Episode 35: Physics and Relationalism: An Interview with Julian Barbour

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Unofficial, reviewed transcript. It may still contain mistakes; check the podcast when wording matters.

Speakers are labeled by first name where identified. Unidentified-speaker labels may refer to different people. Bracketed question marks indicate uncertain wording.

Transcript

[00:00:09]  Bruce: Welcome to The Theory of Anything podcast. We have a special guest here today, Julian Barbour, who, his books, The Janus Point and The End of Time, I have not read them, but Sadia keeps telling me about them, and they were a very big part of my interview with Sadia. And so we decided we wanted to actually talk with Julian Barbour about some of his theories, and he has some really very exciting ideas that I had never heard of before. So I actually am very excited to have a chance to talk with him and to ask him questions directly. So we also have with us Sadia and Cameo here today. So hey, everybody, say hello.

[00:00:48]  Unidentified speaker: Hello. Hi, Bruce.

[00:00:50]  Julian: Hello, that's me.

[00:00:51]  Unidentified speaker: Welcome, Julian.

[00:00:54]  Unidentified speaker: Yes, welcome.

[00:00:56]  Sadia: You're welcome, and thank you very much for your time.

[00:00:58]  Bruce: So Sadia, I'm going to turn most of this over to you because honestly, you're just smarter than me when it comes to physics.

[00:01:06]  Sadia: I just know more physics. That's all I don't know about smarter, but... All right, Julian. So this is really exciting for me because your ideas have been a big inspiration for me when I was interested in quantum gravity, when I was introduced to general relativity in my student days. Just the whole idea of background independence kind of intrigued me. And I feel like your approach, it really took me, I think it made me appreciate physics at a deeper level, to be honest with you, than I had ever gotten from any other books, I'll be honest with you.

[00:01:40]  Sadia: And up till this day, I feel like you make classical physics, general relativity, approaching them fun because of the way, the type of questions that you've asked and how you address them. So I wanted to start by asking you about just an intuition that most physicists seem to have about that there should be some sort of, and I'm not saying every physicist believes in that, but most physicists seem to think that there is some sort of an underlying unity in the universe. And it seems to me that your work, I feel like, has taken that more seriously than I ever saw anybody take. Could you maybe comment on that? And particularly, I'm kind of referring to your Machian approach to physics. What does it mean that there is an underlying unity in the universe? And would you also, as you go through it, maybe tell us a little bit about how that comes about in your theory? Maybe even talk about, I guess I'll let you start and then we could ask questions maybe as we go along.

[00:02:40]  Julian: Yes. Well, certainly Mach has been a great influence for me. And basically, he was reacting very strongly, as had Leibniz before him, to Newton's ideas of absolute space and time. So Newton imagined space as, the way I like to describe it, as a block of translucent ice in which you could draw lines and then you could imagine that some object moves along these straight lines because they're there in the block of ice. And equally, he imagined that time flows uniformly. And in that case, then you can say that the object is moving in a straight line at a uniform speed. But the problem that Mach pointed out is that you can't see space. It's invisible. And what about time? If Newton says it flows uniformly without reference to anything else that's happening. Well, how do you see time? I mean, we don't see time. What we see is objects and we see how they change. We see things change. So Mach has two sayings, which I always repeat, slightly shortened perhaps.

[00:04:16]  Julian: One which is often quoted, which is it is utterly impossible to measure the changes of things by time. Quite the contrary, time is an abstraction at which we arrive by means of the changes of things. And the other one is he says the universe is given once only with its relative motions alone determinable. So that's my starting point. And I think that's not far away from what Leibniz said in a famous disagreement with Newton's ideas quite a lot earlier. And I think that's very intuitive. So then the question is, how do you turn that into a theory? And that's really what I've spent something well over 60 years. It's 59 years since I started thinking about these things. I've worked with very good collaborators. And the idea of the unity of the universe, I think, I always start with just three particles because then you can really do something of interest. Now, what I do assume is that I assume geometry or geometrical relationships.

[00:05:41]  Julian: Galileo said he that attempts natural philosophy without geometry is lost. And I think that's very true. So to give you an idea of how I think about the unity of the universe, just imagine that there are three particles in it. They will, at any instant, they will form a triangle. So that's a unity. In many ways, a triangle is the geometrical figure with which we're very familiar. We can all imagine a triangle. Now, if those three particles are the entire universe, that triangle is everything. So what can we say about it? We can't say that it has any size because there's no ruler outside that triangle to say how big it is. But what we can say is what is the shape of the triangle? Now, the shape of the triangle is determined by the ratios of the sides. So a triangle has three sides, so you can form the ratio of those three sides. And those determine the internal angles of the triangle, which determine the shape of the triangle. I'm assuming that it's in Euclidean space.

[00:06:57]  Julian: And there you have a deep unity. You just can't get away from that. So how far does that answer your question? Well, let me just say that if I only had one particle, there's nothing much you can do with that because you can't form any ratios. So for me, it's very important that you can always form ratios of things of the same kind. So distances, the three sides of the triangle are all things of the same size, so you form ratios of them. And if you had just one particle, you can't do anything with that. If you have two particles, well, you could say there's a distance between them, but you can't take a ratio of one thing. You'd always just get one. You would divide the distance by itself and it always have one. So nothing could change. So the great thing about three is that things can change. So how do you react to that, Sadia?

[00:07:57]  Sadia: No, I think that is beautiful. This kind of highlights that relational view that you hold and that you've really taken seriously. One of the things that I kind of I was wondering...

[00:08:08]  Bruce: Can I ask a clarifying question quickly? So you just mentioned that there's no sizes with three particles. There kind of is in that they could have different sizes relative to each other. So what you're really saying, I think, is there's no absolute size, but rather you can only... Like if you had a triangle that was each side was 10, there'd be no difference between a triangle with each side 10, each side 100. What would matter is that they all have the same ratio between themselves.

[00:08:41]  Julian: Yeah, it's the ratios that count. And I'm envisaging an idealized situation where the particles are really points. They don't have any size. They are just literally points. One of the really main ideas that we have in shape dynamics is that there is no ruler outside the universe. I mean, tell that to the Marines that there's something out there that we can measure the size of the universe by. So all you can say, suppose the universe did just consist of three points that are always at the vertices of a triangle. All one can objectively say about it is that one side of the triangle is shorter than a different side. And you could say meaningfully by how much it might be exactly one half the length and things like that. So basically, you've got three sides of a triangle, but there's only two ratios. Those are pure numbers. And shape dynamics is just insisting that everything we say about the whole universe should be expressed in terms of ratios like that.

[00:09:52]  Bruce: Interesting. Thank you. And you also started to mention that there's an assumption here that the points are infinitesimally, infinitely small. Is that also a part of the assumption when we're talking about there's no absolute sizes?

[00:10:09]  Julian: That's really as a model. When Newton created dynamics, he talked about bodies. And then within a few decades, mathematicians like Euler and others had idealized that to talk about point sized bodies and point particles. And the mathematics is perfectly okay. Now, there's still a lot of uncertainty really in the physics community to this day about to what extent you can talk about point particles or whether you should talk about fields, which is just a distribution of intensity. So I wouldn't say that the point particle, that the particles are exactly points is truly significant. The really much more important thing is the ratios that we're talking about, pure numbers.

[00:11:07]  Bruce: Okay, thank you. That answers my question. Sorry, go ahead, Sadia, with whatever your previous question was.

[00:11:13]  Sadia: Well, I had a previous question, but since there is another thing related to that, I'll just ask now that the point particles or whatever the stuff there is. How does, I mean, correct me if I'm wrong in this, aren't masses assumed to be, aren't we assuming that there are actually masses? Is mass an assumed concept? Even though I understand that at the end the ratios are left behind, does it matter if you have masses that are unequal versus all equal masses?

[00:11:50]  Julian: Oh, yes, sure. Certainly, you can assume that these point particles have masses, and as long as you recognize that all that will count is the ratios of the masses. And in Newtonian theory, you assume that the masses remain constant. So basically, if you have 10 particles, you can give them masses, but then you take the ratios of those masses. So you really only have nine independent ratios, and they are all pure numbers. So the one definite guiding principle of shape dynamics is to express everything in pure numbers. And it's very convenient and easy to construct a model with point particles, which is why at this stage we're doing that. And that already opens up all sorts of interesting possibilities, which to my surprise don't really seem to have been seriously considered in theoretical physics or cosmology up to now.

[00:12:58]  Sadia: And when you, so you're also assuming a sort of like a shape dynamic form for the Newtonian potential, right, in there?

