Theories of Everything with Curt Jaimungal - Physics Biggest Quantum Heretic | Jonathan Oppenheim

Episode Date: September 10, 2024

Welcome to Theories of Everything's "Rethinking the Foundations of the Physics: What is Unification?" series featuring Jonathan Oppenheim. Jonathan Oppenheim is a renowned theoretical physicist and professor at University College London (UCL), known for his groundbreaking research in quantum information theory, quantum gravity, and the relationship between quantum mechanics and thermodynamics. Jonathan holds a Ph.D. from the University of Cambridge and is recognized for his contributions to the fields of quantum foundations and quantum computation. https://www.ucl.ac.uk/oppenheim/ SPONSOR (The Economist): As a listener of TOE, you can now enjoy full digital access to The Economist. Get a 20% off discount by visiting: https://www.economist.com/toe LINKS MENTIONED: - Sean Carroll on TOE: https://www.youtube.com/watch?v=9AoRxtYZrZo - Jonathan's first appearance on TOE: https://www.youtube.com/watch?v=NKOd8imBa2s - Jonathan's paper on hybrid classical-quantum dynamics: https://arxiv.org/pdf/2203.01332 - Jonathan's paper on a post-quantum theory of classical gravity: https://journals.aps.org/prx/pdf/10.1103/PhysRevX.13.041040 - Jonathan's website: https://www.ucl.ac.uk/oppenheim/ - List of all of Jonathan's published papers: https://arxiv.org/search/?query=Oppenheim%2C+Jonathan&searchtype=author&abstracts=show&order=-announced_date_first&size=50 TOE'S TOP LINKS: - Patreon: https://patreon.com/curtjaimungal (early access to ad-free audio episodes!) - Listen on Spotify: https://open.spotify.com/show/4gL14b92xAErofYQA7bU4e - Become a YouTube Member Here: https://www.youtube.com/channel/UCdWIQh9DGG6uhJk8eyIFl1w/join - Join TOEmail at https://www.curtjaimungal.org SPONSORS (check them out): - THE ECONOMIST: As a listener of TOE, you can now enjoy full digital access to The Economist. Get a 20% off discount by visiting: https://www.economist.com/toe - INDEED: Get your jobs more visibility at Get your jobs more visibility at https://indeed.com/theories ($75 credit to book your job visibility) - HELLOFRESH: For FREE breakfast for life go to https://www.HelloFresh.com/freetheoriesofeverything Timestamps: 00:00 - Intro 01:08 - Quantum Mechanics and Classical Mechanics 06:05 - Quantizing Gravity 10:30 - How Gravity is Different 16:07 - Classical-Quantum Gravity 21:42 - Quantum Mechanics 25:23 - Example of Continuous Master-Equation 28:45 - Observation Causes a Collapse 35:20 - Path Integrals 49:34 - Intuitions 59:32 - Is Spacetime Classical? 01:03:05 - Outro / Support TOE Support TOE: - Patreon: https://patreon.com/curtjaimungal (early access to ad-free audio episodes!) - Crypto: https://tinyurl.com/cryptoTOE - PayPal: https://tinyurl.com/paypalTOE - TOE Merch: https://tinyurl.com/TOEmerch Follow TOE: - NEW Get my 'Top 10 TOEs' PDF + Weekly Personal Updates: https://www.curtjaimungal.org - Instagram: https://www.instagram.com/theoriesofeverythingpod - TikTok: https://www.tiktok.com/@theoriesofeverything_ - Twitter: https://twitter.com/TOEwithCurt - Discord Invite: https://discord.com/invite/kBcnfNVwqs - iTunes: https://podcasts.apple.com/ca/podcast/better-left-unsaid-with-curt-jaimungal/id1521758802 - Pandora: https://pdora.co/33b9lfP - Spotify: https://open.spotify.com/show/4gL14b92xAErofYQA7bU4e - Subreddit r/TheoriesOfEverything: https://reddit.com/r/theoriesofeverything Join this channel to get access to perks: https://www.youtube.com/channel/UCdWIQh9DGG6uhJk8eyIFl1w/join #science #physics #quantumphysics #gravity Learn more about your ad choices. Visit megaphone.fm/adchoices

I'm going back to university for zero dollar delivery fee, up to five percent off orders and five percent uber cash back on rides. Not whatever you think university is for. Get Uber One for students. With deals this good, everyone wants to be a student. Join for just $4.99 a month. Savings may vary. Eligibility and member terms apply. I think it's reasonable to question whether we should be quantizing space time like we've quantized all the gauge theories. If it was classical, then it has a number of intriguing features like the measurement postulate is not needed, it may help explain dark matter and dark energy.

Some ideas are so radical, they border on heresy. Professor Jonathan Oppenheim, a distinguished theoretical physicist at University College London, has proposed a theory that may just fit that bill. His provocative framework suggests that gravity itself can remain classical in a quantum universe, an idea that's riling up colleagues and undoing decades of theoretical physics gospel, which asserts that gravity must be quantized. Oppenheim

directly refutes Feynman's arguments about the double slit experiment while showing how this controversial approach could solve long-standing mysteries not only with gravity but also with the measurement problem and the nature of dark energy and dark matter. Okay, Professor, welcome. Take it away. Great. So I'm going to be talking about the attempt to reconcile quantum mechanics and gravity or space-time.

And this is joint work with a number of my students and Isaac Leighton, Muhammad Sajid, Barbara Soda, Andrea Rousseau, Zach Weller Davies, Andrew Gurka, etc. So it's a joint project. We can start by asking just a more simpler fundamental question, which is, we have these two frameworks in physics. One is quantum mechanics, and the other one is classical mechanics. And we can just ask the question, are these two frameworks compatible? Can we combine them in a consistent mathematical way? So quantum mechanics, we're used to the Heisenberg equation. We have a density

matrix sigma and it evolves as the commutator with the Hamiltonian. And classical mechanics has a very similar form if we think of a probability distribution rho. So the probability density rho evolves with a Poisson bracket with a Hamiltonian. So those two frameworks have a very similar form. And we can now ask a very, I think, natural question, which is, can we have a classical system which interacts with a quantum system? So here we have a phase space, q and p. So we have a particle which lives in phase space. And then we could have a quantum system like a two level spin half particle.

