where every single thing that the system could be doing is really playing out in this giant wave function. But he no longer thinks that."
},
{
"end_time": 2353.763,
"index": 92,
"start_time": 2326.647,
"text": " He's accepted what seems to be the new idea. And then within the next couple of years, 1930, Paul Dirac writes a textbook in which he summarizes all of the quantum mechanics that was known at the time, and he sews together Schrodinger's wave functions with Heisenberg and Born and Jordan's matrix mechanics, and he realizes they're all part of this deeper reality. There's this mathematical construction"
},
{
"end_time": 2373.473,
"index": 93,
"start_time": 2354.241,
"text": " It's a kind of a space called the Hilbert space, which is kind of a vector space, but it's a vector space with complex numbers in it. And when you look at the vector space in one way, you see wave functions. If you look at the vector space in another way, you see matrices. You see what Heisenberg was doing. They're all parts of this mathematical structure called the Hilbert space. And then two years later,"
},
{
"end_time": 2401.596,
"index": 94,
"start_time": 2374.445,
"text": " John von Neumann, the great mathematician, he writes a book, Mathematical Foundations of Quantum Mechanics, in which he formalizes this theory in mathematical terms. And that's basically what we've had ever since. Today, when people refer to the Dirac von Neumann axioms, or the textbook axioms of quantum mechanics, they mean this prescription for generating predictions about what we'll see in experiments, empirical predictions. And"
},
{
"end_time": 2428.131,
"index": 95,
"start_time": 2401.937,
"text": " This framework is based on Hilbert spaces. Very roughly speaking, the first axiom says that every quantum system has this abstract space called a Hilbert space, which is not a configuration space, it's a different kind of a thing altogether, and that this state in some sense of a quantum system is represented by certain kinds of objects in this Hilbert space. State vectors, in the simplest case, are density operators, somewhat more complicatedly."
},
{
"end_time": 2436.357,
"index": 96,
"start_time": 2429.275,
"text": " The second axiom is that when left to itself, the system evolves according to, roughly speaking, the Schrodinger equation, more generally unitary evolution."
},
{
"end_time": 2459.804,
"index": 97,
"start_time": 2436.903,
"text": " And then there are three more axioms that talk about when a measurement is performed in the system, what you're likely to see. These are the so-called measurement axioms. And one of them is about what kind of mathematical objects represent the things we can measure. These are called observables. One of them is about how to generate probabilities of what you'll see when you do measurements. That's called the Born Rule. And then the final one is that after a measurement, the state vector of the quantum state collapses."
},
{
"end_time": 2489.497,
"index": 98,
"start_time": 2460.299,
"text": " This is the way we introduce quantum mechanics to students in textbooks now. If you go to my shelf and look at any of the textbooks on quantum mechanics, they will present something like these five axioms. Different people will sort them differently. They may not say there's five. They may say there's four or six or some other number, but I like to carve them up as five, right? So we know we have these axioms. We know that they're very good at giving us a prescription for generating empirical predictions. But"
},
{
"end_time": 2519.701,
"index": 99,
"start_time": 2489.94,
"text": " What do they tell us about what's really going on in nature? Are they saying that the seat of reality really is some abstract Hilbert space, some vector space of possibly very high or infinite dimensions over the complex numbers, and that the universe is some object in this space trolling around according to some rule? There are some reasons to be skeptical of this. One is that we can reformulate the axioms of quantum theory in a very different language."
},
{
"end_time": 2546.374,
"index": 100,
"start_time": 2520.333,
"text": " So people who work in various other areas of quantum physics, in mathematical physics, sometimes prefer to formulate quantum mechanics in terms of what are called c-star algebras. C-star algebras are not things you find on the beach. They're not that kind of c-star, but they're abstract sets of mathematical entities that codify"
},
{
"end_time": 2566.476,
"index": 101,
"start_time": 2547.432,
"text": " How systems evolve in quantum mechanics, how to generate measurement predictions in a way that doesn't start with Hilbert spaces. When you take that alternative point of view, you get a very general mathematical framework from which the Hilbert space picture can emerge in certain, well,"
},
{
"end_time": 2591.92,
"index": 102,
"start_time": 2567.329,
"text": " You can almost always pull out a Hilbert space picture in these stories. Sometimes you get a unique Hilbert space, sometimes you get a proliferation of different Hilbert spaces, and there's all kinds of deep questions about what that means. But when I began learning about the C-straw algebraic formulation of quantum mechanics, it opened my mind, as I think it does a lot of people, to the idea that maybe the Dirac-von Neumann axioms, the ones we hear about in the textbooks, phrased"
},
{
"end_time": 2620.691,
"index": 103,
"start_time": 2592.892,
"text": " primeval in terms of Hilbert spaces may not be the end of the story and Hilbert spaces may not be the most fundamental way to think about the structure of quantum mechanics. I think one can go much farther and maybe we'll talk a little bit about how one can go farther than that but once you already begin to see that there are mathematically equivalent ways to formulate quantum mechanics that don't start with Hilbert spaces it makes you become somewhat skeptical that the Hilbert space picture is fundamental and that the objects in the Hilbert space picture state vectors that"
},
{
"end_time": 2649.377,
"index": 104,
"start_time": 2621.271,
"text": " Well, what is it about the C-star approach that allows you to say that the Hilbert spaces that can come from the C-star approach implies that the Hilbert spaces are"
},
{
"end_time": 2679.804,
"index": 105,
"start_time": 2650.384,
"text": " So that's an excellent question. In the standard approach to quantum mechanics, the first of the three measurement axioms says that every observable thing you might want to look at is represented by a kind of a matrix, more technically a self-adjoint operator on the Hilbert space. It's just, it's kind of like"
},
{
"end_time": 2710.111,
"index": 106,
"start_time": 2680.776,
"text": " an abstract mathematical entity that you can add other such entities and multiply them together. It behaves kind of like a number, kind of like a variable X in algebra, but a little weirder, like they don't always commute with each other. They're kind of strange objects, but we have a mathematical set of tools to take these and generate empirical predictions. When you start with the textbook axioms, you begin with the Hilbert space, and then these operators are things that come out of the Hilbert space. In the c-straw algebra approach, you go the other way around."
},
{
"end_time": 2740.401,
"index": 107,
"start_time": 2710.623,
"text": " You begin with an abstract specification of the observables, which are represented by these abstract mathematical symbols. And the symbols have all kinds of mathematical properties, rules for how you add them together, multiply them, just like I said, but they don't begin as objects that live in Hilbert spaces. They have their own existence, their identity. And there's even a funny way that people who work in this field sometimes talk about it. They'll say, are you a Hilbert space conservative?"
},
{
"end_time": 2768.814,
"index": 108,
"start_time": 2740.93,
"text": " Meaning you take the Hilbert space to be the starting point, or are you an algebraic imperialist? Do you take the algebraic objects to be the basic ingredients? When you start with these basic algebraic ingredients, they form a special kind of mathematical structure called a C star algebra. The C stands for closed, which just means that there's like no holes in the algebra. It's all filled in all the way. And the star just refers to the operation of, it's a complex conjugation, but on these objects, roughly speaking."
},
{
"end_time": 2775.606,
"index": 109,
"start_time": 2769.189,
"text": " And there's some other properties you require these to have, but very rudimentary properties. And then what you can show is that there is a way to"
},
{
"end_time": 2799.206,
"index": 110,
"start_time": 2775.776,
"text": " to construct a Hilbert space out of these algebraic objects. And once you've done that, then they become the matrices or operators in the Hilbert space. But once you see this construction, it's called the Gelfand-Neymark-Siegel construction. It's a beautiful theorem. Once you see it done, you begin to wonder just how fundamental Hilbert spaces really are, especially because some of these sister algebras do not generate a unique Hilbert space."
},
{
"end_time": 2820.896,
"index": 111,
"start_time": 2799.206,
"text": " And that's where the Hilbert space redundancy comes from. In a way, yeah. So, you know, for simple systems, if you've got one particle or three particles or 10 particles, it turns out you basically get a unique Hilbert space. So you really can think of either of them as being fundamental. But when you consider systems that have infinitely many moving parts,"
},
{
"end_time": 2841.084,
"index": 112,
"start_time": 2821.34,
"text": " so a system of so many particles that will model it as if it has infinitely many particles we do this in thermodynamics or a quantum field where there's like variables at every point in all of space for these kinds of systems you don't necessarily get a unique Hilbert space out and then there's this question of which is more fundamental and"
},
{
"end_time": 2857.892,
"index": 113,
"start_time": 2842.381,
"text": " Earlier we were talking about Heisenberg and how he started with observables and Schrodinger didn't."
},
{
"end_time": 2888.251,
"index": 114,
"start_time": 2858.285,
"text": " And now you're talking about taking those observables seriously and forming an algebra of just them called the C star algebra. But then you also said that you can take representations of the observables which become matrices. Yeah. And Heisenberg was dealing with the matrices. Exactly. OK. Yeah. Your picture is exactly correct. So now this isn't what I'm working on right now. But when you begin to realize that you can reformulate the rules of quantum quantum theory in a different way, it kind of opens your mind up to other possibilities. I want to know what your mind has been opened up to. Yeah."
},
{
"end_time": 2909.65,
"index": 115,
"start_time": 2888.558,
"text": " Where is your mind these days on quantum time? That's an excellent question. So let me go back to Wigner's thought experiment again, because I think this is a good hook for where I end up and where I think a lot of people end up. So what was this thought experiment about? In a way, I mean, it's a thought experiment that a lot of people in physics and certainly philosophy of physics are familiar with."
},
{
"end_time": 2936.459,
"index": 116,
"start_time": 2910.026,
"text": " It's a real good workhorse in quantum foundations, but I think there's still a lot of lessons to learn from it. And people have extended this experiment in lots of different, there's the so-called extended Wigner's Friends scenarios that a lot of people are working on, but I think the original version of it is actually really, really nice. And like I said, phrased all the way back in 1956 in Hugh Everett's original thesis. But it's a very simple question. The axioms say"
},
{
"end_time": 2941.561,
"index": 117,
"start_time": 2937.261,
"text": " that we have a Hilbert space and we represent the state of the system as some object this Hilbert space."
},
{
"end_time": 2969.872,
"index": 118,
"start_time": 2943.439,
"text": " Questions we can ask observables are represented by these symbols. We can generate probabilities and then after a measurement, we collapse. Why do we collapse? What's the purpose of collapse? Collapse is to ensure robustness of measurement results. After you do the measurement, you're guaranteed to get the same result again. That's what collapse accomplishes. It ensures that once you've gotten a definite result, if you measure right again before you've given the system any chance to evolve further, you're guaranteed with almost 100% probability to get the same result."
},
{
"end_time": 2993.063,
"index": 119,
"start_time": 2970.998,
"text": " Now, the problem of course is that, well, what is a measurement? What kinds of physical processes count as measurements? One view is, we don't need to worry about this. One view is, all scientific theories are ultimately instrumentalist enterprises, meaning that they exist solely to allow us to connect"
},
{
"end_time": 3021.084,
"index": 120,
"start_time": 2993.592,
"text": " Preparations, setups of measurements to predictions of measurement outcomes or measurement results. That's all a scientific theory is meant to do. Doing anything else, painting pictures of reality is all just there for color. It's like a fable. It's not necessary. It's philosophy. It's metaphysics. It's not important for physics to do that. And the theory does that. The theory says that we do a measurement. Here's what comes out."