[00:13:08]  Julian: Yes, that's quite right. So the Newton gravitational potential that exists between two particles, so that you have particles that have mass one and mass two. And so you multiply those masses and you divide by the distance between them. So that's got things that are not ratios, the masses are not ratios, and the distance is not a ratio. But then you add to, if you have a large number of particles, the total potential for the whole complete set is all those products of the masses divided by the separations between the respective particles. And you add that all up and that is the Newton gravitational potential. So what we then do is multiply it by a quantity which is called the center of mass moment of inertia, or rather its square root, which is equal to what is called the root mean square length. So this is a quantity which has the dimension. It's a length.

[00:14:22]  Julian: So if you multiply something which is one over a length, the Newton potential is one over a length. So if you multiply the whole thing by something which is a length, then you take out the length. So that's got you rid of the dimensions in the length. And then you do the same with the masses. You divide by something that's got an appropriate power of the masses. So the moment of inertia has a mass in it. So you have to divide by an appropriate power of the masses. And then you get something which is called the shape potential. And that's been used by people who study Newtonian gravity for a long time. But we're promoting it to much more significance than they have. But it's a well-established concept. So that's how we introduce the Newtonian gravitational force in that manner. Again, as a pure number.

[00:15:24]  Sadia: I guess the thing that intrigues me is that how big of a part the ontology... where, you know, like, okay, there are masses, for example, that because we know that there are masses and they are correlated with each other using, you know, through the Newtonian potential. But which I understand how, you know, how, you know, eventually in shape dynamics, there are pure ratios. But I was thinking that what if instead of masses, it was something else, you know, which would also impact, say, the type of potential. So I guess in that sense, what I'm wondering is that to me, it feels like there seems to be some sort of, something prior to just shapes. Please, I mean, correct me if I'm wrong. Is that something that, you know, I mean, don't you feel like maybe there is something prior?

[00:16:19]  Sadia: Simply because, like I said, here, obviously, we're talking about masses and their correlations are in terms of the Newtonian potential. But what if that was not the ontology? What if you wanted to take shape dynamics to a different theory? I mean, I guess electromagnetism wouldn't be that different if you have electric charges. But what if there was some other basic elements with their associated potential?

[00:16:45]  Julian: Well, I think there are, this is something which has got to be developed. But basically, over the history of physics, two sort of precise notions have developed. One is the one of point particles. And as I say, that was made firm in the 18th century, really, a few decades after Newton had made his discoveries. And then bit by bit, the notion of a field developed in optics, light was explained as a wave phenomenon. And then Faraday had the idea of fields of force and lines of force in electric and magnetic fields. And then Maxwell put that together into his wonderful equations of electrodynamics, huge triumph of theoretical physics. And then a few decades later, Einstein did something even more remarkable, which was create his field equations in general relativity. And in all those cases, fields had replaced point particles.

[00:17:57]  Julian: But basically, you're dealing with the same sort of things. Instead of having point particles with masses or mass ratios, you have field intensities and you have directions of the fields, the Faraday lines of force run in a particular direction. Everybody knows the famous experiment where you sprinkle iron filings over a magnet and you see the lines of force. So you can do shape dynamics with those sort of concepts. And in the 20th century, you've had this huge success where physicists have gone beyond Maxwell's theory of the electromagnetic field, and they've made huge progress with understanding the other interactions, the above all, the strong and the weak interaction, which is added on to the electromagnetic interaction. And they've shown how to unify them in...

[00:18:59]  Julian: It's not a perfect unification, but it's very impressive how they've managed to unify the forces. Now, in principle, all of those forces are represented by analogs of the Newton potential, but they're expressed in terms of fields and not point particles. But in principle, I think it is possible. We're a long way from developing shape dynamics to do that, but the possibility is definitely there. And one of the key concepts that we have in shape dynamics, which is what we call the shape potential, but it's also the complexity. I mean, we give it two different names. There is an analog of that in Einstein's theory. It's related to three-dimensional geometry. So there's a lot of work to do, but I think the possibility of doing it is definitely there.

[00:19:59]  Sadia: I guess what I'm wondering is that in taking the form of the potential in the theory, aren't we admitting something maybe a little bit more than just pure relations? I guess that's what I'm kind of thinking about, that even though I understand that we have pure ratios, but there is a form of the potential, it is one way rather than some other way. And in the form of the potential, is it possible that we have admitted something which goes maybe beyond relationalism, even though the potential is purely relational? I don't know if I'm clarifying my question in a good way. I guess it comes down to really, what I really wanted to ask you was that would you consider yourself a relational purist? Or do you think that there might be something more to the world?

[00:20:46]  Sadia: Do you think that when we're talking about masses versus charges, could there be something intrinsic that you think that relationalism might miss out? That in some shape or form we are admitting, but we're just looking at it at the level of just relations?

[00:21:03]  Julian: Well, I certainly have a lot of confidence in relations and ratios. What is really the whole story of the universe is, of course, another matter and quite why the Newton potential has the form it does is a big issue. I certainly think that if something has really made all the progress in physics, in understanding the world, that has happened. It's all developed out of the application of geometry. Geometry is not, Euclidean geometry and the facts of Euclidean geometry are not far removed from our everyday experience. Galileo has this wonderful saying, which I always quote, he that attempts natural philosophy without geometry is lost. There are certain very basic facts in geometry about right angles, the shapes of triangles you get then from them, you get trigonometry. You can also get spherical trigonometry about how angles and distances on the sky are related to each other, which incidentally was developed before plane trigonometry was because of applications in astronomy.

[00:22:27]  Julian: That happened about 100, 150 years before the Common Era. So that's, I think, all that physicists, theoretical physicists at the moment have been able to work with really. And in fact, really, geometry has come to dominate physics more and more as time passes. So that's my justification. As regards the particular form of the Newton potential, it's very, very interesting structure that it has, particularly when you put it as the shape potential, when you make it dimensionless, because once you've got the idea of a set of points, and they needn't have masses, you could say they all have the same mass, there is one number which is called the root mean square length. So you take all the separations between the particles, you square them, you add them all up, and then you take the square root of that.

[00:23:38]  Julian: That is called the root mean square length. It's the most obvious thing you would want if you want some average of the diameter of a lot of points in space. If the points in space were bees and you had a swarm of bees, it's basically the diameter of that swarm of bees. Then there's another length that you can define, which is actually just the Newton potential, or rather the inverse of the Newton potential. That's called the mean harmonic length. If you had a mathematician who knew all about Euclidean geometry and nothing about gravity at all, but was asked to come up with a mathematical expression which characterizes how much a collection of points is clustered or is uniformly distributed, the most obvious thing it would come up with would be that ratio of the root mean square length divided by the mean harmonic length. And lo and behold, what is it? It's the Newton potential made scale invariant. And I think that's very striking indeed.

[00:24:51]  Sadia: Interesting. And I guess you also connected it to this concept of complexity that you talk about, right?

[00:24:57]  Julian: Well, that's right because it is exactly the same. It is the quantity that we call the complexity, and that behaves in a very interesting way when you actually look at actual Newtonian solutions, how these point particles interact with each other. This is first of all what is really governing the behavior of those particles. If you consider them as a model universe, if you have a finite number of particles and you say, that's my model universe, it is actually that quantity which governs their behavior. It's also the size of that universe, because how do you measure the size of something? You take a measuring rod, which is, say, six inches.

[00:25:51]  Julian: Long, and you measure any object you've got, the width of your table by seeing how many times that ruler goes across it. Given those, if you have those particles, just the particles and nothing else, is there some way in which you could say how big it is? Well, you could imagine that if there were two particles relatively close to each other, you could say, well, that separation of those two particles defines a ruler. I'm going to say that is my ruler. Then you can say, well, how big is the whole universe? Well, a more sensible way to do that would be to take the average of the short separations and the average of the large separations and divide the average of the large separations by the average of the small separations. You would say that's the intrinsic size of the universe. And that, lo and behold, again, is the Newton potential [made] scale invariant. It's what we call the complexity. It's really quite remarkable how much just comes out of that one mathematical expression.

[00:27:03]  Sadia: Yeah, that is fascinating. And it's also interesting to me that you and your collaborators have mentioned that how, when we look at general relativity in its standard formulation, that there seems to be... Could you maybe tell us a little bit about how the scale and size is treated in the standard or the ADM formulation of general relativity versus shape dynamics? Is there some sort of sense in which the... Because you guys have pointed out that there is... The scale seems to be a little bit more absolute, in a sense, in the standard formulation of general relativity or...?

[00:27:47]  Julian: Well, the scale is... In the standard formulation of general relativity, scale is put in in a rather unsatisfactory way, I have to say. I mean, I have one of my collaborators. He says, and he's a cosmologist, and he says that the first lecture, when students go to their first lecture on cosmology, they're told that size of the universe is a nominal quantity at a given instant. So they're told that what you say is that the size or the volume of the universe now, if it's closed up on itself as opposed to an infinite universe, but I much prefer to imagine that the universe is, in some senses, a true unity and closes up on itself in three dimensions like the surface of the Earth does in two. That may be wrong, and that's got to be admitted.

