Theories of Everything with Curt Jaimungal - Simon Saunders: The Unsettling Mysteries of Time

Episode Date: June 29, 2026

SPONSORS: - Go to https://www.plaud.ai/curt and use the promo code "CURT" to get a Plaud device today - Accelerate your efficiency. Sign up for your one-dollar-per-month trial today at http://shopify.com/theories - I personally subscribe to The Economist. TOE listeners get 35% off the annual subscription. No other podcast has this! https://economist.com/TOE This is a podcast all about time: depending on how you look at it, that's either unnerving or exhilarating. Professor Simon Saunders — Emeritus Fellow at Merton College, Oxford, and one of the most celebrated philosophers of physics alive — goes deep on what time actually is, why special relativity demands a block universe, and what any of this has to do with the Many Worlds Interpretation. Why doesn't space inherit the paradoxes of time? What's really missing from the block universe picture (and is it the same thing missing from quantum probability?) Saunders argues that Bell inequality violations aren't evidence against locality but evidence for Many Worlds, presents a novel derivation of the Born rule from a single physical postulate, and sketches a quantum version of Leibniz's monadology as a possible path through the mind-body problem. I hope you enjoy. FOLLOW: - Spotify: https://open.spotify.com/show/4gL14b92xAErofYQA7bU4e - Substack: https://curtjaimungal.substack.com/subscribe - Twitter: https://twitter.com/TOEwithCurt - Discord Invite: https://discord.com/invite/kBcnfNVwqs - Crypto: https://nowpayments.io/donation/TOE - PayPal: https://www.paypal.com/donate?hosted_button_id=XUBHNMFXUX5S4 TIMESTAMPS: - 00:00:00 - Defining Temporal Passage - 00:05:03 - Block Universe and Relativity - 00:11:15 - The Timeless Viewpoint - 00:18:07 - CMB and Global Time - 00:23:19 - Persistence and Spatial Revisitability - 00:31:02 - Philosophy of Physics Foundations - 00:38:46 - Relativistic Localization Problems - 00:49:22 - Reeh-Schlieder and Vacuum States - 00:55:23 - Branching and Actuality - 01:05:41 - Interval Probabilities and Frequentism - 01:14:14 - Decoherent Histories Interpretation - 01:25:49 - Ontic Structural Realism - 01:32:15 - Deriving the Born Rule - 01:38:02 - Leibnizian Quantum Monadology LINKS MENTIONED: - Simon's Papers: https://scholar.google.com/citations?user=htEv3XIAAAAJ - Many Worlds? [Book]: https://amazon.com/dp/0199560560?tag=toe08-20 - A Brief History of Time [Book]: https://amazon.com/dp/0553380168?tag=toe08-20 - How Relativity Contradicts Presentism [Paper]: https://users.ox.ac.uk/~lina0174/kansas.pdf - Trouble With Quantum Mechanics [Article]: https://www.nybooks.com/articles/2017/01/19/trouble-with-quantum-mechanics/ - Locality, Complex Numbers, and Relativistic Quantum Theory [Paper]: https://www.jstor.org/stable/192768 - Bohmian Mechanics: https://plato.stanford.edu/entries/qm-bohm/ - Finite Frequentism Explains Quantum Probability [Paper]: https://arxiv.org/abs/2404.12954 - Chance in the Everett Interpretation [Paper]: https://arxiv.org/abs/1609.04720 - Reeh-Schlieder Defeats Newton-Wigner [Paper]: https://arxiv.org/abs/quant-ph/0007060 - Everett's Thesis [Paper]: https://cqi.inf.usi.ch/qic/everett_phd.pdf - Physics and Leibniz's Principles [Paper]: https://philpapers.org/rec/SAUPAL-2 - Critical Exposition of the Philosophy of Leibniz [Book]: https://amazon.com/dp/1605204536?tag=toe08-20 - Avshalom Elitzur [TOE]: https://youtu.be/pWRAaimQT1E - David Wallace [TOE]: https://youtu.be/4MjNuJK5RzM - David Deutsch [TOE]: https://youtu.be/vKeWv-cdWkM - Sean Carroll [TOE]: https://youtu.be/9AoRxtYZrZo - Tim Maudlin [TOE]: https://youtu.be/fU1bs5o3nss - Sechit Madra (Trainer): https://www.instagram.com/sechit_madra More links at https://curtjaimungal.substack.com Guests do not pay to appear. #science Learn more about your ad choices. Visit megaphone.fm/adchoices

It doesn't feel as though time is passing. Where is time passing? Time remains the central concept in physics that is least understood. There's lots of debates in the reality, aren't there, about whether God exists outside of time. I think there's extremely interesting. Professor Simon Saunders, Emeritus Fellow at Merton College, Oxford, is one of the most celebrated philosophers of physics alive, working on what time actually is. I find it almost insane all of the minutiae of our present existence with all its craziness and insanity built in from the beginning of the world. No, I cannot believe it. It is not necessary.

On this channel, I, Kirchai Mungle, interview researchers regarding their theories of reality with rigor and technical depth. Today, we go deep into the philosophy of time and what any of this has to do with the many world's interpretation. We go over the professor's boldest claim that the violation of Bell's inequalities is not evidence against locality, it's evidence for the many worlds. We even touch on consciousness. I am just in my Everettian branch. You are in your Everettian branch. We can coherently treat ourselves as a sort of extended observer.

Professor, what is time? Ah, yes, the easy questions first. Richard Feynman said something about time. He said this. He said, time is how long you have to wait. And you can't really say anything more than that without getting into trouble. And it goes back to, I forget the name of the philosopher now, that says time if nobody asks me what it is, I know perfectly well,

but as soon as I am asked, then I become deeply puzzled. So, yeah, I mean, time, I think probably remains the central concept in physics that is least understood. I think that's probably right to say. So at some fairly fundamental level, we, I think, do not altogether understand time. But we have very adequate representations of it in physics, and we know how to deal with it in our ordinary lives, but it is extraordinary. I mean, look, but think of it in terms of just your life, whatever, you've lived perhaps only 20, 25 years, heavens, long enough. There are many, many hours packed into those years. Consider yourself in any one of those hours.

There's time to think and comment and reflect and, you know, look around and so forth. This is you being you. This is you being a person living in an ordinary way over a period of, say, an hour. But then there are thousands of such persons on that basis, because there's been thousands of hours where you have lived through those hours. So there's thousands of, call them larger than moments, so I don't want to make it just something instantaneous. There are thousands of times of your life, persons, as it were,

considering themselves at the time to be all that they are, that there's nothing more to them. As I speak now, I'm not considering that there's more to me in the future. So I'm perfectly adequate as a person with my past, but then there are thousands of persons with my past going back in time. I'm one of those thousands, and of course if we make it not an hour but a minute, we make it not a minute, but a second, if we really compress it, you can have as larger number as you like of previous moments. So what is the status of all of those moments? I mean, how do we kind of deal with that reality, that multiplicity of realities? Because each seems like a reality. You know, you ask me what is real. I can't do better than just point to stuff around us

and say, well, look, you know, this is what's real. It's Johnson kicking the stone. So they're all realities, and they all somehow exist? Well, they don't all exist at the same time. They exist with a sequential structure, and more than that, there's a causal structure, and we build and build until we've got quite an elaborate understanding of that multiplicity as something fairly integrated. And yet there remains something really problematic about it all. It seems that we ought to take all of those momentary mees as equally real. They're separated by intervals of time. They're not all simultaneous with one another, but it seems we must take them to be all somehow real. And this follows in particular from the theory of special relativity. To some extent, also general relativity,

but G.R. brings in some extra considerations. But in special relativity, we learned that there's no such thing as a global present. And if that's the case, there's no such, if you think reality is a present, there's no such thing as a global three-dimensional reality that isn't somehow,

I mean, when I say there's no such thing as a global present, there's a momentary presence centered on me. So I can have a momentary reality centered on me, a three-dimensional reality centered on me, but there's no intersubjective, objective,

public space three-dimensional spatial reality. Because if they were such a thing, that would be a privileged frame of reference, and it's the essence of relativity theory that there is no such thing. If that's the case, so there's no three-dimensional reality that is global. So it seems then that the only public reality is the one that takes in all of the presence, all of those different presence. So this is the block universe picture. So you have this picture. So you have this picture of the histories of people, the histories of objects laid out, as it were, static, unchanging, think of it as some extraordinary block of glass in which all of the myriads of threads weaving through it are each, particles, objects, peoples.