},
{
"end_time": 3048.183,
"index": 121,
"start_time": 3021.476,
"text": " The theory is doing what it's supposed to do. What more could you ask of it? The theory says when we do a measurement, we do this thing, we run this prescription, we collapse the state of the quantum state of the system, and then we proceed. It all works just fine. What's your problem? The Vigner's Friend Thought experiment considers two observers. One is Vigner in the outside world, enjoying a nice sunny day, maybe a nice beautiful autumn day like today. And Vigner's friend,"
},
{
"end_time": 3073.012,
"index": 122,
"start_time": 3048.473,
"text": " who is inside a perfectly sealed box. Now, people may wonder in quantum mechanics, can you really seal anything in a box? Can't things tunnel out? Well, particles can tunnel out of certain kinds of enclosures, but if you make the box thick enough, impenetrable enough, in some highly idealized sense, then you can keep everything inside the box, at least for the duration of the experiment."
},
{
"end_time": 3101.766,
"index": 123,
"start_time": 3073.763,
"text": " Wigner's friend is inside this box along with some quantum system, some system that is in a superposition of two possibilities, a particle that is spin up and blended with spin down in some superposition, let's say. Wigner's friend engages in some interaction that you might call a measurement on this superposed quantum system inside this box. Wigner, on the outside of the sealed box, does not do a measurement, does not in any way learn what has happened."
},
{
"end_time": 3131.817,
"index": 124,
"start_time": 3102.244,
"text": " Now we've got two observers and now we have a question. Do we activate the collapse postulate or do we not activate the collapse postulate? We have two observers. We have to now take a stand. We have to say whether we activate it or not. And there are only a few possibilities. One possibility is, yes, we activate it. We activate this measurement axiom. The quantum state of the system collapses. Even though Wigner on the outside has not seen anything, it just collapses."
},
{
"end_time": 3160.145,
"index": 125,
"start_time": 3132.449,
"text": " For everybody, it just collapses. But now we have a question. Wigner's on the outside, why should Wigner think it collapsed? Because Wigner's friend did a measurement? But how do we know that the thing Wigner's friend did qualified as a measurement? Wigner's friend is just some physical system in the box. If Wigner's friend were replaced with an electron,"
},
{
"end_time": 3183.882,
"index": 126,
"start_time": 3160.691,
"text": " that somehow interacted with the other particle. We wouldn't have called that a measurement. If Ignor's friend is replaced with a water bear, you know, tardigrade, one of those microscopic, very resilient organisms that are very hard to see with their naked eye, would that have done a measurement? Like now we just have a physics question. At what point do we cross the line into yes measurement or no not measurement? Now, there's this thing called decoherence."
},
{
"end_time": 3201.766,
"index": 127,
"start_time": 3184.155,
"text": " that one often hears in these sorts of discussions. Oh, when a big system interacts with the quantum system, there's this thing called decoherence. Decoherence changes the quantum state of the system being observed. But decoherence does not collapse anything. It doesn't single out one result."
},
{
"end_time": 3231.049,
"index": 128,
"start_time": 3203.746,
"text": " And you can actually show that there's no way to take the non-collapse axioms of quantum theory and get a definite result out, to get one result singled out from all the others. So the question is, what do we do here? In principle, we need to supply a rigorous definition of what kinds of processes are measurements and what kind are not, and this is called the measurement problem. We don't have such a rigorous definition, and we haven't for a hundred years."
},
{
"end_time": 3259.889,
"index": 129,
"start_time": 3231.937,
"text": " Maybe one day someone will come along and say this is what a measurement is and this is not what a measurement is but at this point we don't have that statement. And without it we just have this ambiguity. This is the famous measurement problem. That's one possibility. The next possibility is to say there is a definite outcome of the experiment but somehow it happens without a collapse. Or collapse is perspective based, perspectival. Wigner's friend sees the collapse but Wigner on the outside doesn't. But if you take that"
},
{
"end_time": 3286.254,
"index": 130,
"start_time": 3260.725,
"text": " That horn of this dilemma, trilemma, quadrilemma, you take this path, then what you're saying is that Wigner on the outside has some quantum state he uses to describe the system, and this quantum state is incomplete. It doesn't know the definite result that happened in the experiment. And if you're accepting that the wave function is incomplete, you're accepting that there are additional or hidden variables beyond the wave function."
},
{
"end_time": 3311.681,
"index": 131,
"start_time": 3286.459,
"text": " which again is not consistent with the textbook formulation of quantum theory, at least according to the usual axioms. The third possibility is you replace measurement with something else, some kind of dynamical process by which things just naturally collapse when they're big enough, and there's a whole collection of approaches to quantum foundations called dynamical stochastic collapse approaches that do this. The wave function or quantum state is this thing and for individual particles it persists a very long time"
},
{
"end_time": 3342.278,
"index": 132,
"start_time": 3312.602,
"text": " before collapsing but you put enough particles together if any one of them collapses the whole thing comes crashing down and this explains why very big objects naturally collapse very quickly that's option three those approaches are very interesting some of them have been tested experimentally they involve a lot of you know new parameters and you have to guess equations and we don't really have a well-motivated way to understand which ones to use the fourth possibility is that there just isn't"
},
{
"end_time": 3371.101,
"index": 133,
"start_time": 3342.807,
"text": " An outcome. No one gets a definite measurement. Either there is no outcome at all, which doesn't really seem to make sense, or all the outcomes happen in some sense. And this is what Hugh Everett argued in his thesis when he considered this problem. There's no collapse, we get rid of the collapse axiom, and Wigner's friend splits into two parallel copies, each of whom sees a different outcome. One sees spin up, one sees spin down, and these are inside the box. Wigner on the outside,"
},
{
"end_time": 3396.476,
"index": 134,
"start_time": 3371.493,
"text": " also doesn't register a definite outcome if the box opens up, then Wigner sees the definite outcome and Wigner splits into two copies. And the universe kind of unzips as the copies propagate and branches or the wave function of the universe splinters into multiple possibilities. This is the many worlds interpretation and it's an ongoing source of dispute. There are a lot of questions about how to make sense of basic questions about identity and philosophy of mind in a universe like that."
},
{
"end_time": 3419.599,
"index": 135,
"start_time": 3397.261,
"text": " It's not clear how to make sense of probability in the universe like that. There's ongoing debates about how to make that work. That's basically what we're left with. That's what this vigorous and thought experiment leaves you with. You have to make a decision. I guess there's a fifth possibility, which is just quantum mechanics is wrong. But until we have good reason to think it's just wrong, we probably have to operate under the assumption that we need to make the theory work better."
},
{
"end_time": 3448.439,
"index": 136,
"start_time": 3420.247,
"text": " So this, I think, is a good motivation for taking seriously that there's something wrong with the axioms of quantum mechanics. We need to do something about them. It's not just that they're instrumentalist, but they're either ambiguous or incomplete or inconsistent in some way, and we need to fix them. Where does that leave me and where do I come in? One way to understand what I'm trying to do is going back to 1922, just when people were ready to abandon the old pictures of"
},
{
"end_time": 3478.695,
"index": 137,
"start_time": 3448.763,
"text": " Particles and fields and actual things out there doing things behaving. And just as people were about to give up on finding laws, acting on those ingredients that would give you an empirically adequate theory. Maybe it's premature to give up. Maybe we need to think a little more generally about what form laws can take. So by 1922, people already understood that you could have laws that were chancy."
},
{
"end_time": 3505.35,
"index": 138,
"start_time": 3479.241,
"text": " Chancy probabilistic laws that didn't tell you in a definite deterministic way what was going to happen. But laws that simply told you probabilistically what would happen. We knew about these Einstein certainly knew about these kinds of models. One of his great papers 1905 was on Brownian motion. This helped provide solid evidence for the existence of atoms even allowed you to figure out how big the atoms were."
},
{
"end_time": 3528.012,
"index": 139,
"start_time": 3505.879,
"text": " And this is a model based on what's called a stochastic process, stochastic from the Greek word stochasticos, which means to aim or guess. These are models where the laws predict probabilistic behavior. So people knew about these things. Markov had introduced the Markov matrix by the early knots 1906 or something like that."
},
{
"end_time": 3557.363,
"index": 140,
"start_time": 3528.763,
"text": " So these ideas were in the air and people were thinking about, well, quantum mechanics behaves in an unpredictable way. Maybe that unpredictability could be captured in probabilistic laws, but people couldn't come up with the right set of probabilistic laws at the time. Over the years, people did try to come back to this question. In fact, in Hugh Everett's thesis, he talks about an effort by a physicist named Fritz Bopp"
},
{
"end_time": 3587.125,
"index": 141,
"start_time": 3558.66,
"text": " that replaced the usual quantum-mechanical formalism with probabilistic laws, with particles moving around according to probabilistic laws. And Everett actually said this was a promising direction. He wasn't going to study it in his thesis, but this was worth paying attention to. Several other people worked on these proposals, Imre Fenyes in like the 1950s, most famously Edward Nelson in the 1960s. But the models were very complicated."
},
{
"end_time": 3615.077,
"index": 142,
"start_time": 3587.363,
"text": " To get the same predictions that you get from the textbook theory of quantum mechanics, you had to, this is the one political thing I'll say, gerrymander, you had to gerrymander, I mean this in metaphorically the same sense, you had to gerrymander the laws. You had to start with what we knew was supposed to be predicted and then work backward and design these incredibly complicated stochastic laws in order to get the same predictions. So it just felt very unmotivated."
},
{
"end_time": 3639.514,
"index": 143,
"start_time": 3615.452,
"text": " The spirit was a very interesting spirit. Let's just have particles bouncing around or fields, whatever, evolving without a Hilbert space, without wave functions. Let's just directly give them rules that are probabilistic. And in such a way that those probabilities agree with the probabilities we see for measurement outcomes in our experiments. But getting the idea to work was hard. It wasn't clear that we had the right kinds of laws to do it."
},
{
"end_time": 3660.674,
"index": 144,
"start_time": 3640.162,
"text": " And the laws to make them work even in the simplest cases required a lot of fine tuning and gerrymandering. And when you look at, for example, Nelson's stochastic mechanics, you know, his laws are super complicated. And you actually have to first find the wave function from the Schrodinger equation, then you plug it into these laws and laws involve rates that go forward and incredibly complicated."
},
{
"end_time": 3686.766,
"index": 145,
"start_time": 3661.715,
"text": " There were rival approaches. So, Louis Dubois introduced a pilot wave theory in the 1920s that was independently discovered by David Bohm and these theories were based originally on hidden variables, particles that were piloted around by the wave function in some sense. When you try to extend these models beyond systems of non-relativistic particles but to like relativistic systems and fields,"
},
{
"end_time": 3716.8,
"index": 146,
"start_time": 3687.739,
"text": " It gets very complicated and you end up having to deduce probabilities and stochastic laws again. So there seems to be this understanding that ultimately to describe most kinds of quantum systems will need something like laws that are inherently probabilistic. But none of the probabilistic laws that people knew about seemed to work well. They either didn't work or required so much fine tuning that they just seemed unmotivated. In 2022, I was trying to teach"
},
{
"end_time": 3740.657,
"index": 147,
"start_time": 3717.21,
"text": " a class and I had a problem. We were getting to the point in the class where I was trying to introduce a little bit of quantum mechanics and I was trying to decide how to do it and I taught this class a few times. Which class? It's called Introduction to Theoretical Physics. It's Physics 19 here at Harvard and we cover a lot of topics in the foundations of theoretical physics in this class."
