Theories of Everything with Curt Jaimungal - Rethinking the Foundations of Physics | Neil Turok

Episode Date: June 26, 2024

Welcome to Theories of Everything. My name's Kurt Jaimungal and today we have a special series, a new series called Rethinking the Foundations. This year the Rethinking the Foundations of Physics is centered around the question of what is unification. I'm honored that I get to bring you an astonishing lecture tying together almost every unsolved problem in physics in a bow. So not only a neat bow, but a simple one by Professor Neil Turok. Professor Turok is a cosmologist who holds something called the Carlo Fidani Roger Penrose

Distinguished Visiting Chair, if I'm not mistaken, at the Perimeter Institute, and also the Higgs Chair of Theoretical Physics at the University of Edinburgh. And to those who are unfamiliar to physics, if this was the 1800s, those chairs would be called thrones. So anyway, take it away, sir. Thank you very much, Kurt. It's a great pleasure to be with you. Let me just start by saying how much I appreciate your podcast. I think it's run in a different way than other ones, more conversational, and I think that's wonderful to get more discussion we can have the better.

I'm looking forward to lots of interaction with the audience. The issues at stake are very basic to our understanding of where we sit, why we're here, how we got to be here, and so on. I think hopefully the ideas I'll explain are accessible enough for everyone to engage with. Great. I'm going to show my screen. So the title of my talk is really designed to address the basic question Kurt is asking

in this series, namely, what is unification? And the answer I would give is that unification, understanding the laws of physics and the nature of the universe in a unified way, means understanding the universe. That the laws of physics and the arena for physics, namely space and time, are really a single entity. And you might think this was obvious that our best way of understanding the unified laws of physics is to look at the universe. That's the maximum data we have available. Not to do that is kind of insane, is that you are trying to invent things about physics

which are outside the universe. Perhaps unsurprisingly, this has led people to worry about a multiverse. This is the road string theory has gone down. I feel that road may well be as likely to be a dead end. What we have to do is pay much more attention to what we actually see and observe in the universe. And I believe that for some reason, we don't yet understand what we see and observe in the universe

teaches us about nature at a very profound level. So we have this sort of information coming in about the universe now, and I believe this is an ideal moment, very opportune moment, to think about unification. But in doing so we must take that data very, very seriously. That doesn't mean believing every rumor or slight difference between the basic picture and observations. Many of those are due to observational problems. These observations are very difficult in cosmology. Sometimes they make mistakes, and they eventually

get corrected over many years or even decades. So don't take the observations absolutely literally, but do be guided by the broad gist of those observations. And of course, as in every area of science, we may always turn out to be wrong, but I believe this is the best route to progress, is take our theories very seriously, insist on logical consistency, but equally insist on realism, that these theories do match and are consistent with what we see in the universe. So for me, pursuing unification in its own right without thinking about the universe

is unlikely to be a successful strategy. Equally thinking about the universe without thinking about unification, as you'll see in this talk, doesn't really make sense because the universe we see includes logical paradoxes, such as the emergence of everything from a single point, namely the Big Bang Singularity. And without thinking about unification, we really don't know how to begin to address those logical paradoxes. So that's the title of my talk. I thought that since Kurt often has a philosophical flavor to his presentations, which I find fascinating, by the way.

Well, that's can only be understood backwards, namely by looking at our past. That's the only evidence that we have, but it has to be looked forward. Namely, the future is, of course, the most interesting thing about life and what we make of the future. And as you'll see in this talk, the past and the future get connected in very profound ways and I think we're just beginning to understand what that means. Now as you well known in cosmology, looking out from our vantage point on Earth, looking out into space, is also looking back in time. That's because light has a finite speed. As we look outwards, we're seeing the universe, or the objects in the universe, as they were longer and longer ago. universe as they were longer and longer ago. As we look outwards, this is what we see.

Of course, our solar system nearby, but as we go further, this is a logarithmic scale, by the way. The distance scale gets very rapidly longer as you go out in radius. What is the origin of this picture, by the way? Is this yours? Yes. I've given the credit Pablo Carlos Barasi.