That then would seem to be the reality. And that reality just doesn't look or feel like time at all. I mean, it looks and feels like space. So in a certain sense, I mean, it's a quick way of putting it. Time has been specialised. It's been turned into a dimension similar to space. There are structural differences. There's the light cone structure, you know,

absolutely inherent to Minkowski's space time of special relativity. And with that, one partitions straight lines, what curves as well momentarily, but take straight lines, time-like or space-like, and if time-like, whether present-time-like or past-time-like. So you have that light-cone structure in the Minkowski space-time, this block universe. But still, it doesn't feel like time. It doesn't feel as though time is passing. If I ask where in that block universe is time passing, what I can do is look at a segment

of my world line, as it's called. We can look at a little piece of my world line. the little piece that is now, if you want. And there in that little piece of my world line, you see me talking, you know, discussing this crazy subject of what is time. And, you know, my lips are moving, the sound waves being emitted, you know, my head is changing and so on and so forth. But all of that is, as it were, a static configuration. So in what sense does that capture my sense of the real, of what is of passage?

I mean, Stephen Hawking put it in a slightly different way. What breathes fire into the equations? You know, we've got this sort of abstract representational thing. What makes it come alive? And surely what makes it come alive is time actually passing that somehow this picture, this representation of space and time, space time together, fails to capture the felt experience of time, of passage. So this is a very ongoing debate, and I think it's a very fundamental one,

and I think it connects fairly closely to the mind-body problem. And I think one of the aspects to it that is little attended to is it focuses on the fact that awareness is local in time. It doesn't have to be, and it's not even instantaneously local. It's a specious present, 50 milliseconds. Sure, whatever. So that is the localization of awareness. Now, I think we must believe, if we look at other animals,

if we look at insects, that as you go down in scale, the time scale of their awareness is much shorter. You've only got to look at a small dog and the way that it moves or cats and so forth. And it's extraordinary. Birds, it becomes even more pronounced. they are clearly living at an accelerate a faster rate than we are. Yes, except my mom's cat, who seems to be living extremely into the future plotting my demise.

Well, of course, maybe that's for a special case here. You know, it's quite bad. But so, there's something, you know, rather extraordinary about the localization of awareness. And presumably it can't get down to an extremely small, small time scales. But why is it local at all? Well, you could say, well, because dynamics is local. You know, physics is built on locality, you know, fields are local.

So, well, all right. But awareness somehow is underpinned by all of this phenomenology. It could have been underpinned by phenomenology spread out over times, you know, enormously longer than, So perhaps that's the point that to really capture space time, to see in it adequate representation of time, it would help if we could see the thought of a creature on an enormously slower time scale than hours as something spread out over hours or days. I mean, I struggle.

So anyway, so these are the issues that arise with time. And they're especially interesting vis-à-vis other topics and physics and particularly in many worlds interpretation of quantum mechanics because there is something absent there too and that comes in particular with probability, the nature of probability. And that absence of something felt

and that is missing in the theoretical representation when it comes to probability is rather parallel to the sense that something is missing in the representation of time. Forget about quantum mechanics altogether. Yes. So it may be that there's something more fundamental going on, which is kind of like what you really is involved in buying into a view from nowhere,

as it's sometimes called, or a godsai view, as it's also called, a timeless view, a view that is not in time. And I think there's lots of debates in theology, aren't there? about whether God exists in time or is somehow outside of time. And I think those debates are probably extremely interesting, actually, if you really drill down into them. But what quantum mechanics is adding, I think, is actuality is now missing too. It's just as the gods eye view is not temporal.

It's not in time. It takes in all the time. the godside view with quantum mechanics is it doesn't take in the actuality, the particularity that we think is also a part of reality. And the way it takes in all of the particularities, in the way that the gods eye view takes in all of the moments in time.

Let me see if I could summarize. So there's reality, then there's physical reality, and most people, most physicists believe physical reality, is all of reality. So let's just go with that for now. There's this physical reality here. Then there's our models of physical reality, which are something like special relativity, QFT, QM, and so forth. Then there's our experience. So we feel as if we have some unmediated access to this physical reality. That doesn't go through the models. Indeed, we didn't come up with these models till relatively recently, hundreds of years ago. And with time

in particular, is it the case? I like to decalculate. I like to decal. I like to boil something down to its rue to find out, at the root of all of these problems with time, is it that we feel as if there's a privileged now? So that's one of the problems. And then furthermore, that we have a flowingness to time, a directionality to this time. And is it also a third that the past seems fixed and then the future also seems open? And all three of these seem to be in conflict with the models of physical reality. So we seem to be accessing this true reality, whatever that means.

And then we have our models of the reality, which are far more explicated and accurate. And we have this tension between our phenomenal consciousness, our experience, and then the models of it. And I'm just wondering, firstly, is that correct? And then do all of those tensions boil down to those three or maybe even these three collapsed to two or something like that? Like what is at the core here? Yeah, yeah, no, perfect summary of the, as it were, the problem situation. Because we are in this problem situation.

We are all of us perfectly at home. There's nothing alien about our world. And yet, when we try to, in intellectual process of discovering analysis, attempt to construct a more accurate representation of the world, we find that it has to somehow nullify the personal perspective. The way to get the thing off the ground is we've got to remove our personal perspective from the picture. And in a way, that's just fine. I mean, it's a bit like drawing a diagram.

You know, you can draw a picture of a garden without saying where you are in the garden, right? I mean, it would be even more lovely to have, as in the Harry Potter map, where you have the map showing where everybody is. we're moving about. But anyway, so you have a map of your garden and you don't have to put yourself in it. And that seems fine. We can deal with that.

But now think about a period of time and envisage that period of time without putting yourself in it. Then you've got a problem. The point about putting yourself in your garden is you put yourself in it as something local, spatially local. The point about putting yourself in a duration of time

is that you put yourself in it as something temporarily, temporarily local, something with a specious present, a particular 50 milliseconds, which is now. You know, it has that immediacy and urgency. Well, that's fine. So it does the place I'm standing in. That has immediacy and urgency. And what is the difficulty?

The difficulty is to say again, because I can represent and understand or represent or conceive of the three-dimensional space without myself being situated in it. But I struggle to understand the duration of time without me being situated in it. I can only see it as somehow something frozen and lacking temporal characteristics. If I imagine putting a little spot on that four-dimensional structure, but we can represent it as one temporal time and one spatial dimension.

So you can do it in two dimensions. So you can't just label a particular point in the time axis and say that's now. And that would be like labeling a particular point in the garden and saying that's where I am. So you can do that. And as long as you are not, as it were, the point is I can put many other dots there too,

which would be myself at different times. And the problem then is that it seems arbitrary? It seems that there's something inadequate about the representation, the spatial representation of time to capture its sense of flow. So anyway, it's very, I mean, it's one of the philosophical debates that has persisted for a very long time, But it became particularly urgent with relativistic physics. That's the point about you as a word make it no longer even an option

to declare there to be a privileged moment of time for the whole universe. There just is no reasonable moment of time that one could pick out in that way because it would be a preferred frame of reference. I mean, this is all within a special relativistic context. When you go to GR, you also go to the real structure of the, universe. And the real structure of the universe includes a microwave background. And the microwave background does very nearly pick out a unique global time. Right. The way to do it is you, at each point, you seek a velocity in which the microwave background is isotropic.

And you can knit together all of those points, neighboring points, each moving with velocities such that the microwave background is isotropic. And that picks out of foliation. a slicing of space time. The trouble is, it only does so up to certain approximations. What do you mean? You cannot get to precision in this way. You cannot get to a precise momentary time,

instantaneous time in this way. Or you can make certain conventional assumptions and so on and so forth. So when you go to GR and the general the actual structure of the physical universe, then the situation is different. and there is even a way of theoretically changing the way that time works in here. But in special relativity, the theoretical way it works is that there's no privileged frame of reference vis-à-vis dynamics.

So dynamics, which is all about change, does not acknowledge a preferred frame of reference. It has a symmetry with respect to changes in frames of reference. And that symmetry is what destroys the option, as it were, of having a global three-dimensional space. As long as you had that, I mean, Newton, people like this, they thought they had a global three-dimensional space. Whatever the issues are to do with four-dimensionalism and are other times or other moments of time real, these are sort of philosophical questions because they can work with the physics which is grounded in a universal three-dimensional space, absolute space. and it is this that was lost in the shift to relativity. For me, the hardest part about most conversations

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Let me ask you a question, a slightly technical, but ill-defined question, and hopefully you can make sense of it. It seems like space doesn't inherit these paradoxes of time. It seems like there's something special about time. Few people talk about paradoxes of some spatial dimension. Yet in special relativity, we're supposed to be on equal footing between time and space. Okay, so if that's the case, whatever that means, if that's the case,

then why can't you take a paradox of time, boost it to space where there is no paradox? solve it in a sense there and then boost it back. So, in other words, why doesn't space inherit the problems of time, or why doesn't time inherit the solutions of space? Yeah, excellent. So I think one aspect, fundamental one, has got to be that we can imagine a space that endures and that we can visit every part of it as we wish. So that's not really an instantaneous three-dimensional space.