},
{
"end_time": 3767.022,
"index": 148,
"start_time": 3741.169,
"text": " Throughout the class, we're introducing some concepts from quantum mechanics, but this is the sort of toward the end of the class and I'm trying to give them a nice self-contained preview of quantum mechanics. But these are students who are mostly very new to physics. Many of them are just beginning to learn college level mathematics. So I can't start by talking about Hilbert spaces or C star algebras or the GNS theorem or any of those things. I need to find a more"
},
{
"end_time": 3790.947,
"index": 149,
"start_time": 3767.585,
"text": " Friendly way to get into quantum mechanics and every year I would just tear apart my curriculum and try again I was never satisfied with how I was doing it Sometimes I would say maybe we'll just start with wave functions and sometimes I would say maybe we should start with matrices and some I just I couldn't come up with a way that I wanted to do it and in the fall of 2022"
},
{
"end_time": 3820.776,
"index": 150,
"start_time": 3791.664,
"text": " I remembered back to a couple of projects I'd worked on as an undergraduate and even in graduate school where I needed to use the theory of stochastic processes in order to, you know, in undergrad, it was like a special extra homework set assignment for a linear algebra class in grad school actually used it for simulations. And, you know, the theory of Markov chains and stochastic processes, it bears some very vague resemblances to quantum mechanics."
},
{
"end_time": 3841.544,
"index": 151,
"start_time": 3821.493,
"text": " It's got probabilistic laws. You represent the probabilities for a system with a vector. Evolution in time is represented with matrices. Now they're all a little bit different. The probabilities don't involve complex numbers. The matrices are what are called stochastic matrices."
},
{
"end_time": 3865.282,
"index": 152,
"start_time": 3842.244,
"text": " But there are these like resemblances. And so I sat down and I thought to myself, maybe I can find some way to bring these two theories together. The theory of stochastic processes on the one hand, and the theory of quantum mechanics on the other hand. I had this sort of image in my mind of like walking along the edge of a chasm. On one side,"
},
{
"end_time": 3892.022,
"index": 153,
"start_time": 3865.503,
"text": " You had sort of the classical world, classical stochastic processes, probabilistic processes. On the other side, you had quantum mechanics and there was this huge gulf between them. And I was looking for a place where maybe the cliffs came closer together and where it was easier to hop across from one to the other. So I began modifying the mathematics of the theory of stochastic processes and quantum mechanics to try to bring these two pictures closer and closer together."
},
{
"end_time": 3912.381,
"index": 154,
"start_time": 3893.217,
"text": " I was doing this without really knowing very much about this earlier work that had been done, the work of Bopp and Fenyes and Nelson. If I'd read all those papers, I would have given up because I would have decided it was impossible. But sometimes you can only do something if you don't know it's impossible. I did know it was impossible."
},
{
"end_time": 3943.524,
"index": 155,
"start_time": 3913.712,
"text": " I brought these theories closer and closer together, expecting that there would be a moment when I would need to make some kind of jump to get from one theory, classical physics, to the other theory, quantum physics. And the strangest thing happened. The two cliff faces merged. And there was just no chasm anymore. For those who are familiar with second order phase transitions in statistical mechanics, it was like I had reached a point of a second order phase transition. On one side, you have the"
},
{
"end_time": 3972.176,
"index": 156,
"start_time": 3943.712,
"text": " You know, two phases of some substance like water, right? And then you go past a point and the phases merge and there's only one super phase, right? There's no distinction between like liquid and gas anymore, right? So, and I didn't understand what had happened. I was very confused. So I began looking in literature to see if other people had done what I had done and no one had done what I had done. No one had, I guess, thought it was worthwhile to try to do this thing that I was doing."
},
{
"end_time": 4002.875,
"index": 157,
"start_time": 3973.985,
"text": " But I began to read some literature on stochastic processes and Nelson's work and I was confused why had they not succeeded when this seemed to work. And it was about October of 2022. I know because I went to the office of one of my colleagues, the great Logan McCarty, who directs science education here at Harvard. He's a quantum chemist. He knows quantum mechanics backward and forward. And I went and I talked to him and I went to his, he had a whiteboard and I"
},
{
"end_time": 4033.422,
"index": 158,
"start_time": 4003.558,
"text": " I began writing out everything I was doing because that point I'd realized that the secret sauce, the thing that made this work was I had implicitly given up an assumption I didn't even know that I was supposed to make or that anyone had made. When people model stochastic processes, they usually assume that the process is a Markov process. Named after Markov, like Markov, the Russian mathematician who introduced Markov matrices. A Markov process is a process where"
},
{
"end_time": 4052.415,
"index": 159,
"start_time": 4034.531,
"text": " If you want"
},
{
"end_time": 4082.756,
"index": 160,
"start_time": 4052.892,
"text": " And the generalizations of Brownian motion, Wiener processes, and many of the familiar processes that we have heard of, random walks, Poisson processes, these are all Markov processes. Nelson's work, a Markov process, they're all memoryless processes. Now, I was vaguely aware that there existed a subject called non-Markovian stochastic processes. And I went and I looked in textbooks to see if anyone had done what I was doing."
},
{
"end_time": 4110.401,
"index": 161,
"start_time": 4083.063,
"text": " And usually at the end of the textbook, the textbook would say something like, and that's it for the theory of stochastic processes. There is a larger subject called the theory of non-Markovian stochastic processes, but this is too complicated. It is beyond the scope of this book. So it was very hard to find any books on non-Markovian processes. And I went into the literature and I discovered some people were trying to develop tools for handling non-Markovian processes. There's some that can be turned into Markov processes with a change of variables. They become what are called hidden Markov processes."
},
{
"end_time": 4134.821,
"index": 162,
"start_time": 4110.401,
"text": " And some of them if they're just sufficiently non Markovian are just super hard to deal with and so it just feels like the wild west there's just this discipline going beyond the mark of approximation that a lot of people didn't really. You know felt a little uncomfortable exploring it wasn't clear how much we needed them i mean mark of chains are really good at modeling the world around us to really need to spend so much time worrying about non markovian processes."
},
{
"end_time": 4165.503,
"index": 163,
"start_time": 4135.964,
"text": " And what I realized was that I had inadvertently introduced a kind of a non-Markovian process without realizing it. As I plumbed this more, I discovered that what I was working with wasn't even a non-Markovian process in the most familiar sense. It was an entirely, it was a more general kind of a process that first shows up in the research literature in 2006. It's called an indivisible process."
},
{
"end_time": 4193.66,
"index": 164,
"start_time": 4166.613,
"text": " Indivisible processes are in some ways the most general kinds of rules, dynamical laws, generally probabilistic, that fail to have that Markov property. They're more general than what we usually think of as non-Markovian processes. I guess there's more than one way to be non-Markovian and people had a very particular idea of what they meant by non-Markovian. This is like even more non-Markovian than a non-Markovian process."
},
{
"end_time": 4222.91,
"index": 165,
"start_time": 4194.804,
"text": " These processes first showed up when people were trying to understand the kinds of dynamical rules that describe Hilbert space objects. So not what I had in mind. They were already in the Hilbert space picture trying to describe how objects in the Hilbert space picture could evolve in time. And for them, an indivisible process was just a law that could tell you how your process would evolve from one time to another, but couldn't be divided up into smaller times."
},
{
"end_time": 4250.742,
"index": 166,
"start_time": 4223.37,
"text": " So you have a law that tells you how to get from zero to the final time, but the theory just doesn't give you laws for the intermediate times. That's it. That's the indivisibility. Certainly not laws that can be iterated and concatenated into a bigger, bigger law. And if you think about it, this is certainly more general than divisible laws. I mean, because there's this bigger category where we don't have some of the properties we might want a lot of have divisibility. Newtonian mechanics is divisible."
},
{
"end_time": 4279.309,
"index": 167,
"start_time": 4251.22,
"text": " You evolve a system from an initial time to some intermediate time, and then you can stop, look at the system state right now, and then if you want, you can use Newton's laws to tell you what will happen next, nice and divisible. The Maxwell equations that describe the evolution of electric-magnetic fields are divisible, and quantum mechanics, as usually formulated in terms of the Schrodinger equation, beautifully divisible. The Schrodinger equation tells you how the quantum state will evolve, and you can evolve it however far you want, and then read off the quantum state in some way, and then predict where it will go next."
},
{
"end_time": 4302.585,
"index": 168,
"start_time": 4279.548,
"text": " Is another way of saying divisibility as a continuous time parameter? That's a good question, not necessarily, because you could imagine an indivisible process where you're allowed to go from the initial time to any time you want, so time is smooth, but once you pick one of those times, you don't have a law that will tell you how to get from that time to later times."
},
{
"end_time": 4330.555,
"index": 169,
"start_time": 4303.012,
"text": " So time is not necessarily discrete here. It's an excellent question. But what you lack is the ability to break time up into smaller intervals. Yeah. So we just don't have much experience with these kinds of laws until this paper comes out in 2006. It's called Dividing Quantum Channels by Ignacio Chirac and Michael Wolff. Ultimately, it was published in 2008 in Communications and Mathematical Physics. And people play around with these. You know, the paper gets a lot of citations. It's not until 2021"
},
{
"end_time": 4360.776,
"index": 170,
"start_time": 4332.056,
"text": " that a couple of folks introduced the idea of a classical process that could be indivisible, like just a process where the system has some configuration and it's changing, it's behaving in some probabilistic way, but the way it's behaving probabilistically is indivisible. That shows up in a figure on like page 15 of this beautiful review article"
},
{
"end_time": 4375.094,
"index": 171,
"start_time": 4360.947,
"text": " by Mills and Modi where they mention the idea that you could have a process like this. I didn't know it existed. I came up with the term indivisible independently because I didn't want to use irreducible, which is used in so many ways in physics. I didn't want to use"
},
{
"end_time": 4405.538,
"index": 172,
"start_time": 4375.606,
"text": " I basically just was looking for a word that would give you evoke the right idea. And it turned out they use the exact same terminology. So this was a year before I did it. They did not connect it to quantum mechanics. They were just mentioning always the possibility you could in theory have a classical process with probabilistic behavior where the laws are not rich enough. They're too sparse. They won't tell you how to go from any time to any other time. You can only evolve from certain times to other times. The process in general doesn't divide."
},
{
"end_time": 4433.968,
"index": 173,
"start_time": 4406.749,
"text": " What I had inadvertently done was discovered these indivisible stochastic processes and shown that there was just a change of mathematical representation that would take such a system with classical like configurations, could be a system of particles, could be a system of fields, whatever we're trying to model. And if it has indivisible stochastic laws, then through this mathematical representation, this correspondence,"
},
{
"end_time": 4458.763,
"index": 174,
"start_time": 4434.735,
"text": " You get a Hilbert space picture. Super interesting. Yeah. And all the weirdnesses of the Hilbert space picture, superposition of states, interference effects, these are all related to what are called coherences, phases, right? They're all the all the connect all these things are connected to, to, you know, superposition interference and coherences. These could be understood now."
