Secrets of the Universe: Neil Turok Public Lecture

Hello and welcome everyone to the Perimeter Institute

public

lecture

series. My name is Emily Petroff and I am Perimeter's Associate Director of Strategic Partnerships, Grants and Awards. I am pleased to welcome you back to the Mike Lazaridis Theater of Ideas here at the Perimeter Institute in Waterloo. His Perimeter Institute was created to be a gathering place where people can gather, as we will tonight, to ask big questions about the

universe

and seek the big answers. Perimeter will soon celebrate 25 years bringing together people from all walks of life, researchers, students, teachers and the general

public

, to explore the fascinating world of physics.

But the people of this earth have been asking big questions about the

universe

for thousands of years, looking at the night sky and understanding that our place in the cosmos is a fundamentally human constant throughout the centuries. We recognize that the perimeter is situated on the traditional territory of the Anishinaabe, Honashone and Neutral Peoples and is located on the Haldeman Tract, the tract granted by the British to the six Grand River Nations and the Mississaugas of the Credit First Nation. We are grateful to those who came before us and are committed to acting responsibly and collaboratively to advance the pursuit of knowledge, for the betterment of all.

For those watching the webcast live, please join the conversation online. We're at Perimeter on Twitter or x and Perimeter scientists are online to answer your questions. If you have any questions for our speaker, ask them with the hashtag PI live. This week, Perimeter is proud to host a fascinating conference called Puzzles in the Quantum Gravity Landscape, bringing together experts in cosmology, black hole physics, effective gravitational field theory, and quantum gravity. The institute is packed with over 125 in-person attendees and many more joining virtually from around the world. And now it is my great pleasure to introduce you to one of the conference attendees and our speaker tonight, someone who may be familiar to many of you.

Born in South Africa, Professor Neil Turok received his PhD from Imperial College London and currently holds the Higgs Chair in Theoretical Physics at the University of Edinburgh, as well as the Carlo Fedani Roger Penrose Distinguished Visiting Research Chair in Theoretical Physics here at the Perimeter Institute. In 2003, he founded the African Institute for Mathematical Sciences, also known as Ames, a pan-African network to train the next generation of mathematical scientists. Professor Turok has had a distinguished career, including numerous awards. He asked me to be brief, but I would be remiss not to name a few, including the John Torrance Tate Medal for International Leadership from the American Institute of Physics, a Ted Award, the James Clerk Maxwell Medal from the Institute of Physics in the United Kingdom, and he is also an Officer of the Order of Canada.

Additionally, as you may know, Professor Turok served as Director of Perimeter from 2008 to 2018. And he was the driving force behind many of the programs and projects that have made Perimeter what it is today. He led Perimeter's growth into one of the world's leading independent centers for theoretical physics and launched, among other initiatives, the Perimeter Scholars International program, which is a master's program. Here at Perimeter, the distinguished Visiting Research Professorship program and the Center for the Universe. Professor Turok's research focuses on the development of fundamental theories about the origin and evolution of the cosmos, as well as observational evidence.

He has collaborated with scientific luminaries such as the late Stephen Hawking. Tonight, he will discuss recent developments in this quest to understand our cosmic home and the laws of nature that govern everything from particles to the entire universe. He will also explain how new measurements will soon be able to test these interesting ideas. Please join me in welcoming Neil Turok to the stage. Thank you, Emily. It's a real pleasure to be back here at Perimeter. I had a lot of fun as a director, it really was a unique opportunity and it's great to see it flourish today.

So what I'm going to talk about is a new approach to tackling the

secrets

of the universe. And it is a new approach that is really born, with a certain sense of frustration with respect to previous approaches. In my opinion, they had become quite complicated and artificial, including my own approaches. And yet the data, whether it came from the very small or the very large, was the opposite. It was amazingly simple. The most powerful microscope in the world, the Large Hadron Collider, turned on and discovered the Higgs boson, something that was almost guaranteed and nothing else since.

And so, somehow, nature has found a simpler way to be coherent than theorists had anticipated. So, the same story on very large scales. Having mapped the entire visible cosmos, what we discover is that the description of the cosmos is astonishingly simple. It doesn't get increasingly more complicated as you go to larger scales. It's the opposite. Apparently, it gets simpler and simpler. So based on that, this really inspired me to try to come up with simpler, cheaper, more predictive, more principled explanations for what we see. And that is not easy. What I am going to explain is very new, very preliminary.

We have taken certain steps on a new path and I am here in part to present these ideas to many experts. The institute is full of these types of people, at least their modern equivalents, and this is very much the atmosphere at Perimeter. He may be the director of Perimeter, but I wanted to get your particular attention. This is the kind of role I'm playing. It seems like this person is cheating. I am, because I am looking at the answer, that is, the universe and what we actually see in observations. And I'm looking over my shoulder.

This is an axamander and he is looking over Pythagoras' shoulder. Pythagoras is discovering the exact logical rules of mathematics and an axamander has one eye on that, so he's pretty good at mathematics, but he's actually taken these major clues from experiments and the world. This person probably invented the concept of doing experiments to test scientific theories. So that's what I want to be. And here is Euclid, discovering the axioms of geometry. We also have many mathematicians in the perimeter institute. So I'm going to tell you about these very new ideas. I'm surrounded by all these smart people and I have to warn them in advance that these ideas could fall apart.

Tomorrow someone here can point out some serious flaw and the whole theory will collapse. And I apologize in advance, but I actually don't think that will happen. I hope that doesn't happen, but if it does, so be it. Good scientific theories can be tested by logic, logical argument, or by measurement. And one simply has to celebrate when they fail and move on. Well, we live in a spectacular universe and for some reason we don't understand, it literally tells us its

secrets

. The ways in which the laws of physics have been discovered illustrate this time and again.

And obviously we live outside the sun. It's spectacularly beautiful and one of the main laws of quantum mechanics, Planck's radiation law, that radiation comes in packets of energy, is perfectly illustrated just by the color of the sun. So all we had to do to discover that light is quantized is simply look at the sun. We now live inside the Big Bang, and the Big Bang is very similar in some ways to the Sun, except that we are inside it and not outside it. The temperature of the sun is about 6,000 degrees, the temperature of the spherical shell of the universe that emitted the radiation we now see from the Big Bang.

