Theories of Everything with Curt Jaimungal - Julian Barbour: The Physicist Who Says Time Doesn't Exist

Episode Date: November 16, 2024

In today's episode of Theories of Everything, Curt Jaimungal and Julian Barbour challenge conventional physics by exploring Barbour's revolutionary ideas on time as an emergent property of change, the universe's increasing order contrary to entropy, and the foundational nature of shape dynamics. SPONSOR (THE ECONOMIST): As a listener of TOE you can get a special 20% off discount to The Economist and all it has to offer! Visit https://www.economist.com/toe TOE'S TOP LINKS: - Support TOE on Patreon: https://patreon.com/curtjaimungal (early access to ad-free audio episodes!) - Enjoy TOE on Spotify! https://tinyurl.com/SpotifyTOE - Become a YouTube Member Here: https://www.youtube.com/channel/UCdWIQh9DGG6uhJk8eyIFl1w/join - Join TOE's Newsletter 'TOEmail' at https://www.curtjaimungal.org LINKED MENTIONED: - The Janus Point (Julian Barbour’s book): https://www.amazon.com/Janus-Point-New-Theory-Time/dp/0465095461 - ‘Relational Concepts of Space and Time’ (Julian Barbour’s 1982 paper): https://www.jstor.org/stable/687224 - ‘The Theory of Gravitation’ (Paul Dirac’s 1958 paper): https://www.jstor.org/stable/100497 - Carlo Rovelli on TOE: https://www.youtube.com/watch?v=hF4SAketEHY - ‘On the Nature of Things’ (book): https://www.hup.harvard.edu/books/9780674992009 - Leibniz: Philosophical Writings (book): https://www.amazon.com/Leibniz-Philosophical-Writings-Everymans-University/dp/0460119052 - Elementary Principles of Statistical Mechanics (book): https://www.amazon.com/Elementary-Principles-Statistical-Mechanics-Physics/dp/0486789950 - The interpretations of quantum mechanics in 5 minutes (article): https://curtjaimungal.substack.com/p/the-interpretations-of-quantum-mechanics - Sean Carroll on TOE: https://www.youtube.com/watch?v=9AoRxtYZrZo Timestamps: 00:00 - Introduction 02:12 - Working Outside of Academia 03:53 - Space, Time, Dimension 10:40 - Mach’s Principle 21:33 - Mach Confused Einstein 24:22 - Two Particle Universe 31:46 - Carlo Rovelli 35:02 - Julian’s Ontology 43:37 - Julian’s Theory ‘Shape Statistics’ 51:11 - Leinbiz’s Philosophical Writings 56:14 - Expansion of the Universe (Scale Invariance) 01:05:02 - Cosmological Principle 01:15:34 - Thermodynamics 01:17:15 - Entropy and Complexity 01:30:40 - Wave Function / Double Slit Experiment 01:39:21 - God 01:44:48 - The Role of Instruments 01:47:44 - Etymology of Pattern and Matter 01:51:25 - Join My Substack! Other Links: - Twitter: https://twitter.com/TOEwithCurt - Discord Invite: https://discord.com/invite/kBcnfNVwqs - iTunes: https://podcasts.apple.com/ca/podcast/better-left-unsaid-with-curt-jaimungal/id1521758802 - Subreddit r/TheoriesOfEverything: https://reddit.com/r/theoriesofeverything #science #sciencepodcast #physics #theoreticalphysics #time #space #dimensions Learn more about your ad choices. Visit megaphone.fm/adchoices

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iGaming Ontario. We are challenging the belief which is now held for 170 years, that the only way to explain our sense of the direction of time, the arrow of time, is that entropy is increasing, that disorder is increasing. But we're finding strong evidence in Newton's theory that it's the exact opposite. Very, very few people working in cosmology know about this. Very, very few people working in cosmology know about this. For over 50 years, working from a farmhouse north of Oxford, Julian Barber has been quietly developing a revolutionary theory that upends conventional physics. Time itself may be an illusion.

While the Academy raced down the path of quantum gravity and string theory, this physicist, who funded his research by translating Russian scientific journals, was busy tinkering with another model of the universe. What if what we call time is nothing more than the way that we interpret changing shapes? Time is just the shape of the universe. It's utterly impossible to measure the changes of things by time. Quite the contrary, time is an abstraction that we deduce from change. His theory, shape dynamics, suggests that the universe isn't evolving through time at all. Instead, what we perceive of as the flow of time is the difference between static configurations of the cosmos, like frames in a film strip. Even more surprising, his mathematical models predict that rather than descending into chaos, as our mainstream physics suggests,

the universe is actually becoming more ordered and complex, directly challenging the sacred second law of thermodynamics that even Einstein himself believed would never be overthrown. The exact opposite of the second law of thermodynamics, which says that the universe goes from being ordered to being uniform and uninteresting. And we've got exactly the opposite behavior coming out of Newton. In this episode, we explore Barbour's audacious ideas about time, shape, even consciousness, a new way of thinking about reality itself.

Julian, there aren't many people like you. There may be one or two other people like you, if that. And what I mean is that there aren't many people who are contributing to fundamental physics who are outside the academy, at least not in a meaningful way and succeeding. So let's talk about what is it like to do that and what are the challenges? Well, I was able to do it because of being interested in something which is not really normally in academia. I mean, years ago somebody said to me if I want to get into academia I should be able to publish one or two good research papers every year studying time and motion. I knew I couldn't do that and as it happened I was able to earn money

quite reasonably by translating Russian scientific journals. So I did that for 28 years. But it left me about a quarter to a third of my time to do research. And that was perfect. So just steadily now, it's now for over 50 years, I've just been beavering away at these ideas and I've managed to have some extremely good collaborators over the period. So it has just worked very well.

So that's how I've done it. There's a whole lot of fields in which that wouldn't work. Although it's getting easier now, I would say with all the things you can do online and access to libraries and talking to people. So I think it might be getting more possible, but that's how I've done it. Okay, now speaking about these ideas and these theories, how about before getting into those, we talk about, well, you define what is space, what is time, what is dimension.

These concepts will come up repeatedly, so let's have this precise common ground. Both as regards time, I always quote Ernst Mach, who says, it's utterly impossible to measure the changes of things by time. Quite the contrary, time is an abstraction that we deduce from change. So I think that there are instances of time, and I would now say that they are complete shapes of the universe, and that time is just a succession of such shapes. That's more or less what Leibniz already said, Newton's great opponent with whom he debated many things. So that's how I think about time.

And we just, I can perhaps illustrate it with this little model I've made here. I think you can see that. Let each of those triangles represent an instance. Suppose the universe just consisted of three particles, then they would be at the vertices of a triangle at each instant. And so the reality are the three particles at the vertices of the triangle. And time is something that we put in between those instant to make it seem that they're evolving in accordance with Newton's law. But the reality is just that you go from one triangle to another.

That's how I think about time. And there is a representation of Einstein's general relativity where simultaneity is restored. In fact, this is how I got into all this by chance reading about an article that the great Paul Dirac, the great quantum theoretician, quantum theoretician. In 1958, he published a paper in which he said that if we're going to create a quantum theory of gravity, we're going to have to restore simultaneity because if you imagine space-time like a loaf of bread, Einstein insisted that you could slice it in any way you like. And Dirac said, but that's an anathema for quantum mechanics, because you're just introducing redundant subsidiary degrees of

freedom, which have nothing to do with what's really happening. And this made a huge impression on me. And I think Dirac was quite right. Perhaps not precisely the way he put it in the mathematics that he did. But in essence, I think Dirac was right. And with collaborators, I think over the years, we've shown that is a much better way to think about general relativity. And it also does match what we observe in the universe because the microwave background defines

a notion of rest to very great accuracy really. In many ways that more or less coincides with the way Dirac thought about the universe. So that's basically how I think about time. Time is just the way we interpret the way that the shape of the universe changes. You said that Dirac had a notion of simultaneity. How does that make sense with special relativity? He was talking about general relativity, which replaced special relativity. Special relativity was made, really, I would say, redundant when Einstein created general relativity.