It's a space that endures. So it's already got additional structure in there. It involves space as well as time, this endurance of the parts of the space. But granted that endurance of the parts and just take the surface of the earth, as it rotates around the sun, we there have continuity, and we can track objects on the surface of the earth and so forth. As that is happening, we can visit whichever parts of the earth we wish. Yes.

and that is lacking in time. So there's the obvious, what time is one-dimensional, space is three-dimensional. You're right that in Minkowski space time there's a sort of fusion of the two. But this aspect remains that if you consider the analog of an object moving through time,

it is not possible to visit any point along that trajectory. Whereas if you had a three-dimensional space that endures, you can visit each part of that three-dimensional space as it endues. It's a more complex idea. I mean, what I, what we've just done, in a way what we've just discovered, is that as soon as you speak about space and time in terms of points, events, instantaneous, three-dimensional shapes, whatever, things

are reasonably clear. As soon as you introduce things that endure, you've got a problem, because you have to say, well, what does that mean for an object to endure, to persist? You know, not to sort of vanish in a puff of smoke. What is involved in that? And the answer is, well, resolve it into a bunch of timeline, time-like lines, representing the points, all of the pebbles, if you like, of a beach. Consider each of those pebbles and give it a time-like line, a line that it changes over, connects together, events and space-time,

but is always time-like, so in the vertical part of the light cone, and look at the neighbouring pebble and the neighbouring pebble, and the neighbouring pebble, and what you've got is a congruence of time-like lines that are all roughly parallel to one another. They don't move about too much, the structure is preserved. So when you've got all of that physically in place, you then have a notion of a three-dimensional space that endures, which is everybody's idea. You know, I think of my garden, you think of your home.

It's a space that, you know, it doesn't suddenly disappear on you. But what is involved thinking about it in terms of the language of four-dimensional events, space-time points, is that you've got this congruence of time-like lines all roughly parallel to one another with many different characteristics that are relatively frozen. They don't change too much. If we're talking about my garden, it doesn't change too much from one day to the next. of course there's the change in lighting that comes and goes. And understood in that way, when I revisit and I visit every part of it,

it's me always going time-like, but I can move time-like and check out different parts of the big congruence of lines. This kind of needs a graph. A graph or two would be nice here just to depict it. So that's an awful lot that's in place, which is behind our intuition that when it comes to spatial structure, we can revisit every part of it and that when you try to do anything

there's nothing comparable like that that can be done with a time-like line. Actually, I'll place a graph on screen so people who are listening if you have the video version you can watch and there'll be a graph of what was just talked about so that you can see the visual. Yeah, yeah, yeah.

Okay, so when you say endurance, what precisely are you meaning? So, for instance, there's a rock. I'm in Toronto right now, and if I look outside my window, I can see a huge rock. Now, I could say, I want to get to that spatial point, so I'm going to go.

But then the question is, did I get to that spatial point when I hit the rock? Or should I be in outer space and the Earth is completely past me to be in the same spatial point technically because the rock was at a certain... Is that what you mean? Or is something different? No, no, but what you've just done is absolutely. You've pointed to two contrasting systems of coordinates. One system of coordinates is just spatiotemporal points, and that can be external to the Earth as it orbits.

around the sun and everything else that it's happening, that's fine. So we have a system of spacetime points, and you can refer the question of when I say revisit a point, you can express it at the level of a spacetime point. And then the answer is, no, you never revisit the same space time point. It's like you never step into the same river twice. So you can't revisit the spacetime point. That is not what is meant. What is meant instead is a different system of coordinates, one where it's a same thing.

set of rigid bodies. Think of it in terms of rigid bodies. Okay, now, and made out of a mechanical, make it a mechanical system. You can think of it in terms of leg or mechano or something. Should I be thinking of these rigid bodies as actual powder instead then? Because if they're extended rigid bodies and we're using special relativity, well, wouldn't we have a contradiction? Oh, sure. We don't. We don't. There are difficulties of making sense of a notion of perfect rigidity in relativistic terms. We don't need perfect rigidity. Approximate rigidity will do just fine. I see. The point is that the coordinate system thus defined as persisting over time, we can then think of events as being labeled by position with respect to the spatial parts of this

coordinate system. Okay, so we can use the spatial parts of that coordinate system to pick out different events at different times. And in particular, As we move around, and later and later times, we can visit many different points of that mechanical system of rods. We can revisit all of those points. And in that sense, revisit the spatial points. But these are spatial points, not meaning space-time points. That's the difference.

Spatial points. It's a hard thing to properly, with precision and clarity, convey. It's part of ways teaching special relativity. it's not so easy. It becomes easier in the sense in terms of visual diagrams and equations, and you learn how to manage those. But in terms of how to really translate

and express these ideas in ordinary words, it's more difficult. It's one of the things that makes philosophy of physics so much fun. And actually also, I think, makes it important to do philosophy of physics

because I think physicists can get away too much with merely relying on the equations. Ah, expound on that. Yeah. Well, I mean, it's just something that I've often found in discussions with physicists, as a lowly philosopher of physics, I can, without damage, as it were, admit my ignorance of physics. I can say, oh, I mean,

I really, please explain, you know, and I'm really, there's something here going on that I really don't know. And so the physicist's present will enjoy, you know, explaining to someone who is admitting their ignorance, and it's great. But then what happens is the other physicist who's present finds that they don't agree with the explanation that's being given. And then I, because I'm sort of no sum of the game, can point out that, oh, well, there's not quite right, is it? And they find themselves having to discuss things that they mostly didn't need to discuss.

Why, you give a concrete example? A recent one, you don't need to name names. Well, I think I probably, okay, Yeah, it would be two people talking about stochastic quantum mechanics, a dynamical collapse theories, and having very different views of how localisation works in that context. And when pressed, but with, you know, sort of saying, look, I really don't understand it, please explain it. So then one will attempt to explain it, you see, but then the other person who was present took a very different line. And I would have to give names, wouldn't they?

I'm not going to it. But those sounds like philosophers of physics. People who talk about stochastical collapse versus dynamical are already philosophers of physics. So what I was wondering is, are there examples of two physicists who don't consider themselves to be doing any philosophical work at all? Maybe they even look down at philosophy.

And then one was explaining to you, and then you found the difference between the other two. Physicists? Yeah, no, absolutely. Both of these guys were physicists. They were not philosophers of physics. These are physicists. These are physicists, and they were talking about certain kinds of diffusion equations

and how they relate to certain conceptual question that I was interested in. I could express ignorances to how the mechanism worked. It's something that we do all the time in ordinary conversations. Very often we express false ignorance, as it were. You know, we pretend to be ignorant. Actually, we know quite well what's going on. But can you explain that? And so somebody does, and then they find themselves actually,

not in their comfort zone. I mean, this is also a part of it, taking yourself out of your comfort zone. I mean, any conversation about the measurement problem in quantum mechanics has this result among ordinary physicists. They are not really prepared to discuss it in a very serious way, usually, usually, and they typically have not thought very hard about it. So that's an example of how it's possible to get away without talking about something.

very fundamental. So that is not an example where I can say, oh, tell me about what happens in quantum mechanics. I don't know anything about it because, I mean, you know, they know me well enough. That's why I'm there. And it's something about quantum mechanics. So that's not an example I can give.

But it's an example of how physicists will not engage in a conversation. Whereas as soon as somebody who is genuinely, you know, without guile, saying, please, explain, how does it work, then they will interestingly differ one from the other. Actually, I mean, somebody else who made the same point. It was Steve Weinberg in one of his last essays, I think, on the Foundations of Quantum Theory. It was in the New York Times Book Review, I think, around 2017, something like that. And he said, I'm not as happy as I once was about the foundations of quantum mechanics.

I used to think, and he went on a little bit, he said, the trouble is that the experts don't seem to agree. and that's a bad sign. So there is this failure to agree, but very often one doesn't want to have a conflict. You know, I disagree with what you are saying about such and such in physics. If it's a matter where it affects the equations, it becomes a real dispute. This isn't something that can amicably be nodded through you. Somehow you've got a problem there.

So if, but if you can keep it at the level of conversation, then one can pretend that it doesn't really matter. Kurt here, note that if you'd rather listen to Toe, we're on Spotify, iTunes, everywhere with a podcast catcher. You can just search my name or theories of everything. And also, remember to hit subscribe. Earlier you talked about when I asked, What is Time?

There was a quote from Feynman that has to do with how long you wait, which to me is more about duration of time. Yeah. But not what is time itself. So unless all investigations into time come down to speaking about duration, then to me that doesn't answer, What is time? Absolutely.

Now, of course, you could also ask me a counter question like, Kurt, what do you mean when you ask what is an X? Like, what precisely are you looking for? Are you looking for equations? Are you looking for me to point out something like a cup? I don't know how to respond to something like that. I actually don't know precisely what I mean when I say, what is time? But I'm going to pose that question to you once more.

