Time & Cosmology / Spacetime & Noncommutative Geometry

0:00 And it really is a basic question of the everyday that we envision ourselves walking through life with our choices, with the possible outcomes that we can have an interaction with in the future. And I want to mention an episode from the history of art and mathematics, which was the development of perspective right after the end of the Middle Ages, the beginning of what we consider the Renaissance. There were some brave souls who considered there was a way that it would be possible to map some mathematical ideas onto the canvas and transform the geometry of the two-dimensional painting into a three-dimensional painting as the illusion that you were looking at, a three-dimensional world. And that amazing moment was an idea, an idea that we could You can translate in a medium, it's a metaphor, mapping is a metaphor, you can translate in a medium the vision of what things could be to take us beyond. And a lot of the work I feel in physics and in philosophy is to give us an idea, to give us a mapping for how to come to terms with the world. It can be very technical, scientific, but it also should give us, at one level, a way to handle our walk through life. and those metaphors are worth investigating as much as we can. And I think we're going to hear many of those metaphors today and tomorrow. So I hope you enjoy them. And with that further ado, I think it's Dr. Rindler's time to speak to you. Thank you. I'll just try and see whether my voice will work like this. I'd like to talk about this morning. and obviously the picture of Einstein, I'm sorry I wasn't there on the premise unit, but it's there because Einstein theory, certainly at the back of all the modern cosmologies, Einstein generally typically is what really empowers modern cosmology. I'd like to talk about modern cosmology and at the end of it I'll try to make a few remarks on how they actually connected with the subject of study at this conference, name and time.

2:30 Cosmology, at the moment, is undergoing a very, very surge of activity. It's a enormous interest of scientists because a lot of things are happening in it. But of course, cosmology is really of interest for everyone. Once you're aware of cosmology, I think, necessarily, it covers your whole philosophy of life, your whole view of life. And if you just go back a few thousand years, three thousand years ago, the cosmos of the universe was a really cozy place. The earth was the center of the universe. We humans were the absolute summit of creation. Sun and moon, stars were there for our dedication. And there was a whole host of gods looking after our welfare when they were trolling around amongst themselves Unfortunately, since then, unfortunately, perhaps our views of the universe have changed enormously. Today's universe is not nearly as cozy a place than it was then. Today's universe is enormous. We're almost certainly not alone in it. We're almost certainly not the summit of creation. In fact, our universe may not even be the only universe there is. Actually, I might immediately comment on that, why there are many reasons for believing that there might be other universes apart from ours, but one simple argument is that, as you know, the universe, we believe, began with a big bang, and if the big bang is a physical rather than a divine event, we assume that it couldn't be a physical event. And if it's a physical event, we are very much using physics to the idea that anything that can happen in physics once will happen again and again and again. Because a proton happens to be able to disintegrate each other. But maybe if it can, then it will again and again and again. So if there was one big band, then surely good reason to think that there may be many, many others and there may be other universes that talk about. So let me just start talking about actual cosmology. the big personality behind it all is Einstein. But another personality, very strongly associated with modernist Friedman, it's not really his word alone, that Friedman was the first man, I think, in all history,

5:00 to have had this revolutionary idea that the universe is just sitting still there, that the universe is expanding, that our universe was a dynamic system which actually expanded and moved, was capable of motion under its own gravity. That was a really revolutionary idea. It wasn't taken up frequently, but this is really a name to remember in connection with modern cosmology. I have written out here a few milestones of modern cosmology. Copernicus was the first man to realize was not the first. There was an old Dick, Aristarchus, who already put forward the view that the Earth is not the center of the universe, but the sun is the center of the universe, and the planets went around the sun. That view was lost, and it was brought up again by Copernicus in 1543 about. Thomas Diggs made the next contribution, and he realized that the sun is just one star that the stars you see in the sky are really suns, like ours. Isaac Newton also had a cosmology. As you know, Isaac Newton had a tonic of an absolute space that existed in the background of everything that was a natural space. And to him, the stars were distributed in all directions. If you didn't get any stars, no matter which way you went. And of course, he was the father of gravity. So how did the father of gravity reconcile this system of infinitely many stars and go to collapse? Well, the argument is simple. If all these stars sit in absolute space, then from any point of view of any one star, there's a lot of four from one side, from all sides of the world, they pull this star by gravity. But then there's just as many stars on the other side, they pull this star the other way, and so it works in all directions. And since these stars fall, by gravity, fall very hard in all directions, in the end it doesn't move by symmetry. So Newton's universe was a static universe, an infinite universe, and his building works for the stars. The next idea came about a hundred years later, not quite, by Thomas Wright and Immanuel Kant. And they had noticed what the astronomers had called nebulae.