It will still hold in local regions the famous business of when you're falling freely in a gravitational field. That's when you can introduce something that is related, well, really to special relativity then, but it's restricted just to your immediate neighborhood when you're in free fall. It doesn't really apply to the whole universe, and that's what Dirac was thinking about. Now, we didn't get to definitions of space, but before we move on to the definition of

space and also dimension, if we go back to that cardboard diorama that you had, if you don't mind holding it up? Yeah, sure. So one way of thinking of what time is, is time has duration and time has succession. And on here you have these different slices. Now are you saying that there is no difference between the different slices? No, the slices are all different. I mean, they're my triangles.

Each triangle is different from the other one. In fact, I would say what really counts is just the shape of the triangles if we're talking about the whole universe, but the shapes are all different in my model. What I'm saying is that they are, I would say they define an instant of time, each of them defines an instant of time, but duration is not really out there in the universe. It's something that we put in. The instance

are there, but we put the duration between them. Do we also put the ordering between them? No, because that's in their intrinsic structure. If they evolve continuously and a certain quantity, in fact, this is exactly what does happen certainly in Newton's theory of gravity. And I strongly suspect in general relativity too. There is a quantity which grows steadily. In Newton's theory, it doesn't grow absolutely uniformly, but it's always increasing with certain fluctuations like that.

And this quantity is what we call the complexity, and that defines an arrow of time, which is nothing whatever to do with the increase of entropy. In fact, it's quite the opposite. It's an increase of order. So there can be, yes, there are differences. I would say each individual instant is distinct, just as the two triangles of different shapes are distinct.

I always illustrate everything with triangles because that's the simplest example you can take. Okay, so let's abandon for now the notions of space and dimension in terms of definitions, because that may take us off course. Why don't you talk about Mach's principle as that central to your work? So, Mach, like Leibniz before him, said Newton's notions of absolute space and time just make no sense.

Newton said that there is a space exists like a like sort of I say an infinite translucent block of ice in which you can describe straight lines. Now you can do that if you've got a block of ice you can take something and score a line along it. But if you tried to do that in an invisible space, you wouldn't leave any mark. So Leibniz said, this is just nonsense. And Leibniz said, space is the order of coexisting things. And when he was pressed what he meant by order, he said, I mean the distances between things. And then he said, time is just the succession of coexisting things. And whenever it was in 150, 160 years later, Mark essentially came back and said the same sort of things. And

Mark essentially came back and said the same sort of things. Mark's criticism of Newton's ideas was a big stimulus to Einstein, led him to create general relativity, was very much part of that story. What Mark wanted, so Mach's first criticism of Newton's ideas in 1870, in a little booklet, led a young German called Ludwig Langer to propose the notion of an inertial system, which is what today we call an inertial frame of reference. So, and Langer showed in

the simplest possible case with just purely inertial motion how given the motions you could determine what that inertial frame of reference is. Marc said, yes, that's fine, but I think you really need to take into account the whole universe. you really need to take into account the whole universe. So, Mark's idea was that the local inertial frame of reference is determined by the relative positions and the relative motions of all the bodies in the universe. That's how I define Mark's principle. Now, I would say Einstein didn't follow Mark too closely.

In fact, in many ways, I think Einstein introduced a whole lot of confusions. Nevertheless, with a lot of help from wonderful mathematics and also other physics, he did create this wonderful theory of general relativity, which we would never have if Einstein hadn't been so determined to create the theory. But I think in the process,

he created a tremendous muddle about what Bach's ideas really were. So a lot of my life has been spent trying to sort out that muddle. But as a solitary person sitting in the countryside, North of Oxford, people don't necessarily take you very seriously. They think Einstein's got to be right. In fact, I once had a discussion with a distinguished astrophysicist who said to me, well, this is what Mach said and this is what Mach did and what he required. And I said, excuse me, if you don't mind me saying

what you've just told me is Dennis Schama's, is your interpretation of Dennis Schama's interpretation of Einstein's interpretation of Mach. Interesting. And he said, you're quite right. I've never read a word of Mach. So here are these people who will tell you exactly what Mach's principle is, but they've never read his book.

Speaking of books, look, there's this book here called The Janus Point, and the link will be on screen and in the description for people who want to click on it. We're going to get to what the crux of this book is, as well as how your thoughts have evolved since this book may be evolved as the incorrect word because that makes a reference to time, but you understand. Let's make this extremely clear. If this book is in outer space and there's the moon, it's moving toward the moon, that's inertial.

Explain what is meant by mock when he says that there's something that's inertial and is determined by something that's distant. Explain it in terms of this book, just moving in space toward the moon. And then what are people supposed to understand? What is mock saying? as you moved it, as I move this to and fro, you see it moving relative to everything else. When you moved the book, I saw it moving relative to your face, the lamps, and the background. And Mark just says, you must describe everything. His idea of physics is not reductionist, it's holistic. You have to take into account

every last material body or bit of matter in the whole universe, and describe the motion of that book of mind relative to all the matter in the universe. in the universe. So that's, I mean, really, when Newton introduced absolute space and time, he made possible reductionist physics. You could imagine that things are just happening in space and time and you don't have to worry about anything else. But in reality, experimental work was always being done with things that the universe had created. When Galileo found the law of free fall, what he actually did was he got a very smooth plank of wood.

He had it at a very slight angle and then he had a smooth ball, which rolled down that board on which there were marks to mark equal distances that had been traversed. And then he had water flowing out of a tank, and he used the amount of water that was collected to measure the time. And then he found a law and that law said that in the first instant of time, it will flow one unit of distance in the next three, in the next five. And Galileo called that the law of odd numbers. But that material, that physical material, which had been created by the universe over billions of years. It wasn't just floating in

absolute space and time with no features around it. All of experimental physics on which all of our theories rely are done with such materials. You couldn't say anything without those things. And you really have to take into account how they got there, because otherwise you haven't got a complete explanation. So hold up that stapler once more, please. In your explanation, you didn't use the word inertia, but initially when talking about

mocks you used the word inertia. So help me understand what's meant by inertia. Is inertia traveling in a straight line without acceleration? Is inertia resistance to being pushed? What is inertia? Oh, this is good. So, inertial motion is moving in a straight line at one of these inertial systems that that young German Ludwig Lange defined back in the 1880s. That's inertial motion. Now, inertial mass is something different.

This is again, I would say, where Einstein made a mess. Newton defined mass in a circular way. Mach pointed out that Newton's definition of mass was circular. And he gave a very wonderful operational definition of mass, which I think still stands 100%. Basically, this is what students at school, at high school learn. It's illustrated with these things that float on carbon dioxide or whatever it is, white ice or something. So you have balls that roll across a table and they bump into each other and they give each other impacts in opposite directions. So

they impart accelerations to each other, which you can say are inversely proportional to the mass. So you'll have one particle gets, one ball gets an acceleration and the other one gets one, and there's a certain ratio of those accelerations. That is what defines the inertial mass according to Mach. Then if you take one of those two and do the same thing with the third ball, you'll get the inertial mass for that third ball and then you do it with the first one or the second one and the third one and you get a consistent system. It's what you say, it's transitive,

speaking mathematically. So this is really how Mach defined inertial mass. And Einstein just had had a sort of strange idea about things there. And very few people take the trouble to distinguish between for my way of thinking two quite different meanings of inertia. One is the inertial motion, which is the straight line when you've got one of these inertial frames of reference, and the other is this thing which always involves interaction between two things.

It's actually Newton's third law, as Mach pointed out, to every action there's an equal and opposite reaction. So that's how you define inertial mass. And I don't think it's ever been improved since Mach's time, but a lot of people are very confused about it. And what precisely did Einstein become confused about? Well, he thought and now it turns out he didn't do it, but it turns out you can just about do it. He thought that somehow or other that resistance to motion was

due to there being matter in the universe. So that if you could get infinitely far away from to there being matter in the universe. So that if you could get infinitely far away from or ever further away from the matter, that inertial, that resistance to motion would disappear. And in fact, it is true that you can make, I've recently learned about this, there are mathematical models where you can do that.