What is time? And how do you think about it? Sir, I can say why, if you're interested. I can say why I'm dissatisfied by duration as a full accounting of time. But I can't tell you what a full account would look like that would satisfy me. Well, let me just say, just give an honest answer to what I think time is, I think time is precisely this geometrical structure. And it's not any old geometrical structure.

It's one which is threaded together by certain dynamics. And it is represented in this four-dimensional picture. And I think that is a correct characterization of the reality. And I think that it's seeming lack of, where is the fire in the equations, or where is the passage taking you from one moment to the next, is precisely a price you've paid for a perspective, a view from nowhere, a gods eye view. So it's very alien to ordinary sensibility. sub-species as Spinoza put it too

it's very difficult to inhabit that view so there's a tremendous challenge involved in really trying to grasp what is space time if you're serious about it

and equally if you're trying to understand cosmology the universe as we understand it it's a very I think character affirming, but life-changing experience to properly engage with the enormity of the universe. I mean, the only way that I can put it is in terms of one of many experiences of seeing the night sky.

I mean, the night sky, I think, on a properly dark night, which is so rare, but a real star-scape is one of the most extraordinary experiences we can have. I hope you've had such an experience because it's profound. So we can't live with that all the time. When we go about our daily lives, we forget about it all, and so on and so forth. But it's there, and this is the reality that we live in. Something similar happens in the foundations of quantum mechanics. Well, let's get there. So what does all this talk about time, the problem of time, time as a parameter versus time as an operator and so on?

What does all this have to do with quantum mechanics? And also, this talk of quantum mechanics, shouldn't it technically be QFT? Why are we always talking about interpretations of QM? and not interpretations of Q of T, at the end of the day, shouldn't it be Q of T, or even QG? But those are a variety of questions I throw out to you. Yeah, no, the great set of questions. Simple ones.

Yeah, yeah. No, I think that, I mean, absolutely, and I was very much to take the direction in my early career. I thought, look, if we're going to be serious in doing philosophy of quantum physics, we really ought to be looking at relativistic quantum field theory. So I spent a lot of time studying relativistic quantum field theory, and it's enormously rich and extremely rich,

extraordinary and so on and so forth. But actually, I think the most important lesson to come away from it is that physics is scale relative, and the physics that is adequate at one scale will not be adequate at another. And they are not in tension. These different scales and the physics that is going on at them are not in conflict with one another. And in particular, what is of importance to things like conceptual? questions about probability and the problem of measurement in quantum mechanics,

can all be articulated at low energy scales. So that doesn't mean you get rid of relativistic stuff altogether. You've always got radiation photons, and that's actually playing a very important role in foundations of quantum mechanics. But it does mean that you can be pretty sure that if you've got an analysis that works in non-relativistic quantum mechanics, that it's not too dependent. on, well, structures that we don't also find in relativistic quantum theory. So as long as we have that confidence and we can do those checks to make sure,

then we can make do with the language of non-relativistic quantum mechanics reasonably well. And what has also been found is that you can express or probe many profound-looking concepts in quantum gravity using elementary concepts of quantum theory, like entanglement, there may be great progress to be made not through looking at the standard model and high-energy phenomenology or structures that are of interest or relevant in high-energy regimes. No, we do not learn about quantum gravity so well like that.

We better learn about it by applying quantum concepts directly to recover something like to recover something like spatiotemporal concepts. I think, and I find these questions to be absolutely fascinating, but they give further emphasis that the answer isn't to go immediately to relativistic quantum field theory,

unless, of course, you're of the view that people are making arguments and claims in the non-relativistic regime that cannot be recovered in relativistic quantum theory. A good example of that, in fact, is localization of particles. In what sense, can particles be localized within regions? Quantum states, can they be localized within region? Answer, yes.

Pose the same question in the relativistic case. Can particles be localized? The concept becomes problematic. We don't mean localized in space-time. That would mean they came into existence and went out of existence. So we mean localized, spatially localized. can they in relativity be spatially localized? And the answer is, well, not in a covariant way,

not in a way that respects the symmetries of relativity theory. So there's something problematic about the localisation concept. If you ground too much foundational work in quantum theory on position, and even the existence for a position operator, because there is no position operator in relativistic quantum field theory, no covariant position operator. As long as you are careful not to rely too heavily on that notion, say, of a position operator in some interpretation or foundational questions in quantum mechanics, then you can be fairly confident.

I mean, that's, as it was, deals with that potential problem. Other potential problems arise with things like numbers of particles. So you can have interpretations of quantum theory that really drill down into the actual number of particles involved. And if each particle lives in a certain number of degrees of freedom for each particle, let's just imagine one degree of freedom for each. You've got end particles, n degrees of freedom. And that's your physical arena, as it were. And you conclude, oh, well, then you've got a three-end dimensional configuration space. And a quantum state is assigning a complex number to every point of a three-n-dimensional space. That's what the quantum state is doing

for those n particles. And you can then ground an interpretation of quantum theory from that structure, recover objects in three-dimensional space. Go from this complex field in three-endensional space down to objects in three-dimensional space. So fine, that's a whole program that you can engage with and perhaps successfully carry through. But it's not going to be workable if you've got

change in particle number. Right. And indeed, what then is the arena where particle number is changing? We know how to do it in quantum field theory. It's called Fox Space. But the people that are doing this kind of game aren't really interested in Hilbert space structure. And Fox Space is a Hilbert space structure.

They're interested in something more attuned to philosophy. You know, the philosophers can get their head around. Okay, we all understand what it is to have a scale of field in three-dimensional space changing over time. So great, you know, we're happy and confident with that. There's lots of interesting philosophical questions to be raised, but in the mind, you know, blah, blah, blah. So now looking at quantum mechanics, can we not construe it as just a now complex field in a much higher dimensional space? And this is a way of understanding all of the peculiarities of quantum mechanics. Okay, so, but then the question is how do you carry that through in a situation where

particle number is changing over time. I mean, it's the same with the pilot wave theory or DeBroyley-Bome theory. You have a reasonably adequate non-relativistic quantum mechanics in terms of hidden variables, non-local, but they give you the same probability distributions as does non-relativistic quantum mechanics. So this is a great achievement.

Fine. Can it extend to the relativistic domain? Work in progress. But then, of course, it's been working progress for a very long time now. And actually, if you look at what's going on in pilot wave theory, what are giving you the guidance equations or the standard guidance equations, introduce the additional variables, the hidden variables, the point of configuration space as it wanders around, which is the motions of all of the hidden variable particles, is just the integral curve of the probability flux,

the probability current, sorry. So it's got a very simple mathematical expression. The probability current is an object you can build up out of the quantum state, and it's like a vector field, and you can look at integral curves of the vector field. And each such integral curve is a DeBroyly-Burm trajectory. Great, brilliant. It's a very natural structure, so you can try to do the same in a relativistic quantum theory, where you've got something similar, and the answer is it completely failed.

And one of the major reasons it fails is because of the lack of permanency of particle number and associated with it the so-called negative energy difficulty that is present in relativistic wave equations. But look, I'm sort of just going a little bit theoretical just to indicate how the examples, you know, where you use non-relativistic theory and you're not doing it in the proper relativistic framework, can be, you know, damaging. You can be misled, I think. I think one can make wrong choices. If you make use of structures that either don't work at all in the relativistic case or work dramatically opposed to what you want them to do,

which is roughly what's happening with, when you try to do with the pilot wave theory in the relativistic wave equations, what you do with the shrilling equation. Anyway, with all of that, I mean, let me just make a personal note. I spent years on relativistic quantum field theory. And at the end of it all I thought, No, it's just not really of substance in addressing, engaging with the conceptual questions I'm really interested in, which can indeed all be expressed or mostly at a non-relativistic level, but allow me photons. So that's my answer, sorry, rather long, as for why I frame things in terms of quantum mechanics. But another answer is to say quantum mechanics is just shorthand for quantum theory,

and it means to include field theory. I subscribe to the economist. Their science and their AI coverage is among the best I've found anywhere. And I say that as someone who reads plenty of it. I'll give you some examples. They just ran an analysis on how attitudes towards science are changing in American politics and what this means for research and funding in scientific institutions moving forward. This sort of high quality reporting is fantastic. They even covered how dark energy may be weakening over time. Now, if that holds up, it completely changes our understanding of the universe's fate. If you watch this channel, those are exactly the kinds of questions that we explore every week. I subscribe to The Economist because their science and their AI reporting regularly surprises me with how deep it goes. And they're also, of course, known for global affairs, both political and economic reporting. They are top tier. And interestingly, and flatteringly, Toa is one of the only podcasts that the Economist partners with.