And we can ask, can we combine these two systems together in a consistent way? Oh, sorry. Can you just go back because I want to make sure that you're seeing what I'm seeing. Can you go back? Okay. So I'm going to screenshot to you what I'm seeing or I'll describe it, but I can also screenshot it. So what I'm seeing is it says QMP, there's a blue box, and then there's nothing inside the left hand side, but then there's the equal sign and then a psi with a dot. Yeah, there's just, is that not what you see? Oh yeah, I see that. So this is my bad graphics. So the equal sign is a two-level system.

So there's the graph. All right, so if any of you are confused as well. So this looks like it's saying nothing equals the wave function and the wave function's up here for some reason. There is, OK, this little dot here is a point particle, is the free particle. And then we have the state of the quantum system,

which is meant to be a two level system. And as you can see, I do my own graphics. I don't have a graphic designer. Let's keep going. Well, this one's far superior. This is a far superior. So this one I also did myself. Oh, great. And it's just meant to demonstrate that we all the time we combine classical systems and quantum systems. So for example, in the double slit experiment, we treat the walls of the box and the slits,

we treat those classically, and the particle is quantum. And in this potential here, the potential we treat classically and the quantum system is quantum. And that's the case where we have a classical system which acts upon a quantum system is quantum. And that's the case where we have a classical system which acts upon a quantum system. So that we can deal with pretty easily and we're used to such systems. What we are not used to, or we're not able to do

or haven't been able to do until recently is deal with a back reaction. In other words, we have a quantum system which back reacts on a classical system. I'm motivated to study this for a number of reasons. One is that these sorts of situations occur all the time where we have a quantum system that we want to treat classically, but it's interacting with another quantum system. But I'm mostly interested in this because I'm interested in gravity. We know that gravity is famously inconsistent with quantum mechanics.

I either want to think of a reconciliation where I treat space-time as classical and maybe modify quantum mechanics a little bit, or I may be also interested in situations where I just treat space-time classically. So an example is in a black hole, then the black hole is evaporating. So the evaporation is emitting these photons, which we treat quantumly, but the back reaction is on a classical space-time.

Another example is in inflation, in the cosmology, you know, we treat the expanding universe classically, but the vacuum fluctuations we want to treat quantumly. So it's often the case that we want to treat one system quantumly and the other system classically. But I'm also interested in the possibility that maybe we should not be quantizing space-time. And so I want to go over the reasons why gravity is somehow different to the other forces which we want to quantize and therefore why we might question whether we should be trying to quantize gravity. Okay. I just have a quick question here.

Good. So when I was speaking with Sean Carroll, he mentioned to me that the holographic principle is quantum gravity and I asked him, how does that constitute quantum gravity? And he said, well, it integrates quantum mechanics with general relativity. He said it's into some unified theoretical construct. I said, well, to me, the way that I understand quantum gravity is that you quantize the gravitational field. So that either is you do some canonical quantization

of Einstein's field equations, or you employ a path integral over the metrics. What is it specifically that you mean when you say quantize gravity? Right. So Einstein's theory of gravity is that space-time bends when a massive object is... A massive object bends space-time bends when a massive object bends space-time. So to quantize gravity has generally meant that the space-time itself, the metric, the gravitational degrees of freedom,

which is how much it bends, that should be quantized. So that's traditionally what people mean. Now, ADS-CFT claims to resolve this in some situations through a duality. And so people would claim that in certain space times, ADS, that the boundary theory, which is a quantum theory, is a fully quantum theory, is a, you know, it's a fully quantum theory. And by definition, you can say, I'm going to define that to be quantum gravity.

And then if you have a mapping from the boundary to what's happening inside in the bulk, then you would, I think, be able to claim that you quantize gravity. Now, the issue with ADS-CFT is that we don't really know if the dictionary is consistent. So there's all kinds of rules that people are still trying to develop. And we don't really know if these rules hold or are consistent. Some people have a lot of confidence in it.

My sense of it is that these rules are still being developed and we still don't really know if they hold. So, for example, you need to have a whole bunch of things need to, in my view, hold in order for certain paradoxes in ADS-CFT to be resolved. And we just don't know if that's the case. But I would agree that if ADS-CFT, if the conjecture holds, then that is a quantization of gravity in a certain space time. In that case, it still sounds like you have a classical background space time.

How is that quantizing? Are there other issues? So in ADS-CFT, it's this very strange thing that we require this background space-time and then claim that there's no background space, you know, that we kind of don't need it in the bulk and it's somehow emergent. And that may be, you know, that may be successful in the end, but it's a little bit strange in my view that you need to rely on a background classical space time in order to get an emergent space time. I guess what I find interesting about, say, an attempt to quantize gravity is that if

you think about what we're trying to do, so you can see in this slide, you start off with, say, some initial data on a Cauchy surface. So you start off with a space like hypersurface and you define your initial fields to live on that surface and give your initial conditions and then that evolves forward in time. And even defining that initial space like surface requires you to know the metric. And so gravity is really different and even the posing the initial value problem is different in gravity. And when we, for example, want to say that we define our quantum fields on the space-time, then we need to, for example, if x and y are space-like separated, then the two fields commute. But you need to know that those two points are space-like separated

in order to define the commutation relations. So if we're going to quantize the causal structure, then how do we even define the commutation relations? That's part of the problem with quantizing gravity from a conceptual point of view. So here what I want to do is just I want to mention why gravity is different to all the other fields in nature. So we have electromagnetism, we have the weak, we have gauge bosons, we have electrons, protons, blah blah blah. And those are all gauge theories. And in a gauge theory, you have a gauge transformations, they act on the field at the point X.

So we have some field psi lives at the point X, and the gauge transformations act on the field phi. Now, gravity is different in the sense that the equivalent of gauge transformations are Now, gravity is different in the sense that the gauge transformation, the equivalent of gauge transformations are called diffeomorphisms or diffs. What they do is they actually move the points x. They're the active version of a coordinate transformation.