What happens is you can have a system of, it's not Newtonian gravity, but you can have a system where particles interact with each other. When two of them get, if two of them are close, you have an island of particles, a whole collection of particles,

that's the bulk of your model universe. If you have two island of particles, a whole collection of particles, that's the bulk of your model universe. And if you have two particles in that, they will have a certain speed as they go around each other, their gravitational effect, you can measure it when it's close to it. When you take them far away from it, they will go much faster. The effective gravitational force is much greater,

or the effective inertia that they have, their resistance gravitational force is much greater or the effective inertia that they have their resistance to motion is much less. And that is a way of doing it, but you still, to determine the mass ratios, you still need Marx's definition. So this model was first proposed to my knowledge by a German called Trader. He was from East Germany and he proposed it I think in perhaps the 1970s or something like that. And I've recently been interacting with a German student called Dennis Brown who has been working on this model. And it undoubtedly is a consistent model,

but you still need to specify a mass with any of these things. You still need marks definition through the mutual accelerations that bodies impart to each other. Now, whether that is a model that really describes the whole universe, I think that's an open question,

but it certainly is an interesting model. I think it has done a lot to clarify. I'm hoping Dennis' model, the paper that he's writing about this will get published fairly soon. It deserves to be published, and that will help to clarify the issue. This episode is brought to you by Melissa and Doug.

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And let's imagine now that there are thousands of particles, even though yours just has three. Yeah. Are you to then infer the mass based on the acceleration? Is that Mach's way of defining mass? Rather than each particle has the property of mass, you infer mass based on acceleration? You infer mass based on acceleration? You infer mass based on accelerations.

The accelerations imparted mutually when two particles interact with each other. It would be much more complicated if you've got a whole lot of other ones. I mean, this works because you can get a situation where you have particles moving more or less in straight lines in the background. I mean, this is what happens in high school demonstrations. You've just got these balls moving across the smooth table. You can do it with billiard balls on the bullion table too.

You can do it with billiard balls on the bollard table too. Would this mean that in a two-particle universe that they necessarily have the same mass? Well, in a two-particle universe, you can't do anything non-trivial, because you've got nothing to describe what's going on. I always insist the first non-trivial universe has three particles, and then you can do an amazing amount. It's wonderful how many conceptual points you can get across with just three particles. What about a one-particle universe? It would see nothing.

I mean, no, no, I mean, I use three particles all the time to illustrate the things because it's wonderful how much you can get across. Above all, it has a triangle has a shape, but two particles don't have a shape. Okay. Is the triviality of a two particle universe the same as the triviality of a one-particle universe, namely nothing happens, nothing interesting, or is it even slightly more interesting in the two-particle case than the one? First of all, if you imagine you've got a ruler outside in addition to it, then you

can tell how far they are apart. The only sense in which, but without a ruler, all you can say is either they're sitting on top of each other or they're separate. But if they're sitting on top of each other, it would be difficult to see this too. So for me, one particle and twoicle universes just don't make sense. Now, of course, you get... One of the reasons why people think two-particle universes make sense is these wonderful discoveries of Kepler.

Kepler's laws were particles, two particles according to Newton. They go in Keplerian ellipses around their center of mass. But you would never be able to say they were doing that if you didn't have the framework defined by the fixed stars and the rotation period of the Earth, sidereal time. So Marx said Newton's laws were not confirmed, this was back in the 19th century, Newton's laws were not confirmed

relative to absolute space and absolute time, but relative to the fixed stars and the rotation period of the Earth to define time. And that's often forgotten. What is the mechanism by which something here that's local knows about the global? I personally think it's in just in it's in geometry. Just in its geometry, I would say that just in the simplest geometry, Euclidean geometry, there are correlations. If you have N particles in Euclidean space, you can measure the distances between them and

those the number of those it's n times n minus 1 divided by 2. That's the number, so you've got those number of numbers. Now suppose somebody doesn't tell you where those numbers came from but you've been given the numbers. Well, then you would find that actually they satisfy a whole lot of algebraic relations. Certain quantities, certain determinants formed from them are equal to zero. This is what's called distance geometry. Back in ancient Greek times,

some Greek whose name I forget, had a formula which tells you what the area of a triangle is in terms of its sides. And that's expressed through the value of a determinant. But if all the three particles lie on a line, then that determinant is equal to zero. And then that tells you that those separations are in a one-dimensional Euclidean space. And then in the 19th century,

in the middle of the 19th century, a mathematician showed that if you have four particles, then you can make a determinant out of those distances between the four particles that tell you the volume that's enclosed between them. But if that determinant vanishes, it tells you that they're in two dimensions, that they've flattened down into two dimensions. So I would say that there isn't any interaction between the particles. They are just, the distances between them are correlated and that's what we call geometry.

And by the way, this is very similar to the famous Bell inequalities and the correlations that in quantum mechanics with entanglement, where you cannot send any information, but if you know some fact over here, later on you can find that it's correlated with the fact over there. People think this is very mysterious because that correlation is established instantaneously, but no information can be sent by means of that correlation.

You can only do it afterwards by establishing what's there. I think this is very like the situation in geometry that I've just described. So I wonder whether the most mysterious things about quantum mechanics aren't just a reflection of the fact that we're talking about relationships in space. Have you read up on Carlo Rovelli's relational interpretation of quantum mechanics?

I have. I have to say, Carlo's a good friend, but I'm not, I have to say I'm not, my problem with that is that he doesn't really describe, define for my satisfaction what are the things that are being related. And I actually, I may also say that his use of the word relational comes from me. Because right back in 1972, I was getting increasingly aware that people were confusing what I would call Einstein's special relativity or general relativity with what Marx said by and Leibniz by the relativity of motion. So I wrote a paper, it came out in 1972, which said the title of the paper is relational concepts of space and time, in which I said we need to distinguish between relational things which can happen,

exist at a given instant, that my hand is a foot from the edge of my desk and things like that. That's nothing to do with Einstein's special theory of relativity. So I suggested that that distinction should be made, and we needed to introduce the word relational. Well, Lee Smolin took it over from me and Carlo took it over from Lee. Since then, a lot of other people have taken it over from Lee and since then a lot of other people have taken it over

from Carlo and otherwise. So I think I can claim to be the person responsible for that word relational coming in there. But I must say I think Carlo's on the right intuition, but I think the theory is not complete because in the end there are relations between definite things and I don't think he defines them sufficiently clearly. But to be fair to Carlo, I haven't really read his paper in great detail, but I think that's about all I can say. Yes. As far as I know, with Carlo, it's an infinite regress of relations. So what's being related? Well, other relations, and what's the relations that define those are other relations and the relato are also relations. That could well be. I am at the moment with my main collaborator at the moment, Tim Mikoslowski. He's German despite the somewhat Polish sounding name. We are working on a definition of what we call complexity when there aren't

not just a finite number of particles but infinitely many particles. I think that's a very interesting problem on which we're working. In your theory, there is something that's being related, namely particles. namely particles. Yes. I, at the moment, I'm trying to work, I'm trying to start with the absolute simplest possible

ontology. What is the world made of, that could possibly explain all the observations, all the experiences we have. The simplest conceivable one, I think, is point particles in Euclidean space. They could all have the same mass. They could be equal mass particles. And I think out of that in principle one could explain all the structure of the world, not

the fact that I see and hear you because that's the mystery of consciousness. But I think all of the structure, I mean the ratio of the distance between your eyes to the from them to the tip of your nose and things like that. That's what I would call the structure. Then I would say it's a gift of existence that then I see the color of your eyes and the shape of your nose and your dark hair and all that other stuff there. This is the, I would say the gift of consciousness. But the underlying structure could be just points in space.

Have you ever looked at the famous book on the atomistic theory of the Greeks? In fact, what the Greek atomists really said has more or less, there's not much survived. The main text is by the Roman poet Lucretius in the first century BC, De rerum naturai, On the Nature of Things. Now, it's very interesting there because what the atomists and above all, Lucretius is concerned with is to explain all the extraordinary shape that there are in the universe.

So many shapes, you see, it started with looking at the heavens and seeing the constellations and putting stories into the shapes there. So I've recently read, I've only got halfway through Lucretius's poem. It's a very long poem. It's a miracle it survived. And how does he explain all these shapes, the different shapes?