That projectile was at about 3000 degrees when the radiation was emitted. So only a factor of two different from the sun. So our place is outside the Sun, but inside the Big Bang, and both shine with light according to the most fundamental principles of physics. So here is the first groundbreaking satellite from 1992 that measured the Big Bang radiation with very high precision. And you see the curve here. This Planck spectrum is the most famous curve in physics because it is the origin of quantum mechanics. So Planck discovered this from light bulbs, fitting the data to predict the color of a light bulb.

But it turns out that the sky shines exactly with this spectrum. It's based on ideas of heat and thermodynamics developed by Boltzmann, this exponential law that the probability of getting an energy e is given by the exponential minus e over K, Boltzmann T. And that describes this tail of the distribution at high frequency. But the most important thing is that the energy is given by Planck's constant multiplied by the frequency of the photon. And so the entire universe literally shines before us with the elemental spectrum of quantum mechanics that tells us that light is quantized. It is a surprising fact.

And the error bars on this curve are tiny. In fact, cosmic black body radiation is the best black body we know of in nature. It's very difficult to make an artificial one that good. In fact, we could have learned this about the sun if we could observe the solar spectrum. We can't because of the environment. So the atmosphere creates lines, absorption lines. This spectrum is the extraterrestrial solar spectrum. If you rise above the atmosphere, this is what you see. And it also fits very, very well into Planck's black body spectrum. Again, you could have learned this just by looking at the sun.

We just had to overcome the atmosphere to do that. Here again are the theoretical curves. This is at 5000 degrees. It is emitting colors that are yellow and red. As you lower the temperature of the sun, it will become redder and redder. This is the classical theory, which is absolutely useless. And so quantum theory gets the right answer. So the universe literally tells us its laws. And that's the fundamental thesis of this conference: we have to look at the incredible variety of data we have now, figure out which parts of that data are really telling us something fundamental, and learn from that.

Here, then, is Planck's basic postulate. Planck did not arrive at this postulate easily. He said it was an act of desperation to try to make sense of what was happening. The problem is that if you know that light is a wave, waves come in many wavelengths and you can fit small waves in a given volume into a wide variety of waves, just in a wide variety of ways. Imagine putting a wave of a certain length in a box. The smaller the wave, the more ways there are to distribute them. And essentially, the problem they had in thermodynamics is that if that was really the way light worked, if that was all there was, that light was waves that could have any amplitude and any size.

You could just put big numbers in a box. Now, the sunlight is basically in a box because it is scattering the particles. It takes about 100,000 years for a light wave emitted in the sun's core to leave the sun. So this light will be going around for a long, long time. And if it were true that it could literally be shredded into arbitrarily short waves, the sun could not exist as a stable object. You would simply crush all the light waves down to the shortest possible waves and the sun would disappear in a flash of extremely short wavelength radiation.

It takes quantum mechanics to stop that. The quantification of waves into units of energy, in particular that short wavelength waves must have a certain amount of energy to even exist as a piece of light, a photon. That's what stops this leakage towards very short wavelengths. So he came up with this postulate. It is what allows the world to exist stably and objects like the sun. So it's very, very fundamental. And here it is that the energy of a light wave is given by a constant multiplied by its frequency, and the frequency is related to the speed of light and the wavelength in this way.

So short wavelength photons have a lot of energy and you feel that when you listen to the radio. The radio waves pass through you, the room and everywhere, and we feel nothing. But if you're exposed to sunlight, you're obviously feeling that radiation. Radiation comes in high energy packages. And that's why X-rays or gamma rays are dangerous, because each packet of energy can do something destructive to the molecules in the cells. So here we are inside the explosion, and now that we look in more detail at this layer of radiation coming towards us from the big explosion, we see this random pattern.

And this was first mapped by Kobe with very low resolution, but then by this Planck satellite. And so it just looks like a random pattern of waves. In some ways, what emerged from the big bang was something like this, just a random pattern of waves. The waves, in this case, are the density of the universe. It varies slightly from place to place, as does the temperature when we see this surface emitting radiation. But it's nothing random,because it is and it is not. It is random in the sense that the precise location of the waves is random.

But the radiation spectrum of the waves, like the Planck spectrum, is very, very precise. Okay, so this power spectrum means that if I look at a certain angular scale given by this formula, as I vary the angular scale, the strength of the waves varies according to this very precise curve. And these curve characteristics are not really surprising. They are just the sound waves of this hot plasma that emerged from the big bang. They have a characteristic scale that has to do with the speed of sound in the plasma, and that causes these peaks and valleys. So this curve was predicted long before the observations of Jim Peebles, among others.

Jim Peebles won the Nobel Prize, among other things, for predicting this. I was very lucky to be the first to calculate this curve, which is the curve of the polarization power spectrum of light from the Big Bang. Experts in the field had published articles saying this was zero. But we realized that that didn't make any sense, neither me nor my postdocs, and we calculated it. And surprisingly, this curve is a prediction without free parameters. If you adjust the cosmology, the cosmological parameters to fit this curve, then this curve is absolutely predicted. Well, this was one of the first influences on me to tell me that whatever is happening in the universe is really simple, it's not arbitrary.

The laws that the universe obeys are truly universal. And if we understand them correctly, in this case, the laws that come into play here are Einstein's theory of gravity and the laws of plasma physics, which were developed in the 1920s, a long time ago. Here is our model of the universe called lambda CDM. It has only five fundamental parameters. The matter and energy content of the universe is described by three numbers. One is the cosmological constant. It's a little surprising, but not too surprising, because this was the first type of energy that Einstein imagined to be relevant in the universe.

I'll explain it a little in a moment. Dark matter, which I used to think was extremely mysterious. It is one of the great enigmas of cosmology. But recently I have come to believe that there is actually a very economical explanation for dark matter. And finally, the ordinary atomic or nuclear matter that we are made of and the abundance of that matter in the universe, that is another parameter. In addition to that, there are two additional parameters. One is the amplitude or strength of these density waves, which emerged from the Big Bang, is approximately one part, 100,000, the variation in temperature from one place to another when leaving the big pocket.