[00:28:52]  Julian: But if that's okay, then under those circumstances, what budding cosmologists are taught is that you say, the size of the universe now is one, and that's a nominal choice. Then the size of the universe at any other time is some fraction of that. It may be larger or smaller. Then my collaborator says, and thereafter the professional astronomers seem to completely forget about that and carry on as if size is absolute. And you can see countless examples of that if you read the literature. And in a way... They know, so to speak, in their brains that there is no ruler outside the universe, but in their gut they still continue to believe in it. The same really goes for time. This is very interesting because Einstein, towards the end of his life, about seven years before he died, he wrote some autobiographical notes, and he said that he had actually committed a sin when he created general relativity, because he said the theory introduces two completely unrelated concepts.

[00:30:09]  Julian: One is the concept of the spacetime metric, which tells you how far apart in space things are, two points are, or how far apart in time they are. And then he said the theory brings in something completely unrelated, without bringing it out of the theory, which are rods and clocks. And these rods and clocks measure spatial separation and time separations. And he said that is, and he calls, he says that literally is a sin. And he says that a decent theory should develop a theory of rods and clocks from within the fundamental equations of the theory. And he admits that he wasn't able to do that. And he said it was, he admitted it was a makeshift. And he said that this, this sin should be rectified at some stage. And I just think it hasn't been properly done. And I think it's sitting right at the heart of relativity theory and cosmology to this day. When you really look at how general relativity works. Now, this was as a dynamical theory.

[00:31:22]  Julian: This was shown in the 1950s. This was developed by Arnowitt, Deser and Misner. That's called the ADM Hamiltonian formalism, Hamiltonian dynamics. And simultaneously, it was done by Dirac in the 1950s. And Dirac was actually so surprised at what he'd found. He said, this result inclines me to believe that four-dimensional symmetry is not a fundamental property of the physical world. And that's actually what brought me, started me thinking about, well, what's time then? So, and then later on, a method was developed. There's very complicated issues in general relativity, how you can actually use it. And well, perhaps let's stop at that stage, because we might come back to that, because you may want to come back and answer some... question me about what I've just said.

[00:32:20]  Sadia: Yeah, actually, I was wondering that how far do you think shape dynamics has gotten to addressing that question? And by the way, this is one of the reasons that I've thoroughly enjoyed following your work. It's really made me appreciate physics at a deeper level. And the sort of questions like what you were saying about cosmology, it's one of those things you do come across, and you do wonder what all that means. And then somehow, because you're just bombarded with so much, you're learning so much that you just tend to overlook, but you actually didn't let go of it and actually kept asking those questions. So how far would you say that shape dynamics has gone? What do you feel at this point in time how successfully has shape dynamics addressed that question that Einstein left and took the operational route?

[00:33:14]  Julian: I think we've gone quite far, but not yet within Einstein's theory. We have shown really how the theory comes. What Einstein was calling for actually does come out of Newton's theory very beautifully. And now, first of all, Newtonian, when you take relational ideas seriously, which go back to Leibniz's criticism of Newton's concept of absolute space and time, and to Ernst Mach's very forceful criticisms in the 19th century, and try and just say that... So, Mach said you really got to think about how the whole universe works. And he suggested that the inertial motion, which is so important in Newtonian theory, and it was to formulate the idea of inertial motion, that the body moves if it's not affected by the forces, that it either stays at rest or it moves uniformly in a straight line at a uniform speed.

[00:34:24]  Julian: That was why he introduced the notions of absolute space and absolute time to give some mathematical meaning to that statement. And Mach said, there's something manifestly wrong with this, because you can't see absolute space and absolute time. And he conjectured, and this is what Einstein then called Mach's principle, that somehow the universe in its totality, all the masses in the universe, somehow or other through an as yet unrecognized mechanism, is what is actually guiding the particles in their inertial motion. That inertial motion is the local manifestation of the interconnection of the whole universe. And that's, I think I can say, that is the contribution that my Italian collaborator Bruno Bertotti and myself, I think one can say we definitively showed that that makes sense. And if you have a universe of point particles, we showed how you can explicitly implement that idea of Mach.

[00:35:33]  Julian: And in fact, when you then look at the formalism of general relativity, the dynamical structure of general relativity that Arnowitt, Deser and Misner found, and Dirac more or less at the same time, you see that, and if the universe is spatially closed up on itself, then you see that Newton's, the way Bertotti and I showed it with point particles, basically the same structure is realized within general relativity. So if the universe is closed up on itself. And so I think I'm encouraged by that. And so this is this is shape dynamics. Now, it's the really important mathematics that goes behind this was, first of all, the work of Dirac and an ADM. And then it was followed up another 10, 12 years later by Jimmy York in in North Carolina.

[00:36:35]  Julian: And Niall Ó Murchadha, the Irish collaborator with whom I worked for 10 years for 10 years. They did some very important mathematics, which is called solving the initial value problem, which literally lays out the mathematics and proves that it works in a very impressive way. In a much more sophisticated way than Bertotti and I did in 1982. But the overall reason why it works is essentially the same. It's an implementation of Mach's principle in that case there. I just wanted to say that encourages me.

[00:37:23]  Sadia: No, you kind of answered actually one of the questions I wanted to ask at the beginning about that Machian unity, that in standard physics you kind of take the inertial frames of reference for granted and you never really get an answer of, okay, how do the inertial frames of reference come about? Or even the question of what equilocality means, for example, or if a bucket is rotating, how do we know that it's, how do we meaningfully say that if there's water in the bucket, that, you know, clearly we see that there is even acceleration in some absolute sense, but why can't we, according to relativity, say that the universe around it is just rotating around it? Maybe I'm putting too many things here, but I guess what I really wanted to ask was, so it seems to me that there seems to be some sort of almost like a non-local type connection.

[00:38:19]  Sadia: I mean, I know non-locality is a loaded word and different people mean different. Sometimes it's used, talked about in different ways, but it seems to me like there is some sort of almost like an instantaneous type of a connection that determines our locality or whereby locality seems to be more of an emergent thing than anything. Would I be wrong in saying that or?

[00:38:44]  Julian: No, but let me start off by saying that geometrical relationships are non-local. Just imagine, just suppose, I mean, this is just a fact about Euclidean geometry. So you have, so first of all, there are things, there are measuring rods, and I call these gifts of nature. I mean, you wouldn't find them anywhere near the Big Bang in time, but shall we say surveyors in Egypt three, four thousand years ago could take bamboo canes and they could survey fields, which they almost certainly did. And with these bamboo canes, they might have discovered Pythagoras' theorem. It's entirely possible. And the great thing about measuring rods is that they don't misbehave, unless something is done to them. So you could start off putting two bamboo canes next to each other in Alexandria, and then you could take one of them to Luxor and bring it back again and lay it next to the one that had stayed all its time in Alexandria. And you'd find that they were the same length.

[00:40:03]  Julian: And if they weren't still the same length, then it's never too difficult to find out what's gone wrong. Somebody came along and cut a bit off one of them, you know, or one of them's got a bit hotter, so it's expanded a little bit. So this is this wonderful thing about measuring rods. Now, with measuring rods, you can measure distances between a finite number of points. So if there are, there's a formula, it's very easy. So if you're in three dimensions and you've got n points, so you take n, then you multiply it by n minus one and you divide by two. And that's the number of distances there are between those n points. And if there's only three points, those separations, those distances that you've found must satisfy the triangle inequality, but they don't satisfy an algebraic equation. But if you have five or more such points, these can be as far apart as you like.

[00:41:13]  Julian: They satisfy algebraic relations, they satisfy equations. Certain expressions have to be equal to zero. And zero is a very special number. That's telling you something very profound about interconnections in the world. And in Euclidean geometry, these connections, these relationships can be just as big as you like, so to speak. I mean, the overall size is meaningless, but they can hold between any number of particles. You can have these relationships holding between a thousand particles. And that is, I would say, this is a incredibly tightly knitted, so geometry is what holds the world together. I like to quote from the opening scene of Goethe's Faust, well, one of the early scenes, where Faust is in despair about the universe and the world and what it is.

[00:42:18]  Julian: And he says, well, I'll quote the German, he asks, was im Innersten die Welt zusammenhält? And my translation into English is, what is it in its innermost core holds the world together? And my answer, inspired by Galileo, is geometry. It's incredibly non-local. So if those points, if the distances between the points change, as they change, those relations have got to stay valid. And that's happening non-locally. There's nothing local about that. So this is why I think you don't have to be alarmed at all about Mach suggesting that distant parts of the universe are having an effect here, because geometry is already like that. And it's the law. The question that really counts is, what is the law that operates when the distances change? And there's a rather natural way to say what that law is. And in the case of point particles, that's the one that Bertotti and I found.

