Theories of Everything with Curt Jaimungal - The Theory Beyond Einstein: Fay Dowker

Episode Date: June 7, 2024

Fay is a physicist and is currently a professor of Theoretical Physics and a member of the Theoretical Physics Group at Imperial College London and a Visiting Fellow at the Perimeter Institute. Fay conducts research in a number of areas of theoretical physics including quantum gravity and causal set theory.  Please consider signing up for TOEmail at https://www.curtjaimungal.org Links:https://www.kitp.ucsb.edu/activities/hartle-c24 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  

Professor Dauker, thank you so much for joining us. What I'd like to know, or what I'd like to start off with, is why is it that reconciling general relativity and quantum field theory is so difficult, yet so important? Thank you for having me on your podcast, Kurt, and please call me Faye. Will do. In my view, because the reason it's difficult to reconcile general relativity and quantum theory, quantum field theory, is because assumes that there is a space-time background, a fixed background of space-time. Whereas in general relativity, space-time is a dynamical object. And we simply don't know how to deal with a quantum theory where space-time itself is dynamical, where it's fully dynamical and where structures like the causal structure are themselves dynamical.

In quantum theory, as we know it, those things are assumed to be fixed and the conceptual struggles that we have in trying to reconcile these two theories arise in my view because it's really a conceptual struggle. I don't see it so much as a technical struggle at the moment. Of course, there are technical problems within each particular approach to the problem. But really we're struggling over what the right concepts are to work with in this presumed deeper theory that will incorporate both general relativity and quantum theory. Because it's a struggle over concepts, it But it has given rise to many different approaches and we don't have a rich manifold of experimental data to help guide us and help us eliminate particular approaches. Say that doesn't work because it doesn't agree with the data.

So we're using our conceptual intuitions. What feels right? What are the right ideas and physical entities, physical concepts that are going to survive in the deep theory, what are the new ones that are going to arise. So it's hard because we don't have the guidance of experimental data and observations. There may be some quantum gravity phenomenology out there and we just haven't recognized it as such yet. But on the whole, we're just not in a situation where, where the, there's a lot of X, a lot of data, a lot of observations that don't fit our current theories.

So you made a distinction between quantum theory and then quantum field theory. Like you first said, quantum theory or quantum field theory, something akin to that. So my question is going to be why, why that, what's the difference? Okay. Um, so it's a matter of debate in the community whether or not quantum gravity will turn out to be a quantum field theory. So when you said reconcile quantum field theory and general relativity, I was kind of, I let to the conclusion you were thinking of making general relativity into a quantum field theory, but maybe you didn't quite mean that. So I was trying to say that we don't know yet whether quantum gravity will be a quantum field

theory of the sort that we are familiar with that underpins the standard model, for example. Right. So quantum theory, so I think, so my view is that quantum gravity will turn out to be a quantum theory, but not in the same mold as a quantum field theory. We will need to make advances in understanding quantum theory more generally in order to find a working theory of quantum gravity. So I just wanted to broaden the idea of quantumness to encompass not just quantum field theory, but other sorts of quantum theories. If the difficulty is at the conceptual level, well then to me that would imply that

you can't even combine linearized gravity in a quantum way, or sorry, you can't talk about linearized gravity in a quantum way, but you can. And so I just surmised, is it just that there's no back reaction or is there something else, like is it not dynamical enough? Is that just a difference of degree versus type? Like I don't know. I think what linearized quantum, so if you quantize the linearized perturbations around some space time background, ala quantum and treat it as a quantum field theory, a local quantum field theory with, without back reaction, then as you say, it does work up to a point. So it works up to

the point where the energies of the processes you're considering start to approach the Planck scale where you can't ignore the back reaction and then you don't know what to do at that point because you want the effect of this quantum field to be on the background. You want to release the background from being a background and allow it to be dynamical and you want it to be itself fully quantum. And that's where the conceptual... So the theory is fine as far as it goes. It breaks down and the scale at which it breaks down tells you, which is the Planck scale, tells you where the new physics is that you should look for.

So it's a sort of phrase that people use for this linearized series, it's not renormalizable. And that's a good thing. And it's a good thing because? It's a good thing because the theory breaks down and it breaks down at where it breaks down tells you something physical. It tells you where to look for the new physics and where you look for the new physics is at applying the skill. So before we get to your fascinating approach, which more people should know about called

causal set theory, I'm curious, there are various problems in physics. Quantum gravity is just one of them. I'll rattle off a few just for you for some context to this question and for the listener who is interested in looking these up. So there's the problem of the magnetic monopole, why haven't we seen it and why is it SU3 cross SU2, etc. The vacuum catastrophe or there's the horizon, or the fermion doubling problem, which is a mathematical problem, or why is there chirality, why are there three generations of

matter. So reconciling GR with quantum theory is just one problem. Quantum gravity itself is just one solution to said problem. Why do you think it is that we hear so much about quantum gravity? said problem. Why do you think it is that we hear so much about quantum gravity? It seems like there's something privileged about quantum gravity as a solution or as the most pressing problem. What are your thoughts on that? I don't think physics makes that judgment. I think there are people who are drawn to all of the things that you mentioned. People are pursuing those questions avidly. Some are, you know, they have more hope of getting observational evidence, they can hope that certain experiments which are currently underway will give them some clues about what's going on. I don't see that reflected in the community. I mean, if it's a personal question to me why I'm attracted to the problem of quantum gravity, I suppose it's because

it's a historical happenstance, which is just when I was an undergraduate, I started out doing mathematics, so I was a maths student. My finding maths harder and harder coincided with my learning about general relativity, which I totally loved. And because of that, I just loved gravity. I loved the revelation that our best theory of gravity is a theory of space-time itself. Just grab me and has never let me go. So I've always been interested in gravity. it naturally occurs that the general relativity predicts, people say it predicts its own downfall, so that my lecturer, my GR lecturer said that, he said it predicts its own downfall because you can predict that in physical circumstances in the universe, there will be singularities inside collapsed objects inside black holes. At that time, we didn't have the absolutely drop dead evidence that black holes really exist that we have now. But most relativists believe that black holes did exist in the universe. And because of that, the theory

of general relativity just simply doesn't hold anymore close to the singularity inside a black hole. If you want to understand what happens inside a black hole, you have to address the problem of quantum gravity. At the singularity of a black hole, the curvature of space-time is so high and the matter is so hot and dense that you can't ignore quantum effect anymore. The classical description of gravity will break down, so you need a theory of quantum gravity there. It leads to the next stage itself. It tells you that It leads to the next stage itself. It tells you that it's not enough to understand the universe and you have to go beyond it. You have to find this theory of, understand this, a theory in which both quantum, quantumness of space time and dynamical spacetime, both at play.

So that was it for me. I just had to know more about gravity and I wanted to try to contribute to this program of finding the theory that will tell us what happens at the singularities inside black holes and also what we call the singularity of the Big Bang. That's another regime in our universe where both quantum effects and gravity are relevant and have to be taken into consideration. So it's just a historical thing. I just happened, you know, it just happened to me. Right, right.