So the radiation we see is three degrees Kelvin, but the fluctuations are about 30 micro Kelvin. Approximately one part and ten minus five. It's just a number. And then there's a slight red tilt, which tells you that the fluctuations are slightly stronger at longer wavelengths when you look at longer wavelengths in the universe. That's all? That's all. There are no other conclusively measured parameters. There is no evidence of anything beyond this. There is no conclusive evidence. Well? There are slight anomalies here and there. These can be strengthened and made compelling. But for now, this could very well be the full story.

Now, however, our theories couldn't be more complicated. People talk about a multiverse. They talk about extra dimensions and ten to 500 possible universes and chaos on a grand scale. That's not what we're seeing. Well? And so I've come to believe that what we need is a truly minimal theory that is highly economical, and that should be judged on whether or not it explains these numbers. Okay, it's a difficult task, but I'm going to tell you about a theory that at least explains the last two numbers of the first principles. What is red tilt? I said it means the longer waves are a little stronger.

To make it a little more precise, it means that if you go to wavelengths that are seven times longer, you get 4% more amplitude, so not much. Why seven? Because seven is the square of e, and this slope is zero four. This applies to a very wide range of scales. And one of my assumptions toward the end of the talk is that that would apply to a really wide range of scales, from the Planck length to the scales that we observe. If so, this is an example of a critical phenomenon. Critical phenomena are what happen when systems go through a phase transition.

An example is critical opalescence. You see this in very heated water, which at high pressure, if you heat the water enough, what happens is that it turns into gas, but the gas and the water, that very hot water, and the steam are indistinguishable. And you go through this fun phase, which has very far-reaching fluctuations. And that is exactly what we see in the universe. They are very long-range fluctuations with a particular red tilt. And this is a classic example, if true, of a critical phenomenon. Here it is in the laboratory. You see, this is a mixture of liquid and gas under high pressure.

You heat it up. This is the opalescence that has these long wavelength fluctuations that make it slightly opaque to light. And then if you go further, it becomes a completely transparent, superheated liquid. Just an example. But this really is everywhere. This type of phenomenon is really everywhere in physics. So it may be that what we're seeing is somehow critical behavior in the Big Bang, which is pretty exciting, if true. This was a very expensive photograph taken by the world's dark energy telescope. In fact, there is a telescope. Oh, sorry, dark energy studio. There is such a telescope that costs millions of dollars.

This is what he saw. That is dark energy. So dark energy is the simplest form of energy. It is absolutely uniform in space and time, it is immutable, immutable and constant. And that's why Einstein introduced it into his equation as the simplest type of matter that could be relevant to cosmology. And he was lucky. It turns out that most of the energy in the universe appears to take this form. The strange thing about this is that it is gravitationally repulsive. And so, unlike ordinary matter, which is attracted by gravity, it repels and causes the universe to explode.

And there's this rather beautiful cartoon of Professor Desiter who solved Einstein's equations with a cosmological constant and chose that as the symbol we use for the cosmological constant. So it has the form of a lambda. And the question, he says, what makes the balloon burst? The lambda does that. There can be no other answer. And people found out about this in the 1920s. It's a very old idea. Now I'm going to do it. So I have introduced some of the ingredients. Dark matter is not the cosmological constant, it is a type of matter that accumulates gravitationally.

People tend to be a little suspicious of this in cosmology. Why do you introduce some strange form of matter and then assume that it accumulates under gravity and so on? They are right to be suspicious. But in reality, thanks to recent observational advances, we can now see this dark matter using gravitational lensing. So when light is emitted from this surface, the hot surface toward us, it travels through this distribution of matter along the way, and that bends it through lenses, literally by gravity, bending the light by gravity. And as you can see, this lens pattern is what we actually measured.

And by measuring that pattern we can infer what the dark matter was doing. And this has been done recently. Just this year, another telescope observed the radiation from the Big Bang and inferred this distribution of dark matter. And here is the actual projected density of dark matter along the line of sight from the Big Bang. And now we can literally see that. When you see a drop of water on the tip of your finger, if you look at a light behind it, you see it because of the curvature. The water is transparent, but its effect is seen by deflecting the light.

This is the same effect, but gravity acts as a lens. So we can see this dark matter. We don't know what it is yet, but I'll tell you in a minute or two. Now, of course, there is a gigantic conundrum: the whole thing, the big bang in which we live, seems to have originated at one point. It seems that everything we see dates back to a single point 14 billion years ago. And that's a big surprise. And again, what I'm going to claim is that by addressing this strange point and formulating a very specific hypothesis about it, many of the riddles of cosmology are solved.

So before we do that, I want to tell you a little more about microscopes. Obviously, microscopes are how we see the subatomic world. The Large Hadron Collider is the largest microscope ever built. But these cosmological measurements are even better microscopes and potentially take us all the way to the Big Bang and this special point. So let's talk about microscopes. Here is a page from Heisenberg's book on quantum mechanics. And I just want to give you an idea of ​​how he defended uncertainty, the uncertainty principle. From Planck's observation it was deduced that light had to be quantified into packets of energy.

So I'm going to explain now, actually, the Heisenberg explanation here, the Bohr tributes down there. And one thing about Heisenberg is that his diagrams really weren't very good. This isn't even horizontal, nor does it really tell you what that x means. But anyway, it's a surprising argument. The basic point of the uncertainty principle is that waves propagate. Well? And you can convince yourself of this just by taking a stick and touching the surface of a lake, like a silver lake outside here. And when you touch the surface of the water, ripples appear that spread if you try.

Imagine that you are trying to emit a wave that goes in one direction. That's impossible to do with a stick if you only use the tip. If you insert the tip, all you will get is an expanding wave. It won't go in one direction. It will spread in all directions. And the only way to get it to go in one direction is to use the stick sideways. So when the stick is extended like this and you put it in the water, the wave will move in that direction. But of course it will extend to the extremes.