Yes. No, it's an artistic picture, but I think it's a very beautiful picture. Essentially it's telling us what we see when we look out in the universe. So nearby we see what we call a cosmic web, which is basically structure as it was emerging from an initial smooth, almost uniform, almost perfectly uniform universe. That's the cosmic web, the sort of fringes on the outskirts of the picture. If we go even further out with the red circle here is the last, what we call the last scattering surface. It's the hot surface of the radiation coming out of the Big Bang as it was radiating the microwaves which we now receive as the remnant radiation from the hot Big

Bang. So we're essentially sitting in the middle of a microwave oven. As we look outwards, we're seeing the hot surface that was emitting those microwaves. When it was emitting them, incidentally, its temperature was about 3,000 degrees centigrade. Only a factor of two different than the Sun. So essentially we're outside the Sun but inside a cavity whose surface looks pretty much like the surface of the Sun. And then if we go even further out before that surface, imagine we're using

a form of light which can penetrate the hot radiation of the Big Bang, for example, gravitational waves, which would do so. We reach the white circle, which is the Big Bang singularity. That seems to be the beginning of the universe, which we are surrounded by, although actually it's a point. Now, to see how that works, keep in mind that this picture I'm showing now is really a cross-section of a four-dimensional universe, namely time and space. We are connected to every point on this picture by a light ray. This is what we actually see. And we are connected to every point on this picture by a light ray.

So this is what we actually see. But if I try to draw the full four-dimensional picture, I've got to add the time dimension as well as space. And you see, if we are sitting on the right of this picture, in the center of this patch of space around us, the green curves here show the trajectory of light or something traveling at the speed of light. As it came out of the Big Bang singularity,

As it came out of the Big Bang singularity, it then traveled outwards at the speed of light. But of course, you've got to also take into account the fact that as you go backwards in time, the universe is shrinking in size. looks to us in this picture as a big circle on the outskirts of what we can see is actually this focal point on the left where all those light rays in fact came out of the same point in space. Professor, is there anything special about this point where if you look toward the middle of this, Professor, is there anything special about this point where if you look toward the middle of this, it initially is going up, it's sloping up to the right, and then it starts sloping down to the right. Is there anything special about that point where it changes? No, no, there's nothing special. This is just, if I, you see, so if I had drawn this, the curve for an observer living a billion years ago, you know, only 12.7 years, a billion

years after the Big Bang, the light would converge a little bit to the left of where I've drawn it. And so it would bend downwards a bit sooner than the curve I show. So this curve is really, if you like, the curve that we see being where we are in space and time in the universe. It's our past horizon or our past light cone. or our past light cone. So normally in special relativity, you learn about light cones, but they are, you know, they're obtained just by drawing straight lines

and then making them into a surface of revolution. The difference in an expanding universe is that the light cones themselves shrink down to a point at the Big Bang singularity because the universe is shrinking as we go back in time. So this is what we can see. We see a slice of the universe and weirdly enough, the outskirts of the slice are actually a single point,

which is the Big Bang singularity. And that's what we want to resolve. And so everything I'm going to tell you about today rests on a resolution of that strange paradox that the whole universe came out, the universe we see, came out of a single point. Now, as well as the arena for physics, we need to, of course, think about the laws of physics. And the laws of physics we know are shown in this picture. We have the particles, namely the quarks and the leptons.

And so the quarks make up nuclear matter, protons and neutrons, and versions thereof. There are three families of quark, each of them containing an uptight quark and a downtight quark. And then we have leptons, which are sort of generalizations of the electrons, which orbit around atoms.

And they're similarly three families of leptons, each with an electron-like particle which which orbit around atoms, and strong forces, and those are mediated by gauge bosons. The particles we describe as fermions, they're described by Dirac's equation. All of these things are very well established. The Higgs boson somehow connects all of them because the Higgs boson is responsible or the Higgs field is actually responsible for breaking the symmetry in the standard model. And it contributes mass to many up to all of these particles that you see in this picture. So those are laws of particle physics and then I've drawn gravity is this blue curve sort of couples to everything because gravity is really universal and gravity feels everything else in the picture. So we have to somehow

combine all of these laws with this picture of the universe in order to try to make a coherent picture. And where it doesn't work, we have to extend these laws to make it work. Now, as I mentioned, we live outside the Sun, so this is the hot surface of the Sun. And it's completely remarkable that the color of the Sun tells us Planck's constant. I mean, it actually, the fact that the Sun has a single color and it has a temperature of 6,000 degrees, one can infer from the color directly Planck's constant. So, if there were no quantization of photons, hot objects like the Sun simply could not exist. It's the quantization of light which allows hot objects to exist without radiating an infinite amount of energy. If you take the Planck's

constant to zero, you find the rate of radiation from the Sun would go to infinity, and the Sun would disappear in a puff of smoke in no time at all. So this is an example of how the universe teaches us its laws. This is not how Planck's law of radiation was discovered because people didn't really understand what the Sun was at that point in time, but it could have been. By taking the observations as seriously as possible, or trying to make them consistent, one actually learns all about the fundamental