So as a listener, you get an exclusive 35% off. That's not a deal that they have just anywhere. Head to Economist.com slash T-O-E to subscribe. That's economist.com slash T-O-E for 35% off. What are the foundational problems in the philosophy of QFT, distinct from philosophy of QM? Oh, wow. Well, particle localization. I think that's a very distinctive question and problem,

and one that I still think is unresolved. What do you mean? Well, what one does without a covariant position operator? What does it mean not to be able to express that notion of a spatial localisation without privileging a frame of reference? And there's a way of doing it, the so-called Newton-Vickner representation, which breaks the Laurentian symmetries.

So that otherwise has many, it's a fascinating field. I mean, it's a bit mathematical, though. I mean, is it the way you want to go? I mean, I'm happy to make this move. Oh, yeah. Just so you know, the directed audience for this are philosophers and physics and math and computer science, professors, researchers, academics. So it's quite technical.

For instance, you could talk about Coleman Mandula or Ries-Sleiter's theorem or whatever you like as technically as you like. Okay, I hadn't understood that. I hadn't understood that. Hmm. Okay, well, I've been doing a bit of hand-waving previously, haven't I? Well, do I me give you one example of what happens with Newton-Vignor representation? You find that the vacuum ceases to have the Richelida property. And this is, you know, really, very interesting.

I mean, the Richelader property itself, and the Mikovsky's base vacuum, the covarian or invariant vacuum, is rather extraordinary. And, you know, it is the case, it seems that by local operations, you can approximate any state that you want in the whole space of states. You know, it's a sort of, what an earth could, I haven't really expressed it accurately enough. So it is something that I think has led to a great deal of bafflement as to what is quite the right thing to say about it. And it's connected interestingly with Newton-Vigna localization, as is the way that the complex fields are represented in wave equations, the covariant wave equations, the complex numbers that are used there have a different role from the complex numbers used in a Hilbert space representation.

We're used to writing down the client-cordant equation, direct equation, Yangmels equations, equations for QCD, QED and so forth. And the complex numbers that occur in those, they are, as it were, fixed numbers, which do not change in the dynamical evolution of those fields. Those numbers are not complex numbers used in a helper space representation in terms of particle number, and arguably not in any Hilber space representation at all. But what is used in the Hilber Space

representation is something else, a decomposition of covariant fields, these covariant fields, are into positive and negative frequency parts. And that decomposition then works so that each of those parts can function so

to have positive energy and contribute to total number. Now, the way that representation works is a non-local operation with respect to the complex unit that occurred at the covariant field level. The complex numbers in the Hilbert space representation are non-locally related to the complex numbers used in the covariant fields. And it's for this reason that they cannot be a position operator in relativistic quantum field theory. Again, if you do a Newton-Vigner representation, these things essentially go away. What you do in the Newton-Vigner representation, if you were to construct fields local using the complex numbers

in the Newton-Vigner representation, they would then be non-local fields understood in the standard Lorentzcovariant representations. So, I mean, this is just a whole dimension of understanding our analysis of, well, look, the major question that stays you in the faces of philosophy. physics, is you can do statistical mechanics, non-relativistic quantum mechanics, thermodynamics, GR, really with absolute, you know, it's not so hard after two or three years, one or two years of graduate work. But to do anything serious in relativistic quantum field theory, it's much more. I mean, relativistic is like you fall off a cliff. So, you know, there's a mathematical depth and profundity to relativistic quantum field theory

that we still haven't understood properly, I think the fact that there, in demonstrably, there does not exist a non-trivial relativistic quantum field theory satisfying the Whiteman axioms. And that's amazing. You know, it's amazing that these actions are so constraining

that it seems they have an effectively unique solution as free field theory. I mean, relativity is partly involved. Relativity in quantum mechanics go together beautifully. I mean, the DERAC equation is, I think, the greatest work of art in mathematical physics. I do believe that. I do find it has a cathedral quality of beauty and elegance. Why?

Well, I think it's difficult to characterize what is beauty. But I think one other feature of it is the way that you understand the equation can be greater or less profound. So if you understand the direct equation in terms of various symmetries, it acquires an elegance that no partial differential, well, ordinary, to take some random partial differential equation, doesn't remotely convey. It's already in the symbolism and the notation involved as a unification of a whole system of partial differential equations.

I mean, the theory of geo is exactly the same. This spring, denim gets a softer, lighter update. Introducing Old Navy's drapey denim wide leg, a new fit that moves with you. It's everything you want denim to feel like for summer. Easy, breathable and effortlessly cool. With a fit that creates natural movement and a wide leg that feels modern, not overwhelming.

Plus, that signature, wait, for this price, moment. Old Navy's drapey denim wide leg. So how is this related to many worlds? I mean, yeah, because they are related. I mean, because I think that the multiplicity of moments in time, we kind of got our heads around it. We understand that there's a sort of systematic way of understanding it that makes sense. And we're not there yet with the many worlds.

We have yet to have a way of managing and articulating this multiplicity with the same sort of familiarity and confidence and competence that we have in dealing with linear times, as it were. Look, here's where it exists very much in our ordinary lives. It does exist in terms of probability, ordinary notions of probability. I mean, if you think about all the contingencies that happen in our lives, that's what we're managing the many worlds in a way. All of those contingencies carry with them all of the contingences that did not take place. The very notion of contingency, highly contingent, is what so much

much else that is not the case. So we live with that and it's deeply shocking to us. I mean, I think I find it almost insane that from the beginning of the universe, this utterance of mine would be deductively arrived at, deterministically, along with all of the minutiae of our present existence, with all its craziness and insanity, that all of that was some. somehow deterministically built in from the beginning of the world, or was somehow necessary? No, I cannot believe it. It is not necessary.

So this is one of a multiplicity of possibilities we think of, a multiplicity of possibilities. And that multiplicity of possibilities is just vast and mind-boggling, and mostly we try not to think about it. But we do have to think about it when we're making choices relating to events in the future, which are among the possibilities. And the choices we have to make are really, how seriously do we take these various possibilities? You know, there's a possibility you'll be run over by a bus.

The moment you step out of your front door, heaven forbid. So there's a possibility that you'll win a fantastic lottery, and I don't know if you're a betting man. And if you do, then you'll be able to be it in normal. mostly fortunate. So there are these possibilities. But what gravity do you give them? What weight do you give them in how you live your daily life? And the answer is we, you, we, we, we, were all of us extremely adept in, as it were, correctly estimating risk. We mostly, you're really good at avoiding risk. We, we, most of the time, as long as there's not wars happening and crazy stuff going on. And

And we very reliably will, you know, for years after year after year, we'll manage to negotiate all of the, you know, potentially disastrous things that can happen in ordinary lives, you know. So we're very good at handling risk. And that goes with having a sort of kind of primitive theory of everything, which is common sense reasoning, a sort of an Aristotelian way of, you know, analyzing the world or understanding the world and so forth, and there's notions of causation

and propensity and dispositions. There's not quite the notion of probability in there, but we can fairly easily put it in there, and once it's in there, that really then starts to make it all rather clear what's going on. We have to negotiate amongst probabilities all the time. And that negotiation from an Everettian point of view is exactly an understanding, of branching structure. And branching structure, from an Everettian point of view, is the source of the many worlds. It's by virtue of the unitary evolution of the quantum state

having this branching structure, and with nothing else, no other added input, that we take it seriously, not just as representing possibilities, but as representing actuality, of which the actuality that we see, branch the we are in located in is just one. Just a moment.

A quick question. You say the branch that we are in. Now, in the many worlds, in your particular view, would it not be more correct to say the branch that you are in? That even the we here is somehow approximate and it's going to diverge and... No, well, that's a very interesting question. I think the right answer to it is it comes back to this issue of is consciousness localized. I mean, the point is that you and I, as we talk, are able to exchange signals at the rate of, you know, a few hundred or probably several thousand bytes actually a second.

Sorry, a minute. What is the day of submission between us? It's fairly engaged and it's fairly integral to the conversation that we're having that there is this time, for me, my thoughts, oral impact, you hear, think, you respond, I think. That cooperative effort, which is this conversation, it's true as taking place over several thousand miles. But it might as well be understood as a common observer. As long as we're not going to bring in localized quantum systems that we're looking at, we can coherently treat ourselves as a sort of extended observer. and as such speak of

as inhabiting one Everettian branch or a common Everettian branch this is an interesting question I mean I think probably the quicker in this sharper reply must be you're right I am just in my Everettian branch

you are in your Everettian branch but we are correlated. And if you look at the branching structure that unfolds, mostly we are tightly correlated with one another, and in that sense we share a common exchange of ideas and so forth. But if we were to start doing experiments, quantum experiments, you in the US, me in the UK, then we would maybe find some interesting,

from a branching structure point of view, some very interesting, aspects to it that underlie the appearance, at least, of Bell non-locality. So this sort of negotiating with contingency. Now, in a sense, you could say, look, it's nonsense to suppose this is uniquely somehow comes up with the ever-etchin quantum mechanics. It would arise in pilot wave theory, or it would arise in dynamical collapse theory. In any of those theories, you equally have to manage possibilities, and the possibilities

that will come up with will be much the same, regardless of which of those approaches to quantum foundations you take. And, you know, yeah, sure, they're sort of right, but the point is if you go to the theoretical point of view and you really look at what are the contingencies involved in the real world using unitary quantum mechanics, you're doing something that from their perspective is either just a mistake, like in a dynamical collapse theory.