And you also worked under Stephen Hawking. So did working under Stephen have any influence on causal sets, not on your interest in quantum gravity, which I assume it did, but on causal sets in particular? Well, that's a super interesting question. So it's almost as if my scientific progression is Stevens, but in time, sort of in time reversed. Okay. explain. So it turns out, a lot of Stephen's early work was on the causal structure of space-time. So his early work was using the sorts of techniques that Roger Penrose devised for studying the structure of space-time

and predicting essentially that singularities must form inside the horizon of black holes. Stephen used that and he predicted that there must be a singularity at the beginning of the universe at the Big Bang. So He was one of the pioneers of what you might call global causal analysis. In particular, he proved a really important theorem which is, if you know the causal structure of space-time, That is, if you know what events in space-time can causally affect what other events, if you have all that information, then you can deduce from just that information alone, you can deduce what's called the differentiable structure of space-time. That's essentially how smooth the space-time is.

Once you know that, then you have in your hand the ability to deduce almost all of the geometrical and metrical information. He proved a theorem which is somehow, well, we'll get on to causal sets, but it's a key theorem in our approach to the problem of quantum gravity, which puts causal structure at the center. Right. And you gave it a moniker, a large moniker. It had four names with dashes in between them.

What is that? Yeah. So it's a theorem. Well, it's a concatenation of several results over a few years. So it's, the names are Cronheimer, Penrose, Hawking and Malament. So Cronheimer and Penrose, because they, they wrote an amazing paper early on, which shows that if you know the causal structure, then you know the chronological structure. There's a slight sort of distinction there between what events can influence what other events, just full stop. And what events can influence what other events just by

sending a massive particle from one to the other. So the signal has to be what people call a time like signal, something slower than the speed of light. So those are two slight distinctions in this idea of causal structure. So Cronheimer and Penner said that if you know the causal structure, which is just what can influence what, then you actually know the chronological structure, which is what can influence what in a, by sending a massive particle. Yeah. Massively. And then that is, you can show that that tells you the topology of space-time.

And that's a result by Penrose. So Penrose gets in there several times in the theorem. So it could be Cronheimer, Penrose, Penrose, Hawking-Scher. Sure, sure. Anyway, so you know the topology, then Stephen showed you then know the differentiable structure and then David Malaman put the final, he made the theorem as tight as it can be. So he showed what the, he deduced, he proved what the absolutely minimal amount of information you need in order to prove this theorem. What's the minimal conditions under which, the weakest conditions under which this theorem holds.

Then if you have all of that, the causal structure, then that theorem tells you that the causal structure of spacetime will give you all of the geometry apart from one thing. And that one thing is, is local scale. So it tells you the whole, the full geometry of space time, except for one thing. And it just doesn't tell you what, what local scale is. So how, how lot, you know, what the time duration is along some particular world line. It doesn't tell you that. Okay. And then this leads to causal sets.

It's what it's one of the, it's one of it's you might call it the Earth theorem, it's a theorem which gives us hope that causal structure is, can be the underpinning for a deeper theory, a deeper understanding of space-time, sort of deeper than general relativity. I haven't finished the story about Stephen and me. Okay, great. Please continue. The second thing that Stephen influenced me very much with was his adherence to the path integral approach to quantum theory as the basis for theory of quantum gravity. And I think that too. Later in life, Stephen became convinced that the fundamental structure of space-time was not Lorentzian. So the Lorentzian structure just basically means that causal structure, that there's light in it. It's that minus that people see in the mixed signature.

Yes, yeah, so it's all the diagrams you see. Without that, you don't have light cones. So in a Euclidean space time, there is no distinction between time-like directions and space-like directions. They're all the same. Stephen thought that the fundamental degrees of freedom of quantum gravity should be Euclidean space times and that the Lorentzianness of GR would emerge at some effective level. So when I started as a PhD student with Stephen, he had taken up this point of view and I worked on a project within that approach, within the Euclidean

approach to quantum gravity. So I was born as a scientist doing Euclidean quantum gravity. Now I've gone backwards to believing that it's Lorentzian space times and Lorentzian structure and causal structure which is the most fundamental. So I went back to Stephen's early days when he was a pioneer of global causal analysis. But he totally influences me still. But his theorem, that early theorem and also his championing of the path integral approach is something which I learned from him and I adhere to today. So what's responsible for that shift that Wick rotated you from the Euclidean mindset to the Lorentzian one?

Various things. Indian approach, it's very creative, but it didn't satisfy me enough in terms of its conceptual basis. It seemed to me in the end that also it has technical problems, but probably that's, I mean, one can always overcome a technical issue. But the conceptual issues were more, they were more, they gave me more pause, I think, which is to try to understand what's really going on. And I didn't see how you could make headway with that in a Euclidean framework where nothing happens. I mean, everything is, there's no time. And the struggle that one would have to recover any kind of concept of time, the passage of time, causality, one thing being in the past and another thing being, you know, events being causally ordered. Yeah, I totally struggled to see how one could make any headway with understanding how those things might arise in a Euclidean theory.

So that it was very gradual. I mean, these things don't, well, of course, sometimes you have an epiphany, but for me, it was very gradual. Oh, okay. I see. So now the audience is wondering, okay, so what is causal set theory? Sure, it takes into account the causal structure, but then what is it? I would say there are three pillars to causal set theory as an approach to the problem of quantum gravity. And they're all equally important. So they go together. And you can start at any one point and somehow get to the other

two. So I'll just say what the three are. So one is that space-time is fundamentally discrete or fundamentally atomic or granular or pixelated or any of those, you can use any of those words or concepts. So that means that any event in space time, say this whole podcast, that's an event. It has a duration in time and a location in space. Of course, today in modern physics, we don't separate out spatial location and time duration. It's all just one region of four-dimensional space. So there's some event like this podcast. That can be broken up into sub-events. So a sub-event like the first half of it, or the second half, that's two sub-events. And you can keep dividing it so you can divide it into the part of the podcast that involves me and the part of the podcast that involves

you. Sure. So you can keep dividing it into smaller and smaller bits, smaller and smaller events, smaller and smaller sub-events. Ah, I see. Yeah. And, you know, so I can do that. And that's a little piece of the podcast.

So that's a sub-event. But that can be divided into itself into sub-events and sub-events. In general relativity, there's no limit to that subdivision. There's no smallest event until you get to the points of the continuum. And then those events, you could call them point events. So the whole podcast event is made of these point events. But in causal set, there is the hypothesis is that you can't subdivide the podcast event into arbitrarily many sub events.