He wants to understand why children look like their parents, why all sheep look much the same, why there are different types of trees and so forth. Well, what he does in the English translation I have, the word atom appears as a primordial seed. He talks about primordial seeds. He doesn't really have an explanation of the shapes he sees because every shape that he sees, he invokes a different primordial seed.

Now, his primordial seeds are the Greek atoms, indivisible things, but they're solid, indivisible, and they have shapes. They also have relative sizes. After a bit, you get a bit bored with his book because he turns to the next thing he wants to explain. He does it by introducing another type of primordial scene with a different shape. And he does anticipate

the problem of consciousness and where that comes from. And that's because he says then that we've got the tiniest, roundest, smoothest seeds of all that are running around in our brain. seeds of all that are running around in our brain. Because that- Interesting. So, but that does highlight that the great task of science that the Greeks anticipated was to explain shapes. That that's why I talk about shapes rather than the size of things.

So, I always start off by saying, make a distinction between the shape of a triangle and the size of a triangle. So people sort of, I think people instinctively think that things have a size. It's just there. And in fact, I think it's when people talk about the expansion of the universe.

They just imagine that there's a ruler outside the universe which tells you that it's getting bigger. But the way I like to put it, suppose, suppose, you know, this concept of proprioception, when we're aware of where our body parts are, it's a very wonderful thing, you know, I know now that my two knees are about two inches apart, and that if I move my muscles, bang, I've just done it, they'll come together and I'll feel the impact when they come together. Now suppose I hold up my triangles again and I've got a ruler.

Well, I can put the ruler and measure the length of the sides. I've got a ruler somewhere behind me. But suppose the triangle is aware of itself. Each vertex, so to speak, can see the other two vertices. Well, what it will see is an angle between them. It won't see how far away they are. So if the triangle is aware of itself, it's just aware that it has three angles

and that they add up to 180 degrees. That's, I think, how one should think about size. Then, so what is the smallest triangle? Then you can say, which is the smallest triangle? Well, it's the equilateral triangle because all sides are equal. But then as the triangle gets more pointed, the triangle will say, well, I'm going to take the shortest side to measure the other two. And according to that, as it gets more and more pointed, those other two will get further and further away. The triangle will say it's getting bigger, it's expanding. So this is purely intrinsic. So we're talking about the size of the triangle

without a ruler outside it. And I think this is the way one should think about the expansion of the universe. Okay, so let's make that clear for a moment. If we have an equilateral triangle and we have no measure of size, you're trying to get a measure of size. And then you said the equilateral triangle is the smallest and you're wondering, or the audience is wondering, well, how the heck can you measure the size of an equilateral triangle when you said that there is no ruler? And how the heck can an equilateral triangle be said to be smaller or larger than some isosceles triangle or some other form of triangle?

And what you said is, well, let's look at all of the angles. Let's choose the smallest angle. Use that as the objective measuring stick, like the inch, let's say. And then you measure all of the other quantities relative to that shortest one. Yes, actually it would have to be one over the smallest angle. I did actually talk about the size, but better is the angle.

Yes. So I take the smallest angle, but I divide one by the smallest angle. And then as the triangle gets more and more pointed, the size gets bigger and bigger. Now that's singling out one angle, but there's a quantity called the complexity, which takes into account all.

Now I did send you some slides. I wonder whether you can put them on the screen because then I could explain how you can define an intrinsic size. In fact, it's the first slide number one, if you can show. Sure. As I'm loading it up, so give me a minute to do so, please explain to the audience the name of your theory, first of all, so that they can contextualize it.

Is it shape dynamics? Is it called the Janus point? Like what do you call your theory? And then just give the broad strokes of what the theory is. Well, back in, it's 25 years ago, I coined the key idea, shape dynamics, and my main collaborator, Tim Skorzowski, and I now see in some ways more important is what we

call shape statistics. It's all about understanding the nature of shapes defined by points in space. It's easier to express things in terms of separations. So we start off by imagining we have a ruler which tells us how far the particles are apart and then we're going to in a way change the equations, write an equation which doesn't involve that ruler. So I've written it down for first of all three particles which I've given names to, one, two and three, but then there can be any number of particles. So you take all pairs of particles, you can take as many particles as you like, and so

there are then separations between the particles R12, R13, R23 and so forth. And then the quantity that I call the complexity is first of all the square root of the sum of the squares of all those separations. That's a number which we call the root mean square length. So that's a length because each separation is a length. So I've squared all the separations, that makes length squared, but then I take the square root. So that's a length. And the second expression in brackets next to it,

is just one divided by each of those separations. So that's one upon a length. next to it is just one divided by each of those separations. So that's one upon a length. And that means that that expression, which I call the complexity, is independent of any ruler I choose to describe it by. How? It's scale invariant. So if...

Yes, I see that. Do you see that? And I think... I think the readers will, with a little bit of an effort, they'll work that out. I mean, you can put an A underneath the square root and then it'll be an A squared in front of all the separation. The reason I asked how is because it's not clear why scale invariance implies ruler invariance. Like, why are you saying that if it's independent of a ruler, that's equivalent to being scale invariant?

Well, if I was to, if I took my, well, no, that's quite easy. If I just take one of my triangles and measure it with my ruler, it's hidden somewhere underneath all my papers. If I measure it with the ruler on the side that says inches, I'll get a certain value. If I use it on the other side, which gives centimeters, I get a completely different value for the R. So I want something which doesn't depend

upon that arbitrary choice of the unit on the two sides of the ruler. And that's what this expression does. Okay. So now the one underneath it? And the one underneath it is just if you want to add masses. Okay. So each particle then has masses. And then I assume that all the masses add up to one. And then these are pure numbers. In both cases, I arrange it so that they're pure numbers.

You don't need to have a scale to find what the masses are. And you don't need a ruler to do those things. Now, this I think I would say, this is what I call three-dimensional scale invariance, and it plays a very small role in physics. It's very interesting. Let me read you something. The great Henri Poincaré, his book, Science and Method.

Sure. Does that come out mirror image or you can see it all right? Science and method. No, I can see fine. Yeah. It shows a mirror to you but not to me. Yeah. So in this famous book of his, in the first decade of the last century,

he's talking about changing the scale. He says, suppose that in one night all the dimensions of the universe came a thousand times larger. The world will remain similar to itself if we give the word similitude the meaning it has in the third book of Euclid. Only what was formerly a metre long will now measure a kilometre, and what was a millimetre long will now become a metre. The bed in which I went to sleep and my body itself will have grown in the same proportion. When I wake in the morning, in the same proportion. When I wake in the morning, what will be my feeling in face of such an astonishing transformation? Well, I shall not notice anything at all. In reality the change only exists for those who argue as if space were absolute.

So he's perfectly aware of this problem. But Poincare, one of the greatest mathematicians of all time, did nothing about it. He did not produce something which just characterizes shape and changes when the shape does. But this is exactly what that complexity does that is defined in the slide that you showed, or maybe still showing. So what's the justification for that expression? So suppose you have particles distributed in space, and you

want to define a number which characterizes in the simplest possible way the extent to which they're either uniformly distributed or clustered. So that expression that I've that that complexity is, I think, just about the simplest thing that you could possibly use to do it. I think it's an extraordinarily interesting number, and I'm getting more and more the suspicion that it might be the most important way of thinking about the universe. And it's just been just been ignored up to now. Well, the first thing,

I said that it was all the definition, you come to this definition, and this is how I did come to it. So let me give a little bit of background. I read Leibniz's, some of Leibniz's philosophical writings, this wonderful collection of Leibniz's philosophical writings, 60 years old or something. I first read that back in 1977, and it made a huge impression on me. Leibniz said, without variety, there would be nothing.