It's just a mistake. or from a pilot wave theory at your point of view, a very incomplete description. So, you know, in a sense, the perspective, which just looks at this multiplicity, this network of multiplicities, and says this is what we ordinarily, we negotiated it in ordinary lives,

when we really look at it from the perspective of physics, we investigate it from the point of view of Everettian quantum theory. And from the point of view of Everettian quantum theory. quantum theory, what one world requirement is doing, is very, you know, it's rather like with the block universe where you put in a point and say that's where you are. You're picking out a single one of the branches, and you're saying that, and only that is unique, and all of the others do not exist. And with each branching event, that all are culled but one, and so forth. So the Everettian is taking seriously this space of possibilities as all actual.

And if that's the case, then there is no contingency to reality any law, because all of the particularities exist. What seemed extraordinarily contingent was that this unique particular world, as it is now, this instant in time, should exist. That seems something really too specific. The multiplicity in the Everettian quantum theory would return us to something much more... It's not that all possible scenarios exist, not at all. But that there's a...

I mean, if I can just put it in terms of probability distribution over these possibilities. And the ones, the really crazy ones, have zero probability. going to zero or close enough to. Yes, but if it's close enough to but non-zero, then it does occur. Yeah, well, I think it's a difficult question. I mean, I think it depends partly on how you actually analyze probability. A recent approach that I've been developing, which is analyzing probability, quantum probability, in terms of frequentism, involves looking at decompositions of the university,

state into microstates of equal amplitude. Okay. So with such a decomposition, you then examine any proposition or property or projection operator, and you can pose the quote, given the quantum state, the total quantum state from an everaging point of view. And you can ask the question, given such a decomposition which diagonalizes that projection operator, what fraction give the answer yes to that property, what fraction the answer No, you can do that with finite decompositions of the total state.

And if you do do that, and you look at projection operators that correspond to things like records of multiple experiments radically in disagreement with the born rule. So take a projection onto that. And you can never give it a non-zero probability. Okay. Or rather, in order to give it a non-zero probability, you've got to, these microstates, this decomposition of the quantum state into macrostates, has got to be so insanely detailed

that you're looking at distinctions of difference in amplitude comparable to the amplitude of the very low vulnerable-violating branch state. So look, I mean, this is a bit of a complicated thought, but it's a conception probability that makes it, you can never, as it were, see the real extremes in terms of any finitary analysis. On any finite analysis probability in terms of a finite expansion of the state,

you will not see a very low amplitude branch. It doesn't mean it's not there. This is one of the interesting features of this whole framework. Yes. There's always going to be a shredding a cat state, a state which is a shredding cat state for the projection operator or the property of interest. So the general framework of this, we've rather jumped into this, haven't we,

with that perhaps a bit of introductory remark. But I just wish to give it as an illustration of how the extremely low-amptitude scenarios may not have quite the consequence they usually thought to have. I mean, look, another aspect to it all, even if there did exist, I mean, one takes it as straightforwardly,

there exist people staring in the face the huge bond rule violating statistics and all of their experiments have been functioning properly and it hasn't been confected, it's not a put-up job, and they're staring at that. In the very next second, with enormously high probability,

they will see things go on as normal, with vulnerable-compliant probabilities and so forth. But then, of course, you can play the same game again and again and again. So you can always isolate. And I think perhaps another way of answering the question is a little bit like the Boltzmann-Brain scenario, which is also a serious problem. I'm not suggesting that, therefore, one should just forget about it.

But I'm saying that this may be very related, actually, to bosman brains. But again, in the perspective that I'm offering, you will not even see the probability for the bosman brain. You will not see the probability because it cannot be captured in a finitary analysis. It's called finite frequentism? Yes. Well, finite frequentism is, well, the theory comes in two or three. Initially, I presented, this is a theory which only involved finite decompositions of the state. And as such, you can approximate the bond rule quantity extremely closely.

And the nature of the approximation is not that with very small probability it differs. No, no, no, no. It's giving you a number that is very, very close to the borne rule quantity. It's completely categorical. It doesn't involve potentialities or propensual. or anything like that. It's just the number of these microstates that fall within the projector acting on as a eigenvalue one.

But one microstate, usually, almost always, will be indeterminate for that projector, will be a shredding a cat state for that projector. One of those microstates must be. So what you've really got is you've got a set of microstates that give the answer yes to some question. You've got a bunch of microstates give the answer no to that question, and then you've got one, or perhaps more than one, but we can come on to that, in between the two. The ones that neither give the answer yes or no, where there's a superposition of the projector with the one answer with the projector with the other answer.

And for the person who's listening and they're wondering, well, what does yes and no correspond to? Does that mean so-and-so obtains, in other words, is actualized when it's a yes, and doesn't happen or doesn't occur if it's a no or what? Yeah, well, think of it. We're trying to give it probabilities to properties. These could be properties attached to times. So this could be the property of displaying spin-up on a registrar of an experimental apparatus. So it's just a physical property in that sense.

So the question becomes, what is the probability of that property? The question of whether that property actually exists or does not exist, is it hypothetical? We don't have to engage with that at the moment. We're just assigning probabilities. to different properties. Propositions as well. Properties are in one-one correspondence to propositions here. Propositions are often understood as yes, no questions.

But all equally can be just assertions. You know, if I assert something to be the case, you can turn it into a question. You know, the sun is shining. You can turn it into a question, yes or no. So this is very much how properties, propositions, and yes, no questions have been handled in foundations of quantum mechanics

for, you know, there's a whole tradition of it. the logico-algebraic tradition and so forth. Anyway, so on this picture, this is a way of assigning probabilities, and you've got the total number of microstates, say, N and all. Let M of them say yes to the projector, and then the residue, the remainder, say no, except for one. So what this means is you've got a lower bound to the probability of that projection, given by the number of microstates that assigned the,

answer yes. And you've got an upper bound, an upper bound, because you've got that bunch of microstates that assigned it no. And then you've got the one in between, a sort of grey zone, a no man's land, if you like. So what's happened is that rather having probabilities as rational numbers, we're getting probabilities as small intervals of real numbers, an upper and lower bound. Okay, so this construction, it's quite an interesting construction. I hadn't come across it before, but it existed before my own work on it. So-called imprecise probabilities.

I called them interval. Interesting. It's a whole branch, a recent branch in probability probability theory. But the point now about the grey zone, the interval, you've got a lower bound and upper bound, it's a bit like, instead of a point,

probability being a point, it's like a blip. Yeah. And it can be a bigger blip or a smaller blip. And the bigger the blip, then the less informative, the probability. is because it's bounded by zero and one. And if you've got a blip that just takes up the whole of the zero one interval, you've got no information at all.

Yes. So the point about the very low probability stuff using the Bourne Rule is it's always in the grey zone. Huh. Okay. The amplitudes, the precision that would be required to pick it out cannot be increased beyond that grey zone. I mean, look, it needs a further argument to AI. Well, I think at this point what I'll do is I'll place a link to

your paper slash papers on this topic on screen and then in the description so people can find out more. Now I want to spend the next say 20 minutes or so just going over many worlds and I want to see what attracted you to many worlds, what keeps you there and then many people, not many worlds, many people who are listening, they think of many worlds as just one theory, one interpretation, but there are different sects in a sense in many worlds. So there's a Wallachian many worlds type interpretation, there's a Saunders type interpretation, there's a Sean Carroll type interpretation, and so firstly, what is it that unifies all of these, such that they can even be called, the same sort of umbrella of interpretation? And is it merely, are you seeing it as a delightful

place in the sense that it has properties you want that you wish a theory and interpretation had, or is it merely the best of a bad lot? And you're just, saying, well, I mean, if my competition is pilot theory, I'm going to go with many more. Like, you understand what I'm saying. I do. I do. So it's a very interesting set of questions. Perhaps just a comment on the last one. It surprised me the sort of cacophony that emerged over the last 20 years, if I may call it that, of a very different views. It seemed to me, because I suppose my own understanding of Everett was very well worked out in my mind and appeared to be how much.