},
{
"end_time": 4486.34,
"index": 175,
"start_time": 4459.275,
"text": " They could be given a meaning. So in textbook quantum theory, these things don't have meanings. They're just pieces of mathematics that show up in the formalism. We don't understand what they mean. We know that interference shows up in experiments. We know that these things called phases or coherences or superpositions, we see these show up in all over the place, but they don't directly have like a physical meaning. We don't know what they represent and what they really mean. What I was able to show is"
},
{
"end_time": 4516.049,
"index": 176,
"start_time": 4487.159,
"text": " that in going from this very physically concrete picture of objects of a clear ontology probabilistically evolving in this indivisible way in going from that picture to a picture with a nice Schrodinger equation where the evolution is divisible it's a nice differential equation very familiar mathematics in going to that picture that looks divisible you have to give something up that indivisibility doesn't disappear"
},
{
"end_time": 4545.725,
"index": 177,
"start_time": 4516.766,
"text": " It becomes all those weird phases, interference effects and coherences. That's how they manifest in this picture. It's like there's no free lunch. If you want a picture that's mathematically convenient and simpler, a picture where you can evolve a system any amount of time you want, pause, re-evolve, a nice divisible dynamical picture, you have to pay the price. And the price is that all that indivisibility becomes these weird phases. In some very loose sense,"
},
{
"end_time": 4574.275,
"index": 178,
"start_time": 4546.766,
"text": " If you want to think roughly speaking of these individual processes as being like processes with memory, all those interferences and faces, those are the memory encoded in this strange way. And that's the picture. That's fantastic. Yeah. So in this picture, there's no fundamental role for a wave function. I mean, you just have objects bouncing around, according to laws that are more general than laws of Newtonian mechanics, or even the laws of a Markov process."
},
{
"end_time": 4601.988,
"index": 179,
"start_time": 4575.009,
"text": " And if you want to model a measurement, you just model another system that interacts with your first system, give the whole thing a nice simple set of stochastic, indivisible stochastic dynamics. And what you'll find is that the measuring device will stochastically evolve into one of its final readout configurations with exactly the correct probability that we would expect from the Born Rule. But there's no wave function, there's no collapsing,"
},
{
"end_time": 4628.063,
"index": 180,
"start_time": 4602.346,
"text": " It's just some big stochastic process happening. Experience a membership that backs your business journey with American Express Business Platinum. When you pay with membership rewards points for all or part of an eligible flight booked with a qualifying airline through Amex Travel, you can get 35% of those points back, up to 1 million points back per calendar year. American Express Business Platinum. There's nothing like it."
},
{
"end_time": 4647.039,
"index": 181,
"start_time": 4628.336,
"text": " Terms apply. Learn more at americanexpress.com business-platinum. So what's doing the choosing of what interval to make that time? He said that you can choose any interval but then you can't choose a sub interval. Right, this is an excellent question. So"
},
{
"end_time": 4675.196,
"index": 182,
"start_time": 4647.449,
"text": " In order to get an indivisible stochastic process started, you need a time at which you can begin, right? And then the process tells you probabilistically where the system will end up at really any smooth choice of later time. But is there just one special time where things can get started? The answer is no. What you can show is that when you have a system interacting with some larger system, so not left to itself,"
},
{
"end_time": 4705.435,
"index": 183,
"start_time": 4675.811,
"text": " interacting with some larger system. What you find is that if this larger system is exchanging information with your original system, as would happen if you've got a measuring device reading out the configuration of your system, then when it does this, you just let the stochastic process tell you what happens. There's no axiom here. You let it evolve and what you discover is that you get a division event. The evolution divides at that moment, seen from the point of view of the smaller system."
},
{
"end_time": 4732.585,
"index": 184,
"start_time": 4706.288,
"text": " And now there's a new time at which the evolution breaks and you can start now again from that new time. So in an individual stochastic process, it's not that there are no times where you can divide. There are times at which you can break up the evolution, but the times aren't given to you at the beginning. They're not fundamental. They arise from mutual interactions between systems."
},
{
"end_time": 4759.053,
"index": 185,
"start_time": 4733.541,
"text": " Now when you ask what does this look like from the Hilbert space point of view, in the standard textbook quantum mechanical picture, the Hilbert space point of view, what are those division events look like? They look just like decoherence. So decoherence again is when a big system interacts with maybe a smaller system, the environment comes in interacts with the system exchanges information, and we get these changes to the quantum state of the other system changes that don't single out one answer, but do change it in some way."
},
{
"end_time": 4787.978,
"index": 186,
"start_time": 4759.48,
"text": " Those changes kill off the coherence effects. They kill off interference effects. From the point of view of the indivisible stochastic process, they just look like the generation of a new moment, a new division event, an event where the evolution can be started again. And this happens in the end of measurements. And this is a physical process in this picture. And it coincides with what you would call a measurement. But it's generated by the laws of this picture themselves."
},
{
"end_time": 4815.128,
"index": 187,
"start_time": 4788.524,
"text": " Okay, I'm confused. So division events, is that just another relabeling of what a measurement is? Good question. So in a way, sort of, if you give me a second system that I model explicitly, so let me phrase it a different way. In the textbook axioms of quantum theory, measuring devices are treated as outside the formalism, right? They're not"
},
{
"end_time": 4838.268,
"index": 188,
"start_time": 4815.572,
"text": " They're kind of in the background. They're kind of like the person behind the curtain, right? We do a measurement and we just sort of change the quantum state of the system being measured, but we don't usually explicitly put the measuring device into the description itself. If you try to do that, if you try to put the measuring device into the description, what you find after a measurement is"
},
{
"end_time": 4867.159,
"index": 189,
"start_time": 4838.677,
"text": " that the measuring device and its possible readout configurations become entangled with the possible configurations of the system being measured. There's this entanglement that happens. And the question is, well, then what? Now they're entangled, what do I do? What you're supposed to do is collapse down to one of those entangled branches. That's the collapse. Now, if there's a bigger environment that comes in, and the bigger environment looks at the measuring device,"
},
{
"end_time": 4895.759,
"index": 190,
"start_time": 4867.91,
"text": " Then it gets entangled with the measuring device and there's this operation, this sort of formal operation where you can kind of ignore the environment and you see that there's a suppression of all the interference effects but still no singling out of one outcome. You have to at some point pull the fifth axiom, activate it and collapse down to one thing at some point. In this indivisible picture, you can bring in that measuring device, you bring it in,"
},
{
"end_time": 4924.753,
"index": 191,
"start_time": 4896.237,
"text": " you let the overall system of all stochastically and what you find is that and bring in an environment the environment comes and you can treat them all as actual systems none of them are are outside the formalism they're all modeled as systems in the formalism when you find is you let the systems of all the system being measured and the measuring device probabilistically evolved toward the configurations that we would expect from the you collapse axiom"
},
{
"end_time": 4952.79,
"index": 192,
"start_time": 4924.855,
"text": " And because of the environment, you can show that the measuring device and the subject system, they experience a division event at almost exactly the moment of the interaction that we would call a measurement. And this division event means that you can now restart the laws and start them from this moment. This division event is not postulated. It's not an axiom. It's something that just shows up from the usual rules of probability theory."
},
{
"end_time": 4980.964,
"index": 193,
"start_time": 4953.148,
"text": " when you actually model the systems explicitly. So in a way it is a measurement, but it doesn't require a conscious being, it doesn't require a human. Any system that has a robustly large number of moving parts, we call them degrees of freedom, in contact with a nice big environment with a big number of degrees of freedom,"
},
{
"end_time": 5004.019,
"index": 194,
"start_time": 4981.527,
"text": " will to an extremely high level of precision, produce measurement results that probabilistically coincide with what we would expect from textbook quantum theory, and will generate a moment at which the stochastic dynamics of the system being measured in the measuring device can be restarted and have their own dynamics. So"
},
{
"end_time": 5033.763,
"index": 195,
"start_time": 5005.111,
"text": " So yes, in a way it's a measurement, but it lets us get inside the measurement. It lets us see the measurement actually happen, and it gives us a way to understand why measurements do this thing, rather than merely positing that they collapse wave functions. So do you require three different systems to be stated? So the environment, the measurer, and the measured? Yes, that's right. And we require that in standard quantum measurement theory anyway, in the usual textbook theory. The environment as well?"
},
{
"end_time": 5063.848,
"index": 196,
"start_time": 5034.189,
"text": " The environment is needed, yeah. Yep. Because the usual argument is that the environment is what generates the decoherence of the measuring device and the system being measured. But when you say the environment, I mean, in any realistic measuring device, you have, you know, the part of the measuring device that's actually directly engaged in the measurement, but then you have the rest of the measuring device. I mean, it's a big object, it's in a box, it's got dials, it's got other experimental things on it. I'm sorry, this is me not being a very good experimentalist again."
},
{
"end_time": 5086.032,
"index": 197,
"start_time": 5064.155,
"text": " So you firstly describe the environment, the measure, and the measured classically, and then you do your version of a quantizing procedure? Yeah, so you model them classically in the sense that they have classical-like configurations. The measuring device"
},
{
"end_time": 5114.565,
"index": 198,
"start_time": 5087.176,
"text": " is some system, some physical object that can be in different possible configurations. Among those we include at some level of coarse graining. We include, you know, the system is empty, it doesn't yet show a reading, the system shows spin up on the dial, the system shows spin down on the dial, you know, like, but these are concrete configurations made of particular configurations of the constituent atoms, whatever you want. So"
},
{
"end_time": 5134.462,
"index": 199,
"start_time": 5114.889,
"text": " That is to say that their configurations their ontology their physical existence is visualized in a roughly classical way. The quantum part is that the laws they satisfy are not deterministic differential equations like Newton's law or Newton's laws or electric or the Maxwell's laws of electromagnetism."
},
{
"end_time": 5161.613,
"index": 200,
"start_time": 5134.821,
"text": " The laws we give them are these indivisible stochastic laws, which we don't usually see in classical systems. The claim is that when you give these systems these more general kinds of laws, that's enough to make them behave like quantum systems. So what is it that's jittering around or being random here? Good question. So all these systems have configurations, and these configurations are evolving according to stochastic laws."
},
{
"end_time": 5181.169,
"index": 201,
"start_time": 5162.073,
"text": " That is to say that the configurations are changing with time in a probabilistic way. Now, why are they changing in a probabilistic way? I don't know. These are the axioms, right? At some point you have a physical theory you have to propose some axioms. I mean, there's a"
},
{
"end_time": 5211.613,
"index": 202,
"start_time": 5181.613,
"text": " What a posture in how we think about basic questions in philosophy called foundationalism. You have to begin with something. The standard textbook version of quantum theory, which works fantastically well, and I'm certainly not making any claims that any of the predictions it makes are wrong. They're all spot on. Those axioms are axioms and they're very strange. We posit Gilbert spaces and"
},
{
"end_time": 5240.418,
"index": 203,
"start_time": 5211.903,
"text": " state vectors or density operators and the Schrodinger equation and self-adjoint operators and all the collapse postulate and we postulate them because with these axioms we get the right predictions empirically. This picture I'm presenting has axioms too. The axioms are simpler. Every system just has a set of possible configurations, classical-like configurations and the laws are these indivisible stochastic laws."
},
{
"end_time": 5269.684,
"index": 204,
"start_time": 5241.425,
"text": " That's it. Um, now, if you want to ask why the laws are into the fantastic, I don't know. The best I could say is that when we try to explain things, there is a case to be made that you want to start with the least constrained possibilities, the most general possibilities, and then argue that in some circumstances, you get more constrained possibilities."
},
{
"end_time": 5291.561,
"index": 205,
"start_time": 5270.247,
"text": " Indivisible"
},
{
"end_time": 5308.524,
"index": 206,
"start_time": 5292.005,
"text": " To me, it makes sense that you would begin with the most general kind of law and then you would explain why in certain special circumstances we would expect to see a Markov process, why in certain circumstances we would expect to see deterministic second-order differential equation kind of a law."