laws of physics. And right now we're doing the same with the other version of the Sun, if you like, which is this cosmic microwave background sphere within which we live. It's a hot radiating surface. By looking at it, we can see what happened at the big bang singularity. Why do you call it the other version of the sun? Well, in this picture, you see the sun is at the center of the picture and we orbit around it, but the red sphere is the represents. Obviously this is a two-dimensional cross-section of a sphere, and the red circle on this picture represents a sphere which surrounds us, a two-dimensional sphere on

the sky which surrounds us, and it's hot. And it was radiating, radiation at about 3,000 degrees C, or Kelvin, when the radiation decoupled. It's called the surface of decoupling. And so the radiation decoupled from the hot plasma in the Big Bang. And the radiation just traveled freely from that surface to our telescopes at the center of the picture. So, you know, we're outside the sun,

we're inside the surface of last scattering or this red surface, and by staring at the red surface, we hope to learn the equivalent of the laws of quantum mechanics, which we could have learnt by staring at the Sun. So here is the surface, here is that surface plotted in much more detail. So this picture shows a projection onto a plane of that two-dimensional spherical surface which surrounds us called the surface of our scattering.

So this is very much like a map in an atlas representing the surface of the Earth. This is a two-dimensional map representing the sphere that surrounds us. And what you notice, what's plotted is the temperature of the radiation on that surface as projected forward to the present day, and that temperature varies from point to point on that surface. And these are the fundamental variations of temperature and density which came out of the Big Bang and which later were responsible for the creation of structure in the universe. So these variations are very small in magnitude. The temperature of the surface, as I mentioned, was about 3,000 degrees Kelvin when it emitted the microwave radiation,

when it emitted the microwave radiation, but the temperature varied from place to place by about one part, by a few parts in 100,000. And so the variations in temperature plotted on this picture are very modest in size, just a few parts in 100,000. But you can see the pattern of temperature variations. This picture has been made by a number of beautiful experiments,

including the Planck satellite. We now have access to it. The top curve, let's start with the bottom curve. The bottom curve shows what happens if I look at this map with a Fourier lens, namely, I Fourier transform it with respect to spherical harmonics on the sky, and then I plot the magnitudes of those spherical harmonics,

the average magnitude against L, the harmonic number. You see this beautiful red curve on the bottom. This was actually predicted in the early 1970s by Jim Peebles and others. Later, Jim Peebles won the Nobel Prize for that. It's a rather clear-cut prediction, but it rests on a particular assumption about the cosmological parameters, which I'll get to in a moment. So the temperature pattern shows this oscillatory power spectrum. Above that is the polarization power spectrum, and I'm particularly proud of this because this is a calculation we did for the first time when I was a young cosmologist.

So we calculated the red curve. Right. Then rather amazingly, the data points are the blue points, and you can see they fit perfectly on that curve. Now, the key point is that this is with no free parameters. You fit the free parameters of the cosmology to the bottom curve and then just predict the top curve. And it fits spectacularly well. That's not because we were particularly clever with our

calculation. We weren't. We simply turned the crank on a way of calculating this invented by Chandrasekhar in the 1930s. But the difference is that we have the data and we can turn that data into predictions and they fit beautifully with what we see. So in other words, for the bottom graph, that's a temperature graph. Yes. You have some knobs that you can fiddle with and these are called the parameters. How many are there? Five.

Just five. So there are five parameters that go into there. And then you've developed when you were a young student, a function that takes in those five parameters and outputs that top graph. Yes. But those parameters were fixed by someone else for the bottom graph. Absolutely. So there were no new parameters

do you have to introduce for the top one? We had no freedom to introduce parameters. So all that went into the top curve are the Einstein equations for gravity and the equations for the propagation of radiation, which were as I say, were developed by Chandrasekhar in the 1930s and they just use Maxwell's equations and interactions of light with electrons. So we didn't do anything we were the engineers in this game. Okay just took the known laws.

We just took the known laws and applied them. Nobody had bothered to do the top calculation because frankly they didn't expect to see it ever measured. And I had to persuade, I persuaded the experimentalists on the point satellite to include detectors to measure the polarization. You see the numbers are tiny if you look at the units and the top curve it's micro Kelvin squared So they had to measure the polarization with an accuracy of you know a few micro Kelvin Two or three micro Kelvin. That's a very big Task. Yes. Well, you must not have been just some whippersnapper then to have such influence over someone to develop such a sophisticated tool by merely suggesting it. Well, I was lucky. As I say, all the equations were lying around in the literature. Nobody had bothered. Actually, some people had bothered, but they'd gotten it wrong. You can make lots of mistakes in theoretical calculations.

