Transcript for:
Julian Barbour's Time and Cosmology Insights

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. 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 are maybe 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. 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. 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's 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. Well, 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 we debated many  things. So that's how I think about time, and 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. So the reality are the three   particles at the vertices of the triangle, and  time is something that we put in between those   instants 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. 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, 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 spacetime 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.   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. With   collaborators, I think over the years we've shown  that it's 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. JS 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 very, well, really it  is 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. JS 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? CB Yeah, sure. JS 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? CB No,   the slices are all different. I mean, 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 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 instants are   there, but we put the duration between them. JS  Do we also put the ordering between them? CB 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. This quantity is what we call the  complexity, and that defines an hour 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. 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. LB 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's central to your work? CB 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 that exists  like, 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 150, 160 years  later, Mach essentially came back and said   the same sort of things. And Mach's criticism of  Newton's ideas was a big stimulus to Einstein,   led him to create general relativity that was very  much part of that story. So Mach's first criticism   of Newton's ideas in 1870 in a little booklet led  a young German called Ludwig Lange to propose the   notion of an inertial system, which is what today  we call an inertial frame of reference. And Lange   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. And Mach said, yes, that's fine, but   I think you really need to take into account the  whole universe. So Mach'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. And that's how  I define Mach's principle. Now Einstein didn't   I would say Einstein didn't follow Mach too  closely. And 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 Mach'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  him 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 to him, excuse   me, if you don't mind me saying, what you've just  told me is your interpretation of Dennis Sciama's   interpretation of Einstein's interpretation of  Mach. 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. Lyle 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. Maybe evolved is 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, okay, it's moving toward the  moon, okay, that's inertial. Explain what is meant   by Mach when he says that there's something that's  inertial and it's 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 Mach saying?  Well, 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 Mach 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   mine relative to all the matter in the universe.  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.  Then he had water flowing out of a tank,   and he used the amount of water that was collected  to measure the time. 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. 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. Lyle So hold up that stapler  once more, please. In your explanation, you didn't   use the word inertia, but initially when talking  about Mach's, 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? RL 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. So this   is again, I would say, where Einstein made a mess.  So Newton defined mass in a circular way. Mach's   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. And that is what  defines the inertial mass according to Mach. And   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 a sort of strange idea about   things there. And very few people take the trouble  to distinguish between, from 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  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, 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.   And 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. 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 to motion is much less. And that  is a way of doing it, but you still, to determine   the mass ratios, you still need Mach's definition.  So this model was first proposed, to my knowledge,   by a German called Treider. 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 Mach's 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, and I think it has done a lot  to clarify. I'm hoping Dennis's 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. Lyle So let's go  back to the sticks with the cardboard. And let's   imagine now that there are thousands of particles,  even though yours just has three. 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? David 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 a table too. Lyle Would   this mean that in a two-particle universe, that  they necessarily have the same mass? David 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 mean, 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. Lyle  What about a one-particle universe? David That's   not it. It would see nothing. 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, a triangle has a shape,   but two particles don't have a shape. Lyle 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? David Well,   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 those two. So for me,  one-particle and two-particle 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, where 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 Mach's 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. Lyle What is the   mechanism by which something here that's local  knows about the global? David I personally think   it's in 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 the number of those, it's  n times n minus 1 divided by 2. 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. So 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 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. And this   is, 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 sort   of looking, establishing what's there. And 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. Lyle Have you read   up on Carlo Rovelli's relational interpretation of  quantum mechanics? Richard 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, 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 Mach  said 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. 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 it… 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. So I think that's about all  I can say. JS 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 or other  relations? And the relata are also relations. IM   That could well be. I am at the moment with my  main collaborator at the moment, Tim Koslowski.   He's German despite the somewhat Polish sounding  name. We are working on a definition of what   we call complexity when there are not just a  finite number of particles, but infinitely many   particles. And I think that's a very interesting  problem on which we're working. JS In your theory,   there is something that's being related,  namely particles. IM Yes. At the moment,   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. And the   simplest conceivable one, I think, is point  particles in Euclidean space. And 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 from  them to the tip of your nose and things like that,   that's what I would call the structure. And 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, 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 not much survived. The main text is by the   Roman poet Lucretius in the first century BC, De  Rerum Naturae, 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. It started with looking at the   heavens and seeing the constellations and putting  stars into the shapes there. So I've only got   halfway through Lucretius' poems. It's a very long  poem. It's a miracle it survived. And how does he   explain all these 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 seed with a different shape.  