That's called diffraction. This was well known as wave phenomenon. If I send a wave to see some object, this structure here is supposed to be the microscope. So I send a wave into an object of size, delta The dispersion angle is simply the wavelength over delta X. So, intuitively, it's a no-brainer. You cannot see an object smaller than the wavelength of light. But what really happens is that light comes in and shakes the object. The object then re-emits or scatters the light, and it does so in this way that it propagates. This was all very well understood before quantum mechanics, but I think it is a good physical illustration of the uncertainty principle.

This is something that cannot be violated, and it is not possible to create a flat wave by sticking a spike into a pond. However, I just told you that light is actually made of particles. It is made of these quanta or photons. And the problem is that the particles kick. So this light wave is coming and it's actually a packet of energy. And now you are telling me that this packet is going to propagate according to the wave. And then that packet could be deflected through this theta angle. And when it deviates, it kicks. So the light was actually this particle that came in, hit the object you're trying to see, and spread out.

We don't know where the particle is. It could be anywhere on that expanse. That's random. That's what quantum mechanics says, that the precise angle you go to is random. But since it can deflect at any angle, it kicks the particle. And basically what that means is you can review algebra. It means that the uncertainty in the position of the particle you are measuring, multiplied by the uncertainty in its momentum, is equal to Planck's constant or approximately equal to Planck's constant. And that is the Heisenberg uncertainty relation. It is a direct consequence of the fact that light comes in packets and that light is a wave and propagates.

So this was one of several thought experiments that Heisenberg and others performed to convince themselves that this uncertainty principle could never be violated. And it's very, very drastic. It leads to all kinds of changes in the laws of physics with respect to classical physics. Now, a slight extension of this microscopic image is to ask ourselves: what is the smallest possible object you could ever see? What is the smallest possible length that I could see? So let's send out a packet of very high-energy, short-wavelength light, and what happens? Then enter it and it will collide with the object you are measuring.

The problem is that you've packed a lot of energy into a small region of space, and when that happens, you get a black hole, because it gravitates on its own and spacetime literally falls inward and you get a black hole. And unfortunately his microscope doesn't work. Therefore, no length shorter than this length can be seen because the light would simply not escape to be seen. Sothis is the Planck length. And if we believe in Einstein's theory of gravity and we believe in quantum mechanics, this is inevitable. The largest visible length is also the largest visible length.

I've told you about lambda and how lambda has a repulsive gravity, and it's just the opposite. It's as if, in this case, we are inside this special surface. Lambda causes the universe to expand at an accelerated rate and that creates what we call the lambda horizon. Anything beyond a certain distance, we will never see. It may emit light, but that region is moving away from us so quickly that the light it emits will never, ever reach us. And this is the largest visible length. And actually, that's not that different from the size of the region we see now in the universe.

So gravity, in both cases, sets the smallest possible visible length and the largest. So, back to microscopes, here's the large hadron collider. And this was his big discovery, the Higgs boson, which I'll show you more about in a moment. And my colleague in Edinburgh is Peter Higgs. He is the person who postulated the Higgs boson. He's standing there like he understands what's going on, and I guarantee he doesn't. He, like me, is a theorist. We theorists spend our time worrying about concepts and questions of principle, and it takes real people to build big experiments, practical people to build experiments and test these ideas.

And surprisingly, that's what they did. It took about 50 years of continuous development to build a Large Hadron Collider. And when it was built, the Higgs boson was there, exactly where it was predicted to be. So now this is all known physics summed up in a single equation. We have gravity, Einstein's theory of gravity, all the forces like electromagnetism and nuclear forces. We have all the particles described by DIRAC. And Higgs is very lucky. He gets three terms in this equation. The last one includes the lambda. I want to point out SOME things. You will have noticed that Planck's law, following Boltzmann, included a high exponential e at least.

The laws of quantum mechanics are the same, except now there is an imaginary number. Me squared is minus one. But again, we get this exponential with an imaginary number. And here is Planck's constant, h. Actually, it's h over two. PI is hbar. But these are all the laws we know. And my current view is that maybe that's all there is. There is no evidence of anything BEYOND this. And perhaps the real challenge of physics today is to calculate all natural processes using these laws. Maybe it has changed. MAYBE there are no new particles. And I'll justify it in a moment.

So, key points to remember. There's an I here, this strange imaginary number, and there are these particles like the electron and the quarks that our atomic nucleus is made of. The rest are, in a sense, connections. And this is a precise mathematical term, a connection. A connection tells you how things travel and how they affect each other. And it seems that everything else is a connection. You have particles, and then you have gravity, which connects them, and you have electromagnetism, which connects them. And that seems to be the logic underlying the laws of physics. So here it is in more detail.

We have quarks that atomic nuclei are made of. We have leptons like the electron, like neutrinos and the Higgs boson, which couples to everyone, just like gravity. And then we have these forces, the strong, weak and electromagnetic forces, and that seems to be all there is. These are all the particles that we have discovered in accelerator laboratories. As I mentioned, Cern has not yet discovered anything beyond this. There is one. These are left-handed neutrinos. You'll notice the l here, we've only observed left-handed neutrinos. Left-handed means that as it travels along my thumb, it rotates this way, and those are the only ones we've seen.

However, now we want to solve the dark matter problem. To start, what is dark matter? I must mention something else. There is an enigma. There are three generations, right? So this pattern up, down, electron neutrino, electron neutrino is copied three times. It's quite strange. Why is that? We do not know. I'm going to tell you that there is an explanation. Now, it is part of this new theory that we believe was mathematically imposed by the principles of the theory. But that is an enigma. Now, left-handed genres are not going to explain dark matter. We have observed them all and they have tiny masses.

But it turns out there is a simple solution. Just remove the l. Okay, let's imagine that electrons, like other particles, come in right-handed and left-handed versions. Imagine that. So you just have to add the right-handed companions to the left-handed neutrinos. This is a very modest change in the standard model, and is suggested by the symmetry, because now everyone has a right-handed partner. Well? This is the most obvious extension of a standard model. It was proposed in the 1970s and is probably true. Why is it probably true? Because if these right-handed neutrinos were heavy, we would not have seen them in experiments until now.