As far as I know, we're the first people who actually did it seriously and correctly, and we got the curve, and it agrees beautifully. So this just changed, it was a turning point in my career, because you look at this curve and you say, my goodness, the universe is simple. We have five basic parameters, as I explained in a moment. We fit those to some data set. Could be the temperature in the lower curve, could be the galaxy distribution, many other forms of data. So fit it to some data and predict everything else. And the claim is that everything we see is fit by these five parameters. And you can measure those five parameters in multiple ways, right?

And this is called the Lambda CDM model. And really, it's amazing that it's so simple and so far fits everything. And the more and more data we've got, the better the fit. It's really quite remarkable. There are always some tensions, people claim the Hubble constant isn't quite consistent, and so on. But be very careful about believing those because quite often they are later found to be wrong and any of them are any two sigma or two and a half sigma.

That's what you're referring to earlier in the talk when you said don't believe every rumor. Yes, exactly. Exactly. I see. So every week or every year, there's a new tension or anomaly. Absolutely. And most of them just, most of them fade away. And people forgot about them.

What has survived is a remarkably simple model, which as I say, is seems to be consistent, you know, within three sigma or four sigma. Or, I mean, particle physicists like to use five sigma, they never believe anything less than five sigma. And that's a good rule. I would say actually in applying it to cosmology, cosmological measurements are much more difficult to control than particle physics experiments. So not in the lab, you're measuring the natural universe. And I would say our criterion for accepting a measurement should be stronger than five sigma.

If it's five sigma in particle physics, surely in cosmology, it's to be seven or eight sigma. If you apply that criterion, there are no anomalies with this model. So here's the model. It's called Landau CDM. It's more or less what Einstein envisaged in his very first paper on cosmology, Einstein asked himself what is the simplest form of matter or energy? And he knew they were equivalent because E equals MC squared. So he knew mass and energy are equivalent. If you just say what's the simplest conceivable form of energy, the answer is very obvious.

It's the cosmological constant, which is what he invented. It's a form of energy which is absolutely uniform in space, in time, and furthermore is what we call Lorentz invariant, namely if you travel at some velocity, this stuff doesn't change at all is it no matter how fast you travel the cosmology constant is exactly the same as it was when you if you're not traveling so can you get the cosmology constant try to make a bottle. of cosmology with only that constant it didn't it didn't work because he he tried to make a static universe actually didn't know the universe is expanding. The lambda CDM model includes the cosmological constant which is 70% of the known energy in the universe. It includes dark matter that's a big mystery but in this talk i'm going to resolve that mystery by explaining what the simplest candidate is for the dark matter and actually i've already shown it to you.

On the previous slide explain why. What the dark matter makes up about twenty 25% of the energy in the universe, and the remainder is in nuclear particles and electrons, just the stuff ordinary matter is made of, and of course photons. So there are five parameters in the model. One is the density of the cosmological constant, how much energy there is in what we call lambda per cubic meter. The second one is how much dark matter there is, again, just how much per cubic meter in the universe. And the final one is the proportion of nuclear matter to photons. And that's a free parameter in the model.

Actually, it will be explained by the picture I will describe. Not predicted, but explained. Namely, there are enough free parameters in the laws of physics to fit the number of nuclear particles per photon from what we already know. Now the fourth and fifth parameters describe the variations in density across the universe. This cosmic web, as you see in the picture, the variations on the temperature map

of the microwave background radiation. Those require very simple form of density variations. It's known as random Gaussian noise, which means it's just like ripples on the surface of the sea. There are no complex structures. It's literally a random superposition of waves where the waves have a particular strength or power as a function of wavelength.

So there are two parameters there. One is the amplitude. This is about the one part in 100,000 that I mentioned before. That's the amplitude of these primordial density waves. And the second parameter is what's called a red tilt. It means that the waves get ever so slightly stronger as you go to longer wavelengths. In condensed matter physics, such a phenomenon is very familiar. It's called a critical exponent. It means that basically the fluctuations either get a little bit stronger with scale or a little bit weaker with scale, but this scales in a certain way. In the case of cosmology, the red tilt means that if I go to wavelengths 10 times as long,

the amplitude of the ripples increases by 5%. That's not much. And if I go, I think if I go a billion times longer in length scale, the amplitude doubles. Can one also interpret that as it being more numerous? No, it's just that the strength of the wave gets a little bit stronger. The waves are all random Gaussian. It's literally just a random superposition of waves.