It's actually made of finitely many atomic events. You can roughly work out how many of these atomic events there are just by measuring the space-time volume of the podcast, which would be in plank units. That that's a four dimensional space time volume, roughly how long it lasts in plank times, how big it is in space in plank length cubed, and then work out how many plank volumes that is. And that will be the very large number, and that will be the number of atomic events

that can compose this podcast event. And that's true of everything. Okay, so if you were to divide space, not space-time, into discrete units, you have problems with Lorentz invariance, because then you could just boost and then you would have a different smallest unit. But if you have space-time, somehow that's different? If you discretize space-time itself. Yes, yes, yes. That's the key thing. So many people think that discreteness is incompatible

with Lorentz invariance because of exactly what you said, that they think of discretizing space, three-dimensional space. If you discretize space, as you say, the Planck length is not a Lorentz invariant concept. But space-time volume is a Lorentz invariant concept. So some region of a particular space-time, four-dimensional space-time volume, if you boost it, it remains that volume. It doesn't change. It's a Lorentz invariant concept. So if you discretize space-time into atomic events, rather than discretizing space into bits of space, if you discretize four-dimensional space-time into atomic events, then you have no problem with, well, at least it's, it then becomes possible to have a discreteness that is Lorentz

invariant. So is the continuum still present implicitly in the notion of volume? No. I mean, volume emerges from the discrete underpinning. So the idea is that volume is a count, what it actually is, is just a count of the number of space-time atomic events that comprise that region of space-time. Volume is what it seems like to us at the emergent level, at the level of the continuum approximation. It appears to us in our continuum approximation Theory, which is GR, our space-time volume. What it really is in the deep theory is just the number of atomic events.

So, it's like if you have – this is an example that Rafael Sorkin, the physicist who's the main champion of this approach to the problem of quantum gravity. He uses an example of an ingot of gold. So it has a certain mass, but what the mass is, it's just counting the number of gold atoms in the ingot. So that's- I see. So it seems like it's a continuum thing, but really it's a discrete thing in the atomic theory.

You used carefully the word continuum approximation, not continuum limit. So why is that? What would be the difference between those? Oh, that's crucial. So yes, so in causal set theory, I'm still on the first pillar, remember? Yes. In causal set theory, the discreteness is fundamental. So the scale, the Planck scale is a theory which well describes the physics at when there are very, very large numbers of space-time atoms.

So, it's an approximation to the underlying theory, just like fluid mechanics is, and say the Navier-Stokes equations of fluid mechanics, they're an approximation to the underlying molecular theory of the fluid. So the molecular scale is a real physical scale. You can derive the Navier-Stokes equations by taking a hydrodynamic approximation to the underlying physics, but the theory is not a continuum limit because the molecular scale is real. The molecules are not actually physically getting closer and closer together. They're just more and more of them. It's

the same paradigm for causal set theory. We want to derive general relativity as a continuum approximation to the underlying discrete theory when we're in a situation where space-time is large, there are lots and lots of atomic events, but not infinitely many. So it's crucial that the continuum approximation is the concept here. I understand. Okay, now you mentioned you're on the first pillar, so there's the second one. Please. So the second pillar is that causal relations are the fundamental degrees of freedom, physical degrees of freedom, if you like. So the causal, the proposal is that the causal structure of space-time, that is this information about, in GR, which is this information about which events can causally influence which other events,

that survives in the deep theory. Some things will not survive. The manifold structure, the continuous manifold, the metric, they don't survive. Those concepts are not there in the deep theory. Topology, that doesn't survive in the deep theory, but what does survive is causal order. These space-time atoms, they are the elements of this discrete space-time. They're the elements of the set, the causal set that space-time really is, and They have an order relation on them. They maintain, they keep this structure of being causally ordered. You can say, take two elements of the causal set, two space-time atoms, then they will either

be causally ordered, one will precede the other or the other way around, or they won't be ordered. This order is a partial order. In the deep theory, the causal set elements have this structure, just as the point events of space-time in GR have the structure. Those things are maintained in this correspondence between the deep theory, the discrete theory, and the continuum approximation. This causal order is the same concept in both the theories, the deep theory and the continuum approximation, and GR, the continuum approximation. Sorry, what is the deep theory?

Causal set theory. Okay, got it. So I don't know whether that underlying theory is the... Oh, I see what you're saying. I see what you're saying. Okay, okay. I don't know whether that underlying theories or the... Oh, I see what you're saying. I see what you're saying. Okay, okay. Like the ultimate theory, the one that gives rise.

Yeah. The more fundamental one. Ultimate might be too strong, but maybe deeper theory. You're not Stephen Wolfram. I see. Yeah, so it's, I don't know what, maybe deep structure. So the deep structure of space-time is a causal order. Okay.

So that's the second pillar. So, so first pillar is discreteness, atomicity, finite, that there are finitely many atomic events in this podcast. in this podcast. The second thing is that the fundamental degrees of freedom, the fundamental physical structure is an order relation, causal order before and after. The third pillar is that the quantum theory of this entity will be a pass integral quantum theory. So the quantum theory of causal sets will be based on the pass integral or the Feynman sum over histories. That's a sort of synonymous phrase for pass integral, Feynman sum the histories. That's what we will have to base our quantum theory of causal sets upon. That the canonical approach or the canonical theory where there's a, a state

vector in a Hilbert space is not, will not fundamentally be what the quantum theory looks like. So just for people who are taking quantum field theory, they know firstly, they learn about the canonical quantization and then they learn about the path integral quantization. They don't often learn that there are other types like geometric quantization and loop quantization and stochastic quantization I believe. Maybe there are more. I've never seen if there's a proof that says that these various quantization approaches all give the same answer. Are you aware of that? It depends what your questions are, for whether or not they give the same answer. So there are questions that you can ask such that geometric quantization would give a different

result or theory than the path integral quantization. I'm not sure. I don't know how to answer your questions, that specific question. But for example, if one were to compare the canonical quantum theory of just like ordinary quantum mechanics, non-relativistic quantum mechanics and the path integral, then depending on the question that you ask, you can prove that they are equivalent. You can derive the results that you would get from the Copenhagen interpretation of the canonical theory. You can derive those using a path integral to basically construct a propagator to evolve the state vector in time. The path integral gives you more, or at least it holds out the hope, it holds out

the promise of being able to solve the measurement problem. In other words, it holds out the promise of being able to make sense of what's really going on in a quantum theory when there's no external measuring device and no external apparatus and no external observers and no measurements going on. So it all depends on your question. So you can reproduce the Copenhagen predictions using a quantum, using a path integral, but it contains a whole lot more information. And the question is, can we use that? It holds that promise and I can't say that we have achieved this solution of the measurement problem. But it sets out a path towards a direction to doing that. To my mind, that's crucial for quantum gravity because

the canonical approach, the Copenhagen interpretation, they rely on there being measurements, measurement situations. The places that we really want to use our theory of quantum gravity. The very early universe, very close to the Big Bang inside, very close to the singularities of black holes. There are no measuring, there's no measuring going on there. There's no measuring device. There's no measuring going on there. There's no measuring device. There are no repeatable numerous trials where you can. It just doesn't, the Copenhagen interpretation is just,

simply can't be applied in the situations where quantum gravity is really relevant. To my mind, we're forced to confront the problem of what people call the problem of the foundations of quantum mechanics. The path integral approach is a understudied and somewhat neglected approach to the foundations of quantum mechanics that I think holds out this promise of being able to say what's really going on. So we'd be able to use it to talk about the early universe, even in the absence of measurements. So given that you're interested in the foundations of quantum mechanics, does causal set theory have anything to say about Bell's theorem or the inner workings of some effect that

appears non-local? I also understand that there are various ways people use the term local and thus there are various ways people can use the term non-local. So you can feel free to outline those. Yeah, sometimes the same person will use them in different ways. One moment and then the next moment. Yes. Good.