But they do explain why the neutrinos we see have a tiny mass. Okay, they don't have mass. It turns out that neutrinos can travel, couple to the Higgs, and transmute into a right-handed neutrino. This is very heavy and therefore requires a lot of energy. So you can't continue being a right-handed neutrino. It is a dexterous virtual neutrino. You oscillate on this for a very brief moment, basically the inverse of this right-handed guy's mass. And then you have to oscillate again until you become a real neutrino. Then the left-handers would mix in slightly with the right-handers. And the heavier the right-handed ones, the less the mixing, because it is increasingly difficult to oscillate in a right-handed neutrino, the more massive it is.

That's why this is called a see-saw mechanism. The heavier you make it, the lighter you will make it. And what we realized recently is that these right-handed guys are the perfect candidate for dark matter, because they don't couple to light or other forces that we know about, they just couple to gravity and the Higgs. So these intrinsics on the right could be dark matter. And we discovered that we could explain it. Now this is starting to get cosmological. The question is, how is its abundance in the universe explained? What would explain it? We find an explanation for its abundance if we assume that the universe was invariant under another symmetry, which is called CPT.

So CPT is the most fundamental symmetry known in physics. It says that if I take a system and for each particle, I replace it with its antiparticle, and I reverse space and time, that has to be a symmetry of the system. I get another system, but it will obey, it will behave the same way. Okay, so there's CPT symmetry. Our hypothesis is that the universe itself respects this symmetry. It is a symmetry of the fundamental laws. The universe could respect it or violate it. What if he respected it? If it respected it, then in our matter part of the universe, we would have more matter than antimatter.

In the visible universe there must be a companion that has more antimatter than matter. Time would run in the opposite direction for the partner. But what is surprising is that the size of the universe, when reduced to zero in the big bang, does so linearly in time. And if it scales down linearly, if the scale factor scales down linearly, you can just extrapolate it. It is called analytical continuation. It's unique. And you can basically continue from the right side only to the left side through the Big Bang singularity. So that's a possibility. If you do that, it turns out that you predict the abundance of dark matter.

Ah, I should say. You see, doing this is like the image method in physics. If you have a mirror and want to solve the equations of light in the presence of a mirror, there are two ways to do it. Either you calculate how much light leaves your face, bounces off the mirror according to the prescribed boundary conditions on the mirror, and then returns, or you do something simpler, which is just make a copy of yourself. And if you're right-handed, you do it with your left hand on the other side of the mirror, throw the mirror away, and just follow the light from one copy to the other.

That's what this is doing. So it is simply the imaging method applied to cosmology to impose here a boundary condition that respects CPt. So there is no reality in the pre-bang universe. It's just a convenient mathematical construct. From this point of view, the Big Bang was a mirror, a special kind of mirror, but quite unique. It is a type of mirror that respects the basic symmetries of the laws that we know that the neonucines on the right hand appear in this image, you can calculate how many are produced. They are produced as hawkish radiation from the Big Bang itself, and we can predict exactly what their abundance is.

There is an adjustable parameter, which is its mass. If it turns out to be so large, that it is much greater than the mass of a proton, they explain dark matter. And this is the simplest explanation so far. It doesn't mean it's true, because I need some evidence. I need to make a prediction and verify it. Fortunately, there is a prediction. If one of these neutrinos is right-handed, and there are three, like the other left-handed neutrinos, if one of them is stable, it implies that the lighter neutrino does not exactly have mass. And you can see that in this image, because if the right hand is stable, it means you need to turn off this vertex.

Otherwise it would break down into lefties and higgs. Okay, so we turn that off, but if we turn off that vertex, we also turn off this. It is the same vertex. So this left-handed Reno cannot be combined with the right-handed one at all. So this one has no mass. And that is the prediction. And, surprisingly, it can now be proven that the masses of neutrinos are measured through their influence on the accumulation of matter. And so the best current galaxy studies, one called Euclid, is a satellite, a European Space Agency satellite, and the large-scale space-time study in Chile.

These studies now measure galaxy clustering so precisely that they should be able to test this hypothesis. Then we will see if it is true or not. If it is true that it is massless, then in my opinion this easily becomes the most compelling theory of dark matter. Well, I'm back to this, the Big Bang. The hypothesis is that the Big Bang was a special type of singularity. The scale factor disappears linearly. This was anticipated by Roger Penrose, mentioned above in the 1970s. Penrose hypothesized that the initial singularity, that thing where all space reduces to one point, is what is called conformal.

Now, conformal means that the light doesn't see it, okay? Light waves, as he sees, come in all wavelengths. They are all basically copies of the exact same thing. And light itself does not know the size of the universe. The equation that follows is independent of the size of the universe. So the light is compliant. And Penrose's hypothesis was that the Big Bang was conformal. And if everything in the universe behaved like light during the Big Bang, nothing would actually be conscious. No matter within the universe would even know that a singularity exists, because they don't care what the size of the universe is, as it is.

If I take a grid and try to turn it into a circle, try to distort the boundary of the square into a circle, I can do it in such a way that it preserves the angles. This is called conformal mapping. And if you look closely, you'll see that the angles at all of these vertices are exactly 90 degrees, even though the entire shape has been distorted. And essentially because light or photons only care about angles, not overall scale, they wouldn't notice any difference in this situation. So that might be the uniqueness of the Big Bang in one image, but if you stretch it out, it's perfectly regular.

So here's Roger Penrose giving a public

lecture

on the perimeter some time ago, and yes, I'm honored to have a visiting president named after him. Incredible guy, and here is one of the beautiful photographs of him. Penrose has emphasized the difficulty of explaining why the universe is so simple on a large scale. Well, as I mentioned before, whichever direction we look in the universe, the universe is pretty much the same. It just varies according to these random waves whose amplitude is just ten to the power of negative five. It's essentially very uniform, very isotropic, very. It is a very, very special geometry.

It's nothing wild or complicated. And here is the creator creating the universe and choosing this extremely special geometry, the one we see, for the universe to be in. And he emphasized what a puzzle this is. So what I'm going to state now is that I believe we have a solution to that conundrum. We know why the universe is so fluid and simple, and the reason is that it involves some extrapolation of ideas from Stephen Hawking and others. But the reason is essentially the same as why the gas in this room is homogeneous. And do you know why air molecules are distributed so smoothly?