},
{
"end_time": 5325.623,
"index": 207,
"start_time": 5308.933,
"text": " You know, that's the job of understanding the quantum classical transition, understanding the so-called classical limit. How do we get from the laws of quantum mechanics to laws that look like Newtonian mechanical laws or that look like classical Markov processes and those arguments carry through just as well in this picture."
},
{
"end_time": 5355.179,
"index": 208,
"start_time": 5326.067,
"text": " We don't start with deterministic laws. We don't start with a Markov chain or anything like that. We start with these much more general laws. And then by adapting the usual arguments people usually make in trying to get to the classical limit, the classical regime, we see why in certain circumstances we get big classical looking systems whose laws look deterministic or at least look like their Markov probabilistic laws. And to me, that's the right direction of explanation. You start with the more general, the least constrained kinds of laws and you move to the more constrained ones."
},
{
"end_time": 5385.179,
"index": 209,
"start_time": 5355.691,
"text": " So I guess I would say it's not that I feel like I need to explain why particles or objects behave probabilistically. Probabilistic behavior is the default. It's what happens if we don't have a good reason to think the laws need to be deterministic. And then the goal is to show why in some circumstances we get predictably deterministic behavior. But the truth is I don't have a deeper explanation for why we expect the particles to be jiggling around probabilistically."
},
{
"end_time": 5407.585,
"index": 210,
"start_time": 5386.169,
"text": " That's what it means to have an indivisible stochastic law, really stochastic law in general. And your probabilities, are they classical probabilities or are they quantum amplitudes? It's a great question. They're classical probabilities and that's kind of key. So this underlying picture, the claim that every quantum system in its beating heart is really"
},
{
"end_time": 5434.292,
"index": 211,
"start_time": 5408.353,
"text": " some system with configurations. If it's a particle, we're talking about where the particle could be. If it's a field, we're talking about what are the different intensities the field could have in space. If it's a system of abstract bits, like in a computer, it's some configuration of zeros and ones. This is what I mean when I say a classical-like ontology or a classic-like configuration space. And the probabilistic laws are assigning"
},
{
"end_time": 5460.572,
"index": 212,
"start_time": 5434.565,
"text": " ordinary probabilities to these things. They're saying that the system begins in some configuration and then the indivisible stochastic law takes the form of laws that probabilistically tell you where it will end up. And those are just ordinary probabilities. They're real numbers between zero and one. They sum to one. There are no complex numbers at all in this picture at this point. But if you want to describe the same process in a more mathematically convenient way, I mean, indivisible processes are really"
},
{
"end_time": 5493.353,
"index": 213,
"start_time": 5463.746,
"text": " So instead, we use this mathematical change of representation to the Hilbert space picture. We translate all of the ingredients in this underlying process into this Hilbert space picture. In the Hilbert space picture, we have nice differential equation type laws, the Schrodinger equation. We've got complex numbers that show up. And then the probabilities that you have in the indivisible stochastic theory become what we call mod squares of"
},
{
"end_time": 5523.251,
"index": 214,
"start_time": 5493.695,
"text": " complex numbers. The complex numbers that you mod square to get probabilities are called amplitudes. So it's only in going to the Hilbert space picture that we have the need for amplitudes. And the amplitudes do all kinds of funny things. They interfere with each other. If you want to write down a process where a system could go one way or the other, you're supposed to consider all the possibilities and then add all the amplitudes together and there's interference, right? But that's all happening in this sort of mathematical representation, this Hilbert space side. And the claim is that's not telling you what's physically happening in the system."
},
{
"end_time": 5550.094,
"index": 215,
"start_time": 5523.763,
"text": " That's just very convenient mathematics. And again, makes all the right predictions, right? The idea here is you get back the usual textbook axioms of quantum theory, but now you understand where they come from. And now they're not inconsistent anymore because at a fundamental level, there's no special role of the observer. There's no special rule for measurements. All the processes that we think of in quantum mechanics are just ordinary processes. They just look weird and exotic when you see them on the Hilbert space side."
},
{
"end_time": 5578.49,
"index": 216,
"start_time": 5551.34,
"text": " Have you encountered any resistance from people who like their quantum mechanics mystical? Yes. Explain. Well, I mean, quantum mechanics is so exciting. Actually, let me rephrase that. Not that they like their quantum mechanics mystical. Have you encountered any resistance from people who like their quantum mechanics mystified? Mystified."
},
{
"end_time": 5602.688,
"index": 217,
"start_time": 5578.985,
"text": " Yeah, they like it shaken not stirred, right? I mean, a little bit. Yeah, I think it's so there's a sense in which this picture is deflationary. It deflates. It takes exotic statements. Oh, the cat is alive and it's dead. And it deflates them and says, actually, it's really one or the other. And"
},
{
"end_time": 5632.637,
"index": 218,
"start_time": 5603.183,
"text": " We merely represent it mathematically with a state that looks like it's a superposition of live and dead, because it gives us divisible evolution we can use. It's easier to study mathematically, but it's not the reality. It deflates that, yeah. Just to be clear, deflationary is the philosopher's term for saying there's nothing to see here, folks. Just calm down. Yeah, it's basically that. It just like sucking the air out of a balloon, right? It brings it down to Earth, which is basically what this does. It makes quantum mechanics, I think, in some ways much more boring."
},
{
"end_time": 5663.046,
"index": 219,
"start_time": 5633.268,
"text": " And, you know, as I was working on this, I kind of felt that because when young people go into physics and they begin learning about quantum mechanics, it's super exciting to think that you can be able to understand what's going on when the cat, Schrodinger's cat, is alive and dead and particles can go through both holes in the interference experiment at once and it interferes with itself and everything is entangled with everything else. And maybe when we think about things, humans are special, we collapse things."
},
{
"end_time": 5686.391,
"index": 220,
"start_time": 5663.848,
"text": " It says that at some level quantum systems might, if this all works out right, might just be kind of prosaic. There's no wave function in Hilbert space, there's just objects, atoms, chairs, whatever, and they're just evolving just in an indeterministic way, a very indeterministic way."
},
{
"end_time": 5714.514,
"index": 221,
"start_time": 5686.681,
"text": " Well, still probabilistic. We can still assign probabilities to things, because you could imagine laws that are so badly indeterministic that we can't even assign probabilities to them, but we can at least assign probabilities to them, but then a lot of the magic is gone, right? There's no special world for humans. In some sense, I mean, what is it? The history of science has pushed humans farther and farther out of the center of the story. You know, first we were the center of the universe, then we weren't."
},
{
"end_time": 5741.527,
"index": 222,
"start_time": 5714.855,
"text": " Then maybe we were the center of all observations and quantum mechanics and this takes us out of that altogether. There's nothing particularly special about human observation or the human mind. And I guess with AI development, we might soon not even be the smartest people on the planet, the smartest organisms or entities on the planet. So I don't know. I mean, I can only speak for myself. I have felt a little sad to think that there's a way to think about quantum mechanics where there's no wave function."
},
{
"end_time": 5763.882,
"index": 223,
"start_time": 5742.073,
"text": " Nothing is splintering into multiple realities. So there's a way to take Newtonian physics and introduce kinetic energy, which is an energy associated with things moving and potential energy, which is an energy associated with configurations of things."
},
{
"end_time": 5793.985,
"index": 224,
"start_time": 5764.241,
"text": " And you take these two quantities, they're a bit more abstract than like particles and forces and stuff, but you can imagine kinetic energy and potential energy. And you subtract them from each other, which is kind of a weird thing to do. Usually, we think that the total energy is the sum of these things. You can subtract them, and then you can integrate this thing over time. And you get a mathematical construction called an action, the action functional. We're actually covering this in my class right now. The thing you're integrating, kinetic minus potential energy, is called the Lagrangian. At least in the simplest cases, it's kinetic minus potential energy."
},
{
"end_time": 5809.241,
"index": 225,
"start_time": 5794.838,
"text": " And you can use this to encode the laws of your system. You can use this to describe how the system will behave. But you could ask, what is the action? Like, is it a physical object?"
},
{
"end_time": 5837.995,
"index": 226,
"start_time": 5810.128,
"text": " You can make the action evolve in time. You get what's called Hamilton's principle function. It obeys a partial differential equation, and I didn't mention it, but this is the beginning of Hamilton-Jacobi theory, and it was by studying the time-evolving action, the Hamilton's principle function, and its differential equation that led Schrodinger to discover the Schrodinger equation. It was a beautiful extrapolation from the partial differential equation satisfied by this action. So this action as a function of time or Hamilton's principle function"
},
{
"end_time": 5868.558,
"index": 227,
"start_time": 5838.626,
"text": " is a lot like the wave function of quantum mechanics, so much so, like I said, that it inspired Schrodinger to develop the wave function. In some sense, Schrodinger's wave function was like an exponentiated version of this Hamilton's principle function. So you could ask, what is the meaning of Hamilton's principle function? Is there an object out in the world evolving according to this partial differential equation, the Hamilton-Jacobi equation, the equation satisfied by this principle function, this integrated kinetic minus potential energy?"
},
{
"end_time": 5897.756,
"index": 228,
"start_time": 5870.009,
"text": " I think most physicists would say no. They would say that it's just a mathematical convenience. It's an appurtenance of the theory. We can use it to generate predictions. We can use it to make predictions. And that's wonderful. It's beautiful mathematics. But there is no object in physical reality it's describing. And what I'm saying is the wave function is basically just like that. It's in the same conceptual or metaphysical category as Hamilton principle functions."
},
{
"end_time": 5926.766,
"index": 229,
"start_time": 5898.422,
"text": " Sure, it's in the mathematics, it's convenient, but there is no physical object that it is describing. And because there's no physical object, there's nothing branching, there's nothing splintering into branches. So you would never even think that there could be many worlds or anything like that. There's just nothing in the ontology of the picture as I've presented it that would play the role of branching realities. So things like many worlds don't even get off the ground in this picture."
},
{
"end_time": 5951.237,
"index": 230,
"start_time": 5927.602,
"text": " I think that's kind of what I mean when I say that there's no wave function. I mean it in that somewhat precise sense. I don't mean that we shouldn't use wave functions in the mathematics or use them to make predictions, but we should be a little more modest in how we talk about them. Have you spoken to Sean Carroll about this? That's an interesting question. Not yet."
},
{
"end_time": 5981.442,
"index": 231,
"start_time": 5951.783,
"text": " But at some point we'll chat, hopefully. Yeah. I say it's an interesting question because I have not done a lot of traveling in the last year or so, so our paths really haven't crossed. But I'd love to have a chat about it at some point. Well, any Everettians or many worlds, people? A little bit. A little bit. But I think, you know, you talked about mysticism, you talked about how people like their physics. The truth is that people get really good at doing physics in a certain way."
},
{
"end_time": 6008.968,
"index": 232,
"start_time": 5982.295,
"text": " And we develop intuitions. When you learn to play an instrument, learn to play the piano, right? You learn to play chess. You learn gourmet cooking. And you do this over many years. And if you've got the right combination of motivation and talent and skill and the right environment and the right mentors, the right combination of all these factors, you end up becoming very proficient at it."