A coordinate transformation relabels the points x, the space-time points, whereas a coordinate transformation relabels the points x, the space line points, whereas a gauge transformation acts on the fields at the point x. So they're very different. A gauge transformation, I wouldn't say very different, but they're different to a coordinate transformation or a diffeomorphism. So gravity is not a gauge theory in the usual sense. And all the theories that we have quantized so far

are gauge theories. The other thing that makes gravity different is that gravity is the only, it's not even a force really, gravity gives us universal geometry, this background geometry in which all the other fields live. So we have this arena of space-time,

and we have these gauge fields which live in the space-time, and it's only gravity which can be described by a space-time. So when you put it like that, gravity is different to the other forces. It may be that this background space-time is necessary in order to properly define quantum theory. Another difference between gravity and the forces of nature. And so I say, you say gravity is not a force.

Well, it's because when a particle is following a geodesic, no force is acting on it. Gravity is not a force, right? When people say gravity is a force, in particle physics, sometimes people will say that. Are they just referring to the presence of a graviton? Because we have a graviton, we can analogize that to a gauge boson of a photon, and a photon's a force carrier.

Right. If gravity was a quantum field like the others, and then there would be a graviton, and then it would be a force, and particles would be attracted to each other through the exchange of gravitons. But maybe it's just the fact that space-time is bent and particles follow geodesics. Those are two very different pictures. And you can often, so for example, I can often recast a gauge theory in terms of geometry, but it is only gravity, which

gives a universal geometry for all the other forces. So it's only gravity that can be recast in a fully geometric way. And that's because of the equivalence principle. That's why I say that, you know, in some sense, people say gravity is not really a force. People will argue about it, but there's definitely a sense in which it's not a force because particles just free fall. The other thing that makes gravity different to the forces of nature is the Wheeler-Dewitt equation.

So when you want to try and quantize gravity, then the fact that the theory is diffusomorphism invariant or is coordinate invariant means that you have this constraint equation. So you impose this constraint, and what that constraint tells you is that the Hamiltonian is effectively zero and so states don't evolve, the wave function doesn't evolve. And that I think is very conceptually confusing. There are ways that people try and resolve it, for example, by considering relational degrees of freedom or ADS CFT tries to solve it by having a boundary time and relating everything to the boundary. And so there are ways that maybe you can get around the fact that the Wheeler-DeWitt equation

of gravity imposes, tells you that the wave function doesn't evolve. There may be ways to get around that, but at least on the surface, that appears to be a big conceptual difficulty, which any theory of quantum gravity has to somehow resolve. Finally, unlike the rest of the standard model, naive, if you try and perturbatively quantize gravity in three plus one dimensions, you find that it's not renormalizable.

So it doesn't hold at the highest energy scale. So I think this is my key message, which is that gravity is different to the other or to the forces, let's say, or to gauge theories. So I think it's reasonable to question whether we should be quantizing space-time like we've quantized all the gauge theories. And I don't know the answer to whether we should be quantizing geometry or not, but I think it's a reasonable question to be asking.

Are you looking to hire? Well, when it comes to finding the most suitable candidate, searching isn't always the ideal option. That's where Indeed comes in. With over 350 million global monthly visitors and a powerful matching engine, Indeed helps you find quality candidates fast. Whether you're screening, scheduling or messaging, Indeed makes hiring easier and more efficient, allowing you to connect with candidates quickly. 93% of employers agree that Indeed delivers the highest quality matches compared to other job sites, and that's

backed by data. One of the aspects I love about Indeed is how it simplifies the entire hiring process. I had a film incubator and I struggled with slow, ponderous hiring platforms, but I wish I had used Indeed. It would have saved me so much time. With Indeed's ability to leverage over 140 qualifications and preferences, it's like having an expert recruiter in your corner. The more you use it, the better it gets. For a $75 sponsored job credit to boost your job visibility, head to indeed.com slash theories.

That's indeed.com slash theories, terms and conditions apply. We're going to be exploring this idea that rather than quantizing gravity or quantizing space-time, we should instead keep space-time classical, but modify the evolution law so that it can be mathematically consistent. And what we're going to find is that if this program holds, like if we are able to be successful, well, I should say a number of things are already true. If this program holds, if we are able to be successful, well, I should say a number of things are already true.

So it already is true that the theory appears to be renormalizable. It's certainly power counting renormalizable, and we have a lot of strong evidence that the pure gravity theory is renormalizable. And it doesn't suffer from something called a ghost, which is, or a tachyon, which is something that some other theories which are renormalized, gravity theories which are

renormalizable, they tend to suffer from things called ghosts. There's lots of different ways of using the term ghost, so this is like a state with negative norm. It doesn't suffer from those issues while it still appears to be renormalizable. That's I think evidence that maybe we should not try and quantize gravity. The other nice thing about having a classical system which

interacts with the quantum system is that we find that the Born rule, the measurement postulate of quantum theory, is no longer needed. Are you going to explain that in this talk? Yeah. I have a, so I guess I have the, so I can talk for a little bit about the different, the formalism of the classical quantum dynamics, but I can also talk about why you don't need

the measurement postulate. And it's very intuitive as to why you need the measurement, you don't need the measurement postulate. And it's very intuitive as to why you don't need the measurement postulate. And it's basically because if a classical system interacts with a quantum system, then it causes the quantum system to become more classical. I can explain that intuitively. This title, the classical quantum gravity, is this a moniker for the theory that you previously called post quantum theory of gravity, or is it referring to something else? We call it a post quantum theory of classical gravity because quantum theory is modified in the sense that you don quantum theory where in some ways you have

this fundamentally stochastic nature to quantum mechanics and to classical mechanics and to space time. So there's a modification there, but generally these go by a number of different names and there are various versions of them which are not consistent and there are versions which are. And so I'll just refer to them all as classical quantum theories because you have a classical system and a quantum system. And so we might call this classical quantum gravity or a post-quantum theory of classical

gravity, which is maybe the particular theory that our group has proposed. I see. So your theory is an example of a classical quantum gravity. I think so, yeah. But here you're describing the class of classical quantum gravities. Right, that's right. That's right, yeah. There's a few nice things that happen as well. There's something called the decoherence versus diffusion trade-off which I'll give an intuitive picture of which means that this theory is experimentally testable and another thing is I will say that the theory

predicts that Einstein's equations break down at a certain scale and produce some anomalous behavior. And I think it's a reasonable candidate for this. This anomalous behavior is a reasonable candidate for dark matter and perhaps dark energy. The idea that you could somehow combine classical systems and quantum systems has been around for a long time. There's been a lot of no-go theorems which claim to show that we can't do it. And there's been some models that people have tried.