And it's a good thing they are, because if everyone backed themselves into a corner, we wouldn't be able to breathe. Okay, they don't do that. And why not? Just randomness. The thing is that there is a much better chance that the molecules will be spread out smoothly than that they will all be in one corner. It's entropy. Maximizing entropy explains the homogeneity of air. It's thermodynamics. Noyou need a mechanism, it's just what happens most of the time, the vast majority of the time. So I'll show you now. We have an explanation for the large-scale geometry of the universe, which has a similar, thermodynamic character, it does not require any mechanism, so it is based on the ideas of Stephen Hawking.

That's why he was interested in black holes. And black holes are these wonderful objects that, in a sense, are like giant elementary particles. They have very few parameters, they are totally smooth, they can have spin, they can have charge, they can have mass, and that's it. They are just absolutely nondescript objects, like an elementary particle, but they can be huge. We have seen black holes of hundreds of solar masses. In reality, much more than that: millions of solar masses. A black hole has a temperature called the peddling temperature. And it was a big surprise that black holes are slightly hot.

It is a very small temperature, but they give a little heat. More importantly, they have entropy. And, generally speaking, it tells you the number of ways you could have created that black hole. And the entropy is proportional to the surface area of ​​the black hole. Here's Stephen Hawking on the perimeter. When the Stephen Hawking center was under construction and he visited several times, I must say he was treated exceptionally well in the bistro, which he enjoyed and it was absolutely inspiring to visit. Here he is with someone else, you might recognize who, Perimeter Institute founder Mike Lazarides.

And we're at Lake Huron during one of Stephen's visits. They both look very good. So Hawking used a very profound mathematical trick, which I mentioned: this imaginary number that distinguished the Boltzmann type, the thermodynamic arguments from the quantum arguments. And Hawking used that trick to link the two. And the way he told them is by doing time, calculating in imaginary time. It sounds very speculative, but it is not. It is a very precise technique. And that's why he used imaginary time to calculate the Hawking temperature and gravitational entropy of a black hole. Now, essentially what he did was take the spacetime of a black hole, which is a function that has a certain description in terms of real time and real space.

And he said, what if time becomes imaginary? It turns out that when time becomes imaginary, the black hole is actually periodic in imaginary time. It repeats itself in an imaginary time and that is the signal of a temperature. If you have a system that is periodic in imaginary time, the period actually defines the temperature. And that's at least one way to calculate the Hawking temperature. And entropy is calculated in a similar way. Recently we were able to do the same with cosmology. Calculate the Hawking temperature and entropy. For cosmology, I will first show you a simple example and then show you the general case.

This is what Hawking and his collaborators did. A cosmos with only lambda. This, in fact, was Einstein's first model of cosmology. Let's just have lambda and gravity. Well, it's repulsive. And so the universe, if it's a big circle, in this case, I'm just plotting one dimension of space. So it's a circle. It contracts and expands again due to repulsion. Well, that's called spacetime desiter. And when you make time imaginary, space-time increases, time now becomes periodic. And this is what Hawking called a gravitational instant. It is the imaginary temporal version of the desiter space-time. It has a temperature that is exactly the length of a great circle on that sphere and it has an entropy that can be calculated.

Thus, we were recently able to solve Einstein's equations for general cosmology with spatially curved radioactive matter and analytically curved lambda. And we discovered that it looks something like this. It is no longer a sphere, it is distorted. Here is the cosmos of imaginary time from which you can calculate entropy. And you can think that the cosmos in real time emerges from the imagination. Because? This is interesting because it turns out that this gravitational entropy, if it is an entropy, like the entropy of gas in a room, tells you which cosmologies are most likely and which, according to this formula, are most probable. spatially flat, as we see it homogeneous, isotropic and isotropic.

And secondly, this calculation also favors the cosmological constant being small and positive, which is just as we see. So this is still very new. We are discussing with many other experts about what this means. But from my point of view, this is a thermodynamic explanation for the large-scale geometry of the universe. Therefore, we do not need smoothing or flattening mechanisms. Some of you may have heard of inflation, which is a postulated period of very rapid expansion right after the Big Bang singularity. It doesn't seem like we need it now. Our telescopes are also microscopes, and when we look into space, we look back in time.

The universe is shrinking. That's what this image shows. Currently the radius is 20 gigapars x. Let's say if we shrink that region down to the Big Bang, it's about ten microns, and then if I take that same region and follow it to someone's eye, that's what we see. This is the largest visible region of the universe, the one in green. Of course, if we look back in time, the universe is smaller. What that means is that a structure that was only one Planck length or a wave that was only one Planck length wide. In Planck's time, the smallest length imaginable at this time would be about a millimeter wide.

It would have expanded to about a millimeter. If we can capture gravitational waves on millimeter scales, we can literally observe the Big Bang, we can observe the singularity. That's very exciting. These are being developed. It will most likely take decades before this is feasible, but prototypes already exist. That's why I want to explain it now. What I'm getting at is explaining two things. One, why are there three families. I told them that would explain it, three generations of particles. And two, where do these waves, the density waves, that we see in the sky come from? Did they somehow originate in the Big Bang singularity itself, and then move forward and end up creating, leading to the formation of galaxies and stars, etc.?

So I'll explain that now. To understand this, we have to understand how the Standard Model couples to gravity. And currently, there is a very fundamental paradox in that coupling, which is that the Standard Model fields, electromagnetism, electron fields, all the other fields, fluctuate in a vacuum in empty space. The reason for these fluctuations is basically the Heisenberg uncertainty principle. If you try to set them to zero, then if you essentially set their position to zero, their coordinates (the amplitude of the wave) to zero, then their speed is indeterminate. They cannot be set to zero and be consistent with this Heisenberg uncertainty principle.

This is a picture of what is happening in the void right now; This is actually for strong interactions, but it would be the same for electromagnetism or other fields. Unfortunately, the energy in these zero point fluctuations is infinite. And that's a problem because how do you couple it to gravity? So we have several procedures to ignore that, but they are quite artificial and leave you very confused. Somehow, something is happening in a vacuum, which seems deeply paradoxical. They also happen to mess up this conformal symmetry and therefore we cannot describe the big bang. So our starting point was actually to take a hint from cosmology.