[00:43:37]  Julian: And it's a restriction. So you still get Newtonian motions, but they're restricted. They say that a very fundamental quantity called the angular momentum of that system of particles, treated as the whole universe, must be exactly zero. And somewhat related, but this is to do with time, it's very, I won't say it's quite so definite as the vanishing of the angular momentum, but you can also argue that the total energy of the system must be exactly zero. And I don't think this, once you've got used to it, and you've accepted the fact that geometry is this incredibly tight knitting together of the whole universe at a given instant, that this Machian fact about how the universe changes its shape should hold, I don't think that's at all surprising.

[00:44:31]  Sadia: Interesting. And then I guess I kind of wanted to, so that would require that the universe is finite, right? Or would that also require, I guess the universe have to be closed as well?

[00:44:48]  Julian: Yes, it would certainly, I mean, there is perhaps some possibility that this, some sort of approximation to Mach's ideas might work in an infinite universe. But I think it's much more attractive to have one that is a true unity. The particle model is not completely satisfactory because you always have to have a finite number of particles. You can make it bigger and bigger and bigger, but you're still going to hit up against the end and say, well, I can't let the number of particles become infinite. But if you go to the field ontology where you're talking about fields, well, then you can have an infinite amount of variety.

[00:45:41]  Julian: So as you look out at the, as astronomers look back to, as far as they possibly can in the universe, to whatever it is, 300,000 years after the Big Bang, they see what is called the microwave background. I'm sure you've seen that it's all over the place, this image of the microwave background looking like a rugger ball or an oval with spots on it. And those are the fluctuations of the temperature. They're one part in 100,000, tiny fluctuations in the temperature, but there are variations. Now, mathematics is, so to speak, infinitely deep. Those fluctuations could actually, so they spread over a relatively small fraction, so that their temperature variations of one part in 100,000, and they have a diameter. I'm not quite sure what the diameter is, but you've seen that thing. It looks like a speckled rugger ball or an egg. You might even make it so it looks like one of these beautiful Easter eggs that they paint in Eastern Europe.

[00:46:59]  Julian: And there's no reason why those, that detail should not be infinitely deep, because you can go to, you can go to infinity in the sort of infinitely deep, and you could sort of, sort of use a microscope to look ever closer, and you would find that the structure goes on forever. It's mathematically perfectly possible. So in that sense, when you go to the field ontology, you could literally have an infinite universe even, and it would be a true unity because it would close up on itself.

[00:47:35]  Sadia: In other words, we're thinking, one way to think of the fields would be you could, to think that there is some sort of almost like there's no bottom layer that you could keep going deeper and deeper, but you're always going to find relations that, you're always going to find relational aspects where everything is just kind of related at different levels. Is that what you're saying? But if it is that deep...

[00:48:04]  Julian: Yes, it's perfectly possible. If you have waves, I mean, if you have a loop of string, this is like string theory, if you have a loop of string or an elastic thing, you have waves of different wavelengths. They have nodes where the fluctuation is zero, I like a violin string, and there's a longest wave, there's one, the lowest frequency and the longest wavelength, and then you just go all the way up to infinity, and in quantum field theory, that's called, then you're getting into the ultraviolet. So when you go to the infrared, you come to an end, but when you go to the ultraviolet, you don't, you can go on dividing forever. And so, I mean, that's just the same. You can imagine standing in the middle of a circle and seeing dots around the circle equally distributed.

[00:49:11]  Julian: First of all, there might be just one dot in one place, then there would be another dot exactly opposite, then there would be four dots or three dots equally spaced with 120 degrees between them. And you could just go on filling dots forever and ever and ever. It'll never stop.

[00:49:29]  Sadia: But I guess from our point of view, we will always then see the dynamics to be like the universe, the universe to be approximately closed, dynamically closed, because there's always more to it. Would that be the right way of thinking about it? That from our point of view, you know, we will see it as kind of approximately dynamically closed because there's always more to the universe?

[00:49:57]  Julian: Well, we wouldn't see if it really goes down forever. I mean, you know, the structure never comes to an end. We would never... there would be a limit to what we could see. And I mean, that's just a technical practicality. But in principle, it could go on down forever.

[00:50:29]  Sadia: All right. And I guess a related question that I had was I was listening to David Sloan's talk on that shape dynamic workshop. I kind of looked at his paper, too, where he basically did a scale-free, I guess, reformulation of the current theory of cosmology, where starting from a scale-free action. And there was some sort of a friction-like term that he talks about, that we're seeing here that if you give up on the scale, if the scale is intrinsic, then you end up getting this friction-like term in the cosmology model. So would that be kind of suggestive of this type of openness to the universe?

[00:51:18]  Julian: Yes, I guess so. Yes. Now, I mean, David's mathematics is very interesting. It's one way of looking at things. And in fact, actually, there's another way, which also introduces a friction-type thing, which already came in. That was actually before my tour. So back in 2015, I, Tim Koslowski and Flavio Mercati, had this paper in Physical Review Letters, Identification of the Gravitational Arrow of Time. And in that, we said that you could look at the way Newtonian theory behaves, as if there was a friction term. So basically, the great form of dynamics, which evolved in the 19th century, was by this great Irish mathematician, Hamilton.

[00:52:24]  Julian: And that's called Hamiltonian dynamics. In the late 18th century, a beautiful form was developed by the mathematician Lagrange, and that's called Lagrangian dynamics. And they both derive really from Newtonian dynamics, but they're very elegant ways, and very particularly the one that Hamilton devised, came up with is incredibly powerful and very beautiful. And there's no friction in that. So that will describe a pendulum with small oscillations. Well, it will describe a lot with large oscillations and things like that. So, but you can have also friction terms in the dynamics, but then the dynamics is not Hamiltonian. But the interesting thing is, if you take the scale out of Newtonian theory, and there are various ways of doing it, and David has got one particularly elegant way of doing it, or starting without it even rather. But it was my collaborators who did the mathematics in our paper in 2015.

[00:53:33]  Julian: You can take the scale out of Newtonian theory in its Hamiltonian form. And when you do that, you get a modified form of dynamics, which seems to have friction in it. But it's friction of a rather interesting form, because normally friction will bring motion to a stop. I mean, if you roll a ball on a sticky table, it will come to an end, the motion. But this type of friction doesn't. Things go on forever, but it looks as if they're subject to friction.

[00:54:11]  Sadia: All right. In other words, like an open system, right? It doesn't necessarily have to be where it's just losing energy, but it's suggestive of more of an open system, right?

[00:54:22]  Julian: Well, once you take out, energy is a dimensionful quantity. So when you take it out, it's not really such an appropriate concept. If you have a Newtonian system for which the energy is non—is zero, then the shapes change in a certain way. If the energy is non-zero, then the shapes change in a different way. There's a different law that governs the way the shapes change.

[00:54:59]  Sadia: So you're saying that's better to think in terms of, because like you said that we were saying that the energy of the full, if we apply it to the whole universe is zero. So we have to think more in terms of how it affects the changing, the shapes changing, right?

[00:55:13]  Julian: Yes. Well, the thing about just only looking at the shapes is that it removes all the redundant part of your description. If you have the ordinary Newtonian description, well, nowadays students are taught it's an inertial frame of reference. But you start off, for example, with you say where the center of the mass of the system is. That's three arbitrary numbers where you imagine that the center of mass is somewhere in space. Then you say, what is the direct, if it's got angular momentum, you say, what is the direction of that angular momentum in that space? So that's another three things. So that's another two, that's a direction. Then you say what the magnitude of that is.

[00:56:11]  Julian: So you bring in a lot of things which are nominal at the start. So there's a lot of redundancy in the normal description. So if you then use Newton's equations to find out, to get a solution, then you can throw away all of the information about where the center of mass is, what the orientation of the angular momentum is, and what the overall size is, and just look at the succession of shapes. And in doing that, you've done two things which I think are very important and should tell you that's the way to think about the universe as a whole. First of all, you've thrown away every single bit of information which is redundant, that you can get rid of, but you haven't thrown away one single bit of it which is essential. So if you give me a Newtonian solution in the conventional way, I then just take out of it the successive shapes, and then I give those successive shapes to a different mathematician, that different mathematician can reconstruct a Newtonian solution.

[00:57:23]  Julian: It will be one of a whole family of possible reconstructions of the same thing because it will have the same succession of shapes, but it won't have the extra things which come in because of this redundancy, which really goes back to the way Newton formulated dynamics in the first place, which is fine if you're talking about something moving relative to the surface of the Earth, because the Earth provides a frame of reference, and you know what it means to say, I'm going to start at the top of the Empire State building in New York, and I'm going to do it at a certain time, because the time can be defined by the rotation of the Earth relative to the stars, sidereal time. But if you're talking about this in empty space, and with a clock which is not realized by actual material things, you're just bringing in a whole lot of, well, they're not really there. I mean, this inertial frame of reference is really a swindle.