But when I said the strengths of the waves, I mean the amplitude of waves, the fractional change in the density. What I meant was that if you were to add two waves, of course they have to be directly on top one another, then you can interpret that as two medium sized waves giving rise to something that's one large. You could, but when you say random Gaussian noise, you're saying that I just

take a bunch of waves of a given wavelength, point them in random directions with random phases, and throw them on top of each other. Then I pick waves of another wavelength, need to tell you how strong those waves are, again, make a random superposition of them, and put them on top of each other. Everything we see is consistent with that. Random Gaussian noise with two parameters describing the power spectrum.

One is the amplitude and the other is this slight tilt. Now, at the end of the talk, I'm going to tell you that our theory predicts numbers four and number five, almost on the nose. Based on the laws of physics, we already know. It's very striking. We'll see. If this holds up, you know, essentially it's problem solved. But we'll see. So as you can imagine, I am

really quite excited about this. Now, dark matter. So I used to believe that dark matter was the one sure indication we had of physics beyond the physics we know, right? The laws of particles and forces which I showed you. We thought, many people thought, the dark matter must be made of something else, another particle, right? And literally there are tens of thousands of suggestions as to what the dark matter might be. And many, many people have built their careers inventing and then trying dark matter particles or other explanations and then trying to test those in experiments. In fact, we can see the dark matter quite directly now. This is a beautiful picture from the ACT experiment. ACT is a Atacama cosmology

telescope and it's actually measuring the microwave radiation. That's what the picture shows is the surface on the left is emitting light. What we see is the map on the right and as the light travels through the universe it gets deflected by dark matter, by the gravity of the dark matter. Just like, you know, water in a glass of water will deflect the whatever's behind the glass of water so that when you look through it you'll see it lensed by the water. So dark matter does the same thing. You can use this to literally measure, using the bending of light, you can measure the density of dark matter and you can measure the density variations in the dark matter.

And this all fits beautifully with the Lambda CDM model. Would you in order to do that have to know the leftmost CMB? No, you don't need to know it. What you need to do is to assume that the leftmost CMB is random Gaussian noise with a power spectrum, which has been measured by the Planck satellite. So just two numbers specify the spectrum. And then what you do is the thing, the only thing you measure is on the right, which if you can sort of see, they put streaks on that map.

The streaks show the effect of the lensing. It basically stretches spherical peaks. If you have random Gaussian noise, the peaks tend to be quite spherical. But if you lens it, that tends to share the pattern and it turns out you can just measure the sheer in the pattern due to gravitational lens and from that sheer, you can infer the density of the dark matter. It's really amazing all this works. With those five parameters, you can fit everything and there is no inconsistency.

This has all become rather precise. I mean, these gravitational lensing measurements are now involved huge amounts of data, and they're all absolutely compatible. In some sense, it's very disappointing. People design these enormous, expensive telescopes that go through this huge data analysis. They would love nothing more than to find a contradiction. That would be super exciting. Well, they haven love nothing more than to find a contradiction. Okay, that'd be super exciting. Well, they haven't found one.

On the contrary, everything fits remarkably well. So let's come back to the biggest puzzle of all. How on earth did everything we see come out of a forces, the laws of light and electric and magnetic fields, and the laws of particle physics we know, which were written down by Dirac, the Dirac equation, those two theories happen to have a symmetry under rescaling space. So this is actually the reason why a light wave is in fact is essentially the same as an X-ray. An X-ray is just a scaled down version of a light wave. You just shrink the length scale, shrink the wavelength of the light, and you'll get an X-ray. Expand the wavelength of the light and you'll get a radio wave. Light is essentially the same thing

scaled up and down. It can come in all forms. They all obey the same equation. They just have longer or shorter. It's uniquely specified by the wavelength, the reason the theory behaves like that, it has a symmetry. And the symmetry is scaling symmetry, rescaling length and time. And you get shorter or longer wavelength, higher frequency or lower frequency light. Now Dirac's equation has the same property as long as you ignore the masses of the particles. In other words, when these equations are taken to be massless limit and the Big Bang is exactly such a place because the plasma is extremely hot, so masses are irrelevant there. So it's very tempting to believe that at the Big Bang Singularity,

essentially there was nothing but light and light-like particles, and they all have this scaling symmetry. Now, that scaling symmetry is very deep, very profound, and what it's telling us in sort of colloquial terms is that the matter did not know about the size of the universe. It evolves in such a way that it doesn't care that the universe is shrinking as we go back in time. And so the matter is evolving as if the universe were in fact not shrinking to a point, or can be described mathematically with ignoring the shrinking away of the universe. And this is what we noticed about the Einstein equations and the laws of radiation, they have that the Big Bang singularities, a very particular type of singularity called a conformal singularity. Conformal, and I'll tell you a little bit more about conformal. Conformal symmetry, this is a picture which illustrates this. So light and particles are described as gauge fields and fermions in

the standard model, a la Maxwell and Dirac. Now conformal symmetry is asymmetry of light and massless particles. Conformal symmetry means that you can actually rescale space and time locally, and the equations are invariant. So here's an example. Imagine I was solving Maxwell's equations inside a cylinder. So the boundary of the cylinder was a circle, as the left picture shows. Alternatively, imagine I was solving Maxwell's equations inside a square pipe. The cross-section was a square.