What type of field, if it fluctuated, would give rise to a pattern like the one we see in the sky? And it turns out there is a single answer. It is a zero-dimensional field. It is basically a field that has no dimensions. So if you ask about the correlations of this field, it correlates. There is no scale, just as the fluctuations we see have approximately the same strength at all scales. That's what this field has. And in fact, these fields had been thought about before and shown to be a simple gauge theory in the. Here are the particles of the standard model.

What we discovered is that if we add up precisely 36 of these extra zero-dimensional fields, you might wonder where the 36 comes from. And one clue is that there are six of these and six of those. But I'm not going to say more. It turns out that these exactly cancel the energy of the zero points and also restore conformal symmetry. Good. They are non-trivial cancellations and, furthermore, it only works if there are three generations. So this is a very new discovery. We're still trying to make sense of it. These zero-dimensional fields are peculiar because they simply change the vacuum, but have no particles.

So, without adding anything, you are simply adjusting the standard model vacuum so that it doesn't have these violent energy fluctuations, and is consistent with this conformal symmetry that would allow you to describe the big bang. Based on this, we were able to predict the amplitude. And there's a big formula here, but you see all kinds of PI, fives and numbers, the number of degrees of freedom in the standard model. These alphas are couplings that are measured in experiments like CERN. But the principles that I have explained say that we want this conformal symmetry, and we do, because we want to describe the big bang, where apparently the universe had size zero.

So we calculated all these numbers. This one in particular is interesting, because alpha three is the strong coupling constant. We extrapolate it to the Planck scale. It is a huge extrapolation of energy and it turns out that it is what is called a critical exponent. In other words, I told them there was a tilt. The waves get a little longer as you move towards long wavelengths. That's how strong they get. And this inclination must be compared with zero four. It turns out that we have included this number from CERN measurements, extrapolating the CERN measurements, the Planck scale.

And this number is exactly very close to zero four. So our prediction is 00:42. This is the measurement from the Planck satellite. That's just an explanation of first principles. Much more theoretical work is needed to confirm this, to calculate the corrections and make sure they are under control. Observations are also improving. If this agreement holds, then the theory will be convincing. So we may have an explanation for all this. Everything is basically in the physics that we know, we have to do something to fix the vacuum a little, but otherwise the cosmology is under control. So thanks for listening.

Very good, thanks Neil. Thank you. So captivated. I almost forgot to get up to ask the question. So now we'll take some questions, both from the online audience and from the audience here. If you have any questions, please come to the microphone that is set up here on the stairs and we will follow the line. And I will also mention the online questions. So if you're listening online, you can add a question with the hashtag PI live. So while we let people down, we'll start with an online question. So let's see, what do we have? Here's one.

So, I think it's fun to start with. Would the mirror universe be an identical reflection to this one with a mirror? The Earth moving with a mirror? Neil Turok giving a lecture in the mirror. No, the point is that we must clearly distinguish the classical from the quantum. Now, quantum geometry is a fluctuating thing. So when I draw this geometry, you shouldn't imagine just one geometry. You need to imagine something that is a little fuzzy, and it gets fuzzier and fuzzier near the singularity. When the universe is small, that lack of clarity means that, quote, the singularity could actually move.

There is some confusion. The way this CPT symmetry is imposed is where the universe is large. Well? So, if you like this, a two-sided universe that appears on each side, you impose a symmetry that if I turn everything around, there is no difference. In both cases there are fluctuations. So actually CPT symmetry is a quantum symmetry, and the two sides should not literally be thought of as carbon copies of each other. So I think of it more as a kind of mathematical device to do something sensible with the singularity. And you don't do it in the singularity.

Instead, you imagine this extended space-time and impose a symmetry on it. If you turn it around, that's what you do. Thank you. Alright, we have a question from the audience. Forward. Hello. It's not me. I am my soon to be 87 year old mother, Doris Matthews of Elmira, 14 years old with Alzheimer's and her third generation great grandchild. The universe from within. From quantum to Cosmos, everything is spring. High frequency compression to low frequency expansion, harmonic oscillation. Everything in our neighborhood I am a child. 1940. 2040. An imaginary time. Little girl in our park having fun. Seesaws, waves in their sandbox.

It is a wonder. Is it true that the universe is made of stories and not atoms? Tell me. So I could tell my mom and dad. And we could tell our neighbors here where we play. In our park. Where Mother Nature teaches us everything. We can not wait. This is Waterloo. Our region,our perimeter. We are you, you are us. We are one. Connections. We are the big bang. The game of life. Come and play. Everything's fine. Our way to where the air is sweet. Mr. Turk, can you tell me how to get there? How to get to Sesame Street?

Please thank him for that. I should mention that one of the most notable meetings I have ever witnessed was between Stephen Hawking and Sidney Poitier, who, of course, was a legendary actor. And they sat across from each other at the table and Sydney said, let me tell you what I think the universe is. And Sydney, in fact, had her own theory. She didn't have math and stuff, but she absolutely had a vision of how she thought things should work. And it was absolutely fascinating to see the passion with which she communicated it. And yes, Stephen was quite impressed with Sydney.

So, yes, we all have our photographs and she is absolutely right. This is nothing more than a story. All physics is just a story. Someone at our conference this afternoon explained it in detail. Very well said. It's a narrative. Physics is a narrative. It's something we tell ourselves about the way the world behaves. The extraordinary thing about physics is that when the narrative converges, we can use it and it has incredible power. But in the end, it's just a story. Alright, we have another question from the audience. Forward. Thank you Professor Turok for the talk. I apreciate it.

I have two questions. One is that when we think about the Big Bang that occurred 13.8 billion years ago, it seems that relativity tells us that time is relative. So, can you imagine the Big Bang as something that is constantly happening, as if it had its own spin, as a constant phenomenon, and like the sun, you said at the beginning, it seems to us as if it were 14 billion years ago, but it actually has its own twist, more or less. Well, when we say 14 billion years, that's what a particular clock measures. Well. And the clock in particular is an object that was at rest throughout this expansion.