[00:58:30]  Julian: It's bogus, and it is actually confusing students, who should really be taught, really. That's not the way dynamics was discovered. Dynamics, the law of free fall was discovered by Galileo in his studio in Padua near Venice. He was at the University of Padua, which was the university that was associated with Venice. And how did he find the law of free fall? He rolled balls down a smooth, a gently sloping smooth plane. And he measured how long it took them to travel a certain distance. And I think there were various ways, but one way which would certainly have been adequate would be to measure it by water clock, how much water flows out of a tank of water as the ball rolls a certain distance. And that way he found a very beautiful law, which he thought was very exciting. It was the odd numbers law. He said if in the first unit of time the ball rolls one unit of distance, in the next it will roll three, in the next five, in the next seven and so on. Now that is absolutely concrete.

[00:59:43]  Julian: You can imagine Galileo there in Padua doing those experiments and the water coming out of the tank. That is concrete. That's the way students should be told about dynamics.

[00:59:55]  Sadia: It's nothing like what high school physics is like. They don't even get to know much. They study in a very different way. Just to kind of one more thing about it, that friction-like term, would that dictate a slightly different path in shape dynamics then or how to think of that then?

[01:00:15]  Julian: No, it's just the very characteristic way of saying how the shapes evolve in reality. That's really how reality changes, certainly if the universe is a self-contained dynamical system. It is actually what David does with that paper, and I think we also did it in a slightly different way, but in essence it's the same thing. We actually say this is what the universe really is. We are just absolutely pinpointing exactly what the universe is doing. Of course, this is the classical universe described by classical dynamics. We're not talking here about quantum mechanics at all. That's a whole new thing we have to contend with as well.

[01:01:07]  Sadia: And then with this way of looking at things, so when we look at, say, the cosmological redshift, when we see the redshift of the galaxies, which are attributed to the expansion of the universe, would it be correct to say that then we interpret them as the shapes changing, or how do you interpret the cosmological redshift?

[01:01:29]  Julian: Well, first of all, the observation is in terms of shapes. So basically, what the observation of a redshift is, is the following. You have, in a laboratory on the Earth, where it was done, you have atoms which emit radiation, and that radiation is going through a laboratory, or it might even be at the telescope, up in the telescope, and there's a wave there, and it has a wavelength, and it's literally there in Mount Wilson or Mount Palomar. There it is. Well, now it's in these fabulous observatories in Hawaii, [place name unclear], and then in Peru, in the Atacama Desert, and so forth. So, there is the... So, first of all, you have a source, you can imagine, you should think of it this way. There's a source there with atoms that are generating waves of a certain wavelength in that, in the observatory, you can have it. And then there's also light coming from distant galaxies, and that too has a wavelength.

[01:02:41]  Julian: It's come from the same atoms, and you actually see them going next to each other. And the one that's come from the galaxy, it may have left the galaxy an awful long time ago, but the radiation you're looking at is here, is there in the observatory, next to the one that's been generated by the atoms in the observatory. And they have a different wavelength. And it's all now here, and that's all. You can say that is part of the shape of the universe at that instant at which the observation is being made. And if you'd made the observation... would come out... the ratio of the wavelengths would come out differently at different times.

[01:03:25]  Julian: If there were telescopes back much closer to that galaxy [unclear phrase], the ratio of the wavelengths would have been different if that had been made, you know, two billion years ago, if it could have been made two billion years ago. And maybe it was, maybe there were planets with astronomers doing those things. But it's all the observations, the facts are all shapes now, in the now. And it's in that sense that we say the shape of the universe is changing. It's not so much really expanding as its shape is changing.

[01:04:05]  Sadia: All right. Thank you for clarifying that. Maybe Bruce, I know you wanted to ask some questions related to thermodynamics.

[01:04:13]  Unidentified speaker: Yes. Yeah,

[01:04:13]  Sadia: maybe I'll let you do that.

[01:04:15]  Bruce: Actually, let me ask, what about you? You stated that very clearly, that it's not so much that the universe is expanding as its shape is changing. That like is mind blowing for me. I've never heard that before I started becoming introduced to your work through Sadia. But what does that mean? Like is the universe literally not expanding? Can you help me kind of understand the difference between the shape changing versus... I can imagine expanding very easily is what I'm trying to say. Whereas I can't quite get into my head what it would mean to not be expanding, but its shape is changing.

[01:04:47]  Julian: Well, I should say that this business is still, I would say it's still very mysterious. I mean, there is one sense in which you can say that the universe is expanding. And it, well, it does show up in those, in how the shapes change. Let me remind you, I don't know whether this will help, but do you know what a geodesic is, Bruce?

[01:05:25]  Bruce: I've heard the term, but not really.

[01:05:27]  Julian: Well, so if you imagine walking in a hilly landscape, and you want to get from A to B, I think you can intuitively grasp the idea that there's a shortest distance between the two points.

[01:05:41]  Unidentified speaker: Oh, yes. Yes. Okay.

[01:05:42]  Julian: That's a geodesic. Now, if there is a law which determines geodesics, which there is on the surface of the Earth, the geodesic is determined if you go to anywhere on that surface, and then you look in a certain direction, then that defines a geodesic from then on. You don't have to specify anything more than just the initial point and the initial direction. And in two dimensions, the initial point requires two numbers and the initial direction requires only one, because you only have to say it's an angle between 0 and 360.

[01:06:30]  Unidentified speaker: Sure.

[01:06:31]  Julian: Now, what is very, very mysterious, I think, about the expansion of the universe, when you look at it in shape space, although the universe is only at any instant has a shape and that shape is changing, when you want to describe it, you ask, can I describe it, can I describe the change of those shapes as if the universe was following a geodesic, as it's changing its shape? The answer is no. You need one more number. And that number is really what the, it's really what the cosmologists think of as the rate of expansion of the universe.

[01:07:13]  Unidentified speaker: I see.

[01:07:15]  Julian: And so that I'm not so, and in some senses, it's perfectly all right for the, I did say that earlier when I was talking about how the students are introduced to cosmology. The facts in cosmology do give real sense, really, to saying that the universe now is twice as large as it was at some earlier epoch. That's a meaningful statement, but it's in both cases, it's extracted from the way the shape of the universe has changed between the two things. The information is in the two shapes at the beginning and the end of that period.

[01:07:56]  Sadia: In other words, you're saying that in that sense of looking at things, one size is almost treated as a little bit more physical or absolute, and everything else has increased relative to that.

[01:08:10]  Julian: I didn't quite catch the start of your question, Sadia. Could you say it again?

[01:08:14]  Sadia: So in the standard way of doing cosmology, one would think as if one of the size, like you're saying, you're comparing the size of the universe to some size that you've already taken for granted as in some sense absolute, whereas in shape dynamics, all that matters are the ratios. So that question becomes kind of meaningless.

[01:08:33]  Julian: Well, I would say it's put in a different perspective, and from my point of view, it highlights a real, what I increasingly think is really the great mystery in cosmology and perhaps in physics that you, and this goes back to what I was talking about, a geodesic law. So if you really want to, so the great ideal of a theoretical physicist is to find a law that is more predictive. You want the simplest, most predictive law that you can have. And if we're talking about a law in shape space that governs how shapes change, you would want it to be a geodesic law where a point and a direction determines the law. And that is just not the way the universe works. You need one more number.

[01:09:36]  Julian: I can tell you what the universe is really doing in terms of my geodesic story. You've got this clear picture of going along on a hilly landscape between two points along a geodesic. And what the universe is doing as its shape is changing, it's not going along that geodesic, but there's constantly something which is tugging it away from the geodesic. It doesn't exactly follow the geodesic. It gets tugged away from it all the time. So it's turning and turning. And it's always being driven to a particular point where this, to particular points where our complexity or the Newton shape potential, that thing is higher. It's dragged toward this point. So in shape space, it does look like the effect of friction. And that's what David Sloan's talk and paper is about. And that's the way to think about it. And this, I think, is very, very mysterious, because when Newton introduced absolute space and time, he introduced position.

[01:10:55]  Julian: That was never a real thing because of Galilean invariance. So the famous fact that uniform motion can't be detected within a system. I mean, we don't feel the Earth moving. So that, although that appears in Newton's picture of absolute space, it doesn't have any physical effect, but orientation does. Rotation is possible, so that's there. And energy, absolute time, has an effect because you can have different energies. So you can get rid of those, and they disappear from Einstein's theory in a sensible model of that, and they disappear in a Machian universe. So you get rid of those absolutes, and they completely disappear if you have a system which has energy and angular momentum zero. And that's what you expect from the Machian point of view.