7:30 Notice fuzzy things in the sky, but interestingly enough, some of these fuzzy things look elliptical. And the idea was, if you see a fuzzy elliptical thing, well, a elliptical thing may be a disk seen sideways, like this disk that I've drawn there. And if those elliptical things in the sky, these fuzzy things, were actually disks, then that might explain how But in the night sky, you see this bright streak of, well, not very bright, but at least there's an infinite streak of light going down where the light is brighter and in other directions. And Kant and Thomas Wright are interpreted our Milky Way as being the edge of a disk. We live in a huge disk of stars, and the Milky Way is just, when you look sideways in that disk, you see fewer stars. We see many stars, that's the Milky Way. So the idea of other such galaxies began in about 1750. The idea of the universe of galaxies, galaxies way outside of ours. But of course, people had no way of measuring the distance of those fuzzy things. And so there was a long debate whether those things were actually other galaxies or whether they were really just nebulae as they had originally been thought to be. The first real proof that those things, those may be made, were actually, outside of our galaxy, galaxies on their own, came in, well, the question would only be said about the big telescopes. The bigger telescopes came online in 1917, and the question of these galaxies was settled in 1924. 1924, Hubble proved that those fuzzy things, in fact, were of the galaxies. And so the idea arose that our universe of the universe of galaxies, galaxies, probably infinitely distributed in all directions, just like Newton thought the stars were distributed in all directions. From then on, people thought, well, the galaxies, just like our own galaxy, were distributed in all directions. The next big thing came in 1929, when Hubble actually to prove that the universe, just like Friedman had thought, was not just sitting still, but expanding. Hubble proved that these galaxies were moving away from us

10:00 and that could be proved by the spectrum, which was redshifted, an indication that they were moving away from us. The faster they were, the harder they were from us, the faster they moved. And so the idea of an expanding universe was proved in 29 and explained in 1930. At first, that seemed a little puzzle. What was expanding? Was space expanding? Was his pen expanding? Was everything expanding? In the end, it was explained rather simply by a new vector a year later, and he simply said there was a big bang. It wasn't quite a big bang, but nowadays it's called a big bang because the big bang was closing, which gave rise to the expansion of the universe. So according to the Bredge's theorem, there was a big bang, threw stuff out in all directions, Finally, this stuff formed galaxies, the stars first, galaxies thereafter, and that explains the expansion of our universe. Now, until the 20th century, cosmology was essentially speculation because you didn't have really the means to remember the world of husbands. Telescopes could see the stars in our own galaxy. The old astronomy concerned itself with planets, the motion of the nearer planets, the motion of maybe the aspect of the nearer stars, and so on. But there was no way to look outside of our galaxies until the huge telescopes in the early 1802-meter telescopes came online early in the 20th century. So a real science cannot exist unless observation and theory can drive. The theory by itself is pure speculation, non-prime speculation would be anywhere, and it isn't useful, but it isn't very conclusive. And observation alone doesn't do very much for you either, until it is all . So real science needs both. And luckily, these two strands of cosmology came together precisely in 1917. Strangely, in 1917, Einstein, through his general relativity, took forward his first cosmological model. It was static, because he still talked to the universe of static, but at least there was a theory of a huge universe which was held together

12:30 by its own gravity. And then in the same year, the first huge 2.5-meter telescope came online on Mount Wilson. And that really gave rise even the bigger telescopes came online any later. But only when, on the one end, the observations allowed people to go way outside of their own galaxy observe the other star galaxies on the one end. And on the other hand, theoreticians predicted and systematized what was seen by the observation, by the observers. Homology has made huge strides since then. Let me just mention a few of the things that are known today. Actually, within the last 35 years, astronomy has made even bigger strides than it had done in the previous century. First of all, as I said, Newton thought of the base candle box of the universe depending on the stars. Then, after about 1934, when Nobel had proved that the galaxies were actually outside of our own reality, depending about the universe were galaxies. But by now, it was also realized that galaxies tended to put clustered together. So they had clustered with galaxies, huge super clustered with galaxies. But nevertheless, although they clustered, the whole universe was more or less This clustering by now has taken on, by now it's much better understood. So the galaxies actually, the clusters are huge numbers of galaxies in each cluster, thousand maybe, 10,000 galaxies, and in the sky they form the filaments in cells as a strange form-like structure that they've only been really discovered within the last 20 years. So now it is these cells of a cluster of galaxies that form the base of the universe, but nevertheless the universe is still homogeneous on a very, very large scale, one after the other of the scale of these cells, but on the whole, if you take very large volumes on the whole, it is still homogeneous. In the obviously important discovery that was made fairly recently is the expansion of the universe, which is very counterintuitive.