So there is a kind of preferred framework in the cosmos that is defined by radiation. If you are, quote, at rest and you look around you, you will see that the radiation is the same in all directions. If you move, you will see the difference. So for such a clock, the time it would measure to the singularity is 13.7 billion years. But yeah, I'm not sure I fully understood the question. But it is true that time, in generalRelativity, different objects, different observers see different times. But we think we understand that, and we think that, in the end, the story is remarkably simple.

What seems to happen in the big bang, the singularity itself, is that the notion of time. I mean, if this image is correct, the notion of time stops making sense. Because? Because everything becomes light. Literally, the only thing that exists is light. Light does not see the expansion of the universe. The light doesn't see time either. If you ask a photon, what is time? A photon will tell you: I see the entire universe, all of existence, simultaneously. So photons are pretty amazing things that have no time or notion of time. And that seems to be, if this is correct, how singularity is addressed.

There was no time at the big bang, or at least there was nothing around to witness the second part. Alright? Yes, thanks. And just because you had that kind of. That expansion of the universe that we observe in your kind of universe, a kind of mirror model. Yes. And I think Penrose had developed the conformal cosmic cyclic. Yeah. So, I mean, I don't know if that makes any sense according to your model, but as the universe becomes all black holes, and then the radiation and heat dies, would that be where it connects, like it connects in the middle?

But would it connect to the universe at the time of heat death? No. I have the greatest possible respect for Penrose's ideas and, as I indicated, what we are connecting is an idea of ​​his from the 70s, which is about singularity. Since then, he began to defend this image of the cyclical universe, I think partly influenced by me and Paul Steinhardt, because we were talking about cyclical, while I abandoned it because I considered it too complicated. Now he defends it. But the problem is that we don't really have a way to match the future of our universe with the next big bang.

He doesn't have a mathematical prescription for how to do it. He has a prescription, but it doesn't really work. Whereas what we are doing here is called analytical. It means that the connection between these two sides is unique. But we are in discussion about it. I'm trying to persuade him that your previous idea was much better than this one, but we'll see. I mean, I could very well be right. He has turned out to be right about many things. Thank you. Thank you. We have another question. Thank you very much for the pleasant chat. I was wondering about a comment you made about the production of right-handed neutrinos.

Yes. So if I understood this correctly, it would be like a walking radiation effect from the early universe. Yes. And normally, Hawking radiation is associated with some type of horizon or some cosmological horizon. If we are now in this very early time regime and the scale factor is linear, there is no horizon. Yes, good. So it's good that you ask. So at some level, it's totally obvious to suggest that the neutrophin on the right is dark matter, because it doesn't couple to light or other forces. Why wasn't this done? The reason was that everyone thought that the abundance of particles was determined by the thermal equilibrium in the hot big bang.

If you turn off this coupling so that it is stable and could be dark matter, it was never in thermal equilibrium, so they didn't know how to calculate its abundance, so they assumed that wasn't the case. And they literally made that assumption just so they wouldn't have to worry about it. So we worried because we wanted it to be dark matter. And then when I said hook radiation, what I really meant was that it's the time dependence of cosmology that creates the particles. So it is not with a horizon and with a black hole, it is associated with the horizon.

But in general, if the spacing changes, the scale factor changes. You produce much more general particles than having a horizon. And in this case, that's what happens. It's just that the mere fact that the universe is changing size creates a particle. Thank you. Good. We have time for a couple more questions. Forward. Hello. You had mentioned that one explanation for dark matter could be right-handed neutrinos, but that depended on a left-handed neutrino having no mass. Yes. My question to you is: haven't we measured the mass of a left-handed neutrino to be non-zero? No. Great question. So what has been measured?

There are three neutrinos, three light neutrinos that we know of. The only thing that has been measured are the differences in the squares of the masses of those three neutrinos. So we know two numbers. We know essentially two differences between the masses of light neutrinos. We don't know the general scale. So our prediction is that you have these three masses and the lightest one has no mass. Then we predict all the masses from that, from the known measurements. And what these galaxy studies are going to do over the next three to five years is fix the sum of the masses of these neutrinos.

So if they find that the sum is essentially the sum of those two differences, then they will confirm that the lighter one has no mass. Thank you. It's a great question. Alright, let's answer one last question from the audience. Thanks for the conference. It was incredible. My question is simply, you were talking about this type of mirror universe that is similar to ours on cosmological scales, but not identical due to fluctuations near the Big Bang. Feynman had the idea that electrons and positrons were not separate particles, but simply the same particle traveling in different directions in time.

Yes. Could those particles travel between our universe and this mirror universe through the singularity because two positrons and an electron collide? It's a great question. There is a very fundamental view that antimatter is simply matter fighting backwards in time. And in fact, Feynman, the greatest expert on all of this, stated that he believed that quantum field theory, which is what we use to describe a standard model, was nothing more than a way to hide the fact that particles recoil in time. In fact, CPT is, you see, if I have a particle that travels from a to b with a world line, and that, let's imagine that time increases and space goes sideways, then the particle can go back and forth in time and so on.

What is CPT? You are simply reversing the arrow on that line. So instead of going from here to there, it goes from here to there. That's CPT and, in fact, it should be possible. Okay, so in a way we are doing the same thing with the cosmos. But one way to represent this two-sided diagram is that it's actually U-shaped, and you can imagine a universe going back in time for a while, and then spinning around, moving forward, reconciling these images of the particles and the universe is something that I haven't done it yet and it should be fruitful, but I don't know how to do it yet.

Still working on it. Thank you. Thank you. Okay, do you have a quick question? Well. Yes. I was sitting there and thinking: this is very complex and I can understand why you haven't come back from Britain, because you were having too much fun. But I'm thinking that if we start from the most basic, existence, what is existence? How did it appear? I mean, we're pretty much going to the second step, right? From looking at the ball bearings of the world. No, you are absolutely right. The more basic the question, the more difficult it will be to answer.

So all physics does is follow our nose and try to figure out what we might learn next. But the motivation is exactly what you say. We're trying to understand what the hell is going on in a very broad sense. Why does it exist? We do not know. The best we can. That should give you a clue as to what all these molecules are. Absolutely everything is about. It would be called enlightenment. It's a nice thought to end on, so thank you very much, Neil. Thank you.