[01:11:54]  Julian: But the one thing, what also Newton introduced was a notion of absolute scale, as if there was a ruler outside the universe. And that's one way of interpreting what the universe is doing. I prefer to think of it as this thing that is tugging you away from a geodesic. But that's the objective way of saying what the universe is doing. There is something which is tugging its curve in shape space away from the instantaneous geodesic that it could be following. And you can say that's the effect of absolute scale that Newton brought in. And I think, what on earth is going on there? Why is that there? I would say that is the, for me, at the level of classical physics, and it may be intimately related to what's going on in quantum theory, that is the great mystery. And I think this is the value, this is what shape dynamics has done, is it has pinpointed this one fact. I think it is just the great mystery.

[01:13:07]  Unidentified speaker: Interesting.

[01:13:08]  Sadia: Could that have something to do with dark energy by any chance?

[01:13:13]  Unidentified speaker: I was about to ask that.

[01:13:17]  Sadia: I mean dark energy is such a vague thing, it's almost like saying, oh, this is something that we just don't know about, that's where we just, you know, it's...

[01:13:25]  Julian: I don't think, I certainly don't think it's anything, I would be very, I don't think it's anything to do with dark matter. So dark matter makes up about a quarter of the mass in the universe. And I share, I mean, I'm not an expert in these things, but I think the evidence from astronomy and cosmology is that there really is some dark matter out there that they just haven't yet managed to pin down. But dark energy, I would say, I don't want to... I think maybe one... If shape dynamics is the right way to go, I think it may say something about dark energy. And also the very early universe, when modern cosmology invokes something called inflation, I think shape dynamics has the potential to say something about that. And I've written about that, not so much about dark energy, but about inflation in my book The Janus Point, which came out nearly a year ago now.

[01:14:32]  Bruce: All right. Let me ask a couple of my other questions here. I was watching an interview that you did. I can't remember which one. And you were talking about how at the point of the Big Bang is the point of the least... The universe was its most boring. It was the most similar. And then going out both directions from there, only one of which would be able to see, you would see increasing in numbers of complexity from that Big Bang point. Did I explain that correctly? Is that what I...

[01:15:02]  Julian: That's more or less right. I can't remember. There are two options that I discuss actually in my book. And in some senses, the title of the book, The Janus Point, applies to one of them, which I now think is the less interesting, but it is still very interesting because it looks to me as if it could say that there is actually no real... Ultimately, there won't be any mystery about why time seems to go in one direction. But in that model, the universe is at its most uniform, at a central point on, so to speak, the timeline of the whole universe. And in either direction away from that central point, which I call the Janus Point, the universe gets more clustered, more structured. And that is basically the dominant thing, which is determining the direction of time. And that matches exactly what the universe does seem to have done since the Big Bang.

[01:16:01]  Julian: It started clearly very soon after the Big Bang, at least it was very uniform. And it's got more and more clustered and structured ever since. But there is another possibility in Newtonian theory that there's not two sides of the Janus Point, but so to speak, that the universe starts from zero size. Now, that such solutions exist in Newtonian theory has been known for about 130 years. In fact, so there are solutions in Newtonian theory where the particles are sort of doing their thing, and then somehow or other they seem to conspire or they're sort of set up in a very fine-tuned way, where actually they come together and they all collide instantaneously at their common center of mass. And that's called a total collision, and that such solutions exist within Newton's theory was, as I say, discovered about 130 years ago.

[01:17:01]  Julian: There was a very fine paper by a Frenchman called Jean Chazy, which spelled out all the details in 1918, 11 years before the expansion of the universe was discovered. Now, if you reverse the direction of time, which you can do because the Newtonian equations don't distinguish the direction of time, then that type of solution becomes a total explosion. It is a Newtonian Big Bang. And what is very interesting about those solutions is that the shape is very special. It's what's called a central configuration. It's a very interesting shape.

[01:17:39]  Julian: And in fact, there's just one of them where the shape is more uniform than any other possible shape can be, as measured by this quantity we call complexity, which is simultaneously the Newton gravitational potential made scale invariant. And in my book, The Janus Point, I call that alpha. And in that case, you would have a model of a universe which starts not exactly uniform because it can't be perfectly uniform according to the formula, but it can be as... [unclear] In accordance with the formula, no distribution of the points can be more uniform than that. And when you actually look at what they look like, they're incredibly uniform. They've been calculated for up to a few thousand points, and they're actually all concentrated in a perfect sphere with very uniform density. And then there's just an abrupt edge to the sphere, but the separations between the particles are not exactly equal.

[01:18:46]  Julian: There's just ever so slight variations within the separations. So I think that might be a Newtonian model for what the Big Bang was like, and I think it's just possible that inflation, which is quite a successful theory, but they have quite difficulty in explaining why it should start, and there are some issues, I think, with how it ends, it might replace it. So I think, I mean, then if we could really show that something like that is also what is really happening in general relativity at the Big Bang, about which there's a lot of uncertainty, then shape dynamics would really have triumphed, but that's sort of for tomorrow.

[01:19:32]  Sadia: I was also wondering if you could, since we're talking about that, like how the arrow of time, the asymmetry kind of emerges out of that then. So we are looking at a very kind of uniform type of configuration. How would we look at the asymmetry that we associate with time, the arrow of time?

[01:19:54]  Julian: Well, just briefly about the history. So ever since the laws of thermodynamics were discovered and the notion of entropy was discovered, physicists have all believed that this is what's called an arrow of time. And they think the most important one is the entropic arrow of time. And that says that if it's applied to the whole universe, which virtually everybody does do, that says that the universe must have started off rather ordered and to be the disorder, entropy is a measure of disorder in the normal interpretation, and it's increasing. And then Richard Feynman was one of the first people, in fact, he may have been the first person who said it really clearly, there must, you can't explain this, the universe must have started with a low entropy, but there's nothing in the laws of known laws of nature, which would explain that that would be the case. So that got called the past hypothesis by the philosopher of science, David Albert.

[01:21:04]  Julian: And it's been a great mystery. [Unclear connector] that it was a great mystery became clear with the work of Boltzmann in the 1890s in the famous debate he had with somebody called Ernst Zermelo. And so that's a great mystery. But what we showed in, and in fact, actually, we were just exploiting things that have been known for 200 years in Newtonian theory. In Newtonian theory, all you require is the energy to be non-zero. And in a Machian theory, you would want it to be exactly zero. And then you will always have these Janus type solutions where at one point on, just one unique point on the world line of the universe, in the conventional Newtonian sense, the size of the universe is minimal. But in the way we think about it, the uniform is more uniform than in either direction from that point. And then the universe gets more clustered in both directions away from that point.

[01:22:07]  Julian: Intelligent beings must be on one side or the other of the Janus Point. They will see laws which seemed not to respect, to not to have a direction of time, that the time could flow in either direction. But everything around them is going in one direction. The universe is getting more clustered. The main significance of that paper of ours from 2015 is to show that there may not be any mystery at all. You don't have to add anything onto the existing laws, which was what Feynman said.

[01:22:46]  Julian: It just comes straight out of Newton's law. If it comes out of the oldest dynamical law in the history of dynamics, it may well come out of everything else in dynamics. Now, we haven't yet shown that, but I think there's a distinct possibility. Is that the case? So that's the significance of there. Now, the interesting thing is the same. You can have these very special solutions, which I think, because in general relativity, characteristically, the size of the universe does go to zero or it all comes to a point in the normal way they describe it. I think that Newtonian model, which starts with a total explosion, might be a good one. And in which case it starts, the universe starts, not exactly uniform, but as uniform as it possibly can be. It's born with a few wrinkles and then they just get bigger and bigger as time goes on. And maybe the arrow of time could be completely explained.

[01:23:47]  Sadia: So let me ask you a question on that.

[01:23:51]  Bruce: Can I ask a question quickly on that one? Would the people on the other side of the Janus Point, would they be for all intents and purposes in a different universe?

[01:23:58]  Julian: Yes, because you couldn't communicate and they would have the sense of time going forward in exactly the same as the ones on this side.

[01:24:05]  Unidentified speaker: Right.

[01:24:06]  Julian: But I mean, as I say, I'm increasingly getting more attracted to this model where there isn't a Janus Point, but the same effect really comes for anybody in the universe. But with the added bonus that if these ideas are right, then we explain why the universe started in such an incredibly uniform way.

[01:24:28]  Bruce: OK, go ahead, Sadia, and then I'll ask you this question.

[01:24:30]  Sadia: So I was thinking about the arrow. Like, what would be the reason to think that the arrow is pointing away and not towards the Janus Point? Is that to do with what we see when we look at the cosmic microwave background radiation?

[01:24:43]  Julian: Well, that's a question of bringing in the other arrows of time. And you could think about this in terms of what you call gradients. So you can say this, if you say that increasing clustering is like going up a hill, then you've got a gradient going uphill. So that's one arrow of time, but there are other arrows of time, like our memories. We remember the past, we accumulate more memories. So you could put a gradient there of the number of memories we have. And there's the collapse of the wave function and there's the increase of entropy and things like that. So the question is, what would justify us in saying that the gradient defined by the clustering, the increase in the clustering, is the same as all the other arrows of time, the one to do with us forming memories. And when you can talk about entropy properly, that that should go in the same direction.