At the end of the day, it turns out that you can consistently couple classical systems and astro systems. There's been some examples of that which have been known since the 90s. So Blanchard and Jarek and D'Yossi in the early 90s gave some examples of such dynamics. There's been some toy models of Newtonian mechanics, which people have been able to fit into this classical quantum framework. And recently, a whole bunch of different experiments have been proposed to test these theories. So, you know, this is a consistent theory, which is experimentally testable.

So the plan of my talk is the following. I will give, we'll get a bit technical and we'll talk about what the form of the dynamics is, this classical quantum or CQ dynamics. I will talk about this decoherence versus diffusion trade-off, which you can see where the measurement posture is, why it's not needed, and why it can be used to test the quantum nature of gravity. This might be a bit beyond our time, but we might be able to kind of get

into the renormalization issue. And maybe we can even get to the enormous behavior of this theory. Okay, so let's just go back to remind ourselves about quantum mechanics and classical mechanics, which you can see have a very similar form. And now we want to see if we can combine them. And the first thing we want to do is we want to describe our state of a system.

So we have a quantum system, which has a density matrix psi, and let's just take this two-level system. So we have a two by two matrix. And then we describe it by a point in phase space and a probability density over phase space. And I'm afraid I've used a Zed here instead of Q and P. So let Zed be the point in phase space. So we are going to describe our quantum system, you know, it can be have the zero state and the probability that it is in the zero state depends on the point in phase

space. So we have the probability of the quantum system being in the zero states conditioned on where it is in phase space. It has a probability of being in the one state conditioned on where it is in phase space. And then it has a coherence, which again depends on where it is in phase space. So that's how we describe the classical quantum system together. And there's a few slides which look a bit, I hope not intimidating, but I like to show them because I like to show how similar classical mechanics is, quantum mechanics is, and the classical quantum mechanics is. So, you know, the formulas is very similar.

We have in quantum mechanics Q, we have a Hilbert space, we have a density matrix sigma which lives in the Hilbert space. The matrix sigma is normalized, so its trace is 1, and probabilities are positive, so the matrix has to be positive. So the fact that sigma represents probabilities, gives us probabilities, tells us that it has to be a positive matrix normalized to 1. Likewise, in classical mechanics. We have phase space. We have a Density which lives in phase space that density has to be normalized. So if we integrate over phase space the density must integrate to one and It must be positive because it represents a probability density. So the same properties of a probability density

So the same properties of a probability density and the same, you know, the probability density has very similar properties in comparison to a quantum density matrix. The classical quantum state, it's going to be very similar. It, you know, it's normalized, but when we say normalized, what we mean is that we take the trace and we integrate over a phase space and then it's integrates and traces to one.

And it's a positive matrix at each point in phase space z. So it has the same properties of being positive and normalized. And now what do we mean by consistent dynamics? We just mean that it's another way of writing it. Sorry, writing these density matrices and the CQ state. So we just want that the dynamics preserves maps state to state. So if a dynamic is consistent,

it'll be a linear map which maps a state to another state. That's what we mean by consistent dynamics, and that's a necessary and sufficient condition for our dynamics to be mathematically consistent. I've written here, you can always embed a classical system into a quantum system. There is a fully quantum way of writing the state and that's what I've written here.

I want to give an example of the classical quantum dynamics, and I'm going to give an example, which is the one we are so used to, which is a Stern-Gerlach. This should have a D1 in front of it that's missing. But we have a free particle. So the Hamiltonian is p squared over 2m. It's a free particle, which is classical. And then it has a position q that's also classical.

But then it has a spin, z sigma z and so the particle lives in phase space but then there's this two level system which lives on the Bloch sphere and here's the Hamiltonian and so what's going to happen well when the spin is up we expect the force to push it in one direction and when the spin down, the magnetic field will push the particle in the other direction. So, um, and the D one is what? Um, the D one I is here. I'm here written it correctly.

So the D one is the force of the magnetic field. So it's the force of the back reaction. So if D one is big, then the spin has a very strong back reaction. Right? If D1 is very big, it means you have a very strong magnetic field, and it means that the spin particle will cause the classical particle to exert a very large force on the classical particle. That manifests as a change in slope, as an increase in slope, or what? That's right.

P dot is the acceleration, so P dot is if this is time over here, thank you, then it'll take you not time, it's Q, but you can take it to be time. It'll have a very large force, so the acceleration will be large if D1 is very big, and the force will be either in one direction or the other direction depending on the spin. So here you have an example, you start off with the spin, the two-level system, quantum system in the plus state in the superposition, and it will either go and end up in the zero state or it'll end up in the one state. And it'll push the classical particle, the free particle, it'll either give it a force in one direction or a force in the other direction.

And so you can see what's happening here is that the quantum state is collapsing. It starts off in the plus state, like a Stern-Gerlach, right? So in the Stern-Gerlach, if its spin is in one direction, the particle moves in one direction. If the spin is in the other direction, the particle moves, gets a force in the opposite direction. And if we observe this particle, you know, if we observe it having a force in one direction, we will know that it's the zero state. If on the other hand, we observe that this particle moves in the other direction, then we will know that it's the one state. So by observing this classical particle,

we in some sense learn whether this quantum system is in the zero state or the one state. So I want to write down what the full interaction looks like. Oh, just a moment, sorry. What is the collapse here? The observation collapses it? Yeah, so exactly, good, good. So what is doing the observation? Well, it's the classical particle

That's doing the observation the classical particle moves you know gets a force in one direction or a force in the other and Based on that we will learn whether the spin is Whether this two-level system is a zero or one because the system is classical You know another observer could measure it to arbitrary accuracy at any point. So we can imagine that an observer looks at this classical particle and tries to see if the force is in one direction or the other direction. And if the force is in one direction that they will then know that the quantum system is a zero and

if it moves in the other direction they'll know that the quantum system is in a one. So we can imagine that there's an observer who measures the classical particle, but we can also just imagine that it's the classical particle itself that is causing the spin to go from the plus state to the zero state or the one state. So this is why I said that the measurement postulate isn't needed. This dynamics automatically gives the result that if I have an initial superposition it'll go to the zero state or the one state and with a probability given by the Born rule which is the modulus of the wave function squared.