We couldn't say anything, we couldn't see anything. The whole of our existence relies upon the existence of variety. Then Leibniz was a perfectionist, so he said, what we really want is a universe which is more varied than any other possible universe. So in his famous monodology, he says, we live in the universe which is more varied than any other possible universe, but subject to the simplest possible rules. And so far as I know, nobody had ever given that mathematical expression until I introduced Lee Smolin to Leibniz's ideas. And he came up with a mathematical expression to do that. And I came up with a slightly different one. But then after a while,

I began to feel both Lee's version and mine was not very satisfactory because there was to increase the variety. So then when you really look at Leibniz's philosophy, it's not so much that the universe is eternally maximally varied, but that it's striving to become ever more varied. The only way you could make either Lee's or

my definition of variety increase would be just by increasing the number of particles. You wouldn't be able to get that by changing the separations between the particles. So I was always on the lookout for something that would do that. And then it was in 2011, through the fact that I've been interacting already for 12 years with some of the top people who work on Newton's theory of universal gravitation, that discussing with one of them, we came to the conclusion that something that they call the shape potential or the normalized Newton potential is the quantity that would characterize variety.

is the quantity that would characterize variety. So if you, are you still showing the expression, my expression for? No, no. Well, I don't know whether you can show it again Kurt or? Yeah, we can bring it up. Perhaps you can bring it up. If you look at that expression and say, a couple of particles, you want to say how it will react to clustering.

So the first, all the stuff under the square root won't change much if a few part, two or three particles. I'm imagining lots of particles, so lots of separations. If two or three particles I'm imagining lots of particles so lots of separations if two or three get closer to each other that doesn't change much because the other ones are squared and it's not very much but in the second factor where you've got one upon the separations that is very sensitive that increases hugely if the if just two particles get closer to each other. And in fact, if they coincide, it becomes infinite.

So that complexity is extremely sensitive to clustering. Okay. So that's exactly the sort of effect that I wanted to, it characterizes variety. In fact, maybe it would have been better to call it the variety rather than the complexity. Now, what is very interesting about that expression, particularly when you look at the one with the masses, the second one is just the Newtont, except for the sign, it's just the Newtonian gravitational potential. It's the gravitational potential from which

the famous one upon R squared forces are derived. Right. And the other one is the quantity which measures the size of the system. So that the Newtonian n-body problem, that's n particles, a finite number, n of particles interacting with each other, those, it's all about how those two numbers change. And lo and behold, it comes out of

the desire to implement Leibniz's idea that without variety there would be nothing. So neighbor's nightly saxophone practices? Er, nope. You're on your own there. Could have skipped it. Should have skipped it. Skip to the good part and get groceries, meals, and more delivered right to your door on skip. Breaking news happens anywhere, anytime. Police have warned the protesters repeatedly, get back.

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then let's take that second equation. We have the square root of M1 times M2 times the square of r plus a variety of terms that are similar. You could also have chosen the cubed root of m1, m2, r cubed plus so on so on so on, or any to the n. And I'm sure there are a variety of other equations that satisfy both scale invariants as well as clustering being proportional to high complexity. So what landed you on this one? Well, I think there's a nice rule that Einstein had. When you, this is what I do approve of. When you've got a new non-trivial idea, try it out first on

the simplest non-trivial case. And this is just about the simplest that you can get. Now if you went to all these more complicated ones, you would get still the same sort of results because the key thing is that it's scale invariant. The actual way you implement it, you can implement scale invariance in many different ways, but the interesting thing is that there's an underlying general property which will be common however you do it, and that because of the key principle that you want three-dimensional scale invariance. Hmm, okay. Now, what do you say to that passage that you had read before about if we had doubled

everything, every single thing or tripled every single thing, there would be no difference, we wouldn't be able to tell. That seems to me to be reflective of the 19th century or prior, but the standard model isn't scale invariant. So what do you say to that? Well, first of all, I'm very, I must say I am skeptical about the way think about the way cosmologists think about the expansion of the universe. I think they do just imagine that it's as if there was a ruler out there. They illustrate it in various ways with stretching elastic and they put buttons on elastic and they stretch it apart and they talk about space expanding. I have to say I'm very skeptical about that.

I haven't really gone into the standard model in particle physics. But I'll come back to what I said before. What is the absolute minimal ontology that we can possibly hope to describe the universe? Let's see how far we can get with that. And I think we may not have got things right by any means still. We're a long, long way from saying we've got a new theory of the universe, but it is striking what we have got.

And I've got one or two more things to show that will illustrate that fact. Of course. Well let me just before we do that, a very key property of the one that you're still showing the complexity is that everything in it is positive. It's a positive number. It's what you call positive definite. And being positive definite, it must have an absolute minimum.

And I'll anticipate something by saying that absolute minimum is essentially always realized on a unique shape and I'll already give it a name. I call that unique shape alpha. And that shape, just by the way of the definition, that shape is more uniform than any other possible shape that you could have. So that's already quite an interesting thing. I should say that Richard Batty, who's an astronomer in Manchester,

very kindly made that image available to my collaborator and then found its way into my book, The Janus Point. But if you're leaving this still, if you're not editing this out, I should give thanks to, acknowledge thanks to Richard Batty. Yes. Great. So you'll see that it shows a sort of,

as if it was in three dimension, you see an extremely uniform ball. This is, I think, I'm pretty certain it's 5,000 particles. So it might just be 500, it's a little bit difficult. You can't count them. But on the left, it's shown as

if you were looking at a ball of them. And on the right, it's an equatorial section through. And you'll see that it's not perfectly uniform, but it's very uniform. And it may well be at, or it's certainly very, very close to the absolute minimum of that quantity, my complexity. And you'll see that it's remarkably uniform. And the fact that it is so uniform is a consequence of a

famous theorem that Newton proved, Newton's potential theorem, which explains why non-rotating stars like the Sun are spherically symmetric. So Newton's potential theorem says that if you're outside a spherically symmetric mass distribution, the gravitational effect of that distribution is as if all the mass were concentrated at its center. Right. And if you were within it, you would be, it would be just the mass that's at less distance from the

center than you are, that's concentrated at the center, that's what you feel. So this is Newton's theorem. Now, the structure of the complexity is such that really, there's a balance of forces. That shape is actually also called, well, it's got two names. It's called a central configuration, and it's also called a relative equilibrium. Now it's called a central configuration because if you think of that distribution of particles then the net force that each particle is subject to, exerted by all the others,

points exactly towards the common center of mass, and increases, gets stronger with the distance, so that gravitational force. So that's why it's called a central configuration. If it was just pure gravity and they started at rest, then they'd all start moving towards the center of gravity where they would all collide at once in what's called a total collision. But the much better way of thinking about that distribution is what's called a relative equilibrium. equilibrium, because what is really there is that there are repulsive forces, hook after the famous hook HOOK, who was also another great rival of Newton's. So there are, you can either say there are attractive Newtonian forces that get stronger

with the distance, balanced by repulsive hook forces, which also get stronger with the distance, balanced by repulsive hook forces which also get stronger with the distance, so the thing is held in relative equilibrium. But equally you could just as well say that there are repulsive gravitational forces and attractive hook forces. It doesn't make any difference which way you think about it. So these are very interesting structures indeed. They're held in balance. Just to say again how interesting is, if it's in two dimensions and I'll show one in two dimensions where you don't have uniformity because

that wonderful theorem of Newton's just holds in three dimensional space and for potentials that are one upon R. So the forces are one upon R squared. It doesn't hold under any other circumstance. And I begin to think that this could be a very fundamental hint to what is going on in the whole universe. Explain. Well, there's the cosmologists, there's a holy grail of the cosmologists, which is what they call the cosmo, it used to be called the Copernican principle, but it's now called the cosmological principle, which is that if you look at a large enough region of the universe, it will look like any other equally large region anywhere else in the universe. It looks the same anywhere you are.