},
{
"end_time": 6037.91,
"index": 233,
"start_time": 6009.616,
"text": " And you can do wonderful things. You can play beautiful pieces of music. You can make just fantastic cuisine. You can become a grandmaster in chess. And if someone comes along and says, I think you should do this differently, you should go back to the to the starting board, you should sit on the piano bench like this, and you should hold your hands like this, or you should play chess. And the pieces should start off in a different position. And we should change all the rules, right? The chess pieces should move differently."
},
{
"end_time": 6058.234,
"index": 234,
"start_time": 6038.66,
"text": " You're going to render a person back to square one. And you could imagine why someone probably wouldn't want to do that. And it's not for any negative reason. It's just that they've optimized themselves to do really good work, right? And to ask them to go back to the drawing board and start again is a huge ask."
},
{
"end_time": 6088.404,
"index": 235,
"start_time": 6058.882,
"text": " And so I would basically say anyone who's been doing quantum mechanics in a certain way their whole career, who's developed all kinds of intuition, they just have a good feeling for what to do with wave functions and stuff, you know, I could imagine someone, you know, in that position, being reluctant to want to go back and rethink all the foundations from the beginning, especially if most of their career, what they've heard is the foundations are fine. Quantum mechanics is just a device for generating predictions. Why should I go back and even think about any of this stuff? So I don't think that"
},
{
"end_time": 6116.715,
"index": 236,
"start_time": 6089.002,
"text": " I certainly am not critical about any of that attitude, but what I have certainly found is that people who are newer to physics, students, tend to be much more interested in talking about a project like this. But there are absolutely exceptions among professors as well. I'm going to have some wonderful colleagues who've been incredibly receptive and open-minded and we've talked about this project a lot and I've gotten a lot of really good input from people."
},
{
"end_time": 6132.892,
"index": 237,
"start_time": 6117.517,
"text": " You know, but so I think it's a combination of intuition building and also what calls us to do quantum mechanics. I mean, quantum mechanics is such an exotic theory and to think that you're going to spend your time imagining the world is some wave function."
},
{
"end_time": 6162.551,
"index": 238,
"start_time": 6133.558,
"text": " Or state vector or some abstract object living in a high dimensional configuration space or in somewhat modern sense in a high dimensional Hilbert space. Hilbert spaces are beautiful. The mathematics is incredibly elegant and it has a certain kind of spiciness to it. But complex numbers floating around. We don't know why, you know, at least the way we usually talk about it. I can imagine being romanced by that. I was. I feel like that's what brought me into quantum mechanics."
},
{
"end_time": 6181.51,
"index": 239,
"start_time": 6163.012,
"text": " So I can definitely see why some people would like to keep that. And I think among all people who take that romantic view about quantum mechanics, I don't think anyone takes a more romantic view than Everettians, people who work in the many worlds interpretation, because their picture of the world isn't just exotic. It's profound, right? The idea that"
},
{
"end_time": 6211.101,
"index": 240,
"start_time": 6182.261,
"text": " Every time a quantum event takes place, the universe splits into, in the cartoon picture it's like two or three branches, but in the sort of more sophisticated, more fine-grained version of the Everett approach, it's an uncountable profusion of branches. I mean, it's mind-blowing and amazing and it forces you to confront some very deep questions in metaphysics, in philosophy of mind. It's just so rich with inquiry"
},
{
"end_time": 6240.265,
"index": 241,
"start_time": 6211.732,
"text": " I can imagine people working in that field would like to hang on to it. So I'll give you two examples, because I can relate to this to being inveterate and obstinate. So when I was learning about the categorification of quantum mechanics, and I'm reading papers like, okay, here's another way you can think of quantum theory as a daggers symmetric monoidal category. And I'm looking at him thinking, okay, but but so what? I still have that so what but I think a part of it is that I'm used to doing quantum mechanics."
},
{
"end_time": 6255.93,
"index": 242,
"start_time": 6240.845,
"text": " Windows XP"
},
{
"end_time": 6285.657,
"index": 243,
"start_time": 6257.005,
"text": " Couple years ago, Windows XP on his computer because he's familiar with Windows XP and wants to use DOS and can't run QBasic on Windows 10 without some emulator or virtual machine. So my dad is like what you're classifying as the or what you're characterizing as some people who are used to quantum mechanics in the old way, at least when it just comes from not their dislike of it for being deflationary, but their dislike of it from being different."
},
{
"end_time": 6314.804,
"index": 244,
"start_time": 6286.22,
"text": " Now the question could be, well, Jacob, what does it provide me? What does your approach give? Why should I learn it? You've just said that it seems like regular quantum mechanics. Okay, cool. Perhaps to you, it's a more beautiful version. Maybe to someone else, it's more convoluted. But whatever, what does it give you? What's the upshot? It's a great question. So the first upshot is it patches up the axioms. The axioms had this ambiguity or inconsistency or incompleteness to them."
},
{
"end_time": 6344.65,
"index": 245,
"start_time": 6315.299,
"text": " They had this mystery about what a measurement is that seems to play a role in the axioms but isn't defined by the axioms. And you run into problematic thought experiments like Wigner's Friend experiment. And the Wigner's Friend thought experiment is, it's not exactly the same thing as the problem of black hole information loss by any stretch, but there are some resemblances, right? There's this big problem in quantum gravity, black holes appear to radiate according to work going back to Stephen Hawking."
},
{
"end_time": 6370.947,
"index": 246,
"start_time": 6344.974,
"text": " um and there's this tension between evaporation of black holes quantum mechanically and unitary or schrodinger evolution which is information conserving in some quantum mechanical sense and the fact that black holes supposedly can't allow information to escape there's this tension between all of these things um that's the kind of tension we're seeing with thought experiments like the vigner's friend thought experiment and it's not like the black hole evaporation problem is more accessible experimentally"
},
{
"end_time": 6399.582,
"index": 247,
"start_time": 6371.425,
"text": " I mean, to go out and actually do experiments on black hole evaporation, you'd have to set up 10,000 identically prepared black holes, which we don't have to do, wait many times the age of the universe for all of them to evaporate, ensure they all evaporate inside of a completely sealed chamber with perfect detection mechanisms to collect all the Hawking radiation that comes out, with sensitivity enough that we can detect, you know, incredibly tiny, tiny entanglement effects, right? And then subject all the data to a level of analysis that we think may be computationally impractical."
},
{
"end_time": 6425.742,
"index": 248,
"start_time": 6400.606,
"text": " I mean this is not a practical problem at least as far as we know yet that could change but as far as we know it's not a practical problem yet this is considered a serious area of research whereas the inconsistencies in quantum mechanics are not considered as serious for some reason I don't quite understand there's some sociology there what I would tell quantum physicists is one advantage this approach is that it it resolves some of those inconsistencies which is itself may be a good thing"
},
{
"end_time": 6452.005,
"index": 249,
"start_time": 6426.578,
"text": " It does it in a way that doesn't require that we model only one kind of quantum system. One of the disadvantages of like Bohm's pilot wave theory is it works really well for very simple kinds of systems consisting of finitely many fixed numbers of non relativistic particles but has resisted being neatly generalized beyond that. So it's nice to have a model that's a little more model independent and simpler than the Bohmian approach."
},
{
"end_time": 6480.435,
"index": 250,
"start_time": 6452.312,
"text": " And it doesn't run into many of the confounding metaphysical mysteries that one has to deal with with Everettian quantum mechanics. You know, we're not making zillions of copies of us in this picture. So it provides, I would argue, one, and maybe at this point, maybe the only attractive, in my opinion, way to resolve these inconsistencies with quantum mechanics, although your mileage may vary, and I don't want to speak for everybody by any stretch,"
},
{
"end_time": 6508.797,
"index": 251,
"start_time": 6480.708,
"text": " That to me is already something. The second thing is it provides a picture. Quantum mechanics, when I teach quantum mechanics to students, they're expecting me to talk about waves moving in 3D space. And when I show them the axioms, a lot of them are very disappointed. They're like, but where's the picture? And isn't it like there's an electron and it emits a photon? And I'm like, well, the textbook axioms don't really talk about an electron here emitting a photon there. According to the axioms, that's just added for color. We draw pictures of electrons emitting photons just"
},
{
"end_time": 6538.831,
"index": 252,
"start_time": 6509.121,
"text": " Just to help tell the story, but none of this is actually legitimated by the axioms of quantum mechanics. There is just also the problem that there are a lot of phenomena out happening in the world that aren't measurements. You know, when early gases are mixing in the primordial universe, when stars far away are colliding, when, you know, a piece of aluminum sits on the surface of Mars and doesn't collapse under its own weight, when birds forage, when humans fall in love,"
},
{
"end_time": 6554.616,
"index": 253,
"start_time": 6539.548,
"text": " These don't appear to be measurements, and yet the axioms of quantum theory only make predictions about measurement outcomes, probabilities of measurement outcomes, and averages of measurement outcomes weighted by measurement outcome probabilities, and that's it."
},
{
"end_time": 6582.09,
"index": 254,
"start_time": 6555.828,
"text": " That's a very narrow category phenomena. How do we get from that narrow category phenomena to the wider category of all the other things that we think are happening in nature? Or are we just going to say that our talk of all those other things of birds foraging and early gases mixing is just for color, is just storytelling? So this allows quantum mechanics to be a theory of all the much larger category phenomena rather than just this narrow category of measurements. I call this the category problem of textbook quantum theory."
},
{
"end_time": 6608.456,
"index": 255,
"start_time": 6582.91,
"text": " But ultimately, I think physicists are going to be interested in applications, practical applications. Or you'd hope. Well, we would hope, but yeah. But in my experience, physicists, they want to know, what can we do with this? I think there's some things you could do with this. One is, indivisible stochastic processes, at least classical indivisible stochastic processes, are currently three years old."
},
{
"end_time": 6638.353,
"index": 256,
"start_time": 6609.411,
"text": " This is an area of dynamical systems theory that is completely unexplored. It's like opening up a sketch pad that's full and turning the page and finding like a totally blank new page. How often does that happen in mathematics or science that you turn a page and you open the door to some completely new area of inquiry? I don't know a lot about the mathematics of indivisible stochastic processes because nobody does yet."
},
{
"end_time": 6666.374,
"index": 257,
"start_time": 6639.343,
"text": " I think that's just interesting. I think it would be very interesting for people to think about these kinds of systems and work out their properties. It may be that the best way to study an indivisible plastic system is to write down a Hilbert space for it and basically do quantum mechanics. Just like sometimes the easiest way to study Newtonian system is to write down Lagrangian for it and do Lagrangian mechanics. But it may be that we can understand things about these systems on their own merits."
},
{
"end_time": 6691.647,
"index": 258,
"start_time": 6666.8,
"text": " It may be that when you don't start from a Hilbert space but instead start with these different axioms, you can point to new ways to generalize quantum mechanics that would have been impossible to imagine before. If you're starting with a Hilbert space, that limits your imagination about what else you can do. If instead you don't start with a Hilbert space, you start with a more general kind of probabilistic system like I was talking about in this picture, this indivisible stochastic process."