[01:25:56]  Julian: Well, once in this model of the universe we have, we pointed this out in a later paper than the one that we published in 2015. No, actually, I get it wrong. The one in physical review letters was in 2014. 2015, we pointed out that in such a universe, if subsystems form, they will have negative energy. And as they form, they start to behave in the normal way with, as in thermodynamics. And you would have something like an entropic arrow within the subsystems. And that entropic arrow within the subsystems would point in the same direction as the overall clustering in the universe at large. And I don't think anybody really doubts that the way we accumulate arrows also agrees with the direction in which entropy increases. So I think that's the reason why you would say that's the sensible way to define the direction of time.

[01:27:03]  Julian: By itself, you're right, Sadia, you could say just the clustering by itself. You could say the arrow is pointing to or away from the Janus Point or to or away from the beginning of time. But once you add in the other ones, if you've got a theory for the other ones, and we certainly have at least a reasonably good outline of a theory of the entropic arrow, I think we, you know, that settles it.

[01:27:30]  Bruce: So in that same interview, you mentioned that as things move away from the Janus Point or whatever we're calling that, complexity increases, and you even went so far to say that this seems like a sort of teleology.

[01:27:44]  Julian: Well, now we're getting, you know, when people reach my age, I'm [unclear] into my 80s. People say, no, they get senile and get sort of carried away with crazy ideas. I have to say, I begin to wonder. And I have been greatly influenced, like my friend, Lee Smolin, by Leibniz. I introduced Lee to Leibniz. Now, Leibniz is a very fascinating thinker. The great logician Gödel with his famous Gödel's Theorem was a great admirer of Leibniz. So Leibniz talks about perfection of laws and perfection of the universe. Well, I already mentioned that the ideal of a theoretical physicist is to find a theory which is perfect and more predictive than any other theory. So Leibniz was sort of advocating things like that. And if you read Leibniz, and I do recommend it, he's very thought provoking. A basic point that Leibniz makes really is that if there were no variety in the world, you couldn't say anything. I mean, you couldn't begin... A completely uniform universe has no meaning. It's just a blank.

[01:29:07]  Julian: There's literally nothing there. So Leibniz has this idea of perfection, which is to make complete or to progressively make more complete, more perfect. And so that suggests that a universe which starts off with very little variety would get more interesting. It would get more perfect if the variety increases. And in fact, he argued very late in his life in his famous Monadology, very much along the lines which I did earlier about structure could go on right down infinitely deep forever. You know, you could keep on looking with microscopes.

[01:29:49]  Julian: And in the Monadology, he has a very famous passage where he talks about, he was very influenced by the Dutchman Leeuwenhoek's microscopic observations with these incredible microbes that he discovered with his microscope and had described. And Leibniz was hugely impressed by this, and he argued that every living tissue has more living tissue within it. And he talks about every pond has fishes in it, and every fishes within fishes, you could find ponds with fishes within those ponds all the way down.

[01:30:32]  Julian: I mean, like the rhyme about fleas upon their backs to bite them, and they have lesser fleas, and so on, ad infinitum. And that idea of Leibniz was killed when quantum mechanics was discovered, because quantum mechanics really puts a lower limit at the present stage, at the present stage of the universe. So what's rather interesting about the universe, I find, is it does seem to have started very uniform with very little variety, and certainly the variety has been increasing very impressively up to the present epoch, but there seems to be that idea of Leibniz's ponds within ponds and fishes within fishes and fish ponds within fish ponds all the way down.

[01:31:17]  Julian: That's not right, but I don't think it's entirely impossible that the universe could go on, that so to speak, there would be increasing levels of ponds within ponds. This is at the stage where some professional physicists who happen to, by chance, to listen to this will say, Ah, yes, there's Julian, he's really getting senile, or he's just naive, or, you know, he's a hopeless optimist. I mean, Leibniz was made fun of by Voltaire in Candide as Pangloss. So you could dismiss me as being Panglossian.

[01:32:00]  Sadia: Let me ask you one thing on this. So if there is a unity to the universe, that type of geometric unity we were talking about, wouldn't that mean that identity, like that would give a very precise meaning to identity? Because each view would be unique, which means that we may not really have pond within pond, but maybe other stuff within kind of like the infinity we were talking about, but just the infinity in diversity and not as the sort of thing that cosmologists sometimes talk about, that where there may be repeating parts of the universe where we're doing exactly what we're doing right here, but somewhere else.

[01:32:40]  Julian: Yes, these are all metaverse ideas. I have to say I'm skeptical about the metaverse because, well, first of all, my understanding is it requires an infinite universe and it's all within one space-time, and it all assumes this external scale. I'm skeptical about it. And it came out of, these ideas came out of eternal inflation. It came out of the success of inflation. So cosmologists who developed inflation said, well, if it could happen once, it can go on happening again. And then before, you know, they've got these things. But then they get into terrible probability difficulties with trying to make any predictions about the multiverse. Lee Smolin has written very effectively about this and so have other people. So I put more faith in there being just one universe. And then it is very Leibnizian that you could look. I mean, Leibniz says that Monads and he identifies us with Monads.

[01:33:55]  Julian: He says we are just views of the universe from a particular point of view. And I think that's quite an idea. What I'm now suggesting is conceivably those views in some senses could be infinitely rich. Perhaps in the distant future, there are centers of consciousness. I mean, we know so little about consciousness and we understand it. Understanding of consciousness is pretty limited. You know, maybe there are richer things in the future. Who can say?

[01:34:39]  Bruce: Just a moment ago, you mentioned that quantum mechanics, at least at this stage of the universe, puts a lower bound limit on sizes. Are you suggesting that as complexity increases, that that could change at some future point in time?

[01:34:56]  Julian: I think it's possible.

[01:35:01]  Julian: I mean, there's no doubt in my mind the amount of variety in the universe can just go on growing and growing and growing. And in some senses, it can be measured. I mean, in the simple model we have with point particles, we have complexity which measures how much it is. Now, there is an interesting possibility that my collaborator, Tim Koslowski, came up with. So basically, our Newtonian models have, as we developed it, just have a fixed number of particles. I mentioned that before, the number of particles is fixed. And then any shape that the particles come in, any distribution which defines the shape, that has a given complexity. Now, but that complexity depends, changes, you can have a larger, the complexity depends upon the number of particles and the way they are arranged relative to each other. So you could imagine a universe in which, first of all, the complexity literally is time, that what we call time is just the universe becoming more complex.

[01:36:16]  Julian: And literally is a pure number defined by the value of the complexity. And then that could increase also by more particles coming into existence. You would have genuine creation of particles, as well as them being able to move into different positions relative to each other. And in that way, the complexity could go on growing forever. And there would be more, there would be creation forever. I don't know. I mean, this is, as I say, I'm sure there were, if some professional theorists get to listen to this, they might be shaking their heads and say, shoot that man. But it's not impossible.

[01:37:06]  Sadia: But to be honest with you, Julian, I think if anybody in their own time isn't really kind of letting their fancy kind of go wild here and there, then I don't know. They're not being creative. I think we should, as long as, you know, your papers are to the point.

[01:37:21]  Bruce: So actually related to that. So first of all, would that mean, in essence, that the Planck length can change over time?

[01:37:29]  Julian: Well, the way I think, well, sort of all the Planck length changes compared with in standard cosmology, the Planck length changes relative to the size of the universe. So the normal size of the universe that cosmologists talk about is the Hubble radius. And very early, very soon after the Big Bang, the Planck length was not much different from the Hubble radius. Now it's a tiny fraction of it. I don't, just guessing it, is it one part in 10 to the 60 or something? It's a tiny fraction of the Hubble radius now. So to say that the Planck constant is not really a constant because it's a constant relative to the things that are used to determine it. And basically that's the cesium atom. But instead of the cesium atom, you could think about cosmological scale. So there's nothing inconsistent in what I'm saying. And in fact, I would say that the inverse of our complexity, you could call that a dimensionless Planck length. And that will change.

[01:38:48]  Julian: It will be different for different shapes of the universe. And that's no different from the present situation when you say, what's the ratio of the Planck length to the Hubble length? That is changing. That's getting smaller all the time in standard cosmology. So there's nothing particularly untoward in what I'm saying there.

[01:39:11]  Bruce: Now, going back to teleology, though, I realize that's kind of a dirty word to a lot of people in science. But in evolution, it's not. Like, I can easily talk about a heart having a purpose is to pump blood, because of its evolutionary setting, invoking a sort of teleology in evolution, at least in a certain way, is considered acceptable, as long as it's consistent with, like, Neo-Darwinian evolution. What would be the equivalent for physics, though? Like, we've got this complexity increasing over time. Where does that come from? Where does the complexity come from? Is there something equivalent to evolution that allows us to invoke teleology without violating anything? Or is this just a mystery at this point?