15:00 When the major invented the Big Bang, the Big Bang shot stuff out in all directions. And the idea was that, of course, it should matter out in all directions. But then gravity will slow down, so the expansion would start enormously, and gravity would gradually slow down. There's always a question, maybe it will slow down enough, maybe the universe would expand, come to a halt, and then re-collapse. Or maybe the energy was bigger enough from the beginning, and the universe would expand forever. But always slow down by gravity. In other words, although it starts with velocity with infinite, then velocity will slow down, slow down, slow down, and it will slow. It may never slow down altogether, but it is going to slow down. Counterintuitively, it was discovered that instead of slowing down, the unit is actually accelerating. But that is something that is a possibility within Einstein's general relativity. Einstein had invented a term in his field equation, the so-called pathological constant, the universe, there's a force in Einstein's theory, a sort of countered gravity force. It's called the cosmological term. It's not really understood, but what its exact meaning is it could be just part of the geometry of the universe. It could be something else. Anyway, people nowadays think there's some mysterious stuff called sharp energy, which is responsible for this acceleration of the universe, and it's a big problem. So there's this dark energy, which is a present problem. There's also a problem of dark matter. When you, dark energy is what you need to accelerate the universe. And dark matter is the opposite. When you look at galaxies, when you observe galaxies with very strong telescopes, we find that they hang together in a way which is stronger than will be justified by all the matter that we can see in a galaxy. All the matter that we can see in a galaxy, it wouldn't actually hold it together. You need more matter to account for the various motions that you see in the galaxy. So dynamically, more matter is needed, and it can't be only matter. There's some good arguments to say that the actual matter in the galaxies which hold them together is not just the ordinary matter, like this table

17:30 or whatever you see on Earth. It's, again, something that they don't quite understand. and it's not dark matter. So dark matter is another unknown component of the universe which holds the galaxies together and is the opposite of what dark energy does. When you then take a balance sheet and ask yourself how much of the universe, how much stuff in the universe actually makes it understand, it's small. This 5% is the only baryonic matter which we understand, which is the stuff that's one of the exams in the laboratory, 70% is the dark energy that accelerates the universe. One knows how much you need, but one doesn't know what it is. But it doesn't count about 70% of the density of the universe. And there is this 25%, which is that dark matter that resides in galaxies that are also not at this point. So it's funny that only 100%, only 5% are really understood by it, and the rest is rather mysterious. Another thing, of course, that has happened recently, all these additions are getting better and better. Telescopes are stronger and stronger. In the old days, 2.5-metre telescopes like 10-metre telescopes, much bigger ones than that. 100-metre telescope is in the current stage. As a cosmology which once was a pure specter did something, now it's been called precision. Precision cosmology can make really very accurate measurements. People, for example, believe they know the exact age of the universe. People believe the exact age of the universe is 13.7 billion years. That's how long ago the Big Bang happened. Anyway, you do have precision universe. and also people think they know precisely that the curvature of the universe is zero. That may or may not be true, but anyway, that's what's thought. That's what people think. As well, the fine structure, I'll skip that for a moment. Inflation is another thing. It's an alternative idea of what immediately after the Big Bang. Some people have called it the most important theoretical development in cosmology

20:00 in the last half century, I don't really think that's what it is, it may or may not be true. It's one of those fashionable physical theories, which when I was a student, the state-of-state theory was fashionable, and everyone believed in it, and then it fell out of favor. And I have a feeling maybe inflation is one of those fashionable theories which everybody latches on, but it may in the end not be true. Gravitational wave astronomy is over the horizon, it will, it's not there yet, but not there yet, but it will provide a new window on the cosmos, and then, of course, the idea of many universes is also fairly new. This is just an overview of what's happening, of what is happening, what is happening recently. Let me just put on the slide. There's some characteristics of our universe that it is useful to bear in mind. First of all, the fact that it's enormously big. The second is that it's regular. The regularity of the universe is actually a huge puzzle. The regularity of it, if you really believe that the universe started with a big bang with huge explosions and stuff up in all directions, then it is rather the present, while the present universe is actually homogeneous. It's true that on a smaller scale you get all these filaments and cells and coins and walls. But if you take an average over large enough regions, every huge region, say you divide what you can see into a million parts into a million cells, then each of these cells is in fact more or less like every other. You have regular homogeneity on a large scale. And why that is, it's a huge puzzle. It's enormously lucky for cosmologists, because if you didn't have that, if you didn't have that homogeneity, it would be very hard to build cosmology and make cosmological markets and cosmological theories. The regularity of the universe allows you to have a theory. And then, of course, the third point, the universe is expanding. That's uncontrovertible. The universe may be curved. That's quite interesting also. And that idea is to divide stuff. In other words, the universe either leave it flat, it couldn't start flat in all directions in space, or it could possibly be curved back in itself. A flat universe could be an infinite universe.