},
{
"end_time": 6721.715,
"index": 259,
"start_time": 6692.449,
"text": " Maybe there are deformations you can do to the assumptions, changes you can make to it to generalize these systems in ways that do not give you a Hilbert space. You could generalize these systems and get something else that doesn't give you a Hilbert space and that you never could have gotten to if you'd started from Hilbert spaces. And maybe we need a generalization like this in order to make progress on foundational questions in say quantum gravity. So I think that's another potential area of use. And then another area is"
},
{
"end_time": 6752.346,
"index": 260,
"start_time": 6722.568,
"text": " If there's this correspondence between Hilbert space representations of quantum systems and classical looking probabilistic systems, especially beyond the Markov approximation, this might suggest that there are efficient ways to simulate non-Markovian classical stochastic systems using quantum computers. So one open question is, if we had a quantum computer today,"
},
{
"end_time": 6781.988,
"index": 261,
"start_time": 6753.336,
"text": " What would we use it for? There are already a number of known algorithms. There's no proof that the algorithms are stronger than what you could ever do with a classical system, but it's widely believed that many of the things you could do with these quantum algorithms are far more efficient than you could ever do with classical algorithms. But it's not like every question you'd want to do in a classical computer can be done more efficiently or more quickly in a quantum computer. So figuring out what are the kinds of things"
},
{
"end_time": 6809.838,
"index": 262,
"start_time": 6782.5,
"text": " That a quantum computer would help us do more efficiently is a really open question. And when you set up a correspondence between quantum systems and a large class of stochastic systems, you open the door that there are some problems that may be difficult to simulate classically that are easier to simulate quantum mechanically. I don't quite know what those are yet. That's an area of research that I'm working on right now."
},
{
"end_time": 6838.643,
"index": 263,
"start_time": 6810.725,
"text": " But I'm talking to people who work in the theory of quantum simulations of classical stochastic processes. And we're trying to determine maybe there are ways to use this correspondence to provide more efficient ways to simulate these systems and provide a new application for quantum computers. So now there's also the possibility that in some circumstances, indivisible stochastic systems might actually behave differently from quantum systems, at least textbook quantum systems."
},
{
"end_time": 6859.343,
"index": 264,
"start_time": 6839.599,
"text": " There are maybe slightly different predictions for a Wigner's Friend thought experiment. Unfortunately, doing the Wigner's Friend thought experiment is probably out of our experimental capacity for the next thousand years. Who knows? But there are some cases in which you want to model the quantum system and you need to throw in additional assumptions in order to actually make predictions, assumptions that go beyond the textbook axioms."
},
{
"end_time": 6889.241,
"index": 265,
"start_time": 6859.957,
"text": " For example, if you want to model a very, very complicated quantum system, you may have to add certain additional axioms about, you know, what are typical initial states for the system? What kind of typical evolution would we expect? These go beyond the textbook axioms, and it's possible that when you start with different axioms, you would actually modify some of those assumptions. And so for some classes of very complicated quantum system, it's possible you could get slightly different predictions. But these are all highly conjectural claims. A lot more work needs to be done to determine if or when any of these could pan out. So I want to be very clear"
},
{
"end_time": 6912.944,
"index": 266,
"start_time": 6889.599,
"text": " We're only the very beginning here, but even to have this correspondence at all, I think opens up a lot of doors and there's nothing more exciting to me in science or philosophy than having open doors. Well, this is certainly cutting edge. My cutting edge is in it's been developed in the past couple of years and also it may have wide application soon and may actually be on the right track."
},
{
"end_time": 6941.203,
"index": 267,
"start_time": 6914.787,
"text": " Does it provide any insight into QFT, which depends on a Fox space, which depends on Hilbert spaces? Yeah, so it's an excellent question. So quantum field theories are situated within the axioms of textbook quantum mechanics. So those axioms, I mentioned Hilbert spaces and showed all that stuff. Quantum field is a particular kind of a system that lives within the framework defined by those axioms. What makes quantum fields"
},
{
"end_time": 6970.896,
"index": 268,
"start_time": 6941.698,
"text": " Well, there's many things that make them complicated. One thing that makes them complicated is they have infinitely many moving parts. Unlike a system of, like, five particles, they have infinitely many moving parts. We see that these are systems with infinitely many degrees of freedom. And this causes all kinds of mathematical complications. When working with a quantum field theory, like regular, everyday physicists using quantum field theories today, often you have to regulate the theory. I mentioned Planck introducing Planck's constant to regulate."
},
{
"end_time": 6993.831,
"index": 269,
"start_time": 6971.34,
"text": " The regulators we use temporarily make many of these infinite things finite so we can do the calculation and then what we do is we try to send the regulator to infinity and usually we can do that, then it goes away and we believe we have a good solid prediction that doesn't depend on the regulator. Unlike Planck's constant, the regulator goes away and we believe that we have a robust result that holds in the continuum infinite limit."
},
{
"end_time": 7015.862,
"index": 270,
"start_time": 6994.667,
"text": " And there's a whole beautiful intricate story called renormalization and effective field theory. That's all about how to do that in a mathematically consistent way, reasonably consistent way, and generate good predictions. I'm not going to have time to go into all of that. But at the end of the day, right, this is still just a quantum system, a very complicated quantum system. And to the extent that you can generate the axioms"
},
{
"end_time": 7037.944,
"index": 271,
"start_time": 7016.578,
"text": " For any quantum system, you can generate them for quantum fields starting from an indivisible stochastic process. According to this picture, a quantum field is a collection of entities delocalized, spread out in space with configurations, and these configurations evolve in this indivisibly stochastic way that can be modeled in Hilbert space language."
},
{
"end_time": 7061.613,
"index": 272,
"start_time": 7038.541,
"text": " In a sense, it's just like any other kind of a system, you are still going to run into the same mathematical complications, maybe new ones, from the fact that we have infinitely many and you have to do mathematical tricks to make these things tractable. But yeah, so the answer is quantum fields fit into this framework, but it's inherently going to be very complicated because quantum fields are super complicated."
},
{
"end_time": 7089.189,
"index": 273,
"start_time": 7062.278,
"text": " And do you reproduce the exact postulates of quantum mechanics or do you have some deviations that there's an experimental way of testing whether the stochastic approach is the more underlying correct one? It's a good question. So at the level of the correspondence, there's just a mapping that takes you from the ingredients of the invisible stochastic theory into the corresponding Hilbert space description of its quantum Hilbert space representation."
},
{
"end_time": 7118.712,
"index": 274,
"start_time": 7089.787,
"text": " There are in principle deviations because collapse doesn't fundamentally happen in this picture. However, the deviations are going to be pretty much the same as for any no-collapse formulation of quantum mechanics. So, Bohmian mechanics, the pilot wave theory of de Broglie and Bohm with particles being guided around by wave functions, Everettian quantum mechanics, you know, the many-worlds interpretation, these are all no-collapse interpretations. Collapse is not fundamentally happening. There's no collapse axiom."
},
{
"end_time": 7148.712,
"index": 275,
"start_time": 7119.514,
"text": " And so you're going to get tiny discrepancies in the predictions of these theories as compared with textbook quantum theory. And I can make this super explicit. Go back to Wigner's friend. According to textbook quantum theory, Wigner's friend on the inside does a measurement, collapses the quantum system inside the box. That system is collapsed. It's collapsed for everybody. It's collapsed for Wigner's friend in the box. It's collapsed for Wigner outside the box. It's just collapsed. In a no-collapse approach, like many worlds or Bohmian mechanics or my approach,"
},
{
"end_time": 7177.056,
"index": 276,
"start_time": 7149.531,
"text": " There isn't really a collapse that's happened. And what this means is that the wave function Wigner is using on the outside, the quantum state, is a non-collapsed quantum state. It contains those superposition interference phase effects that have not been erased. They haven't been erased because there's not been a collapse. So in principle, Wigner on the outside, with a sufficiently powerful measurement apparatus, could detect"
},
{
"end_time": 7203.319,
"index": 277,
"start_time": 7177.585,
"text": " those small discrepancies, which would be discrepant from textbook quantum mechanics, but detecting them would be extremely hard. So there's a paper from a few years ago that Scott Aronson and Lenny Suskind and I believe one other author published in which they prove what people call the quantum necromancy theorem, which is just to say that"
},
{
"end_time": 7229.445,
"index": 278,
"start_time": 7204.224,
"text": " If you could, if Wigner could design an experimental apparatus sophisticated and sensitive enough to detect those tiny little discrepancies between the no collapse interpretation and textbook quantum theory, then that apparatus with some relatively simple modifications could take a long dead cat and bring it back to life."
},
{
"end_time": 7254.616,
"index": 279,
"start_time": 7230.896,
"text": " Which we usually regard as a thermodynamically impossible feat, right? That's why they call it necromancy, like magically bringing the dead back to life. It would be akin to unscrambling an egg, right? Like taking a scrambled egg and turning it back into the original egg. I mean, this is beyond really any technological capacity we could imagine. So, yes, it makes somewhat different predictions."
},
{
"end_time": 7278.797,
"index": 280,
"start_time": 7255.299,
"text": " But only as far as other no collapse interpretations make those same slightly discrepant predictions. And fortunately, those discrepant predictions are so minuscule that they would be extremely hard to measure. Easier to measure probably than the black hole information problem could be measured. But kind of the same level of like extremely tiny suppressed effects."
},
{
"end_time": 7306.084,
"index": 281,
"start_time": 7279.565,
"text": " Hola, Miami! When's the last time you've been in Burlington? We've updated, organized, and added fresh fashion. See for yourself Friday, November 14th to Sunday, November 16th at our Big Deal event. You can enter for a chance to win free Wawa gas for a year, plus more surprises in your Burlington. Miami, that means so many ways and days to save. Burlington. Deals. Brands. Wow! No purchase necessary. Visit bigdealevent.com for more details."
},
{
"end_time": 7338.319,
"index": 282,
"start_time": 7308.66,
"text": " Okay, before we end, I want to know what is a particle in your view? Also, is your view called an interpretation? Is it a theory? Is it a correspondence? What would you call it? Why don't we settle that right now? I don't have a good answer to that question. I think you could call it whatever you want. One could think of it as a physical theory. It has variables and ingredients in it and those ingredients have laws."
},
{
"end_time": 7360.691,
"index": 283,
"start_time": 7338.49,
"text": " So it's a physical theory. It's a physical theory that makes the same predictions as textbook quantum theory in all realistic scenarios, as far as I know. You can think of it as an interpretation of quantum theory in the sense that if you start with the formalism of quantum mechanics and ask, how do we interpret the things? What do the things mean? This provides a platform for actually talking about what's really out there in nature possibly. I should say it's not a unique picture."