Conformal symmetry tells you those two situations are actually identical as far as the light is concerned. Often, so the grid you see on the right, that's just a coordinate grid. It's useful for writing down equations or putting them on a computer but has no particular physical significance. Now, if I distort the square on the right into

the disk on the left with a conformal transformation, that means a local change of scale, which does not change angles, it only changes lengths. I get the picture on the left. So that's another grid. I could solve the Maxwell's equations on that grid. And then the statement of conformal symmetry is that these two things give exactly the same result. So these funny points, when you see this pile up of grid points

in the left-hand picture, they're a little bit like the Big Bang singularity, right? There's a sort of pile up of space into a point. And what it's saying is you just have to blow that up with a conformal transformation, just expand your grid, and the equations are just the same in the new picture. We actually use this picture to make

sense of the Big Bang singularity. We go back to the Big Bang singularity. We go back to the Big Bang singularity. Now, imagine blowing up that singularity. I don't mean in the sense of explosion, I mean in a mathematical sense, like changing the scale of space. One can do this mathematically, and then the singularity actually becomes a finite.

It's not a point. It's now a finite patch. And then we impose a boundary condition on that patch, which implements mirror symmetry. So that initial patch at the Big Bang, we treat as if it were a mirror. So normally when we deal with, let's say Maxwell's equations in a mirror, the propagation of the light in the presence of mirror, there are two ways to do it.

Either you impose a boundary condition at the mirror, you say that the electric field parallel to the mirror has to be zero, and you literally solve the equations showing how the light travels to the mirror, bounces off the mirror and comes back. That's one way of doing it. It's actually a very rather tedious way of doing it. There's a much nicer way of doing it, which is to say, look, I'm looking at myself in the mirror. If I'm right-handed,

let me make a left-handed version of myself, put that behind the mirror. Okay? So it's a fictitious person. That's literally a mirror image of me. Put it behind the mirror an equal distance from the mirror, throw the mirror away, and just solve Maxwell's equations for the light coming from that person to me.

That's called the method of images in physics. It's a very elegant way of solving boundary value problems. What we're claiming is that you can apply the same method to describe the Big Bang. The Big Bang is a mirror. I literally take the post-Bang universe, make an image of it before the Big Bang, and then I would just propagate light and particles from that pre-bang universe through the big bang singularity, because of conformal symmetry, that propagation is completely smooth and regular and predictable, and I propagate that forward to see what we see. So we claim that this extended or mirror universe picture is absolutely compatible with everything we see in

the universe. So in a certain sense, when we look back towards the Big Bang, we are seeing our own image, okay, that the Big Bang is a boundary condition. It's not, you shouldn't think about, you see the conventional way about thinking about the Big Bang, which I think leads to terrible paradoxes, is that somebody input all the stuff in the universe at the Big Bang and sort of threw it apart. Right. What we're doing is the opposite of that. We said no, the big bang, all that happens in the big bang is a boundary condition, which the matter has to respect. If you look at this, the traditional way is that someone or something just spurred everything into existence from that single point. Exactly. But then you're saying that this is an improved

picture. Yes. However, it just looks like someone or something spurred all from all points at once. So it doesn't seem like much of an improvement. So tell me why this is different. Right. No, good question. You might say our picture looks like somebody made two universes. So surely it's twice as difficult. Yes. No, good point. What we're saying is that there is a, yeah, in fact, the answer is Twice as difficult. Yes. No, good point.