So, it's my view that quantum mechanics is non-local. So the import of, what should we call them? Thought experiments or thinking around situations like the EPR setup and other sort of what you might call logical contradictions, logical antinomies that arise in quantum mechanics. The Bell's theorem and the Bell inequalities are a little, they're subtle because they don't quite, I don't know quite how to think about them because they involve probabilities. And when anything that involves probabilities embroils you in the question of what probability is.

Yeah. Anyway, but you don't need to think about, in order to be confronted with the conclusion, or confronted with evidence that quantum mechanics is non-local, you don't need the Bell inequalities themselves. There are these other logical contradictions to classical rules of inference. One of them is something called the GHZ setup. That's Greenberger, Horn, and Zeilinger setup where you have three spin-half particles in a particular state. And you can set things up so that the prediction that you would make using classical rules of inference is exactly contradicted by what you would measure if you actually do the experiment. It's a one-shot experiment rather than having to gain probabilistic information. Anyway, it's my view that quantum mechanics is non-local, but it's not non-local in space.

It doesn't imply that there's superluminal influence or what Einstein referred to as spooky action at a distance. He meant spooky action at a distance in space. I don't think it implies that it doesn't imply that. It implies that there's a non-local influence in time. It means that an event can influence something that happens in the future without influencing intermediate things. Okay. So that the influence is not local in space-time. It's non-local in space-time, but it's still causal. So the cause, the effect of the cause is still within

the effect of light. That's still the case. But the influence doesn't propagate locally in space-time, but jumps, if you like. Okay. And it can only jump to the future. Yeah, and it can only jump to the future. And is there a limit to how far it can jump? No.

Okay, and is that necessary? So in other words, when something is non-local, is it necessarily infinitely non-local? Like is there a degree of measurement to non-locality or is it zero or one? Like it's all the way or none? Um, I suppose we don't really know fully because we don't have our theory of quantum gravity, but if one takes the lessons of quantum theory as we know it and causal set theory, which is a non-local theory, then there is no limit to how far into the future the effects of a cause can manifest itself. So I would hazard that, yeah, I mean, it has to be finite, but arbitrarily far into the future.

I see. This word quantum theory comes up over and over and it would be great to just define when someone hands you a theory, how do you know if it's a quantum theory? Like what are the necessary and sufficient conditions if there's a consensus on that? Is it h-bar you have it or is it just non-commuting observables? Like what is it that makes a theory a quantum theory? So in the past integral, from the path integral perspective, you can think of the path integral quantum mechanics as a species of a more general type of theory called a measure theory. So in a measure theory, there are events, things that can happen, and then there's some measure on those events. In a classical theory, that measure would be a probability measure.

So each event has some probability of it happening. And in a quantum theory, there is again a measure for each event, but that measure is no longer a probability, or not necessarily, it's a probability. What it actually is, well, that's the whole then welcome to our world of trying to figure out what it actually is or what it means or how to interpret it. But it's a measure that when you calculate it, you can see there's interference between histories. So the probability of an event in a classical theory is just you just add up the probabilities of all the histories in that event. So all the possible ways that that event can happen, you add up the probabilities of all those

ways and that's the probability that the event happens. In quantum theory, roughly speaking, you take all the histories that make up that event and then each one has an amplitude, not a probability. You add up those amplitudes and you square it. We take the mod squared, roughly speaking. It's that squaring which is the quantum. That's where you see the quantumness because that gives you interference. It gives you the signature of quantum mechanics which is, say, the fringe patterns of the double slit experiment. It's interference between histories when you calculate the measure of an event. That's quantumness for me. Yes, I see. I see.

Was there some landmark result that came from causal set theory that convinced you, wow, we're on the right track? So for instance, there's something about Hawking radiation or the entropy of a black hole or anything that has discreteness solves some of the problems with the path integral because you don't go all the way down to zero. So you don't get these UV divergences. So that's a win, but there are other discrete approaches to physics as well. So it's not a unique win, which will also get to causal dynamical triangulations

later. But the point is that what was along your journey in studying causal set theory and developing it? What was some result that led you to feel, okay, man, this is super cool. We're on the right track. A few things, but one that's particularly nice or fun to recount is the discovery of the accelerated expansion of the cosmos. So that was when the measurements of distant supernovae and their luminosities showed that the universe, the equation of motion of the expansion rate of the universe had to be modified by adding what is known by various monikers. One is dark energy, another is the cosmological constant. So you have to add a fudge factor to the so-called Friedman equation for the expansion of the universe in order to account for these supernovae results.

It's nice you can go onto the Nobel Prize website and there's little clips of the three people who won the Nobel Prize for that discovery and And they all say, they thought it was preposterous and they all delayed releasing their results because they thought they must've made a mistake. They all said that, all of them. They said, oh, it's clearly a mistake. We better go back and check. It'll go away. Of course it didn't go away.

And then they won the Nobel prize. So, so that fudge factor is real. I mean, you need to add that to the equation. And it's a mystery what it is. That's the puzzle of dark energy. But what was nice for us working on causal set theory was that Raphael Sorkin had predicted that this effect should be there, that there should be this accelerated expansion and he predicted

the order of magnitude using basic ideas from causal set theory, basic expectations of what a quantum theory of causal Set Theory will look like. It's kind of a back of the envelope calculation. It's a heuristic calculation. It's not something we can, because we don't have a Quantum Theory of Causal Sets, we can't rigorously show that or derive this result. But it's so sweet. When you make a prediction in advance of the measurement of the observation and at a time when no one wanted or expected it or everyone simply assumed that the cosmological constant was zero and it was only gradually that certain cosmologists were starting to say, well, actually our cold dark matter cosmological model is not really fitting the data anymore.

We might need to add a bit of lambda, a bit of cosmological constant just to fit cosmological data. from cosmological data. That started before the supernovae results. But Raphael's prediction was even before that. So we were getting excited because the cosmologists were starting to say maybe we need this cosmological constant. Not too many people were taking that up, but it was starting to happen. It reminds me a little bit now of the situation with the Hubble tension. Yes. How so? Well, at first, of course, you know, at first it was sort of a mild tension. Now people are saying that it's a tension at the level of five or more sigma.

So it's a real, you know, it's a real... There was something that was just released on that, like within a week ago, about how with the new James Webb telescope data, some other research team has found that the tension disappears. I haven't looked into it, but it's within a week that this came out. I better look that up. I like tension. Yeah, exactly.