[01:39:54]  Julian: Well, first of all, I think quite a lot of biologists would be quite cautious in saying that evolution is teleological. I mean, there is this thing that I think the human brain now is 10% smaller than for the Neanderthals, and that's just because we've got much more efficient at getting food. So we don't have to have such big brains to know where all the food sources are or things like that. So, I mean, evolution doesn't necessarily always go in the same direction, but that's a minor issue compared with this.

[01:40:35]  Bruce: Yeah, I'm not suggesting that evolution itself is teleological, but within evolution you can invoke certain kinds of teleology by the existence of evolution.

[01:40:47]  Julian: I think in the sense that you say that organisms will evolve to suit the niche in which they find themselves there.

[01:40:59]  Sadia: Yes, that is the best explanation, functionalism, sort of.

[01:41:07]  Julian: At the moment, I'm having very interesting discussions with three people. One is somebody who was in finance and has now gone back to study because he's decided in midlife that he wants to really think about the universe again. And then I'm talking as well to a couple of physics students. They're both in their fourth year. One is in Iran and the other is in India. And we're looking at Leibniz. And I must say, he's very interesting. He makes all sorts of suggestions. And in Leibniz's time, I mean, metaphysics was not a dirty word. One looked for deeper reasons for why things are the way they are. And it's only comparatively recently in... I mean, I don't know when in...

[01:42:06]  Julian: Since the Scientific Revolution that came in with basically with Newton, when scientists started to say science cannot answer why questions, it can only answer how questions. So if you have a law, it can then tell you what the consequences of that law are, but it can't tell you why that law is there, why the law is there. But Leibniz is constantly arguing about that law and what possible laws there could be and what the universe could be like. And very often the criteria he comes up for are the sort of ones, and I've already hinted that, the theoretical physicists love, which is the search for the theory of everything, the big TOE, the great, you know, the theory of everything. That's a very Leibnizian metaphysical principle.

[01:43:10]  Julian: If a theoretical physicist is listening to this now, he'd say, oh, yeah, but it's justified because first Maxwell unified electricity and magnetism, then Einstein unified inertia and gravity. And then more recently, particle physicists got a long way with unifying the forces. That's fine. But what's driving them on to get it even better is still nevertheless that Leibnizian ideal for the perfect theory. So in a way, Leibniz would say perfection is a metaphysical principle.

[01:43:50]  Sadia: So, but let me ask you, Julian, about this. So in that sense, aren't we kind of talking more sort of like a meta law, which is taking us a little bit beyond relationalism then?

[01:44:02]  Julian: Well, we may, but Leibniz is, I think Leibniz would, I mean, I said early on, I'm sure some years ago, well, it's about 40 years ago, I read that Leibniz reserved, he wrote very little in German, but apparently what I read was that he expressed his deepest thoughts in German. And in one of his German writings, he says that variety is reality. That is what reality is. And that very notion, if that's what he said, and I keep on trying to, I mean to try and search for that, every time I meet a Leibniz expert and I say, is that what he said? And they said, yes, he did say that. And then I said, can you send me the reference, please? But I never get it. But it makes perfect sense from, I mean, everything I've read of Leibniz, that makes perfect sense, that variety is reality. And then perfection will mean perfection. The etymology of perfection is to make complete. Per is thorough, to go through something perfectly. And perfect is from [Latin word unclear], to make.

[01:45:20]  Julian: So it's to make something perfect. And so the idea that the ideal law of the universe would be to increase variety forever is not unreasonable. And it does come out of Leibniz's way of thinking. And certainly I'm finding it very stimulating discussing it with these people. And the three of them really are very interesting. And I mean, at least the one from Iran is very knowledgeable about philosophy. And he's very sharp, comes up with very interesting comments. So I'm getting a little less worried about coming up with a little bit of metaphysics, but making clear what the idea is. And one has got to have some stimulus to look for a law. My goodness me, the universe is fascinating when you think about consciousness and all these issues. Maybe we do have to think a little bit out of the box.

[01:46:32]  Sadia: I agree with you, because to be honest with you, when I look at the world around me, I feel like this sounds like a pretty reasonable thing to say. I mean, I think what happens is a lot of times physicists from within the view that they've held, what's worked for physics, when we're studying very simplistic systems, somehow they tend to kind of generalize that to the whole of reality. But it seems like, at least when we study biology complex system, it does seem to me that that is best explained in some form of functionalism. And there has been an increase in complexity. The world seems to have gotten more interesting.

[01:47:13]  Bruce: You mentioned reading Leibniz. Do you have a recommendation, like as a starting point, for learning some of his ideas that you're referring to here?

[01:47:22]  Julian: Well, the book that I've got two books. One is just called Leibniz Philosophical Writings, and it's published by, it's called Everyman's University Library of Leibniz's Things. I bought it back edited by somebody called Parkinson, and this was published in 1973. I mean, the book is incredibly rich. It's only actually all of the ones, the ones that you read, that you see cited a lot, it all comes in quite a slim volume. It's in just over 220 pages, and you can dip into them. Leibniz is not always easy to read because he started off very much with scholastic medieval philosophy, which he never entirely shook off. So it's quite difficult to get into what he's really driving at. So it does help to have a bit of an introduction. But, I mean, he talks about simple substances, and you think that's just like a pat of butter. Far from it. It means something that's got all sorts of relationships within it, which are holding, knitting it together, to use my expression.

[01:48:47]  Julian: It's something which is knit together by its, that its attributes sort of all hold it together. But if you, I don't know whether I've, I've never actually, I mean, Bertrand Russell wrote a book about Leibniz philosophy. I, I read it many years ago. I mean, I started reading Leibniz, it's now, back in 1977. So it's about 45 years ago. And it made a huge impression on me without sort of clarification of exactly what he meant. But there are things, but I would say just get that. Then there's a bigger collection edited by somebody called Loemker, L-O-M-K-E-R [letter sequence uncertain]. And having extra, I mean, there's a, there's a huge project going on in Hanover to publish everything of his. A few years ago, they reached volume 50, each volume about 800 pages. That sort of, with notes and letters that were sent to Leibniz. And they're only half, they were only halfway through the project.

[01:49:54]  Julian: I mean, it's colossal. Unbelievable what he generated. And of course, he was a very great mathematician. He was joint discoverer of the calculus with Newton. He proposed the use of binary numbers, created the first calculating machine. You know, he's a very, very remarkable person.

[01:50:18]  Bruce: Yeah, it sounds like he's had a lot of interesting contributions. Okay, thank you. I will look up some of those books. Now I'm very curious.

[01:50:26]  Julian: Yeah, Parkinson. Make a note of the name Parkinson, like the unfortunate neurological disease. See if you can find it. The book I've got is called Leibniz: Philosophical Writings. I dare say it's still in print. And if not, you could get it in a library, and I don't.

[01:50:46]  Unidentified speaker: How much?

[01:50:46]  Unidentified speaker: 800.

[01:50:50]  Unidentified speaker: There are versions you can get.

[01:50:54]  Julian: That's probably the hardback or something.

[01:50:57]  Unidentified speaker: Yeah.

[01:51:00]  Julian: I'm quite intrigued that my first book, which came out as a hardback, is Absolute or Relative Motion. If you try and buy that on Amazon, it's around $900.

[01:51:14]  Sadia: I must say, I highly recommend that book. That's a beautiful book to read.

[01:51:19]  Julian: In a way, that's the one that gave me more satisfaction than any other. Particularly, what I really loved was discovering what Kepler had really done. It's a phenomenal achievement that Kepler had. That's actually, by the way, which gives me so confidence in saying that it's geometry that holds the world together, because Kepler really was the first person who, in his mind's eye, could travel in space and imagine that he could go anywhere. He was always saying, what will the solar system look like if I were on Mars when from the Earth Mars is in such a direction relative to the fixed stars? Then I'm going to imagine myself, I'm going to then know if I were on Mars, I would know where I would see the Earth from against the background of the stars that way. And then he then could use that to check various conjectures. It's just phenomenal. He did that. And he also wrote one of the very first science fiction novels, which is An Imagined Journey to the Moon.

[01:52:38]  Bruce: Well, we're quite a bit over time, so we probably ought to wrap up.

[01:52:44]  Julian: It's about time for me to start making my supper, yes. But anyway, good to talk to you both.

[01:52:50]  Sadia: Good to talk to you, Julian. Thank you so much for your time. This was such a treat.

[01:52:55]  Bruce: It was. It was awesome.

[01:52:57]  Julian: Well, it was a pleasure. Bye then.

[01:53:01]  Unidentified speaker: All right. Bye-bye, Julian.

[01:53:02]  Unidentified speaker: Bye-bye. Bye.

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