},
{
"end_time": 7386.186,
"index": 284,
"start_time": 7361.084,
"text": " A given quantum system may represent many different indivisible stochastic processes, just like a Lagrangian or better yet a Hamiltonian formulation of classical physics can describe many different Newtonian systems. There's not a one-to-one relationship between these pictures. You could think of it as a formulation because it's a new mathematical framework. I think what you couldn't call it is a prescription, a recipe, because"
},
{
"end_time": 7417.09,
"index": 285,
"start_time": 7387.295,
"text": " It's more than just a list of steps to follow. It's more than just an algorithm the way the textbook axioms of quantum theory are just an algorithm to follow. It actually tells the story of things happening. So I don't know if that answers your question, but did you want to follow up on that or do you want me to talk about particles? Yeah. What's a particle? What's a particle? So classically, a course of particle is a point-like entity characterized by a mass of some kind, could be zero mass,"
},
{
"end_time": 7442.142,
"index": 286,
"start_time": 7417.671,
"text": " I guess it's a tachyon, it could have some weird imaginary mass. It's characterized by spatial degrees of freedom, meaning it has a location in some notion of physical space, usually XYZ coordinates when I think of it that way. It will generally have something like different locations, different moments in time, which we can think of as being like a trajectory. And"
},
{
"end_time": 7468.063,
"index": 287,
"start_time": 7443.831,
"text": " You know, if it's a truly point-like particle, then it has no internal structure. It has no volume. Nonetheless, it can carry certain other quantities. It can have other attributes like electric charge, which are related to how it interacts with fields and other kinds of particles. It can have an intrinsic form of angular momentum. So just as"
},
{
"end_time": 7495.503,
"index": 288,
"start_time": 7468.916,
"text": " You can have kinetic energy, but kinetic energy can kind of be frozen in and become kind of rest energy like an internal energy of a particle. Angular momentum is a kind of emotional kind of momentum, a kind of rotating momentum, but you could also have a frozen in kind that's called intrinsic spin. Particles can carry that intrinsic spin that can be converted into other forms of angular momentum just like rest mass can be converted into other forms of energy. So these are what a particle is. It's a thing with this collection of possible properties. In"
},
{
"end_time": 7520.538,
"index": 289,
"start_time": 7496.254,
"text": " Quantum mechanics, at least since Wigner's work on representation theory, particles have been understood as the simplest kinds of quantum systems that have a well-defined nature or behavior under space-time transformations. So if you ask what's the simplest kind of quantum system with a Hilbert space that is as small as possible, doesn't include anything extraneous,"
},
{
"end_time": 7542.244,
"index": 290,
"start_time": 7520.981,
"text": " But for which, when we move around in space or turn around or change inertial reference frame, change frame of motion, we just get a new element of the same Hilbert space. We don't get something new, but it's like minimal, it's irreducible. Then you have a math problem. What are the irreducible unitary, which just means they're represented by, you know, certain kinds of operators in the Hilbert space,"
},
{
"end_time": 7569.633,
"index": 291,
"start_time": 7542.927,
"text": " representation of the space-time symmetry group, the Poincare group, the abstract representation of moving around in space, changing frame of motion, rotating. And that's a math problem, you can classify it, and what you find is there are distinct kinds of Hilbert spaces with these properties, and they are characterized by mass, and by spin, and by charges, and they have motional degrees of freedom, and so forth. That's usually how we think about particles in quantum mechanics."
},
{
"end_time": 7598.473,
"index": 292,
"start_time": 7572.585,
"text": " And that's all we can say in quantum mechanics, because all we've got are Hilbert spaces in the textbook formulation, if you're going to describe a system of particles, you just got a Hilbert space. And so all we can do is talk about what that Hilbert space, what a structure is, and its structure for particle is related to these transformations of spacetime. In the picture I'm proposing particles go back to the classic like picture, a particle is a point like object in space."
},
{
"end_time": 7613.404,
"index": 293,
"start_time": 7598.916,
"text": " in three dimensional physical space, if we think that physical space is three dimensional, with various properties or dispositions interacting with other particles."
},
{
"end_time": 7631.647,
"index": 294,
"start_time": 7614.155,
"text": " Yeah, that is when you interact with a particle, it may be disposed to give you certain results on your measuring device, is all I mean. So if you measure its position, you'll read off what its position is, but if you measure some more complicated feature, then what you get on the measuring device will be some more complicated result of the interaction with the particle. So it has a disposition to produce certain kinds of"
},
{
"end_time": 7659.548,
"index": 295,
"start_time": 7631.647,
"text": " In metaphysical speak we would say that certain properties are categorical. They just explicitly exist as they are and others are dispositional. That is you look at them and what you're seeing is really like how the particle will be disposed to show you what it's going to do. But at the end of the day particles are much more like they are the classical picture. Just point like entities with some properties with different positions through time. So that's all particle is according to this picture."
},
{
"end_time": 7677.415,
"index": 296,
"start_time": 7659.94,
"text": " And I should say that I'm not saying that particles are the fundamental ontology of nature. I don't know what the fundamental ontology is. But so far in your theory, what is the fundamental ontology? We go back to the old classical way of doing things that if you want to model a given system, you propose a certain ontology for it."
},
{
"end_time": 7706.476,
"index": 297,
"start_time": 7677.79,
"text": " You have to say what you think the configurations are. If you want to model particles, it's going to be arrangements of particles. If you want to model fields, it's going to be, you know, delocalized field intensities distributed throughout space. If you want to model strings, if you want to model bits on a computer register, you pick the right ontology for the right kind of a system and then you model it. It's possible there is some truly fundamental ontology of all of nature. I don't know what that is. I think to some people, especially people working in Everettian quantum theory,"
},
{
"end_time": 7736.51,
"index": 298,
"start_time": 7707.346,
"text": " The idea that the fundamental ontology is state vectors or wave functions in a Hilbert space is very appealing. It would mean we already know what the fundamental grounding of all of reality is. A Hilbert space. There's some Hilbert space and there's an object or objects in a Hilbert space and that is the fundamental ontology of everything. I'm not saying that. Hilbert spaces are not fundamental in this picture. We go back to really having to be kind of metaphysically humble."
},
{
"end_time": 7766.852,
"index": 299,
"start_time": 7737.927,
"text": " We know about some systems. Some systems appear to be particles, some appear to be fields. Maybe particles are emergent from fields and we don't need particles as a separate category. Maybe fields are fundamental, maybe they're not. I think it's premature to try to guess at what the fundamental ontology is just yet. And in this picture, you don't have to. You just pick whatever ontology you need for the model you want to talk about. Particles, fields, registers on a computer, and then you proceed from there. Maybe one day we'll discover that there is one model"
},
{
"end_time": 7790.094,
"index": 300,
"start_time": 7767.585,
"text": " With one ontology from which we can get all the other models. That would be a very exciting day, but I don't think that we can guess what that is today. And I don't think that we can just take that to be Hilbert spaces and be done. I think that's premature. There's so much more I want to talk to you about. We didn't talk about causation either. And there's a whole other, you know, connection to causation."
},
{
"end_time": 7813.37,
"index": 301,
"start_time": 7790.896,
"text": " Reichenbach's Common Cause Principle."
},
{
"end_time": 7838.097,
"index": 302,
"start_time": 7813.78,
"text": " It was wonderful to see you in person. I've been following you for again, following politely, diplomatically. You understand for quite some time now. And why don't we end? I know you're about to rush off to see your students. Why don't we end with your advice to students? Oh, actually to your advice to students who are watching and researchers who are watching. Um,"
},
{
"end_time": 7867.517,
"index": 303,
"start_time": 7839.804,
"text": " I'll just use my standby advice, which I think has been really helpful to me. And people have told this to me and maybe I'll share this. We all come at the work we do with a distinct profile of strengths and weaknesses, like I just said. Every person is, you know, our particular set of strengths and weaknesses is like a point in a very high dimensional configuration space or parameter space. So we're not rankable."
},
{
"end_time": 7896.203,
"index": 304,
"start_time": 7867.961,
"text": " You can't order people. We're not an ordered set. It's very easy for students going into science to think that they lie on a linear ranking system. There are people who are better or smarter than they are. And if they're not as smart as those people, they can't make contributions. They can't do good work. And in my experience, having worked with so many students over the years, but also having read a lot of history, history of science, we discover is that it really is true that we all"
},
{
"end_time": 7923.78,
"index": 305,
"start_time": 7896.544,
"text": " We're all points in some very high dimensional parameter space. We're not rankable. And figuring out how your unique profile of strengths and weaknesses can be brought to bear to make progress on work that you find meaningful. Figuring how to do that is part of what it is to go into an area of scholarly work and grow and learn and develop. So I would say don't worry too much about where you think you fall."
},
{
"end_time": 7954.445,
"index": 306,
"start_time": 7924.445,
"text": " Interdisciplinarity is wonderful. We should have more focus and spend more money on the places where disciplines"
},
{
"end_time": 7979.855,
"index": 307,
"start_time": 7954.821,
"text": " intersect. I work at the intersection of physics and math and philosophy, and I guess now, you know, statistics, like, you know, dynamical system, there's so many different, different fields that sort of meet where I'm currently working. And I think this is not novel to say, but I think some of the most exciting work happening in"
},
{
"end_time": 8003.814,
"index": 308,
"start_time": 7980.128,
"text": " scholarship generally and certainly in science or philosophy in particular is happening at interdisciplinary boundaries. So I would say that maybe not for the researchers, but for the people who pay researchers. Yeah, spending a little more time thinking about how to promote work at the boundaries of disciplines where there's real cross pollination between disciplines, I think would bear a lot of fruit for progress in all of our work."
},
{
"end_time": 8030.998,
"index": 309,
"start_time": 8004.053,
"text": " I agree. Last night, one of the reasons I'm here in addition to see you was at MIT, there was an event by Addie right here yesterday last night called Echolopto, which was about neuroscience, cognition, biology, physics, language. Yeah, it was a combination of basically every sort of major field in STEM and the arts where they intersect and can be used to create something that's actually useful. But you have to be rigorous about it. You can't just"
},
{
"end_time": 8057.824,
"index": 310,
"start_time": 8031.596,
"text": " So that was fun. Anyhow, thank you. It's been a pleasure. And I know that you're itching to get going. And I appreciate that your students have been kept waiting for this. This is wonderful. I appreciate your time. Thank you for inviting me. This is wonderful. I really appreciate the invitation and all the work you've been doing on this amazing podcast series. It's it's amazing work talking to the public and and talking to, you know, people who are working in all these different fields about their work and"
},
{
"end_time": 8073.217,
"index": 311,
"start_time": 8058.575,
"text": " Clarifying complicated topics for everybody I think is amazing work. Thank you. And next time the interview we'll do will be more technical. We may even use the blackboard. We'll see. We'll see. Anyway, it was a delight. Thank you so much for the invitation. Thank you."
},
{
"end_time": 8101.425,
"index": 312,
"start_time": 8074.189,
"text": " 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 Kurt, you've spoken to so many people in the fields of theoretical physics, philosophy, and consciousness. What are your thoughts?"
},
{
"end_time": 8113.473,
"index": 313,
"start_time": 8101.425,
"text": " Also, thank you to our partner, The Economist."
},
{
"end_time": 8138.097,
"index": 314,
"start_time": 8115.725,
"text": " Firstly, thank you for watching, thank you for listening. If you haven't subscribed or clicked that like button, now is the time to do so. Why? Because each subscribe, each like helps YouTube push this content to more people like yourself, plus it helps out Kurt directly, aka me. I also found out last year that external links count plenty toward the algorithm,"
},
{
"end_time": 8162.756,
"index": 315,
"start_time": 8138.097,
"text": " which means that 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."
},
{
"end_time": 8186.732,
"index": 316,
"start_time": 8162.756,
"text": " 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 gained from rewatching lectures and podcasts. I also read in the comments that, hey, toll listeners also gain from replaying. So how about instead you re-listen on those platforms like iTunes, Spotify, Google Podcasts, which"
},
{
"end_time": 8209.821,
"index": 317,
"start_time": 8186.732,
"text": " If you"
},
{
"end_time": 8227.398,
"index": 318,
"start_time": 8209.821,
"text": " 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."
},
{
"end_time": 8247.654,
"index": 319,
"start_time": 8240.128,
"text": " Think Verizon, the best 5G network is expensive? Think again. Bring in your AT&T or T-Mobile bill to a Verizon store today and we'll give you a better deal."
},
{
"end_time": 8270.179,
"index": 320,
"start_time": 8250.691,
"text": " Jokes aside, Verizon has the most ways to save on phones and plans where everyone in the family can choose their own plan and save. So bring in your bill to your local Miami Verizon store today and we'll give you a better deal."
}
]
}No transcript available.