I hope it doesn't go away. Anomalies are interesting. Yeah, there's something to understand. So when Raphael did that calculation, did he have to put in any matter? No, it doesn't. Well, there is matter in the model. I mean, in the cosmological model, there's the usual matter. But what Raphael's model and idea cleverly does, it means that the cosmological term, the cosmological

constant is not a constant, just like the Hubble constant is not a constant. So it's a parameter that, so the cosmological, so lambda varies, it's not a constant. In fact, it fluctuates, it fluctuates throughout cosmic history between positive and negative values. But the envelope of the fluctuations always tracks the ambient matter density. Sometimes people call these tracker models. In that sense, it solves this why now problem. The why now problem is why is lambda, this is dark energy, why is it starting to dominate the universe now? So the transition between matter domination and lambda domination is happening now. Why is that?

Is that a tuning problem, if you like, for the cosmological model? So the lambda has to be just so, so that it's just coming to dominate now. But in Raphael's conception, it's always true. So that another phrase that he and his collaborators coined for this model is ever-present Lambda. So it's always the case that the expected value of lambda is of order the plus or minus the ambient matter density. Anyway, it's very hard to express just how powerful or influential amongst thinking that experience of having a prediction in advance of the actual observation is. It's, yeah. Wonderful.

So instead of saying, well, there's this data we need to explain, let's go make our model explain it, you predict something unexpected. Yeah, like a retro-diction. Right. Yeah, you've done a pre-diction, got it, yes. Yeah, genuine pre-diction. So that was fun. That was a red-letter day for us. Wonderful. And are there any technical difficulties, I know you mentioned technical difficulties can be overcome, but are there any technical difficulties

with a varying cosmological constant? So the way that general relativity is derived, at least one way is you just vary the action of R, like the Ricci scalar. And then you can also plus a constant. Okay, but if you were to plus a constant that is not a constant anymore, it depends on something then does just that introduce a different degree of freedom?

Is there something else that becomes incompatible? I don't know. The model is very, it's not GR and it's not, it's not local and it's not, it's not of the same sort as just fiddling with the Lagrangian and producing a cosmological model like that. It's genuinely stochastic. Raphael's original conception is that the fluctuations of lambda are quantum. Now the model that he and his collaborators have come up with that realizes some of these ideas is actually classically stochastic. So the, the value of Lambda is it, it's like a noise, you introduced

this noise term, this fluctuation. Yes. But it's classical noise, classical fluctuation. I see. So that's why you use the word expected value of Lambda earlier. Yes, exactly. So it's very unusual and different kind of a cosmological model. So it raises all sorts of questions about how to judge whether the model is doing well or not doing well. So I said, for example, that

the lambda can be positive or negative. So the value that we measure today is actually positive. But the model equally predicts positive and negative. So it could just as easily have been negative. It just happens to have been positive. Well, the string theorists would love it if it was negative. They would have loved it. Yes. It just turned out not to be so, but it could very easily have been negative according to this, these ideas of Raphael's. And in fact, in 50% of the models that when you run them.

I see. So it's directly centered at zero. Yeah. The mean is zero. Yeah. The mean over the runs is zero. So that's, that's, um, a question, right? How many, what proportion of the runs have to give you what you see in

order for you to say this is a good model. That is a question that I think is very difficult to answer. Yasemin Yazdi and her young collaborators, including my student, have been probing this model further, trying to see whether it can cope with the precision cosmological data sets that we have today. So CMB, the supernovae data themselves, can ever present lambda cope with those? Can it reproduce those? And so the question arises, let's run the model, see whether it produces a universe like ours. So how many, out of how many runs do you need to get a universe like ours for you to say, yes, this is a good, this is successful? That's the question that arises in this framework.

So I think we don't have, we don't know how to answer that. Fei, do you happen to have a preferred interpretation of quantum mechanics or a favorite one? Well, I mean the one that works for the lab is the Copenhagen interpretation. And I think that one can derive it with the assumption that there are measuring devices and observers and all the paraphernalia that you need, you can derive it whilst treating the experimental apparatus as part of the quantum system. So you don't need to treat it in a different way. You can put everything into the quantum system. It's all in all the, all the histories and the sum of the histories. I mean, they're very big and fat, these histories, they contain all the information about what

all the particles in the lab are doing. But you can put them in and then heuristic hand waving that everyone believes will produce for you the predictions of the Copenhagen interpretation. So without having to require that outside your lab there's a super observer looking at the observers who are in the lab. So you can, I think, solve what people call the Vigna's friend problem or this problem of infinite regress using the path integral. So the path integral out does Copenhagen. And in fact, I think it's fair. I think it's reasonable to claim that, that, um, that the Copenhagen interpretation can be derived from the path integral. Is this a theorem or a result that people can look up?

Yeah, it's not a theorem because you can't actually do any of these calculations because the system is just so huge and too complicated to actually do the calculations. It's the same kinds of calculations that people have done when they show that a macroscopic object is decohered very quickly by cosmic micro background photons or that sort of thing. So it invokes the same... Sorry, what I meant was, is there an article or something people can look up to learn more about this? Because plenty of heavy lifting is done by the word measurer.

But you're saying we just throw in the measurer and we... Yes, just throw them all in there, throw them all into the quantum. So I, there's no paper as such, but so I would point people to Jim Hartle's memorial conference, which took place to honor Jim's contributions to physics. It took place in Santa Barbara this last February. Okay. I mean, I recommend all the talks that were given at that conference. So you can find them on the Kavli Center for Theoretical Physics at Santa Barbara website. So just look for the Jim Hartle celebration conference. All the talks are great. I gave a talk on Jim's contributions to foundations of quantum mechanics. So Jim is one of the few people who has really advanced the use of the path integral for

quantum foundations. So his approach to quantum foundations is called generalized quantum mechanics. It's based on the path integral and I sketch out the argument that, which is based a lot on Jim's thinking, that the Copenhagen interpretation can be derived in a completely quantum way with everything in the system is quantum. And yeah, so I haven't written it down, but that's it in there. Okay. So the link to that will be in the description and you can check it out if you're watching or listening to this.

Click on the description. The claim, however, is that you can go beyond that. So Copenhagen and this, what I've just talked about, this derivation of Copenhagen from the path integral, they assume that the only things you're going to talk about are measurement events or instrument events or pointer positions or macroscopic events. So if you assume that, then the path integral will give you the same predictions, the same probabilities as the Copenhagen interpretation. But the path integral can, it has the potential to give you a lot more because you can calculate the measure of microscopic events.

So events that the Copenhagen interpretation is entirely silent about. Copenhagen doesn't say anything about the probabilities of micro events. It just tells you about pointer positions and measurement outcomes and readouts of, you know, if you're on your computer screen and so think macro events. But the path integral contains information, it contains the information about the measure of micro events and the struggle that we face in furthering this project of founding quantum theory on the path integral is what to do about those, how to make predictions about micro events. And I can sketch what the answer is that we have so far, but I can't give you the full

story because we don't know what that is. Sure. Why don't know what that is. Sure. Why don't you sketch it? So the question is, what is the world? What corresponds to the physical world in a quantum theory? What corresponds to it? There's lots of stuff machinery in the physics, in the maths and the physics that you're writing down on a piece of paper. So what amongst all of those things corresponds to the world? And what corresponds to the question of the following sort. Did this event or if you like,

if you want to make predictions, will this event happen or not? Uh-huh. So suppose we want to fully describe the physics in some lab yesterday. Then we make a list of all the events and they can be microscopic or macroscopic. It doesn't matter, just all events. So, for example, the electron went through the left slit of a double slit experiment.