Okay, so the measurement postulate gets replaced with an interaction postulate or no? That's right. Or just the measurement postulate gets replaced with the following postulate. There exists a genuinely classical system, which maybe I want to take to be the experimenter, maybe I want to take it to be space-time, but if there's a genuinely classical system, then it will automatically cause, and there's an interaction, then it will automatically force quantum systems to collapse. Got it. And so here we have an example of the evolution. You can see that it looks very familiar. So we have the evolution of this joint classical quantum state row hat.

We have the ordinary Heisenberg commutation relation, which gives the evolution of the quantum state. And now, instead of having, so previously we had this Poisson bracket. And now we have something called the Alexandrov bracket, which is, it looks like the Poisson bracket, but it has an operator ordering ambiguity. And so we take H on the left and H on the right. So this is this Alexandrov bracket.

In the example of this particular interaction, which is this magnetic field, D1q sigma, then it looks like this. It essentially gives you motion, acceleration in one direction or acceleration in the other direction depending on the value of the spin operator. Okay, so if the spin operator is up, then it will give you momentum in one direction. If the spin is down, it will give you momentum in the other direction, sorry, force in the other direction. There are two additional terms, and those two additional terms, so there's the terms that roughly speaking are the usual Poisson bracket and the Heisenberg commutation. But there are these two other terms.

This term will be familiar to anybody that's studied open quantum systems. This is called the Limbladian, and it results in decoherence. If you've seen the Limblad equation or the GKSL equation that's sometimes called, this is a double Poisson bracket and it leads to decoherence.

So it causes the spin to decoherence. And if anyone has studied stochastic dynamics, they will recognize this as, you know, again, has a very similar form to the Lindblad equation, but it is the Fokker-Planck term. So it leads to diffusion. So in this case, it leads to a diffusion of the momentum. So the momentum diffuses and the spin decohes. And in order to keep the density matrix positive, it needs to satisfy, well actually needs to satisfy this inequality. So this is what we call the decoherence versus diffusion trade-off. If you have a long coherence time, so you have very little decoherence,

then you need a lot of diffusion. So D2 needs to be very large if D0 is very small. So if you have a little bit of decoherence, you need a lot of diffusion. And that's all in relation to how strong the back reaction is, this D1. zero is very small. So if you have a little bit of decoherence, you need a lot of diffusion. And that's all in relation to how strong the back reaction is, this D1. So this is the tradeoff and it's what is going to allow us to experimentally test this theory. And a remarkable thing happens when the tradeoff is saturated, which is that the quantum state stays pure. So I said you have this Lindblad term which represents decoherence,

and you have this diffusion term which causes the momentum to move around. And remarkably, when you saturate this trade-off, when you make d2, d0 equal to d1 squared, then in some sense there is no decoherence because conditioned on the classical system the quantum state stays pure. So what happens is that the quantum state starts in the plus state and it stays pure the whole time conditioned on the trajectory of the

quantum system and collapses to being in the zero state or the one state, but it doesn't actually decohere, it just stays pure the whole time. I can pause there, I would normally pause there for questions. What I, I can do one of two things next, I would, so this is what's called a master equation. If people are familiar with the Fokker-Planck equation or the Heisenberg equation or the Lindblad equation, these are all examples of master equations. So this is a master equation.

And that's one way to describe classical quantum dynamics. I can go through the formalism for discussing classical quantum dynamics through path integrals, but I can also talk more about the experimental tests and this decoherence versus diffusion trade-off and give a maybe some intuition as to why we have this trade-off. Paramount Plus. We come to you from the mountain of entertainment to tell you what's streaming on Paramount Plus. Blockbusters like A Quiet quiet place, day one.

One. Originals, including Yellowstone. Let the world know we're here. Let it out! And hits like Dexter. You're decent and good. I'm not. Paramount Plus, your eyeballs, equals entertainment.

Stream Paramount Plus from $6.99 a month. Kurt, you have any preference? The path integral approach. You want to go to path integral. Kurt, you like the technical stuff. And for those of you who'd like to skip the recondite inner workings and go straight to the intuition, feel free to move forward to the timestamp of 49 minutes. Good.

So actually, this is, I think, fun for people that if you love path integrals, then I hope you like this because I want to talk about the different kinds of path integrals we have. And so maybe you'll find this a bit fun. So this is the standard path integral for quantum systems. We want to compute an amplitude. We start off at some initial time, t initial. We start off in some initial state, psi i. And we want to know what is the amplitude that at some final time the system is in the state psi f final. Now, are we assuming that these phi are vectors or are they fields at this point?

This is quantum mechanics. So I'm going to go through each of the path integrals. I'm going to go through the quantum path integral. I'm going to go through the open quantum system path integral. And then I'll go through the classical path integral, which you may or may not have heard of, but there are classical path integrals. And then I'll talk about the classical quantum path integral. Now I'm super glad that we're gallivanting in path integrals because I'd

like to know more about the classical case. Okay. It's, uh, I'll even, it even has names, um, several names. Wonderful. Um, okay. So, um, this is the quantum path integral. So this is how we describe quantum mechanics through path intervals, and we sum over all paths weighted by the action with an i.

Good. And so that gives us, we sum over all the paths. And now we're going to do something which is done a lot in a number of formalisms, so one is called the Feynman-Vernon formalism. One is called any open quantum systems. Sometimes it's called the Schmier-Keldysh formalism. But now we don't want to just compute an amplitude. We want to compute the density matrix.

We want to compute probabilities. So we have a bra and a ket. So we double the number of fields. So we have the plus and a ket. So we have, we double the number of fields. So we have the plus field and the minus field. So here we are starting off in an initial density matrix, psi i, a pure state in this case. And then we want to compute not just the amplitude, but the element of a density matrix.