So that's called the cosmological principle. They're very pleased that they think they've got that in cosmology thanks to the theory of inflation in there. But I'm wondering if it doesn't really actually go back to Newton's idea and that you don't need inflation at all. Because if you imagine you put a dime, a small coin anywhere down on that section on the right, shall we say that's a tenth of the diameter of the total thing on the right, it would cover shapes that look much the same. It would satisfy the cosmological principle. Uh-huh. And if you had spheres containing the particles,

small spheres containing the particles in the one on the left, they would also look the same wherever you put the sphere, unless it was right at the edge and you were at the rim. So that's pretty interesting. That comes straight out of, that comes straight out of Newton's theory and this quantity that we call the complexity. The specialists in the field call it the shape complexity or the normalized Newton constant. And it is actually

the quantity that really governs everything of interest that happens in the Newtonian N-body problem. The Newton potential is not really what counts, it's that, this quantity, what I call the complexity and what the N-body people call the shape potential. And so, and you can, and what the N-body people call the shape potential. And so, and you can, what is very interesting, very few people except the specialists in the field

know about this thing. You can have these total collisions, they were first discovered in 1907 by a Finnish mathematician called Carl Sundtman and he was the first person to ask in Newton's theory is it possible for three particles to collide all at once at their center of mass and he proved that they could, very remarkable, very sophisticated mathematics, subject to some very interesting conditions.

First, the angular momentum must be zero. There must be no overall rotation in the system. And secondly, as it comes to the total collision, the shape must become very special. Either it must become an equilateral triangle, whatever the mass is, or it must become a collinear configuration where one particle is,

there are three of those because one particle can be in between the others, and that's whatever the masses. So that's very, very interesting. And then a year later, somebody called Block showed that St. Mons result is exactly the same thing happens, more or less exactly the same thing happens, if there are any number of particles.

And so this is 1907, 1908. Now, Newton's equations work both way in time. So instead of thinking of it as a total collision, you can suppose it's going the other way. And then it becomes a Newtonian big bang, extraordinarily uniform. And this is 20 years before Hubble publishes the law for the expansion of the universe. So if that isn't thought provoking, I don't know what is. And very, very few people working in cosmology know about these facts. So are you saying that there's this formula here called complexity, which different people in different fields call it different names like shape potential, you said, the end body

people call it different names like shape, potentially said the end body people call it. If you minimize this, it's like minimizing the action, their version of action. If you minimize this, that is the state of the universe at any given point or any given slice of time or instance. I'm not sure what to say there. It characterizes the shape of, if you accept my idea that there are Newtonian big bangs, so the Newtonian big bangs start from these very special shapes, and in particular they can start from the one which is most uniform, that alpha.

So it would be very like the one on the left, that ball on the left. So that would be the first instant of time, the first instant of a Newtonian Big Bang. So looking at this image with the circles and one is more dense on the left, one is more sparse on the right, you're saying the one on the left. The one on the right is the section through, the equatorial section through. The one on the left is if you were to speak, if it was a swarm of bees, what it would look like if it was a swarm of bees.

So what we're actually looking at on the left one is the 3D version of just points. That's right. Yes. It's a 3D version of, I think it's 5,000 particles, but it might be 500. Sure. But you see how amazingly smooth it is. Why is it odd that it's smooth?

So you're saying that it's not that you started out with a sphere and you're just trying to populate it with some uniform probability over the points inside the sphere. You started out with something else and it became a sphere? Let's go back because I think the story is worth telling. It all goes back to Leibniz and me being so impressed by it. So Leibniz said, I want something that I think variety is the most important thing in the universe. So I tried to find an expression which characterizes that variety and I found it,

lo and behold, in Isaac Newton's theory of gravity. And then I later on, well, I did that more or less at the same time. A little bit later I discovered that actually there are Newtonian big bangs. That the Newtonian big bangs start, the most interesting Newtonian big bangs, but they all start when that takes a very special shape and the most interesting ones start when it's at its most uniform shape. So you're led more or less directly to Newtonian big bangs.

They start maximally uniform, but as they progress, as time passes in the way we think of it, structures form and the universe gets more structured, more ordered. That is the exact opposite of the second law of thermodynamics, which says that the universe goes from being ordered to being uniform and uninteresting. And we've got exactly the opposite behavior coming out of Newton. So this is quite a bit of what my book, The Janus Point, is about. We are challenging the,

it's a belief which is now held for 170 years, that the only way to explain our sense of the direction of time, the arrow of time, is that entropy is increasing, that disorder is increasing, but we're finding strong evidence in Newton's theory that it's the exact opposite. Now, it's a different matter. Within those Newtonian universes, subsystems can form, clusters can form as they get ever more structured. Subsystems can form within them and as they form and then decay, they do behave like thermodynamic systems. They do what's called virialize,

which is characteristic of thermodynamic systems. So in some senses, we are explaining, we're deriving the second law of thermodynamics and saying that it's not as fundamental. Let me read you what the famous English astronomer Arthur Eddington said. The law that entropy always increases holds, I think, the supreme position among the laws of nature. If your theory is found to be against the second law of thermodynamics, I can give you no hope. There is nothing for it to collapse in deepest humiliation. Right. And let me now add something that

Einstein said on thermodynamics. He said, it is the only physical theory of universal content, which I am convinced that within the framework of applicability of its basic concepts will never be overthrown. Now the interesting thing is Einstein did not say what is the framework of applicability of its basic concepts. And I think this is a point that I'm making throughout the Janus point. I think people have just completely forgotten what are the conditions under which thermodynamics is valid. And that goes back to how thermodynamics was discovered.

It came out of Sardicano in 1824, wrote this wonderful little book on the motive power of fire in which he was working out conditions under which steam engines operate with maximal efficiency and that was what led 25-26 years later to the discovery of the first two laws of thermodynamics. Now a steam engine stops working if the steam escapes from the cylinder. The steam has to be in a box. And if you look at the wonderful definition of entropy by Rudolf Clausius, it's all about a system in a box where the size of the box is slowly changed and you control whether heat is getting in and out.

It's absolutely critical the box is there. And then if you look at the atomistic explanation of the laws of thermodynamics, starting also with seriously with Clausius, but then Maxwell, then Boltzmann, and then Gibbs, they all assume molecules in a box. They bump into each other and they bounce off the walls of the box elastically. And nobody, and I'll now stick my neck out, I don't think anybody has seriously asked what happens if the box is not there. This is what the main message of the Janus point is. Things are just completely different. It's as different as night and day. And amazingly people haven't thought about that. Can you please explain the relationship between complexity or at least your measure of complexity?

And we should know, we should state to the audience that there are a variety of measures of complexity like Kalmykhorov and so on. So you have a specific kind. There are also a variety of measures of entropy such as Shannon and Boltzmann and so on. So I don't know if you're referring to all of these entropies, but anyhow explain the relationship between your measure of complexity and entropy as they both increase with the universe. However, your complexity is associated with order. So as the Newtonian universe, in the Newtonian universe, Big Bang, the complexity increases and with it the order increases.

it increases and whether the order increases. The key thing is that entropy is not a scale invariant concept, whereas complexity is a scale invariant concept. If you put a system in a box that immediately introduces a length scale, that's the length of the sides of the box. You've then got ratios, you've got separations between the, the separations between the particles are always some ratio of the diameter of the, of the length of the box. Now, just, if you, if you don't have something like that, you can't define probabilities meaningfully.

Suppose you had a deck of cards with 52 cards in, then your chance of getting the King of Hearts is 1 over 52. But if you had a deck of cards with infinitely many cards in, the chance of getting any one particular card, if you put your hand into an infinite bag, would be zero. Right. Now Einstein, let me quote somebody else. Einstein, so the man who is really highly regarded in physics, Einstein called him the greatest American physicist,

that was in Einstein's time, was Willard Gibbs. Gibbs in this famous book here, Elementary Principles of Statistical Mechanics, he develops how you do it. He has his result, which gives a coefficient of probability. But he then says, he has a caveat. He says that there are circumstances

in which the coefficient of probability vanishes and the law of distribution becomes illusory. That was what I gave with my example of a deck of cards with an infinitely many cards in. You can't talk about probabilities if there are infinitely many cards in that case. So he says that you can't talk. So this is what Einstein should have said, my basic principles,

what was Einstein's words? Within the framework of applicability of its basic concepts. He didn't say what the framework of applicability was. It's that in Gibbs's words, that the system cannot become distributed in unlimited space or the momenta, the energies of the individual particles, become infinitely great. Because then mathematically you're in a situation where you're talking about a phase space of unbounded Liouville measure.