22:30 Infinity is a very difficult concept in physics. Infinity mathematics is very funny. It's the abstract limiting operation of infinity mathematics, that's great. In physics, to think of an infinite universe, to think of infinite class, A big bang produced in one explosion, an infinite amount of mass, it's a difficult concept. Nevertheless, the universe could be infinite. It would be hard to swallow, but it could be infinite. However, Einstein said it could also be curved. It could be curved back in itself. I would be happy if it were there, it would be easy to understand. Like the surface of the Earth could be a two-dimensional universe that's curved back in itself. There's no boundary anywhere, amount of matter, so maybe the actual universe is a sort of three-dimensional analog of a sphere, so it's a very curved. And of course, it's enormously old. The fact that it's enormously old, I'll just have a little diagram here. I start with this last fact, and it's enormously Here's a little diagram. This is billions of years. The Big Bang started about 14 billion years ago, but four and a half billion years ago the sun and the earth were born. Life started rather early, but about 500 million years after the beginning of the earth was formed, already apparently the terms of life were beginning to exist. time of all sorts of little things happening in the waters and wherever, and then about 500 million years ago, the age of the animals. So the last 500 million years, the world was already full of animals of all kinds, and then the last few million years, maybe one, two, three million years, man. The age of man on that diagram would be less than a human the thickness of that line would be less than that of the human hair. So it's interesting. And of course, the sun is, this is when the sun was born, the sun and the earth were born. It's going to live as long again, so the sun, we don't have to worry about the sun going out before we're ready. There's a lot of time to, very pleasant reason to happen. If at the moment, human history is as thin as a hair,

25:00 it's going to happen. I'm very interested in thoughts. We won't discuss that now, but anyway. after the Earth was born, and that's what you said? Just half a million years for the . Yeah, well, it's a short time. Anyway, so that is certainly a thought to bear in mind that human history is enormously short compared to the age of the Earth, the vastness of the universe. The vastness of the universe begins already in our neighborhood. The idea of the vastness of the universe, if you look at the sun, The sun is an enormous ball of gas, but it is so enormous that, for example, if this were the earth, the earth is about, it's the average of 100th part of that of the sun, so the earth, and here's the orbit of the moon around the earth, so the earth with the orbit of the moon would fit very comfortably into the sun, which gives you an idea of how big stars are. So stars are enormous. The distance between stars is also enormous. If a star is a pinhead, then the distance between stars is about 50 kilometers. And then, how many stars are there? This is an equation that's worth bearing in mind. It's not a real equation, but I need to go back down years and years and years ago. It's a sort of tongue-in-cheek equation, but it's useful. But 10 to the 11 stars make a galaxy, and 10 to the 11 galaxies make the universe. 10 to the 11 stars make a galaxy, that's about right. like our own galaxy, which is a surrounding galaxy, maybe it has something like 10 to 11 stars in addition. And then, 10 to 11 galaxies is just about what is within range of the best telescopes. So if you just calculate, obviously no one is counting 10 to 11 galaxies, but if you calculate the number of galaxies that are within the range of our best telescopes, you calculate that they are within reach about 10 to 11 galaxies. is we know that many exist for sure. The universe may be infinite beyond that, but at least it's that big. It may be much bigger than it, but at least it's that big. But if you write down here to the 11th, it doesn't mean very much. 10 to 11, everybody knows the truth. If I say 200, well, that's a huge auditorium, you can imagine what that is. If I say 20,000, maybe that's a huge stadium, you can imagine what that is. If you write down 10 to 11th, it's hard to imagine. I'm going to help you to show you how big is 10 to the 11.