beautifully with the development of decuriant history, I thought this would be immediately obvious to anybody who studied these ideas. So I really expected a decorian history-based Everett's interpretation to be widely pursued, actually, investigated, examined, and so forth as to its various conceptual challenges, blah, blah, blah. So, but that didn't happen. What instead happened is that most people were very distrustful of decoient histories altogether, quantum history's formalism. It seemed something somewhat alien

to ordinary column theory and, you know, blah, blah, blah. So, and instead pursued their own imaginative reconstructions of Everett's ideas, many of them, without regard to decoherent's theory at all. So I did find this hot,

but, I mean, David Wallace and I were, you know, highly at one, in almost throughout this period up until when he left Oxford in, whenever it was 2014 or something. So there wasn't much of difference between us. I suppose what differences there were concerned? I mean, there were certain issues bound up with the nature of divergence and branching and certain metaphysical questions like that

that I was probably more insistent on than worst to his liking. But in the meantime, there did arise these other very, articulate proponents of views, pictures of many wells that involved certain ideas that, to my mind, are completely antithetical to anything that is in Everett or in the development that came out of Everett. For example, Sean's picture, that Wells are in one-one correspondence with the spectra, discrete spectra of the energy operator. I find that very different from anything that I have gathered from Everett. or to take another point of view that some people have been interested in, which is sort of a hybrid of Everettian worlds,

which nevertheless are able to interact with one another. And this involves modifications, perhaps, to quantum formalism and so forth. Sure. And yet further, that there has remained, to my mind remarkably, and I do find it surprising, a tenacious view that Everett himself was not really committed to many worlds and indeed that there is a different reading

of his work that should indeed be an open-end inquiry in its own right. Well, okay, I'm fine with that. I mean, I'm all an open-ended inquiry, as it were, but I do think it's fairly obvious that indeed grasped the many-world's

aspect to his work, even though it's not his favoured way of framing it. And indeed rightly, I think many worlds doesn't quite get at what was special about the Everett interpretation. I mean, the Everett interpretation, it was special about multiplicity, so in that sense, many worlds, but the multiplicity did not have to involve worlds. I mean, they could have involved just trajectories of particles, and multiplicity of trajectories, arising with the same degrees of freedom. So these would be trajectories as in sequences of

localized quantum states, all in a superposition. Okay, so that is Everettian thinking, and you don't have to think of those things as worlds. Right. So it's just to illustrate how the core of Everett's thinking was not so much the global cosmological, blah, blah, blah. Wait, I'm not sure, sorry, I'm not sure how I can think of those as not worlds. So what would be the interpretation? What else would they be? Well, they're very small worlds. No, I agree with you. You know, of course, aggregate and have very large numbers of particles involved,

and then you've got superpositions of them doing very different things, and then, well, heavens above, aren't these like many worlds? And you can blow it up and look at the actual solar system and so on and so forth. I mean, it's quite interesting when you do look at the actual soda system from an Everettian point of view. In fact, I think this is a little known truth, the Everett's most detailed model that he gave of how to interpret

the Schrodinger equation, the evolving Schrodinger equation, was in terms of something very close to a model of the solar system. In fact, had he given, he could have done that. He could have put it in terms of a model of the solar system. forgetting about chaotic orbits and moons of planets like Jupiter and so forth, but just have four or five very large masses in gravitational interaction

and have them in a superposition of, well, have them initially in localized states and then bring about a superposition of two of those localized states and that would involve some very serious collision between the particles involved. so it would be non-trivial. But what would then develop would be a superposition of motions, each of which would be perfectly akin to a classical mechanical system.

Would exactly satisfy, exactly. Very high degree of approximation satisfy classical equations of motion. And Everett more or less indicated that. It was in this last section of his thesis, I think it was the last section, called supplementary topics, if I remember it correctly. And he only sketched the idea of how,

you could recover classical motions from quantum states. So this is the key to everyone's thinking. You've got to, it's not the degree of freedom that gives you the handle on tracking an object over time. It's quantum states of that degree of freedom that may evolve in such a way and involve a superposition of others that you can track them over time because they obey approximate equations. And you've got very large masses, well localized. The rules are the rules of Newtonian gravity or Newtonian mechanics, and they're very precise in those ways. But the rules could be slightly different,

and you can get out Naviostok equations and hydrodynamic equations and brownian motion and so forth. So you get out these rules for how states behave over time in accordance with these equations, but it's always states in superpositions with other states similar evolving over time, obeying definite rules. So that's the Everett interpretation. And he never put it quite like that.

And indeed, the way he put it in his 1957 paper, the rules in question were the measurement protocols. You know, prepare the instrument, measure spin, put the spin into value in memory, reset, measure again. That's a sequence of steps. And those are the rules. You can then analyze the quantum state evolving unitarily in terms of a sequence of states satisfying that protocol,

the same rule, the protocol rule, satisfying the protocol rule, but differing it's depending whether it's a spin-up state or a spin-down state. So it was sort of there. It was present in Everett, but it wasn't very vivid. I mean, to give another example of this, and I do want to push it

because I do think it's quite central to the Everton interpretation. Sure. If you consider radiation, so it's a classical linear theory just like Schroding equation, Maxwell's equations, everything's fine. So you've got the electromagnetic field

and it's evolving over time, just like you've got the Schroding equation and the state, quantum state, evolving over time. Now imagine what is happening in that electromagnetic field evolving over time when you switch on two torches. Well, what happens is you create excitations

in the electromagnetic field, field in the vicinity of the torches where you switch them on, which then propagate through the electromagnetic field. Okay, and they propagate in accordance with multifying rules, and they gradually spread over time and so forth, and it will depend on the medium and various other aspects to the whole setup as to what exactly happens where and when and what time intervals. Okay, but now imagine somebody comes along and says, look, what we've got, for each instant of time of the electromagnetic field, is we've got.

a superposition of a beam of light here and a beam of light here. And at the next instant, we've got a superposition, beam of light here, beam of light here, and so forth. And you end up to think, so what we've got in this evolution is the development of a superposition of a beam of light pointing in two different directions at once, which is a contradiction. Therefore, you cannot have this beam of light pointing in two directions at once, it makes no sense. Okay, to which the answer is, no, it's not a beam of light in a superposition pointing in two different directions.

It is two beams of light. And I think it would be a madman who would deny that on being pressed. You know, the same goes with mobile phone conversations going on all of the time. What's happening in the electromagnetic field? Well, there's lots of mobile phone conversations taking place all at the same time. and it's not that there's a superposition of a conversation taking all of these different words on one of the words at the same time, right?

Okay, so this sort of indicates what is the Everett interpretation? It is this preparedness to recognize, now looking back at the quantum state, this preparedness to recognize the sequence of stories. I've got a story here and I've got a story here, and that amounts to two stories. stories, it's not a single story saying two things at once. No, it's two stories.

Okay, so let me ask you about ontology then. In your mind, is what is ontological, or the most ontologically real? Is it the universal wave function? Say, bosons are not a part of this picture? Because I know you have some issues with bosons versus fermions. Fermions may exist to you. Is the universal wave function what's ontologically real? Or what about reshonsons? reduce density matrices, are those just as real or what? What I say real, I mean, much like how earlier in the conversation you were saying, as you look around, you would say that the tree is real and that this is real and so on. Yeah, right, yeah.

Yeah, I mean, I think the issue is, if we're looking just at low energy quantum mechanics, and you've got a reasonably stable system of degrees of freedom and particles in question, and you're neglecting things like phonons and certainly photons, and you then consider what would be the quantum state for that complex system. You've already suppressed a whole lot of stuff, so it will not be an adequate representation of the physics. But you can imagine that maybe this is a world in which, I don't know what, phonons somehow have been so suppressed,

and maybe there is no radiation, so it's a sort of pretend world, and we just got that quantum state unitarily evolving. Now, does that quantum state unitarily evolving in that way give us everything that we want? Well, I think the answer is yes. It's an adequate ontology, but it's not a perspicuous one. And because it's not even that adequate

because it doesn't account for all of the other bits and pieces. So then you could go to, well, let's take the standard model and we'll take the quantum state for the entire Hamiltonian as defined by the standard model, and we'll look at this representation of the Lorentz group in terms of this, and we'll consider that evolving state, which will now be, I mean, even Fox Space is not really adequate to this. The whole thing is too, it's over-precissified.

It's made precise in an inappropriate ways. But anyway, you could imagine that somehow being unitarily evolving, that is not a mistaken thing to say, although in practice it's a very difficult thing to really make sense of. and that would be an adequate representation of reality, but again, it would not be a perspicuous one. So what is perspicuous? It comes back to the sound waves or electromagnetic waves.

What is a perspicuous representation is not that I give you a snapshot of the electromagnetic field at each moment of time. That may be adequate for you to, you've got reality there, but it's not a perspicuous way of showing you what's going on or getting you to understand what's going on. So what is needed in that showing and understanding of what is going on in quantum mechanics is pretty well the whole Q number structure too.

You need the quantum operators, you need the algebraic structures, you need the group representation theorem above all. So you need all of that in place in order to really... It's not just all in the Hamiltonian, you've got the unitarily evolving state, and it's just all locked up in the Hamiltonia.