Okay. Or... So a possible world, basically anything that's a possible world or a possible event, but it excludes impossible ones? Well, it depends what you mean by impossible. It's everything that's conceivable according to what you have decided are the histories of your system. The first thing you have to do is write down all the histories of the system. A history is an in principle, finest-grain description of the whole finest-grain description of the whole system, a history of the whole system, so from some initial time to some final time. So in principle, what's the finest detail that you can get on

this system? So if it was n-particle quantum mechanics, it would be just the exact trajectories of all these n-particles between the initial time and the final time. That would be a history in this theory. An event is just some statement about those trajectories. It could be that trajectory five passes through this space-time region and trajectories seven and eight pass through that space-time region. That's just some statement about the history of the system. That's an event and it could happen or not happen. That's the concept now that I'm proposing. So in the world, after the system has run its course, the actual world corresponds to a list of all the events. So each event either happens or doesn't happen.

So there's just a yes and no for each event. You ask for each event, did it happen? And it's either yes or no. And the list of all of those yes or no answers, that's the world. Yes. Okay. So there's a joke, which is that it's a Wittgensteinian concept of reality. The world is everything that is the case. It's just a list of the events that have happened. And then complementary to that, everything that's not in that list of things that have

happened didn't happen. So in the Wittgenstein case, there's a tautology. So do you see a tautological aspect to the quantum definition of the world that you just outlined? No, because you have a model. That's the crucial thing, which I think Vickensheim doesn't have. You have a model of the world and your model is very rich already. So you have done, you have done a lot of work already. So you, as a physicist, you, the phys, you know, you've to get to this point,

you've already said that your system has these histories. The basis of your, the kinematical basis of your theory is this set of histories and that's work. You have to, well, why those histories and not these ones? Why are they trajectories and not fields? Which fields? So you've got to do a huge amount of work first, intuitive, careful, scientific, creative work to come up with your list of histories, your set of histories that go into the sum over histories for your theory of your system. Once you have that, you've already got a lot and then you have a list of events. Right. So it's not just, you know, if you've decided that your histories are all about trajectories,

then you can't, the events that happen can't be about fields and vice versa. So it's not, it's not tautological because, because you have your list and that it's not tautological because you have your list and it's not just any old thing. It's not like saying a table is a table or anything goes or it's not like that at all because you have a theory. So that's what a lot of, yeah, well, so Wittgenstein missed, he was missing that. Where does consciousness fit in, Faye? I don't know whether I was hoping you would ask me that and I was hoping that you wouldn't ask me that.

Yeah, so I wrote a paper about consciousness, which surprised me. Yeah, I didn't expect that. Well, you mean to say you didn't expect to start writing the paper on consciousness, or you just were surprised when you wrote it at the end? Oh, there's a paper on consciousness here. Yeah, just somehow it just was there and hadn't been there before. I was surprised that I found that I had something to say about it. So that was what was unexpected. And I found that I had something to say about it because it struck me that the framing of one of the central debates that I see going on or witness going on just

from the outside, I'm not party to these debates, about consciousness was very, very similar to a debate about the nature of the passage of time, which I am more, and then again, I'm not a philosopher, so I'm not part of the community of philosophers of time who talk about these things. But I do talk to such philosophers and participate in meetings on the nature of time as a physicist. So it struck me that the same debate, sort of central, what I consider to be the sort of central debate was really happening in both these two arenas. And I have come to the conclusion, or at least let me say, I would like to propose or put out there for people to think about that they're the same debate. The debate on consciousness and the debate on time is the same one?

Yes. And sorry, just a moment. When you say the debate on time, are you referring to the arrow of time or something else? Something else. So the question of whether the passage of time is an illusion or whether it's physically real. I see. Okay. Now you're going to have to justify why are those two the same?

Okay. So that, that is a debate I claim in the philosophy of time. So you can find, I can find you some thinkers who come down on one side or the other. But the debate that I noticed happening in philosophy of mind, let's call it, I suppose, or philosophy of consciousness was the question of whether consciousness is real or an illusion. I think people, a misapprehension or some misunderstanding about it that means that there's no hard problem of consciousness. So either there's a hard problem of consciousness or there isn't because consciousness is somehow not what you think it is or it's an illusion in some way. And that's this, I claim, mirrors the debate about the nature of the passage

of time. So either the passage of time is real, physically real and not accommodated within our current physics, let's say. Or it's an illusion, it's something to do with psychology or something that doesn't, you know, it's not, it's not, there's nothing to explain. There's no physical passage of time. And I claim they're the same debate. I don't want to spoil the punchline, but it has something to do with a process versus a state, if I'm not mistaken. If I am mistaken, correct my mistake, please. So I'd like to contrast not process and state, but rather process and event.

Sure. So, I want to make the distinction, which seems kind of pedantic or foolish or just a sort of... Well, pedantic distinctions is 95% of philosophy. So, you're well in the philosophical domain. Like to make a clear distinction between an event and the occurrence of an event. An event is something you can write down on a piece of paper. It's something that you can write down on a piece of paper, it's something that it's like saying, rain in London between noon and 1pm yesterday. So I think that's an event. But the occurrence of the event is a dynamical process

and that's true of all events. So I want to encompass this discussion in the first instance or I'd like to locate it in the first instance within general relativity. So, which is great because the language of general relativity is all about events, space-time events, the event of this podcast, the event of your breakfast this morning. So that's it. It's something which has a space-time substrate. Yes. And I don't see process in that, at least in the general relativistic description. So in the general relativistic description, there is no process. There's just events.

That's right. I see. So when you go discrete, so now let's move the debate or the discussion, let's move the discussion from general relativity to the deeper theory, in other words causal set theory, or let's say the speculative proposed deep theory, causal set theory. Now every event is made of these finite and many discrete atomic events. I propose that the process of the happening of the event, which is made of these atomic events, the process of the happening, the occurrence of that event, is the coming into being of those individual atomic events in what Raphael Sorkin calls a birth process. So it's

a process. So for each event, each atomic event, each space-time atom, it's not there and then it is there. So it's born. And that's the process of the birth of these space time atoms. I see, I see. All of them together, that's the occurrence of the event. Is that a mathematical statement or is that the interpretation of the math? I'm not sure. Maybe you can tell me. There's a twist here which is kind of crucial to this proposal that this is what, this has anything to do with consciousness now. Which is that, so an event I claim, this non-dynamical thing, this, you know, your breakfast this morning can be fully laid

out, written down, pictures drawn of it on a piece of paper, and it can be shared. You can lay it out, maybe mathematically, and you can hand it to me and I can hand it to you. We can talk about it. We can do physics using these descriptions of events. But they're just events. So to use some continental philosophy words, there's just being but not becoming. Yes, that would be a reasonable, I like that. Okay. The becoming or in other words the occurrence of an event is the birth of the space-time