What we're saying is that there is a, yeah, in fact, the answer is this. Great, natural lead-up. Yes, the answer is this. So the most fundamental law of physics we know, which is a direct consequence of quantum mechanics and relativity, is called CPT symmetry. CPT symmetry was discovered in the 30s and 40s as an inevitable consequence of bringing quantum mechanics and relativity together. So it underlies quantum field theory. Now what is CPT symmetry? CPT symmetry says the following, that if I turn, if I look at some physical process and I try to make another physical process

using a law of symmetry, okay? So take some physical process, turn every particle into its antiparticle. That's what the C does. P invert space. So literally just send any space coordinate in three-dimensional space to its inverse. X goes to minus x. Okay, that's an inversion of space. That's a very dramatic thing to do, but the laws, you know, you can

do this with the laws of physics. T is time reversal. So whatever's going forward in time, make it go backwards in time. The CPT theorem in relativistic quantum physics tells you that the rate for any process and its CPT conjugate process is identical. So this is kind of analogous to time reversal in Newtonian mechanics. In Newtonian mechanics, you can take any laws of motion and reverse time, and because they're second order equations in time, they are invariant. So Newtonian mechanics has no arrow of time, and in relativity, the generalization is CPT. So we take our observed universe, the right hand part of this picture, it has more matter than antimatter. OK, so it is not invariant under C.

And it's not invariant under T. It's going one way in time. And so the right hand side of this picture violates CPT. What you would, but if you apply CPT to the right-hand side of the universe, what you get is the left-hand side. Namely, every particle goes to its antiparticle. What was going forwards in time moving to the right, in the right-hand part of the picture, is now going forwards in time moving to the left, in the left right hand part of the picture is now going forwards in time moving to the left in the left hand part of the picture.

And so the statement is that if you want the universe to respect the laws of physics. I'm in the most obvious way namely that it is invariant under CPT. Then you are led to this double picture. And in the doubled picture, there is then a very natural boundary condition, which is symmetrical under CPT. And the boundary condition is the one that we use. So we're saying the Big Bang

is a CPT mirror. And this resolves the fundamental puzzle of why the universe appears to us to violate its own laws. You know, we send more matter than antimatter. That looks like the universe is not invariant under C. Likewise, we see time going one way, and that's incompatible with the fact that the laws of physics are invariant under reversing time and changing matter to the universe. And the consequence is this mirror universe hypothesis. So to put it differently, anyone who makes any other hypothesis is going to have to violate CPT. And you know, that's a losing battle. So so yeah so we were very surprised. So in Newtonian mechanics, if you take a ball and there's no friction and you drop it, right,

it hits and then it comes right back up. Exactly. Okay, now if you were to look locally, if you were to just look at the two half a second, you would say, well, look, there is a difference between the future and the past, because in the in the past, it starts to go down, but in the future, it starts to go up. But you're saying, well, you have to look at the whole picture. Of course. So let's take the full movie. Of course. So now, philosophically speaking, we use that word earlier. Sure. What is someone who's watching this supposed to feel? There's some religions that say something or someone or universe started itself and you experienced this world once, right?

Then there are some other right traditions that say you experience it cyclically, infinitely, right. And then there's here, which seems to suggest, well, you experience everything twice. No, because, um, you see, when I say we're using the method of images to impose a boundary condition at the Big Bang. So this picture is a mathematical picture, a device, which is useful in order to impose a particular boundary at the Big Bang. So in this picture, the universe in a certain sense creates itself.

It's extremely minimal. Everything I described could be described by just taking the right half of the picture with this boundary condition, which is, in effect, the result of doubling it and imposing the symmetry. You see, if I doubling it and imposing the symmetry. You see, if I double it and impose a symmetry, the doubling goes away because the left and right halves are identical.

So then to be specific, is it correct to say the Big Bang is a mirror? Yes. Yes. For mathematical convenience, it's useful to model the Big Bang as a mirror. Is that the more elaborate correct statement? No.

Or the Big Bang is a mirror is the correct statement? Correct statement is the Big Bang is a mirror. For any mirror, it is useful to double the universe. I see. Yeah. The doubling is just a mathematical trip, which you can use for any mirror. We're saying that literally the Big is just a mathematical trick, which you can use for any mirror. And we're saying that literally the Big Bang is a mirror.

So I would say that this, I mean, certainly in my experience, and I've worked with Stephen Hawking and I've worked with a number of other such people on scenarios for cosmology, there is no doubt this is the most economical hypothesis you can make. Because it's consistently compatible with the laws of physics and extremely minimal. So, you know, either it's right or it's wrong. We'll see. That's the attractive feature of this whole setup is that it is eminently disprovable and that makes it interesting. So, as I mentioned, these laws, the particles and forces, actually do have this symmetry under local changes of scale and that allows us to resolve the Big Bang singularity, to blow up the point everything came from into a patch.