27:30 10 to the 11 is this thing. If you make yourself a box, and the box is 15 foot by 15 foot by 15 foot, a rather large room. It's a cubic room. So a large, huge box, 15 foot by 15 foot by 15 foot. You fill it with pinheads. Pinheads are by pinheads, one millimeter in the glass. Filling with pinheads, no pinheads you get into that box. is more or less 10 to the 11. So that gives you a picture of how big a number is 10 to the 11. It's a number of pinheads you can fill into a rather huge chunk. Well, that's the number of galaxies. That's the number of stars in one galaxy. So that many stars, each pinhead, they would make one galaxy. But then again, there are that many galaxies in the sky. So 10 to the 11 times 10 to the 11. with that many stars, and then that many galaxies you get, so they are like, well anyways, there are 22 stars for sure exist. That's 10 to 22. Hard to imagine if you don't have a diagram. If you have a diagram, if you have a cube 15 miles wide, 15 miles high, 15 miles deep, fill that cube with pinnets, and that's the number of, that's 10 to 22 pinnets for 10 to that cube. of stars that exist for sure. We're one of them, the sun is one of us. And if people think that that's the only place where they'd like a universe, well, that's just strange. I think the chances, if you look at the enormous universe, that we're not alone, that we're not alone in this universe. So it's big. The other thing is, the regularity of the universe, is, how much time do you do? Stop shooting. Stop shooting. Well, the regularity of the universe. That's the problem. The regularity of the universe is regular. I'll tell you about it. One of the best, well, oh yeah. I won't mention that. I will mention, I'll go back to the, because I've got this in hundreds of time. If I have time at the end, I'll show you three more slides. But what does all this have to do with time?

30:00 What it has to do with time is that once you have an expanding universe, like the one you believe in 11th, with an expanding universe, and if it's all machines, it is regular. So the density decreases of the universe, and everywhere. it's less and less and less and less, but the density is quite instant. It's the same everywhere. But it gets less and less and less, and the universe gets more and more expanded. Well, you can say that universe itself acts as a clock. It acts as a synchronizing mechanism. Because as the universe expands, you can say, well, if an event happens here and an event happens there, when will I call them simultaneous? Well, the density here is the same with the density there. So the density of the evolving universe, of the whole continuously evolving universe, that density provides a clock. It provides a unique way of defining time throughout the universe, which is interesting, but it's not quite inclusive. As you may know, I make this conference and consider that in special relativity, which is Einstein's theory of Einstein put together space and time. And going to Einstein, space and time are related. And special activity is a simple way of studying it. Special activity studies space time, at least empty space time, there's no magic to confuse the issue. So in special activity you consider put together space time, but even in special activity time is rather problematic. Special, empty space time is free of any features And you can really slice it in several ways, in many ways. So simultaneously slices in empty space time, this kind of slicing, this kind of slicing equally good. In other words, in special relativity, there's no unique concept of simultaneously. You can slice it this way, these two events are simultaneously. You can slice it this way, these two events are simultaneously. Because of the symmetry of empty space time, Although you need to define what time is in special activities, it depends on the observer. Fast-moving observers are slices differently, but still there are nice time slices in special activities. Then you want to generate it. You generate it before in Einstein, time, space, and imagine are all mixed up.

32:30 So for example, if you had a chaotic universe, if you had a chaotic universe, Well, you prepare to say, well, I have very little special coordinates. In a very regular universe, well, you have special coordinates. We can get out of the universe. And don't forget, especially in the United States, there's no boundaries of background space. There's no boundaries of natural space in the back of the world. So all we've got is chaotic matter. So how do you define coordinates in there? Well, there's no space anywhere. You can't have an XYZ. Spatial coolness are rather arbitrary in a completely chaotic universe. But in the same way, because space and time and matter are in the areas, time is completely arbitrary, loses its meaning in a completely arbitrary universe. However, when you then go to a homogeneous universe, like the treatment universes that are in the base of modern mythology, then by their opportunity, by their expansion, you are back and you will have a preferred time. But for example, philosophers like Gödel pointed out that time, it's true that in the universe we have it, by a happy accident, we possess a preferred time. The time that we have is the oneness that is in fact forced to rest by the expansion of our own genius universe. But Gödel said, if the concept of time is dependent and how the magnetism should be. This account of time would be lost, or the unique time would be lost if the magnet were chaotic, then time is rather different from what philosophers and Jewish and Catholic ones. I suppose that's a very good example. Isn't that right? I'm surprised to take one question, and we'll have plenty of our videos in the next two days. I'd like to pick this question. Do you believe that we should separate really space and time, space time basically from matter? I would say like a concept of background time, background space time, and then something Yes, I do agree, yes, yes, yes.

35:00 Space time will become one, but matter is not going to become one. space value on one name man on the other end are relinqued by anti-filiers, but man because of space in your place. So there's a relation between them, but certainly a conceptual difference. Thank you. Thank you. Thank you. Thank you. Thank you.