So we have, you know, an amplitude is just a vector, but now we have a matrix because density matrix is a matrix. So we have the amplitude and we label it by, we have a ket field and we have a bra field. So what does that look like? We have two fields and we have e to the is for the bra field and e to the minus is for for the ket field. Actually it's the other way around. This is the ket field and this is the bra field. So it's a little bit

confusing when you first look at it but you will be rewarded if you stare long enough or read Feynman and Hibbs and learn about these pathineurals. The point is that because you're computing a probability or a density matrix, you have two amplitudes in some sense, and so you have the bra field and the kit field. Uh-huh. Let me just go back up. Remember, this was the normal path integral where we're computing the amplitude,

and now we want to start off in this initial state where we want to compute both the row and the column and so we have two fields one representing the row in the column or the bra in the ket and so we have this doubled path integral. Got it. And so this is computing the density matrix. So we can write it as a density matrix. So we have a density matrix. And this is one slot, the row. And this is the other slot, the column. And we sum over both the bra field and the ket field

in order to compute the density matrix at some later time. So that's just quantum mechanics. And now we can add this Limbladian term, the decoherence term. It's also called the Feynman-Vernon term. And it's the term that's gonna cause the system to decoherence. So remember, decoherence is when the off-diagonal elements

of your density matrix decay. And so here we add this term and you can see what it does. It causes exponential decay of off diagonal elements, right? Because when the bra field, the plus and the minus field are the same, it does nothing, this term vanishes. But if the bra field and the ket field are very different, then these terms in the density matrix will be exponentially suppressed. So this suppresses any terms in my density matrix in which the bra field is different

to the kinked field. So again, you have to stare at that for a while or read, I recommend Feynman and Hibbs, but you can see that this path integral or Schringer-Kaldis, you can see that this path integral, or Schringer Caldash, you can see that this path integral is like an open quantum system where the off-diagonal elements of my density matrix are exponentially decayed. But here we're using a field rather than a... you know, this phi could be a field here. Good. So that's the path integral for decoherence of an open quantum system. And now we're going to jump to classical mechanics. Here is the path integral for classical mechanics. It's the most boring path integral you could imagine because there's only one path.

Yeah, there's only one path. It has to satisfy, you know, at every point in time, you have to satisfy Hamilton's equations. And so it's a very boring path integral. It just has delta functions and it's Q dot has to satisfy Hamilton's equations, P dot has to. And we sum over all paths which satisfy Hamilton's equations. And it's very boring.

Now, if we have a stochastic theory, it gets a bit more interesting. So then we have a genuine path integral in the classical case. So this is a classical path integral. It's the path integral for Brownian motion. And so Brownian motion, we usually have f equals ma, so this is f equals ma. But Brownian motion, the deterministic evolution is f equals ma, but we're allowed to have stochastic fluctuations

away from Newton's law. In this path integral, you sum over all paths given by q, and if it satisfies Newton's equations of f equals ma, then those are the paths which are given the most weight. But if it just has some small fluctuations away from Newton's law, that's okay. And those will still contribute to the path integral. But if we deviate too much from Newton's force law, then that will be exponentially suppressed. So this is Brownian motion.

It represents a stochastic evolution. You could also be, you know, this is the way of writing the Fokker-Planck equation. It's a way of writing the Langevin equation, if you've heard of those. And it goes by the name of Onsager match loop. It's sometimes also related to something called Martin Seguia-Rose, if you want to Google things. But these are all different path integrals for classical mechanics when you have a stochastic emulation. Okay and the random variable here is F? F is the force and so you have a

random force which is not shown here. The path integral just tells you that there's kicks in the force which you don't see because there must be a kick in the force to move you away from F equals ma. So previously what you would have said for the deterministic case is you would have given some initial position, some initial velocity, but now you also have to tell it what the acceleration is and we have to sum over all possible accelerations and they're suppressed if they deviate too far from Newton's law. The thing which is undergoing stochastic evolution, Kurt, to answer your question, is q, right? So q is the position of the particle gets stochastic kicks.

It's generally satisfying f equals ma, but it has these little kicks that move it around. I see. And make it deviate from the log. So that's another thing you just have to stare at for a while and you say, OK, I see that f equals ma is, those are the paths which have the most probability, but there's other paths which contribute. And there's a general thing here that what we're doing is we're taking an equation of motion,

so the action is given by an equation of motion squared with a minus sign. So the equation of motion squared basically says that generally you respect the equation of motion, but you're allowed to have deviations away from it. So here we have the Euler-Lagrange equations. And so I can have a path integral which is given by the Euler-Lagrange equation squared. Maybe you can guess what's about to happen. If you want to have a stochastic theory,

we can take equation of motion. Here's Einstein's equation in the vacuum and we can contract it with itself to square it. So in that way, you can consider a theory of gravity where you have Einstein's equation, but you have deviations away from Einstein's equation. And so you have stochastic fluctuations of the metric. And I'm slowly moving towards the classical quantum theory, but if you go back to the example I gave, you need to have – so here's the Fokker-Planck term – you need to have a stochastic – in

order to be consistent, you need that the classical degrees of freedom are stochastic and the quantum degrees of freedom have decoherence. And so what we need to do is we need to consider a stochastic evolution of gravity in order that we can now reconcile it with quantum field. So here's maybe just to show up some things which maybe are familiar to people. Here is the Langevin equation so it's the acceleration is equal to the, equation so it's the acceleration is equal to the you know this is f equals ma but then we have a random kicks these these this Langevin noise, Bernian noise and on expectation this noise is zero but it has some covariance and that is one way to describe stochastic evolution and the other way that's equivalent to this path integral formatism. So I think it's nice because I guess in my view what I

like to do, I like to see the formal similarities between quantum mechanics, classical mechanics, and now the classical quantum formalism. So here is here is the quantum path integral, here's the action with the Feynman-Vernon term. Here is the F equals MA classical action, which is usually by the name of onslaught or match loop. And now here is this classical quantum action. It contains the Feynman-Vernon term. It contains this evolution. So you have decoherence term

which decoheres the back reaction term and it has a stochastic force but the force is given by the bra field and the catch field. So it's maybe a little bit hard to kind of absorb it all at once, but I guess the main message that I want to give is that really what this classical quantum path integral is is it's a kind of smushing together of the classical path integral and the quantum path integral for open quantum systems. So it has all the elements. It has a decoherence term here, which looks very similar to the Feynman-Bernon term.