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. But that does highlight that the great   task of science that the Greeks anticipated was  to explain shapes. 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 I think people instinctively think that   things have a size. 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 you know  this concept of proprioception when we're aware of   where our body parts are. It's a very wonderful  thing. 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 add up to 180 degrees. That's, I think,  how one should think about size. 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 can 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. LBW 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. RH Yes, actually, it would have to be one  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 slide number one, if you  can show it. LZ 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? What   do you call your theory? And then just give the  broad strokes of what the theory is. RH Yes. Well,   back in, it's 25 years ago, I coined the key  idea, shape dynamics. And my main collaborator,   Tim Skolovsky, 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, 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 these 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. And that means that that   expression, which I call the complexity, is  independent of any ruler I choose to describe   it by. It's scale invariant. LBW Yes, I see that.  SL. Do you see that? And 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 separations. LBW The reason   I asked how is because it's not clear why scale  invariance implies ruler invariance. Why are   you saying that if it's independent of a ruler,  that's equivalent to being scale invariant? Well,   it's quite easy. If I just take one of my  triangles and measure it with my ruler, which   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. LBW Okay. So now the one underneath it? LBW  And the one underneath it is just if you want to   add masses. LBW 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, I would say this is what I call  three-dimensional scale invariance. And it plays   a very small role in physics. Let me read you  something. Henri Poincaré, his book Science and   Method. Does that come out mirror image? Or you  can see it all right? Science and Method. LBW No,   I can see it fine. It shows a mirror to you, but  not to me. LBW Yeah. So in this famous book 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  meter long will now measure a kilometer. And what   was a millimeter long will now become a meter. 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, 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 Poincaré, 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 complexity is, I think, just  about the simplest thing that you could possibly   use to do it. And 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 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   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. And 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. And 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  monadology, 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 Lee, both Lee's version   and mine, was not very satisfactory because it 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.  And 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. Are you still showing  my expression? LBW No, no. SL. Well, I don't know   whether you can show it again, Curt. LBW Yeah,  we can bring it up. SL. Okay, 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   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 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.   So that's exactly the sort of effect that I  wanted. 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, except for the sign, is  just the Newtonian gravitational potential. It's   the gravitational potential from which the famous  one upon r-squared forces are derived. And the   other one is the quantity which measures the size  of the system. So the Newtonian n-body problem,   that's n particles, a finite number n of  particles interacting with each other, 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 that's a pretty remarkable thing to   start with. So if we want to prioritize scale  invariance and also the second factor looking   like Newton's potential or with additions  here, 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 invariance   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. 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's because of the key  principle that you want three-dimensional scale   invariance. 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? SL. Well, first of all, I   must say I am skeptical 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. I mean, 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. So 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. Well,   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  Battye, 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 acknowledge thanks to Richard Battye.  So you'll see that shows as if it was in three   dimension. You see an extremely uniform ball. 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. 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, what the effect,   the structure of the complexity is such that  really there are two, 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. And 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 because what is  really there is that there are repulsive forces,   hook after the famous hook, H-O-O-K. It 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. 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. And they're held   in balance. And just to say again, how interesting  is it? If it's in two dimensions, and I'll show   one in two dimensions where that 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. Hmm, explain. Well,   there's the cosmologists, there's a holy grail  of the cosmologists, which is what they call the,   it used to be called the Copernicususan 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. And  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 it's a 10th 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. 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 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. It's 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,  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 Sundman. 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   mass is. So that's very, very interesting. And  then a year later, somebody called Bloch showed   that Sundman's 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. Lyle Troxell 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 N-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. Lyle Troxell 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... Lyle Troxell 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. Lyle Troxell 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. Lyle Troxell Sure. Lyle Troxell But you see  how amazingly smooth it is. Lyle Troxell 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 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 discovered, well, I did know  it more or less at the same time. No, a little   bit later, I discovered that actually there are  Newtonian big bangs, that the Newtonian big bangs   start, well, 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 a Newtonian big bangs,  and 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. And so 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 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. 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. 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 Sadi Carnot 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 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  Kalmygorov 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. The key thing is that entropy   is not a scale invariant concept, whereas our  complexity is a scale invariant concept. So 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. The separations  between the particles are always some ratio of   the diameter of the length of the box. Now, if  you don't have something like that, you can't   define probabilities meaningfully. If you have 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. Now, Einstein, let me quote somebody  else. 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. And 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 his 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 infinitely many  cards in. You can't talk about probabilities   if there are infinitely many cards in that case.  