37:30 from Syracuse University. Incidentally, those of you who are leaving will not be coming forward. I guess I was too late to forward those people who are leaving. You're not going to get accredited if you get up or something else. Yes, you will. I'm kidding. I'm very pleased to welcome Professor from Syracuse University. today. He's actually an old friend, a former teacher from my graduate days at Serenity University. I'm so happy that you have persuaded him to come visit us. He's a world-recognized expert on this very strange thing called non-commutative geometry, also goes under the name Fuzzy Physics. And you probably will be convinced, at least in the Latin of the scripture, following this talk. So let's welcome Professor Dalek Balocham. I will try to explain to you what is going on with this subject called non-committed I am very unhappy, because I had made all this in colour, because of the low tick availability here, I can't show it, but okay. Then we start with some orders of numbers, some orders of information. And eventually I will try to tell you from these numbers why these ideas, these extremely novel ideas are imagined. We know that the size of an atom is roughly 10 to the power of minus 8 centimeters. And this is roughly the wavelength of visible light. In fact, it is because the light is emitted by atomic transitions, so it has to, the wavelength should have the characteristic length, size length of the atom itself. Now, the atom itself is composed of a nucleus of size 10 to the power of minus 13 cm.

40:00 And the electrons are moving around it at a distance of about 10 to the power of minus 8 cm. far from the atom itself. In fact, the distance between the nucleus and the electron is five orders of magnitude. The size of the nucleus, as I told you, or the proton and the neutron is about 10 to the power of minus 30 centimeters. Whereas the size of the electron itself, which is orbiting at a distance 10 to the power of minus 8 centimeters, is very small. It is Next, the next small scale occurs when we deal with new elementary particles of weak interactions. For example, when we look at beta decay of nuclei, we are then, like radioactically, we are going to a different length scale. In fact, it is a length scale that is governing the size of the electron, and that is about 10 to the power of minus 15 centimetres. We believe now that we have a very good understanding of the physics up to these scales. In fact, the accuracy, the agreement between theory and experiment up to this kind of landscape is quite impressive being in the range of something like 5 percent or less. So it is an extraordinary achievement that we have understood more or less the physics, the nature of reality down to this scale. But something completely different happens when we start from this scale and go into gravity. When we go into gravity the typical length scale is not this thing but it is something like 10 to the power of minus 32 centimeters. That is 10 to the power of 90 times smaller than the size of an atom. It is huge, the difference between the scale between the size of an atom and the scale that is controlling the gravitational forces is huge. It is 10 to the power of 90 times. The odds of magnitude that are involved is 10 to the power of 90. So, if I go to the next scale, next thing, now, first question that arises is, is there any way whatsoever of testing physics at these scales? We will come to that in a minute.

42:30 But the first observation to make is that at such small scale, we have really no reason, up to your reason, to imagine that the nature of space time wouldn't be anything like what we imagined today. In fact, start by applying some qualitative arguments coming from gravity. We can argue in fact that we can expect the physics to be totally different, radically different. The point I want to make here in this case is that in this case we expect also actually a fundamental limitation on probings as one-length scales. In fact, what I am going to claim is that there is good reason to imagine that we cannot really see these We cannot probe them with great accuracy. So, for example, what is the reason? Suppose I want to probe very short wavelengths. Then we need very short wavelengths. That is physically quite obvious. So the matter with which, say light or whatever it is, with which I am probing this lens case must have very short wavelengths. But constantly this is that the wavelength of a particle, if the wavelength is very short then the particle must be very massive. There is something called a content wavelength which is associated to each particle and that content wavelength must be is the wavelength that we are talking about here. That means it is very massive that by Einstein's e equal to mc squared root we have to put a lot of energy. In fact, we can estimate that energy, it is on the order of 10 to the power of 90 nuclear masses in this extremely tiny volume, we mean 10 to the power of minus 32.3 cm3, this being the scale of gravity. So, we are putting this huge mass in this extremely small volume. But then again, we know by classical Einstein relativity that if we put, we have so much mass in such small volume, we are going to create one of our black holes. Roughly speaking, what happens is that the gravity that is created by this huge mass in this small volume is going to be so large and the gravitational attraction is going to be so tremendous that nothing can escape that region. In particular, light cannot escape that region. So, the entire energy wave goes out of our mission. You cannot see it. So, we expect by this quantitative we cannot really, there is a fundamental limitation coming from quantum gravity of probing sense