And that's just like my infinitely many cards in a deck of cards. And this is just not being recognized. And when you get, and I think it's just the same in quantum mechanics, because in quantum mechanics, you have Hilbert spaces. And if you're going to define probabilities in Hilbert spaces, then there can only be a finite number of states in that Hilbert space. If you've got one with infinitely many possibilities, then again you won't get proper probabilities. So I think it just breaks down. Is the universe in a box? I don't think the universe is in a box.

Or it's very questionable and if the universe is not in a box. So what happens in the Newtonian theory is that structure grows and it's nothing whatever to do with growth of disorder, it's quite the opposite. But as I explained, subsystems conform within it. So I tell you what we could look at. Let me show you, get you to, Let me show you, get you to, if you could bring up the one that's called shapesphere first. Okay. So now the great thing about the three-body problem which corresponds to a triangle is that two angles determine the shape of the

triangle. So you can represent, there's a representation of all possible shapes when you've got three particles as points on the surface of a sphere. So the illustration I've got you to show is when it's for three equal mass particles and the particles that are at the same longitude but opposite latitudes are mirror images of each other. The equilateral triangle, its two mirror images, are at the north and south pole and the collinear configurations are along the equator. And along the equator there are six special points.

Three of them is where our complexity becomes infinite. That's when two particles get much closer to each other than they are to the third so that you divide the distance to the third one by the separation between the two and then that becomes infinite. Those are singular peaks. And then the three points which correspond, they are saddle points of the complexity. They're very important in astronomy, by the way. So that's the shape sphere. And then on it, you will see there are contours of the complexity. Those are values of the complexity. It has its absolute minimum at the North Pole, and then you'll see the complexity growing. And as it gets to those special points,

it becomes infinitely high. So that's the shape sphere. So this is like an analog to configuration space in physics? But the key thing about it is it's what you call a compact space. So that you totally- Yeah, so in configuration space, it's non-compact. If you don't take out the scale, if you don't take out the scale, it's an unbounded space, it has infinite measure.

But when you quotient by dilatations, you get a shape space and you literally see it there. Moreover, this is what's really wonderful about it. There's a uniquely defined distance on it. There's something which I call the natural measure, which is actually a measure of the difference of shape. It's a pure number. Right.

You can define a difference of shape. And that difference, so the shape sphere has an area which is 4 pi. And then, so then now you can actually seriously talk about probabilities. So you can now say, suppose I have shapes of triangles which occupy just some small patch on, I put a little coin or patch on the shape sphere, then its area is a fraction of the total of the 4 pi. Then you can say that's the probability that the shape lies within that patch. So is that your analog of the born density?

Let me just say one other thing first. I don't know if you know, it's worth mentioning here that a famous problem that Lewis Carroll, the author of Alice in Wonderland, Charles Dodgson, as a mathematician, posed. He said, given three arbitrary points in an infinite plane, I can tell you what the probability is that they form an obtuse triangle. In other words, a triangle with one angle more than 90 degrees. But the answer he gave people disagreed about, and quite a lot of different seemingly contradictory proposals were given.

Now, a few months ago, a group of students in California with whom I worked out the answer using this probability measure, and they found that the probability is three quarters. And then one of them looked online and found that a former collaborator of mine, Edward Anderson, had published a paper giving that result in seven years ago, it's three quarters, and in an email exchange with me, he said somebody else had got it before him. So there's a probability measure on shape, there are probabilities of shapes. point, I made what I thought was a very conventional proposal to find quantum gravity. So in quantum gravity, going back in 1967, Breister Wick wrote down an

equation not for shape, possible shapes of the triangle, but for possible configurations. So his wave function would be for triangles with both shape and size. And he found that the wave function would be static, nothing seemed to change. So people came up with all sorts of ideas. The first one was DeWitt himself. So they looked for what they called an internal time. So a typical internal time would be to say to take the length of one of the sides to be the measure of time and then see how the other two lengths change as that one changed. So I did something which was very conventional, but instead of taking the lengths,

I took the shape and I took our quantity, the complexity. And I said that because the complexity, once you get away from the start of the big bang in the Newtonian thing, the complexity grows pretty steadily linearly. And so I suggested that the time for quantum gravity should be the complexity. And I wrote down in my paper at the end of chapter 18 of the Janus point, I actually proposed a time-dependent Schrodinger equation. I

immediately knew that it would have a unique solution. That's to do with the fact that alpha, there's that one, just one single unique shape, which has the absolute minimum of the complexity. And that has a huge impact on the whole story. So then I thought there would be probabilities evolving with complexity time over shape space. But then my two main collaborators, Flavio Mercati and Tim Koslowski, they realized that actually that wave function would have the same value on every isocomplexity surface. So I thought that makes the theory trivial. And immediately Koslowski Koslovsky said no no it isn't trivial because there's this probability measure there. It's as if so there is essentially something that

looks exactly like the Born density in quantum mechanics sitting there on shape space without any wave function. So this is why I've now, Koslovsky and I are now seriously exploring whether really there is any quantum mechanics at all, whether it is all just probabilities for shapes. So once you get rid of this idea that there's a ruler outside the universe, quantum gravity or at least Newtonian quantum gravity should be about probabilities for shapes and learn by all you can do without the wave function and Planck's constant. The Planck's constant has got to be emergent in some sort of way. Do you have any idea about, in your model, the perihelion procession of Mercury?

Do you have any ideas as to how to recover that? Um, no, I've got some, I've got some very, very speculative ideas, which I think probably would be a bit stupid. Let me just say something. You're extremely welcome to voice your speculative ideas on this channel. Well, let me say something about the famous two slit experiment, which Richard Feynman says

it's really the entire mystery of quantum mechanics is the two slit experiment. So well, before I say that, let me say something else again. Let's consider how was it that, what was the evidence that the founding fathers of quantum mechanics used to arrive at the idea of a wave function. All the evidence was in the form of photographs taken in a laboratory or essentially is that sort of generalized photographs. All the evidence, John Bell says this,

all the evidence for quantum mechanics is essentially in structures that we see in non-quantum terms. It could be computer printouts and things like that. This is very close to the Copenhagen interpretation that in the end you have to describe the outcome, the setting up and the outcome of experiments in classical terms. So what they assumed, so very important was the discovery of tracks in cloud chambers. So a cloud chamber that Wilson had created, he put it in a metastable state, super saturated, and suddenly he noticed these tracks.

This was the discovery of cosmic rays, these tracks, these curved tracks. If there was a magnetic field, the tracks would be curved. Essentially, what the founding fathers were doing, were trying to explain the structure in photographs by saying before the photograph is taken, there are particles moving in through space and time at the same time as a

wave function was evolving and affecting the motion of those particles. They were very much under the influence of de Broglie's idea. And then a photograph is taken and captures the positions of the particles relative to each other. It doesn't show the wave function at all, shows the particles. And then they essentially really the whole of quantum mechanics, I believe it's fair to say, was deduced from that sort of information. Now there's a possibility that the same fact, the same information, evidence, could be explained in a completely different way.

Suppose some deity outside the universe takes a photograph, a snapshot, and the snapshot captures the universe with just one particular value of the complexity. That's one condition. It's a bit like an eigenvalue in the time independent Schrodinger equation.

And then there are probabilities for those shapes. There's lots of shapes with that complexity, and some of them are in regions that are much more probable than have a higher probability. And suppose you look carefully in all those shapes. You might find in one of them, just in a tiny part of it, exactly that photograph. And then the photograph would have a totally different

explanation that does not in any sense rely upon a wave function or Planck's constant. It's just because it's a shape with a given value of the complexity. So that is a possible explanation. Now people just shake their heads when I say that. But now think about something also with the two slit experiments. So one of those photographs could show the two slit setup. It could show the macroscopic source from

which whatever these particles are that are being used in the two-slit experiment, it could show the two slits and it could show the emulsion on which the individual impacts are captured. And those could be, so to speak, Bayesian priors. That would be prior information. You could get that information, but you don't yet look at the emulsion. Then you could look at the emulsion and say, ah, there are these impact things there

that look like interference fringes. It's just a case of correlation. I was saying earlier, there's all these correlations that geometry just puts there. So maybe if you put the priors that correspond to the setup of the two slit experiment, lo and behold, you will get what the outcome is. And then if you actually, I've now started looking, checking out. So the first thing a bit like a two-slit experiment with extremely low density, I think it's equivalent to a candle a mile away, where actually there can only have been individual photons coming through was 1909 by GI Taylor and then there was another more experiment made a

little about a couple of a few years before Dirac made his famous comment that each photon interferes with itself but if you think about the setup for these things, already just reading the details of the Taylor experiment from 1909, it's incredibly special, very very special setup that was used. So could it be that that incredibly special setup forces correlations to appear in the form of the interference patterns? Let me read another thing which it reminded me. So maybe those patterns were created by the experimentalist.