And it has a stochastic back reaction, which looks very similar to the stochastic back reaction that you get from the Langevin equation. And then this bound of 4D2, which is greater than D or the inverse of D0, where does that come from from the above? Yeah, that was this decoherence versus tradeoff. That was the decoherence versus diffusion tradeoff. And that's what you need in order to keep the dynamics mathematically consistent.

And that's just a mathematical proof of, remember that we started off by saying, OK, this is what the density matrix has to be positive and norm preserving. Well, the dynamics has to be completely positive and norm preserving. And in order for it to be completely positive, and map a density matrix to a density matrix, map a positive matrix to another positive matrix, it has to satisfy this trade off. So that's where the trade off comes from. I see just a moment. So the derivation of this is in the paper with you and Davies,

is that correct? Yeah. It's with, well, no, it's actually in quite a number of us. So it's a paper. It's called The Two Classes of Classical Quantum Dynamics, I believe. OK. It's also paraphrased and forward-sided in my PRX on a post-quantum theory of classical

gravity. So now that was a lot of formalism and you know there's some tables, I like to put a table in most of those papers where you see classical mechanics, quantum mechanics, classical quantum mechanics, you see how formally similar they are. So that's the, I think, you know, for people studying and thinking about the formalism of our theories and the So that's the, I think, you know, for people studying and thinking about the formalism of our theories and the frameworks that we have, those, you know, are the only frameworks we have. And so I think it's interesting to see the mathematical similarities between those three different frameworks now. But I want to take a break from mathematics and formalism and give you an intuition behind it,

and an intuition as to why we'll be able to experimentally test the quantum nature of space-time and why it has to be that a classical space-time would cause the wave function to collapse. So that's what I want to do. And I call this the decoherence versus diffusion trade-off. So we're going to talk about the decoherence versus diffusion trade-off and it comes about, I think it's quite intuitive how it comes about. Let's imagine that we have a superposition of a particle, a superposition of it being here and there. So this is not two particles, it's a particle in superposition. It's here, a superposition of it being here and there. So this is not two particles, it's a particle in superposition.

It's here, a superposition of here and there. And now let's turn on the gravitational interaction. So remember that if a particle is as a mass and it's in superposition, it causes space-time to bend. So here we have space-time bending. It doesn't quite know, should it bend around here or should it bend around there? It doesn't really know. But let's think about what should happen. So we know that if the particle was here, then it should bend space-time around here. And if the particle is there, then it should bend space-time around there if the space time is fundamentally classical then we could imagine measuring the gravitational field we could take some pendulums and measure the bending the curvature of space time and we can try and tell by measuring space time to arbitrary accuracy and measuring the curvature to arbitrary accuracy we could try and tell by measuring space-time to arbitrary accuracy and measuring the

curvature to arbitrary accuracy we could try and determine whether the particle is here or there. So let's imagine someone does it, try and measure the particles here and there and if space-time was classical they would measure to arbitrary accuracy and they would instantly know whether the particle was here or there. So that's why a classical notion of space-time will cause states to collapse to being here or there. We know that that's not what happens because states can stay in superposition for quite a long time. So in order for a classical spacetime to be consistent with quantum superpositions, we need the interaction to be stochastic. So it needs to be that when we measure spacetime, we don't learn exactly whether the particle is here or there because spacetime is

fluctuating. And so when we measure space, you know, this is a diffusion. So when you measure space time, there's all these stochastic fluctuations. There's this diffusion in space time. And so we don't learn exactly whether the particle is here or there. And so this is the trade-off. So if you have a long coherence time, if the particle is able to remain in superposition for a long time, it must mean that there is a lot of stochastic noise which is obscuring whether the particle is here or there. So the particle is in superposition, we measure the gravitational field, it's stochastic, but we measure it for long enough that eventually we learn where the particle is and we learn that the particle is there.

So that is this trade-off. The longer the coherent time, the more stochasticity we need in order to have a long coherence time. So that's the trade-off and that's the thing that we propose people measure. They should measure, you know, we put a bound on coherence times and we put a bound on stochastic fluctuations in the gravitational field and that could rule out any theory in which space-time is fundamentally classical and could verify the quantum nature of space-time or it could verify that space time should be treated.

Let me just maybe give it a game through the double slit experiment. In the double slit experiment, we could imagine we have massive electrons, we perform the double slit experiment, and while we're performing a double slit experiment, we could imagine that someone sits there with, you know, pendulum to measure, try and measure which that the particle went through or use the gravitational wave detector in case this particle emits a gravitational wave. Pretty unlikely, but who knows. And so if the gravitational field is classical, we can measure it to arbitrary accuracy. We'll be able to determine which that the particle went through, and therefore there's

no way that this particle could make an interference pattern. On the other hand, if the, this is some complicated slides, which I probably should explain better, but I guess we're getting close to running out of time and I hope that my previous picture explained it, but roughly speaking, you know, in electromagnetism, the particle when it goes to the left, the right side, it gets entangled with the electromagnetic field, and the electromagnetic field to some extent knows which slit it went through. The neo field definitely knows which slit it went through, the far field not so much. If we measure the far field, we will not be able to determine which slit the particle went through,

because it turns out that the two different states of the electromagnetic field, they're different, but they have a large overlap. That's why we still see an interference pattern. In the case of a classical spacetime, which is stochastic, if we measure the gravitational field, we'll get these probability distributions of gravitational fields, and we won't be able to determine which the particle went through. You will be able to still have interference patterns. Now is this also the same response that the people who quantize gravity would say? That if gravity was a quantum theory, what would the answer be to if you sent, say,

there's some molecules, I think it's 720 atomic units is the largest that they found an interference pattern of. So let's say you send the largest that they've found an interference pattern of. So let's say you send a molecule through, it gives an interference pattern, but you're able to detect a graviton, then does that collapse it? What do they say? Well, so in the purely quantum case, you can actually have a large back reaction. So if you look at what happens with electromagnetism, there's this huge back reaction on the electromagnetic field.