You are really articulating local structures to whatever discrimination you want, depending on what you're interested in doing, and you will need all of those Q numbers. One way of framing it is that the Q number structure, or Q numbers and the whole mathematical technology involved in that, is what allows you to give structure to the quantum state. The quantum state has that structure,

but what expresses it or articulates it is this technology of Q numbers. And what I find particularly perspicuous about it, of course, is projection operators and sequences of such, so quantum histories. But that's also just a coarse-graining of many different types of fine and path-hintechon approaches to quantum theory. So it's a fairly structured way of breaking down

and pretty well any quantum theory, and pretty well any quantum theory as well, into something like quantum histories with a measure over quantum histories. And the particular kinds of history is involved and the kind of structure that they have and the probability relationships that are thereby involved and where the de-coherence is going on

and if it isn't, then maybe we've got to give up on probability as something involved in the dynamics. And so forth. So I know that sounds like a bit of a big fudge. I'm saying yes, but not really. Yes, there's only the quantum state, but no, not really, because we need all of the other stuff in order to understand the quantum state,

in order to express it, in order to write it down, make sense of the representation that we've ended up with. It's a real collaboration. I see. I think philosophers do see some, you know, just some base level where everything else, you know, it just, you've got changes in that, the primitive ontology sort of position.

There's some primitive ontology, which is clearly stated, and a dynamical theory just tells you how it changes over time. End of. Are you an ontic structural realist? Oh, yeah, yeah, pretty well. Yeah, I mean, sure, this structural kind of representation of reality I take as being giving us reality, yeah, yeah.

I mean, I think it got taken in various ways that, you know, I don't think we're very helpful. I mean, one of the aspects to it is what is the role of mathematics? Okay, and as long as you think, think that our mathematics is really ultimately something more like set theory and the structuring questions of set theoretic structure, then I'm not a structure realist at all. So part of what I took to be important about structural realism was that it really was the mathematics that came first.

I have pages and pages of questions for you regarding many worlds theory. We're running out of time. and hopefully in this world, in this branch, we can speak again just on that topic because even a single question to delve into what precisely something means would require maybe an hour for just one question and have a variety of them. So those who are watching and listening, if you have further questions, feel free to leave them in the comments. We can get to them in the next time. I do have a question which you can tell me has a quick answer or doesn't, and then if it doesn't have a quick answer, we can answer it next time. So speaking of set theory,

in ZFC, or in ZF, sorry, the axiom of choice is equivalent to Zorin's lemma. So I'm wondering in your finite frequentism if equal amplitudes giving way to equal probabilities, is that then just another way of saying the Bourne rule in the same way that axiom of choice in ZF is another way of saying Zorin's lemma? Yeah, no, I don't think that's right. And partly because I think I would put it in terms of a postulate. And the postulate is very simple.

if there's such a thing as physical probability at all, and that's highly contentious. There's lots of people in many world approaches who deny that there is any objective probability other than agents, rational agents, and so forth. But if you think that there is anything like physical probability, then let it obey the following postulate. You cannot change X by an action, a physically allowed action on Y,

when Y is disjoint from X. and the action preserves disjointness throughout. So it's an extension of a kind of locality principle. It's a bit like the bell locality. You can't change the probability, physical probability of X, by messing around with Y, which is remote. And I'm saying you can't change the probability of X by messing around with Y which is disjoint.

And if you have that postulate, then that forces equit amplitude states to have equal probability. So any analysis of probability that gives you probabilities of states, if it satisfies that postulate, must give you equal probability to equal amplitude states. And that's translating disjointness into orthogonality. So that's a way, and that's a strict derivation of the born rule from a physical principle, but it's a new physical principle.

And heavens, people may find that a step too far. But notice that it's a principle that is obeyed by the born rule, as long as it's not being supplemented by anything like state collapse, dynamical collapse. And equivalently, as long as the actions that are relevant and permitted are unitary. So when it's

the original pasture, you cannot change the probability of X by a physical change to Y that is disjoint. It's got to be a physical change, something you can actually do. And if, and this is unitary quantum theory, all physical

changes are unitary, then you force that equal amplitude states must have equal probability. I mean, as a mathematical derivation, I doubt it's that interesting. But I think conceptually it's interesting. But, well, we'll see whether others find that. So it is my hope. But look, I'm sorry, we've overrun, haven't we?

And I sort of got the sense that we were getting sidetracked in so many interesting ways, you know. But I think that's probably what you do, and you did it brilliantly. But I worry that the result is going to seem really a bit. haphazard, you know, visiting one topic after another. Discursive discussions into reality is another name for this channel, so. I should have realized that better. It's been lovely, so I do hope for another occasion. So my last question, my last question before you go.

Oh, okay. Is do you have any tension in any of your worldviews that are rigorous? So let me give two examples, to circle back. One was that we have a feeling of a now, and we have a feeling of a moment in time moving, and a feeling that the future is open, not determined, and so forth. And then we have our more articulated physical models of the world. Okay, okay. So those two seem to be in tension.

Now, one way of resolving that tension is to say that the experiential one is more of an illusion. So you just somehow dispense with that in favor of the physical model. And then the other way is to just say, well, I have to live the way. with attention, I don't know how to resolve which one is more correct. It seems like at least this one is more able to be tested in the lab and get results, but it doesn't mean that my experience is wrong. I don't know how to make them compatible. So that's attention. That's living with attention. Hilary Putnam, now the second example is Hillary Putnam said that he goes to temple on Saturday, and he doesn't know how to make his conception of God compatible with his philosophy and his view of

science. And he just said, that's just the tension that I have. I don't know how to reconcile that. And then he had some platitude verbiage of, well, I find this tension productive. I mean, I don't buy that he finds that tension productive. I feel like that's something you have to say when you have a tension because you have to make the tension turn into something positive, otherwise you look foolish. But anyhow, do you have any tensions between your worldviews? Well, absolutely. And what they do is stretch me very far. I mean, I do find myself. I do find myself, stretched and it's not always pleasant. I mean, I'm not in my comfort zone as a result. That's how the tension is expressed. But I think the stretching is mostly productive and it's not to be somehow

alleviated by ignoring one or the other. It is to work with it. And it's potentially fruitful. So, I mean, look, it's possible to make progress on very limited things which may yet really illuminate much more greatly. And I'd give an example, partly as a result, I suppose, of teaching Leibnizian metaphysics, but I found Leibniz's methodology a very interesting way of resolving the mind-body problem. And it was entirely devised to that end.

I mean, that is why Leibniz devised it. It was the only way he could see of resolving the mind-body problem. So, all of the arguments, Chinese, spells Chinese Rome argument, things like that, and Leibniz saw it all very clearly. So there is a quantum version of the monotology. I find it extremely interesting. It is more like, it's not quite idealism, but it is a framework of thinking in which representation or in Leibnizian terms perception is the fundamental.

and that really the world is built up out of perceptions. So this is the monology, and there's a quantum version of it where these are really correlational structures. But, I mean, you could call them perceptual structures if you want it. I mean, I think there may be an appropriate shift of language in that way. And so might it be a way of seeing the physical reality really very differently in quantum mechanical terms.

I think there may be some possibilities of that. So that would be an example where if something like that were to really make sense, I think it would be a shifting of a lot of the things that are under stress, whether it would change the more fundamental of them, I'm not sure. I suppose I doubt it.

But I was struck by one thing, Bertrand Russell, when he read the monodology, he more or less said, well, look, in accordance with this, there'd be no such thing as absolute simultaneity. Something like that. That was in 1904 or three or something. Right, right.

So you said something interesting about stretching. Actually, I just started training at the gym, so I have a trainer now. Oh, cool. And his name is Satchit, for those who are watching. I recommend him. He's at Good Life, and Young and King in Toronto. Fantastic trainer, Satchit. Anyhow, he trains me.

I always tell him, kill me, when I'm. go, if I've slept well, I tell him, kill me, and he loves to hear that, because he's just push me hard, push me hard. And then I started to get some pains, and they started to be relieved by going to stretch therapy, by getting stretched, like actually getting stretched. I can stretch myself, but sometimes other people stretching me, they can do much more than I can do. And so just you talking about the productivity of stretching reminded me of a more concrete physical instantiation of this at the good life here in Toronto. So if that can be good for your body, then the stretching is interesting for the mind.

So I like that use of tension. Yeah. Okay. Yeah. Thank you so much. Well, thank you so much, really. It's been a great pleasure. Really enjoyed it.

I've also got a sense that you had all kinds of really hard questions to ask. Hi there. Kurt here. If you'd like more content from theories of everything and the very best listening experience, then be sure to check out my substack at Kurtjimungal.org. Some of the top perks are that every week you get brand new episodes ahead of time. You also get bonus written content exclusively for our members. That's c-U-R-T-J-I-M-U-N-G-A-L.org. You can also

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