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' words,   that the system cannot become distributed in  unlimited space or the momentum, 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 unboundedly of ill measure. And that's just   like my infinitely many cards in a deck of cards.  And this has just not been recognized. 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. And 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 can form within it.   So I tell you what we could look at. Let me show  you, get you to, if you could bring up the one   that's called shape sphere 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. 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. And moreover, this  is what's so 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. You can define   a difference of shape. So the shape sphere has  an area, which is 4 pi. And 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. I  put a little coin or patch on the shape sphere.   Then its area is a fraction of the total of the  4 pi. And then you can say that's the probability   that the shape lies within that patch. So is that  your analog of the Born density? This is going   to... So 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 work, 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 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. So in  the Janus point, I made what I thought was a very   conventional proposal to find quantum gravity.  So in quantum gravity, going back in 1967, Bryce   de Witt 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. And the first one was de Witt  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 change.   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  and 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, and 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 Koslovsky, they realized   that actually that wave function would have the  same value on every iso-complexity surface. So   I thought that makes the theory trivial. And  immediately Koslovsky said, no, no, it isn't   trivial because there's this probability measure  there. 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 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 lo and behold,   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.  Lyle Do you have any idea about, in your model,   the perihelion precession of Mercury? Do you  have any ideas as to how to recover that?   No, 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. It's the two-slit experiment.   So 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… they're sort of generalized photographs.  All the evidence, John Bell says this, all the   evidence for quantum mechanics is essentially in  structures 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. So this was the discovery of cosmic rays,   these tracks, these curved tracks. If there was  a magnetic field, the tracks would be curved. So   essentially, what the founding fathers were trying  to explain the structure in photographs by saying,   before the photograph is taken, there were  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,   it 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 eigen value 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 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. And  then you could look at the emulsion and say,   ah, there are these impact things there  that look like interference fringes.   So maybe 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 G.I. Taylor.   And then there was another, a 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 two-slit,   the interference patterns? Let me read another  thing, which it reminded me. So maybe those   patterns were created by the experimentalists.  They're not something that just wandering around,   looking around the universe that you would easily  see. And 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 were 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 all the sights and   sounds and the colors and the things. I don't  have it to hand, but there's a W.B. Yeats hated,   like William Blake, hated Newton and science  because Yeats 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 Berkeley, the idealist. So Bishop  Berkeley said, there are only souls or minds   and God implants ideas in these minds. 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 the sky 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. 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   any body 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, 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. And then you get pure   numbers. So, really, that's what the first great  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 have only 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. 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, these are very, very  special structures. Is it possible that we think   that the experiments are just discovering what is  out there, but could it be that, to some extent,   they're playing a significant role in creating  what is observed? I've already made this   point with the two-slit experiment. 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've 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. Curt 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 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.org,  redirects to that sub-stack, or you could   just search my name and sub-stack. It's free,  so check it out, as there are also full-length   podcast episodes released ahead of time there.  Yes, that's, yes, they're right, 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 what's the   etymology of pattern? 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 threeness  of, many religions have a concept of triality. Oh,   yes, yes. Now these are very, I may also say, just  as we got 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, Curt. Yes, no, 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 C-H, 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,   where there's a gap between matter, a chasm, but  it's also our yawn, the gap between- Yawning,   like breathing. Yes. Okay. Yeah. No, well, not so  much breathing, but just the space between two. So   this is, there was a very interesting talk about  Hesiod and the etymology of chaos that I heard   a year or so ago. Like a yawning chasm, I get it.  Okay. Yeah. And I did comment that this is exactly   what the N-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'll 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 Substack. 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 Curt, you've spoken to so many people in  the fields of theoretical physics, philosophy,   and consciousness. What are your thoughts? While  I remain impartial in interviews, this Substack   is a way to peer into my present deliberations  on these topics. Also thank you to our partner,   The Economist. Firstly, thank you for watching.  Thank you for listening. If you haven't subscribed   or clicked that like button, now is the time to  do so. Why? Because each subscribe, each like,   helps YouTube push this content to more people,  like yourself, plus it helps out Curt directly,   aka me. I also found out last year that external  links count plenty toward the algorithm,   which means that whenever you share on Twitter,  say on Facebook, or even on Reddit, etc.,   it shows people are talking about this content  outside of YouTube, which in turn greatly aids   the distribution on YouTube. Thirdly, there's  a remarkably active Discord and subreddit for   Theories of Everything, where people explicate  TOEs, they disagree respectfully about theories,   and build, as a community, our own TOE. Links to  both are in the description. Fourthly, you should   know this podcast is on iTunes, it's on Spotify,  it's on all of the audio platforms. All you have   to do is type in Theories of Everything and you'll  find it. Personally, I gain from re-watching   lectures and podcasts. I also read in the comments  that, hey, TOE listeners also gain from replaying.   So how about instead you re-listen on those  platforms, like iTunes, Spotify, Google Podcasts,   whichever podcast catcher you use. And finally,  if you'd like to support more conversations like   this, more content like this, then do consider  visiting patreon.com slash CURTJAIMUNGAL and   donating with whatever you like. There's also  PayPal, there's also crypto, there's also just   joining on YouTube. Again, keep in mind, it's  support from the sponsors and you that allow   me to work on TOE full-time. You also get early  access to ad-free episodes, whether it's audio   or video. It's audio in the case of Patreon, video  in the case of YouTube. For instance, this episode   that you're listening to right now was released  a few days earlier. Every dollar helps far more   than you think. Either way, your viewership  is generosity enough. Thank you so much.