The back reaction is really big. But what actually happens is that, so it gets, what happens is that the electron gets, we say gets dressed by the electromagnetic field. So what you actually have when you put an electron through the double-sit experiment is that you have an electron with its associated electromagnetic field, so it's highly entangled with the electromagnetic field, and then when it gets to the screen, in some sense, the entanglement with the electromagnetic field just gets erased. And so in the quantum case, there is no trade-off. You don't need to have a decoherence versus diffusion trade-off. So it's only in the classical case

that you are required to have this trade-off. Now, that doesn't mean that in the quantum, for quantum gravity, there will also be stochasticity, because vacuum states are, they have fluctuations. But for quantum gravity, ironically perhaps, the stochastic fluctuations are much weaker. It's a slightly puzzling thing to get your head around because you would normally think of the classical vacuum as having less fluctuations, but it's actually a classical vacuum needs to have more fluctuations in order to be consistent with quantum theory. Okay. But, you know, both, you know, what we expect to see in this post-quantum theory of classical gravity,

we see that the classical spacetime is going to have these big stochastic fluctuations, which interact with the quantum vacuum in a very non-trivial way. So both theories have this, but if spacetime is treated classically, then the fluctuations actually have to be larger. Understood. It's confusing. But the nice thing is that you can experimentally test it. So what we propose is that you do double slit experiments to show that gold atoms, for example, have very long coherence times. And then the trade-off tells you that in a Cavendish experiment, you should see a lot of stochastic fluctuations, because the longer the coherence time,

the larger the fluctuations. So then you, in some sense, you use these two experiments, the double slit experiment and the Cavendish experiment, to squeeze the theory from both sides and potentially rule it out. And so that's the proposal for testing the quantum nature of spacetime, hyper-schizen, double split, long coherence times, and that gives the trade-off.

Is this doable with current technology? So I think we need to do more theoretical work because there is a bit of theory which goes into this, because you can have different, it turns out that the trade off has a parameter in it which is theory dependent and so we currently are trying to constrain that. At the moment we think that one of the best detectors for precision gravity measurements is going to be LISA, the LISA gravitational wave experiment, which will, I guess, I think it's going, will become live in 2035, 2030. Wow. 2030. And so when that goes live, I think, you know, I think by that time our double slit experiments will be enough to

catch up with the bound that it gives. And so that should either prove the quantum nature of gravity or this other theory. Let me just say that it appears to be renormalizable. And I just want to end with just a bit of a summary and the main, I think, open, well, there's a lot of open questions, but just end with the following. I have no idea if space-time is classical or quantum, what its nature is. But I think that there is a consistent theory where we treat it classically. And so I think we have to really first check if the theory satisfies all the properties we want,

namely that it's completely positive, renormalizable when we add matter, which we don't know yet, that it's consistent with the experiment, the vacuum structure that we see around us, and is generally covariant. So we need to do all these tests to see if this theory passes all these bars. And at the end of the day, I have no idea if space-time is classical, but we can perform the measurements. I guess that's the main message, that this is a reasonable theory, it's mathematically consistent, and ought to be tested. I've just thrown up a bunch of open questions. Versus foil, what is that?

Oh, well, I guess, you know, if you're proposing something which has one, so we have a bet, I have a bet with a string theorist and a loop quantum gravity researcher, Jeff Pennington and Carlo Rovelli, the odds are pretty long long and it's always good to hedge your bets. And so, you know, I think this theory, you know, is a candidate for a fundamental theory,

but also as an effective theory. So it's an effective theory, or could be an effective theory, or there's a parameter space in which it is an effective theory where we treat space-time classically. But also it's, you know, it is a theory where we can actually do calculations and see what happens. This is what I mean by a foil. If you want to compare quantum gravity with something, you need the alternative hypothesis. It's an alternative hypothesis which we can use to understand what quantum gravity should predict in comparison to alternative hypothesis. So maybe alternative hypothesis is a better word than FOIL,

but that's what I mean. In order for this theory to – there are a number of tensions that still exist in the theory, so you need to make sure that it's renormalizable when you add matter, that when you renormalize it, it doesn't break covariance, that it doesn't, after renormalization, that it's still completely positive trace preserving, and that you still have locality. And so there's a number of challenges and tensions that need to be resolved.

So at the end of the day, I have no idea if space time is classical or quantum or something else, but if it was classical, then I think it has a number of intriguing features like the measurement postulate is not needed, that it may help explain dark matter and dark energy, that it is, appears to be renormalizable without ghosts. And so, you know, at the end of the day, I feel like we have to go out and perform the

experiment and see what nature has decided. So with that, I'd like to thank you for your attention. Wonderful. Thank you so much, Professor Jonathan Oppenheim. Again, the links to the professor's work are in the description. They're on screen as well. Thank you for staying up. I know that it's almost midnight where you are. Thank you so much, professor.

Yeah, well, thanks very much for giving this platform. It's great. Also, thank you to our partner, The Economist. Firstly, thank you for watching. Thank you for listening. There's now a website, curtjymongle.org, and that has a mailing list. The reason being that large platforms like YouTube, like Patreon, they can disable you for whatever reason, whenever they like. That's just part of the terms of service. Now a direct mailing list ensures that I have an untrammeled communication

with you. Plus, soon I'll be releasing a one-page PDF of my top 10 toes. It's not as Quentin Tarantino as it sounds like. Secondly, 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 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 gained from replaying So how about instead you read listen on those platforms like iTunes Spotify Google podcasts whichever podcast catcher you use and Finally if you'd like to support more conversations like this, more content like this, then do consider visiting patreon.com slash Kurt Jaimungal and donating with whatever you like. There's also PayPal, there's also crypto, there's also just joining on YouTube. Again, keep in mind, it's support from the sponsors and you that allow me to work on toe full time.

You also get early access to ad free episodes, whether it's audio or video, it's audio in the case of Patreon, video in the case of YouTube. For instance, this episode that you're listening to right now was released a few days earlier. Every dollar helps far more than you think. Either way, your viewership is generosity enough. Thank you so much. you