atoms that comprise that event. That birth process cannot be captured objectively externally, not even in a movie. And the reason is that the atomic events that comprise the event of your breakfast, they are partially ordered. So that means that some of the atomic events have no order. There's no relation between them. There's no causal relation between them. And there's no fact of the matter about whether this one happens before this one or this one happens before that one. They're just not ordered. There is no order in which they happen. But that makes it very difficult to conceive of this process actually happening dynamically because when you imagine this birth process, at least when I imagine it, maybe you can, when you imagine this birth process, there are these atomic events. Think of them as dots. So the dots are, you know, they're appearing. But if it's a dynamical process then they're appearing kind of one by one. But then the two events which, the two atomic events which are not ordered cannot appear

one before the other. Object, because there is no order in which they appear. They don't appear, they don't come into being in an order. They're unordered. This seems to complicate the problem of time. Yeah, it does complicate the problem of time. It's like you're digging the hole deeper rather than getting yourself out of it. Well, okay, so let's see what that has to say about conscious experience. So the proposal is that conscious experience is the occurrence of events which are neural correlates of consciousness in the brain. So let's, we have some subject,

let's call them A. So A is the subject and they have their events happen. There are events in their brain which are clever, our clever colleagues have identified as neural correlates of conscious experience. So there's some neural correlative of being conscious of seeing a stop sign or something, some conscious, you know, some sense experience. Sure. And there's some neural correlates, which it's some event in the brain of A, the subject. some event in the brain of A, the subject. So the proposal is that that event in itself is not consciousness because it's a dead thing. It's just something you can draw on a piece

of paper and hand around. So there's nothing alive about that. There's nothing that has any of the qualities of conscious experience about that event. But the occurrence of the event, this coming into being of the space-time atoms that comprise that event, that's what conscious experience is. That's the correlate of conscious experience. The event itself is not the correlate. It's the occurrence of the event that's the correlate of conscious experience. The event itself is not the correlate, it's the occurrence of the event that's the correlate. And now the fact that you cannot imagine this dynamical correlate is actually a good thing because it explains certain features, certain qualities of conscious experience. Because you can understand why you can't know what it's like to experience seeing a stop sign just by knowing the event. If you know the full neural correlate of consciousness

theory, you know what that event is. You can write it down. You say, here it is, here's the new, and you can test it. You can go and induce this event to occur in someone's brain and ask them, do you see a stop sign? And they say, yes, then you know that that's, but it doesn't explain what it's like, but you can't explain, you can't understand what it's like externally from the physics, external to the system, because the correlate of actually having the experience is this process of the birth of the space-time atoms. It cannot be written down. You can't make a movie of it. You can't even imagine it in your own head. So you just can't know it. But you can experience it. So what conscious experience is, it's an internal view. So you can experience it if

you're internal to the system. You can't know it if you're external to the system, but if you're part of the physics, if you are part of the system, physically part of the system, then you can have that experience. So, you can know it directly and without mediation. So there are these qualities of conscious experience that people sometimes list. I mean, there's debate presumably about whether these are accurate or meaningful. But if you take them as being meaningful, then you can understand them because they arise because what experience is, is this process. So for example, the process of the birth of space-time atoms is unceasing. So the quality of conscious experience is that it's, it's live. You can't stop it.

You can't say, oh, hold that thought, you know, and just have a break from it. It's just, it's, you know, it's ongoing. So is the moment of now something that is illusory or is real? It's real. It's real. It's the, but it's, but it's not a thing. It's a process. It's the process of this birth of the birth of space time atoms that is now. Both the process and the thing, aka the events, are real. Yes. I didn't put it in the paper because I thought it was a bit risky, which is to say it's a kind of dualism, that there are two types of thing.

Yes. People don't like that. No, they don't like that. That's why I didn't say it. There's the stuff, there's physical four-dimensional stuff, that's space-time trajectories, world lines of atoms, field configurations, four-dimensional stuff, then there's the process in which that stuff comes to be. So they're very different types of thing, but they're both physical. The birth process is objective. The stuff is not objective because there's an arbitrary

subjective cutoff that you impose if you want to talk about space-time, space-time up to when. As a physicist, you just put on some arbitrary space like hypersurface and space-time is real. So the description of the physical stuff has a subjective element to it, but the process is completely objective. The struggle that one has with the process is that you can't view it from the outside. Physicists would love to have a God's eye view of the world, to see the world there, over there in the corner, the whole thing. You can't do that. The only way you can see or experience or apprehend the process is to be inside it. So there's no God's eye view in this conception. Super interesting.

Of the world as it is. But then there's all sorts of nice consequences of this, all sorts of things that feel right about consciousness that are just natural because they're properties of the process. So this idea that it's somehow private and somehow unshareable with someone else. That's because you can't copy it. There's no objective external view of it. So I can't make a copy of it and hand it to you and you see, ah, yes, that's it. Only I can experience it. Now, when you're saying you can't copy it, my mind thinks in terms of the no cloning theorem, but that's not what you're referring to, is it? Okay, Faye, explain to me the experience you had of coming up with this view.

So was it something that occurred gradually, or was there even a single epiphany? No, it was gradual and I changed my mind and I became more, I made it more forcefully as time went on. So at first I just said, well, there's some connection. And then I just said, oh, let's go bold. Let's just say it's the same. let's go bold, let's just say it's the same. So that conscious experience is the process of the birth of the space-time atoms or the atomic events that make up a neural correlate event. So I became bolder as I went on. And I talked to a lot of people and a lot of people were very helpful about what I should think about, what it could and couldn't do. So for example, I was reading, so yeah, certain things, so I had so many drafts, so many writings that just went straight in the bin.

How long did it take? For the first draft that went, that I put on the archive, um, maybe six months, but then I was giving talks and revising it due to people's feedback, which was super helpful. During those six months, was that almost exclusively what you were working on? I was doing a few other things, but I was a bit obsessed by it. So, okay. So then six months is more reasonable because that's quite quick. Did you also touch on the subject of free will? No. Is that something you're saving? I don't have anything to say about it.

I don't, because I don't, I mean, I don't believe in it in some way, whatever. All right. So before we close, Professor, there's another professor named Tijinder Singh. And he had a question for you. He wanted to know, should gravity or gravitation be unified with other forces? Hmm. I don't know about should, but it would be lovely. I mean, it would be, you know, that would satisfy, That would be so satisfying. So I asked Tijinder, what do you mean by unification? Because there are various sorts of unification. Sure, for sure, for sure. So one way that this unification might happen is that everything is space-time. Even what we conceive of now as being separate from space-time as being matter that lives in or on space-time, as a sort of decoration

on space-time. It might be that everything is space-time, so that seems a bit far-fetched, but there are ideas out there which are, you know, super attractive and people find super attractive and I would like to feel that they're part of the final answer. Not final, bad choice of word, part of some kind of advancement, some progression, some progress. Sure, sure. So, Kaluza-Klein theory, for example, Kaluza-Klein theory is a mechanism for how gauge fields can be just manifestations of gravity in higher dimensions with certain compactified space with certain symmetries, then you can hope that gauge theories will

arise in that way, that other bosonic fields could arise in that way. And then as for fermions, well, they're harder to imagine arising from gravity. But there is a paradigm for how you could get fermions from purely gravitational degrees of freedom. And that paradigm goes by the name of topological geons. And the idea is that particles are, their excitations, topological, their excitations of the gravitational field on space times in which space is topologically non-trivial. So you could have little wormholes or more complicated topology of space. And then the gravitational field, there are collective degrees of freedom of the gravitational field associated with this topological non-triviality and you can quantize them as fermions.