45:00 length scales. So what we are trying to do is to make some kind of a model which will take into a fundamental limitation. But we know already from another source of physics, which I am sure you have heard. There is a limitation on measurements. For example, we know that in quantum mechanics, it is impossible to measure positions and momentum with data accuracy. There is an absolute limitation which is given by the max constant. So, we can imagine, in fact, what we know from quantum mechanics, that the product of uncertainties in position in momentum measurements cannot be smaller than time's constant. So, we can imagine that maybe a mechanism of this same kind that is governing quantum, this limitation in measurements in quantum mechanics also is a one, at least as a model which limits measurements in space and time. So, I remind you that quantum mechanics, the way it is about this limitation is by saying that position and momentum do not commute. Don't worry if you do not know what that is. Some of you might put some course in quantum mechanics and you need to know what that means. Otherwise don't worry. So that means that quantum mechanics is non-competitive geometry. And that is this non-competitive geometry is giving this limitation. And it is this that leads to Eisenberg's uncertainty principle. Well, in the same fashion, for space-time too, we have to consider it non-competitive geometry. And see whether we can make physics on this kind of space-time, where the fundamental limitation on Bechema's is already built. So, if I go on, I should give you a bit of history here. Actually, this idea that space-time geometry, space-time behavior, there may be fundamental He is actually quite good. Heisenberg suggested this and there exists a letter from Heisenberg to Byers in the 30s where he describes this possibility and he actually complains that he does not have enough mathematics to explore the physical consequences of this possibility. Later, Piers, actually, go on, if you can raise it a bit, Piers mentions Heisenberg's, actually Piers wrote it soon after, wrote a paper, saying that there are institute systems in nature where this is realized.

47:30 You are really talking about electrons in a field in the presence of a value field in the third direction. This is called the Hall system where a similar thing happens. He actually wrote a letter on this, but also he mentions Heisenberg's ideas to Wolfgang Paulde. Paulde in turn expressed the whole idea to Hartle and Snyder. I think both of them were at Winston Institute. And later Snyder published a first paper on this subject around this time. where an actual warning is attempted to be created along these lines is in this paper, in this period. I want to mention my own bully, one time bully, Joe Whitewell in this context. Joe was a student of open paper and he was also a gross associate of power and he was He had a very tough life because he, well he was exceptionally brilliant and he was a professor in Minnesota and he lost his job during the McCarthy time because he was accused of passing secrets. He is the one who was accused of passing secrets to the Soviets. So he lost his job in 1952 and was supported for many, many years by his wife, Bertrand. Eventually, Joe Romer got a position in case in 58 and from there he came to Syritus. Joe was quite exceptional. He seemed to know everything. I mean, for example, he knew Sanskrit, I don't know how, and he knew not coming into geometry, he was, after retirement he was translating old music, 12th century music, into modern language. So he knew a lot, and he had written, he had done enormous amount of work in the Schneider model, and he published essentially nothing. But I have seen his manuscripts, and they are now saved in the university archives. So they are available for public

50:00 view. So let me now go back to physics. We can ask what kind of new physics can we expect from this new mission as they start. Let me just mention a few, how they come out. Well I told you already that atoms and molecules are mostly empty. Atons are of the size, the are very large distance, some 5 orders of magnitude distance from this atom. Atom is about 10 to the power of minus 13 centimetres. And this thing is, electron is orbiting 10 to the power of minus 8 centimetres. Which means that the atom is mostly empty. But where is it? If the atom is mostly empty, you can ask, it is very reasonable to ask, my fingers are mostly empty, why can't I pass one finger to another finger? Or for example, a professor has walked, why cannot a professor walk through a window? It's a reasonable question to ask. And here of course I can put in a pitch for the Indians. Go on. Well, I am sure that all of you know that there are people in India, yogis, who routinely walk through mountains But of course it involves a lot of work, a lot of meditation. But the physicist's question is why can't we all do this? This is something in sectional. Based on in sectional principles, why can't we all do this? The reason is a deep physical principle which is called the Pauli exclusion principle. This is a quantification principle which says that no two electrons or no two protons can occupy the same spot. So, when one tries to push, say one electron or proton near the other, there is a very slight depulsion which is impossible to overcome in the standard formation. So, this is one of the guiding factors which prevents the possibility of walking through doors or crossing one field and then through another figure. It is in fact a principle which gives divinity to matter and much other observes in the area. Well, it turns out that the space stream obeys non-community geometry at short length scales, at least length scales, then this principle is violated by very small amounts. That means

52:30 very specific experimental signals to look for. Particularly the kind of signals you can look for are formative transitions in atoms or in certain some nuclei. And these experiments can be done with enormous precision. They are forbidden. For example, one experiment that people do is, they take a crystal where you take a crystal and put it in a vacuum and then you pass a current over the crystal for one month. Then ask, look for a photo of a line which is a forbidden line and thereby see limits, try to put limits on these transitions. There are such experiments which have already been done. So they are capable of extreme precision, which at least at all of this will put limitations on the possibility of the kind of physics that we are trying to do. Okay. Thanks. Okay. Now there is another interesting thing that happens. All of two integrals in these models can occupy the same spot because of the violation of something really strange happens. Then if you put the exclusion principle splits these points. So, for example, if you put an electron in spot x, there is another spot y. This is not x somewhere else, which I can show you how to calculate it in a model. And there you cannot put an electron. So, if you put an electron here, you cannot put an electron somewhere there. Or, for example, if I am here, then you cannot put my drone there, out there somewhere, which I can tell you where it is. Of course, you may say this is too much. That is recklessness suggests making more glass, but there is a different point. Next question. Let's go on. Another striking effect concerns causality, which touches upon an issue which was brought by Professor Rinder. Causality is the principle that it is not possible to save information faster than the speed of light. A consequence is that research and experiments perform the space-time points which cannot be connected by light signals or are not combinated. For example, there is freedom to do experiments with these points without interference with