Then they're not something that just wandering around, looking around the universe that you would easily see. Here's a lovely quotation from Eddington again, from I think it's his 1922 book on general relativity. He says, We have found a strange footprint on the shores of the unknown. We have devised profound theories, one after another, to account for the origins. At last, we have succeeded in reconstructing the creature that made the footprint.

And lo, it is our own. So maybe the human experimentalists who set up an incredibly special situation, actually what created those interference fringes by doing that. It's not impossible. I listen extremely carefully and you use the word deity once and earlier you used the word gift when speaking about experience and consciousness.

I'm curious about your views on God. I think about a year or a bit over a year ago, I started reading books on consciousness, which has made me sort of think about these things a bit. I would say I'm agnostic. I do think though now that there is something incredibly amazing about the universe it is it is all the sights and sounds and the colors and the things I don't have it to hand but there's a W. Yates hated, like William Blake hated, Newton and science because Yates said something along the lines.

Newton took away everything, all the sights and sounds and left us just the excrement of the world. But Bishop Barclay, the idealist, so Bishop Barclay said, there are only souls or minds and God implants ideas in these lines. And an interesting thing is I did actually get around to checking the etymology of idea. Any idea what it is? No, no idea. It comes, it's the Greek word for a pattern, a shape. So going back to what Lucretius was saying

and the ancient atomists, they wanted to have a theory of shapes. So I think mathematics defines the shape, the shapes starting with a triangle, but going up to any tetrahedron, any complicated shape you like. And then somehow or other consciousness for us gives us the gift of seeing all these things, hearing and so forth. Now, whether this makes me more inclined to believe in some sort of divinity. I don't know. I did now start checking out the etymology of divine and this comes from Sanskrit. And it's also related to sky, the island of sky in

in the northwest of Scotland and the sky we see. That's all tied in, I guess it's our idea of wonder where we just look at the stars in the sky. And so, I think it's Sanskrit word, diva for a god, these sort of things there. But I mean, who am I to say? All I can say is it's pretty damn wonderful. That's all I will say with confidence. Oh yeah. But I do like the idea that,

I'm getting more and more confident about this idea that mathematics just creates that structure. And they couldn't even just be points in space. I mean, particles gives you some idea that they're a bit like tiny billion balls or something but they might just be purely mathematical points. By the way it's interesting that the Newtonian n-body problem, the word body there is just a historical leftover. So when Newton formulated the first law of motion, he said, anybody continues in a state of rest

or uniform motion in a straight line unless it's acted on by force. But already he, but then explicitly the great mathematicians who followed him, Leonard Euler and Lagrange in the 18th century, when they were the real creators of the modern N-body problem. It is actually point particles. So what I like about point particles is that they have no size. So the only quantities that come in

are the separations between the particles, and then you make it scale invariant by dividing by that root mean square length, the average, so... And then you get pure numbers. So really, that's... That's what the first great scientific dynamical theory is about.

It's about just points. So I'm now coming, but I mean, I have to say, I have to be honest, these ideas, some of these ideas, when they come to me in the last day or two, that you asked about the perihelion advance. Maybe we should look much more seriously at the role that the instruments that we use to make these observations are playing. Think about, I've already talked about the two slit experiment.

I mean, it's unbelievable, the tiniest little thing in the most special environment. But then think about radio telescopes or these incredible ones at 5,000 meters in the Atacama Desert in northern Chile. I mean, TESAF, very, very, very, very, very, very, very, very, at 5,000 meters in the Atacama Desert in northern Chile. I mean, these are very, very special structures. Is it possible that we think that the experiments We think that the experiments are just discovering what is out there, but could it be that to some extent they're creating, they're playing a significant role in creating what is observed?

I've already made this point with the two slit experiment, that they're forcing the two slit experiment means that we will only look at a very, very special part of a shape. That's required. So maybe all these marvelous instruments, telescopes, all of them, electron microscopes, are playing a significant role in creating what is observed. And I come back to what Eddington said, you know, we have found a strange footprint, and lo, it is our own. Well, there are some interpretations of quantum mechanics that have the experimenter as the creator of the results. There's the Wheeler interpretation.

Kurt here. Quick aside, I actually cover the top 10 most common interpretations of quantum mechanics on my sub stack, explaining them all extremely intuitively. There are a variety of other topics on my sub stack explaining them all extremely intuitively. There are a variety of other topics on my sub stack as well, such as what it means to explore ill-defined concepts, why, quote, explain like I'm five, else you don't understand, end quote, is a foolish idea, and what God has to do with ambiguity. The website C-U-R-T-J-A-I-M-U-N-G-A-L dot org redirects to that substack or you could just search my name and substack It's free. So check it out is there also full-length podcast episodes released ahead of time there. Yes, that's yes

There are there is something along those lines. You're right. I don't know I Want to tell you since you're such a fan of etymology Do you know the etymology of pattern, since you mentioned that? Pattern? But wait a minute, I said the etymology of idea was patterned, wasn't it? Yes, now you're, what's the etymology of pattern? The etymology of pattern is father, so it's paternal.

And then do you know the etymology of pattern is father, so it's paternal. And then do you know the etymology of matter? That's sort of, that's bulk or a mass, just a bulk, isn't it? It's mother. Matter eventually comes from mother. Oh, that's very good. So what's super interesting is that you can think of this world, speaking of speculative ideas, as the merging of you need a father, you need a mother, you need pattern, you need matter,

and that gives rise to this world, the child. And maybe that has something to do with the three-ness of, many religions have a concept of triality. Oh yes, yes. Now these are very, I may also say, just as we're going into etymology, the end body specialist at the observatory in Paris who's been such a help to me, Alan Albury, when I was talking about etymology, he suddenly turned to me and said, what's the etymology of etymology? But you're no very good points occurred. Yes. No, these are, these are very interesting.

Also very interesting is what is the etymology of chaos? Do you know that one? I believe it comes from Greek and it starts with a K and not a CH and it has something to do with gaps or the difference between a boundary and what bounded the boundary or what gave rise to the boundary, something like that. Yes, you're quite right. So first of all, our modern meaning of chaos is not from the ancient Greeks, it's from Ovid, very much later.

So when you go back to Hesiod, it's much more akin to chasm. There's a gap between matter, a chasm, but it's also our yorn, the gap between yawning like breathing. Yes. Okay. Yeah.

No, no, well, not so much breathing, but just the space between two. So this is, there was a very interesting talk about Hesiodon and the etymology of chaos that I heard a year or so ago. Um. Like a yawning chasm. I get it. Okay. Yeah.

And I did comment that this is exactly what the end-body problem is about, because you have a space between particles, between matter. But it is very interesting, I agree. Certainly the father and mother is certainly very interesting. Sir, I have to get going and you have to get going. So it was wonderful to speak with you and I appreciate you dealing with all these technical difficulties. Thank you so much.

It's been a blast. All right. Next time we have to get into some more technicalities, especially about the Janus point, the double sidedness of it. How does that distinguish itself from Sean Carroll's double-sided past hypothesis is something I'm interested in, but I don't have to wait. I don't know what went wrong at my end. Certainly I started wrong, but something didn't work with the mic.

Thank you. Okay. All right. Bye for now. Bye-bye. New update. Started a sub stack. Writings on there are currently about language and ill-defined concepts as well as some other

mathematical details. Much more being written there. This is content that isn't anywhere else. It's not on theories of everything. It's not on Patreon. Also, full transcripts will be placed there at some point in the future. Several people ask me, hey Kurt, you've spoken to so many people in the fields of theoretical physics, philosophy, and consciousness. What are your thoughts?

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