Even though that the field is fundamentally bosonic, the quantization of that, there can be a quantum theory of these collective degrees of freedom in which quantize them as fermions, even though the field is fundamentally bosonic. There can be a quantum theory of these collective degrees of freedom in which these particles are stable or approximately stable, stable for long enough and have fermionic statistics and spinorial spin. It's a beautiful idea, goes back to Raphael Sorkin and John Friedman. We haven't realized that, but the potential is there, the hope is there, whether or not it will bear fruit in the future, I don't know. But that would be, I mean, I said that my journey in physics began with general relativity and just loving space, time and gravity. So if everything is space time, then that would be, that would suit me very well. I would

love that. And it also was Einstein's, as he finished general relativity, he was trying to find a way to make particles just space time, that they're only space time. Probably including also the electromagnetic field, but yes. Yes. Yes, that particles are, yeah, they're configurations of the field. So I don't think he, as far as I know, I don't think he considered the possibility

of topological non-triviality in space. No, I don't think so. So a difficulty I have in the path integral, summing over geometries, or I guess some people call it summing over histories, is that a spinner is a section of a frame bundle, sorry, a section of a spin bundle, and then the spin bundle requires a spin frame bundle to be defined,

which itself requires a metric. And you need that because they're orthonormal frames. So if what we're saying is we're going to allow the metric to completely vary, then it's unclear to me what a muon or an electron is when the basis of its definition is a metric. So do you also see a tension there? Yes and no. I mean, it may be that they're not, those concepts just aren't there in the fundamental theory and that they arise at some stage as we go through levels of effective theories, that they arise at some higher level of understanding after we have achieved the continuum approximation.

If we can derive a continuum approximation in which GR is a good description of space-time, at that stage you do have a tangent space. You have all the structures that you would need to the structure that you would need to have the spin structures that you're talking about. So yeah, it would be nice to be able to have a better… We don't do very well with putting matter degrees of freedom on causal sets because of the problems that you just mentioned. Because there's no continuum, there's no tangent space, we don't even have vector fields, for example. We can do scalar fields, but beyond that, we don't be asking for that to be the seeds that are already there. You can see the seeds of how matter is going to arise. Maybe we need to, you know, I mean, there's a long, Planck scales are very far distant

from any scales that we have probed so far in physics. So there's a lot of space in there for lots of stuff to happen. So yeah, it may turn out to be a failing of causal set theory that matter, it really struggles to account for matter at all. But it may turn out that it's possible to account for it at some intermediate level of some regime, let's say. So if causal sets is the deep theory, then above that you'd get the continuum regime. And then in the continuum regime, then you can see a matter is going to arise. Yeah. So my second last question is that there's a conceptual harmony between causal set theory

and causal dynamical triangulations and that they both attempt to understand some quantum nature of space-time by discretizing, focusing on the causal structure. But other than this, do you see them as incompatible? Do you believe one will be the limit of the other or you see some way that they predict what's opposite or both can't be correct? So, a fundamental difference between causal set theory and causal dynamical triangulations, as I understand the latter, is that in causal dynamical triangulations, the discreteness is a way to define, you use the discreteness as a way to define what you mean by the path integral.

And the path integral for full quantum gravity, the full theory, the theory that captures all of the physics, that is defined in the continuum limit. So we come back to your question at the very beginning where you asked why I had stressed or had used the term continuum approximation. So in causal set theory, the full physics is contained in the theory where the discreteness scale is finite and is, we think, conjecture, is of order the Planck scale. So there is a fixed finite discreteness scale and that's physical and the full theory requires that. So you get the full physics with that discreteness scale in there. In causal dynamical

triangulations, you get the full physics only when you take the discrete ness scale to zero, literally. You have to take the continuum limit. And the full physical theory, the real true physical theory, is the continuum limit theory. And that's the difference, which which is to my mind, important. That separates the two theories and makes it interesting. That's good. That means that we have diversity in our approaches because I think it's only with the diversity of approaches that we're going to make progress because we need ideas to arise in the different approaches that feed into and across the approaches.

And of course, you know, probably no approaches is the full answer. Ah, interesting. Yes. You know, we better, better give ourselves the best chance of, of making progress by covering lots of different ideas. So, so that, that's a fundamental difference between causal set theory. The discreteness is, is fixed, finite and physical. And then causal dynamical triangulation, the discreteness is a way to define a sequence of theories, each with some fixed, each with some discreteness scale. That sequence of theories has to tend to a limit theory when the discreteness is taken away. So the discreteness scale goes to zero

and the full theory is that limit theory. And those are different conceptions and it's important that we have both of them in play at the current time. Thank you for spending so much time with me. I know it's just the sun is gone from where you are. It's late. Oh yeah. Gradually. Now, the last question is just you're speaking to the people who are entering the field of theoretical physics. And they want to know what advice do you have, Faye? Professor Dauker. That's the hardest question you've asked. I think be brave and talk to people is good advice that I try to pass on to my own students. So, physics is, it's, theoretical physics is nice in that you can go anywhere

in the world and you can walk up to someone and say, hi, my name is Faye, tell me what you're working on. And you will get a positive response and you can be the shyest or most unsociable person of all, but that doesn't matter. No one cares. You will get a nice warm response if you ask people to tell you what they're working on or what you're thinking about. And then pretty much most people, although I suppose there will always be a few exceptions, will reciprocate and say, oh, and when they've told you what they're working on, they'll say, and what are you working on? And then you can tell them what you're working on. And that's so nice. And you have to practice it. So the best place to practice it, of course, is in your home institution, wherever you

are, just practice asking people, your peers or fellow students, those who are a bit older than you, post-docs, your professors. Everyone welcomes that question, particularly the professors who are, you know, they have probably spent the day moaning about some admin thing or, you know, some, the latest outrage from the administration, you know, some new thing that we all have to do, which we don't want to do. And, you know, it's, it will be such a relief actually to, to, to have to talk about our work. So, so don't hesitate to do that and practice doing it. Now today, start doing it today.

And then gradually you'll feel, and you get, you know, much more comfortable and confident about The fact that you actually have something to say so Thank you so much. Take care. It's been fun. Thanks Kurt Firstly, thank you for watching. Thank you for listening There's now a website Kurt Jai Mungle org and that has a mailing list The reason being that large platforms like YouTube like patreon 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

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