55:00 each other. So if two evers cannot be connected by a light signal, then they are basically independent. This is a consequence of standard special relativity, but this principle is not valid in non-cominient theories. They fail. Then we can calculate the failure. So, what happens is, what happens is, what happens is, I don't know what to do. Alright. So, non-collimative theories, even if two points are spatially separated or separated by distance, so that line signal cannot be set from one to the other, still these events And there are limits of the precision which experiments can be done at these two points. And there are uncertainty principles governing events happening here at another point which you normally think cannot be connected by life signal. And this would have definite consequences in cosmology which are led to be explored. In fact, if they explain what was mentioned in the last talk, they observe mass in homogeneity at least provide some model where we can see, this work has not been done, but it is a speculation that large scale of homogeneity may be due to violations of positive. So, what is this problem here with homogeneity? As I explained, the puzzle is that this homogeneity is extending over reaches which were not in causal communication even in the distant past. So how come they are looking the same? And maybe it is because of the violation of causality. There is a very related result. That is quite interesting and its implications are not very clear to We saw from the Artemis based on quantum physics and blackboard formation that the whole sector was such that I cannot localize events in space, I cannot measure spatial events or time intervals too sharply, there is a spring. So, time, that means that time of space cannot be sharply localized. That means the statement

57:30 of instant your time loses meaning. That, what does that mean, what do I mean by that? For example, what I mean is, I cannot really say that the electron is at position x. I can only say it is around position x with some uncertainty. It is a probability of finding electron around the point which you say is the most probable point has a spread. So you can find it outside the region also. Likewise here what happens is that any event, you can only say that when an event occurred say at 2 pm but the spread does go many seconds. You cannot sharply say that it occurred exactly at 2 pm. Impossible. Now the funny thing is is going backwards and forward in time. That means, an event is occurring around 2 pm, it is printing also back in time and there is a tick, so the possibility of saving signals back in time arises. Purely at the cotton level. And it is by a small amount. So the hope arises that perhaps you can send signals back in time and influence your long-dead So that is quite interesting and remains to be experienced. Well, meaning of such possibilities are yet to be experienced. So let me conclude, it's exactly twenty-five minutes. I'll try to give you a flavour of emerging ideas in a fairly non-dictive manner. There are a number of experimental consequences of these models. And then also, this is an interpretation, which are not at all clear yet. People are thinking about it, but they are not at all clear. But the mathematical formulation is more or less under control. And I have given some references, and I will stop here. Thank you. So we're right on thread, and I think we can entertain some questions. If you would identify yourself when you ask a question, that would be useful. Yeah, Steve Weinstein. Just something you said toward the end about that.

1:00:00 You're looking at the idea that events don't have a definite temporal location, fuzzy time coordinates, with backward causation. And I'm not quite sure I'm going to elaborate on what the connection is supposed to be. Is it the ? The wave function, they say to prepare a quantum state, if there is no quantum state, the position, time of time, immediately becomes a time operator. By the way, there are some strategies. I am not doing agreement with this Heisselberg concept which was said in this morning. So that time is not operating. It is something else. But here, what's called time coordinator is actually an operator. So if you try to make quantum steaks, you cannot localize it because it doesn't come in with other operators. So it doesn't spread. So it is spreading back and forth in this coordinate time operator. So it makes an ordinary condominium. If somebody tomorrow prepares a condominium stick, I can make a measure when you see it. Is the idea that you have an event, perhaps, involving your grandmother at some point, which is in the past life home with respect to one of the things in its space life with respect to another design if the temporal location is fuzzy, is that the idea? Well, if light poles lose meaning, you know. Well, that's why I think so, yeah. But that's why I'm not sure that you know. But there is a temporal order. You can still give a partial order. Although light poles lose meaning, there is a way to give a partial order to this operator itself, the spectrum of this operator. So with that we can still say something to the future of what something is to the past or something. We must make our face off face with it. So there is a way. So yeah, there is something interesting to think about. Do Einstein integrations play a role if there is no country better?