And then that patch is the mirror at the Big Bang. This is actually all the particles we know. Now, notice something funny about this picture. All right, so the neutrinos in the bottom left have a superscript L. something funny about this picture. follows the fingers of your left hand. So it's rather strange that the light neutrinos we see only come in the left-handed variety. All the other particles have a right-handed and a left-handed version. Now so that is you know what we see in laboratory experiments. We only ever see left-handed neutrinos.

However, if we were to imagine the simplest or the most minimal conceivable extension of the standard laws of physics, what would it be? And I just made it. Right. I went from this slide to that slide by removing the L. Okay. Now all the particles have both left and right handed versions. Okay. And my claim, our claim, this is with Latham-Boyle, our claim is that removing that L, in other words giving the neutrinos a right-handed as well as a left-handed version, allows you to solve the problem of dark matter in an extremely minimal way with the mirror hypothesis.

So now imagine these are the laws of physics. There's no L anymore on any particle. Every particle has left and right versions. Now what happens is I take my left-handed neutrino, it's coming in from the left, it then, what we call, we say that it can oscillate into a right handed neutrino the new right in the middle. Add oscillate back into a left handed neutrino on the right. Now the left handed neutrinos are very light neutrinos are very like particles they don't have much mass if the right handed if the right handedhanded neutrino is very heavy, then this process can only be a virtual process. You can't, you had a certain amount of energy, you can't stay as a right-handed neutrino, you just don't have enough energy to account for its mass. So you've got to go back to being

a left-handed neutrino. So this is what we call neutrino oscillations. a left-handed neutrino. This is what we call neutrino oscillations. The left-handed neutrinos can oscillate briefly into a right-handed neutrino and then they find themselves in, if you like, they've got more mass than they can account for with their energy, and so they go back into being a left-handed neutrino. This mechanism is a mechanism for giving the left-handed neutrinos a small mass. neutrino. This mechanism is a

Namely, if there are right-handed neutrinos which are very heavy, this would explain why the left-handed neutrinos are very light. You see, the heavier the right-handed neutrino, the shorter the time you're going to spend as a right-handed neutrino. And so basically, the heavier you make it, the less and less probable it is that the neutrino oscillates in this way. And so, it's called the seesaw mechanism because the heavier you make the right-handed neutrino, the lighter the mass of the left-handed neutrino. So this was understood in the 70s. And at that time, people could have said, oh, well, maybe the dark

matter is a right-handed neutrino. You see, the right-handed neutrino is a very obvious candidate because it has no electromagnetic charge. It doesn't couple to the strong or the weak force at all. So the only thing the right-handed neutrino couples to is the Higgs field, this thing noted by H, and gravity. So for the right-hand neutrino to be the dark matter, all you need do is A, switch off this coupling. Actually, this is the important one. For the right-handed neutrino to be the dark matter, the only problem is that it can decay.

This diagram shows a right-handed neutrino decaying into a Higgs and a left-handed neutrino. If you want the dark matter to be stable, it has to have survived for at least 14 billion years, you've got to switch off this vertex. If you switch off that vertex, you must switch off this vertex because they're the same vertex. If you do that, it means the left-handed neutrino cannot oscillate into the right-handed neutrino, and this actually means the left-handed guy must be massless.

So just from this picture you can see that if the dark matter is stable and consists of right-handed neutrinos then it's plausible that one of the left-handed neutrinos is massless and that's actually our prediction which is going to be tested in the next five years. So now how do we, the second thing you've got to do is you've actually got to make these right-handed neutrinos, right? How do they get made? And the way they get made is rather beautiful. You see, if I switch off this vertex, the right-hand, put a right-hand, one of the,

the, there are actually three of these right handed neutrinos and three vertices, so I'm somewhat simplifying the story. But if I take one of them and I switch off its vertex, then it actually doesn't couple to anything except gravity. So this poor right handed neutrino is sitting there in the universe, it doesn't see the hot plasma at all. And the mystery is, how did it get created? You know, what determines its abundance?

And so this was actually our first starting point with this whole picture. We realized the right-handed interferers are produced as Hawking radiation from the Big Bang, that it is simply the time dependence of the universe that creates these right-handed particles. It literally pulls them out of a vacuum, which is a process called Hawking radiation. It's due to gravity, it's due to their coupling to gravity, and due to the fact that the universe is expanding. So what we showed is that if their mass was 500 million times the mass of a proton, then they account for all the dark matter we see.

And this is the simplest yet explanation for the dark matter. It's just right-handed neutrinos. They were created by the expansion of the universe. To calculate that creation, we had to assume a particular quantum state for the right-handed neutrinos. And what we do is to use the state defined by CPT symmetry and the mirror hypothesis. Okay, so all of this is kind of self-consistent. And is that a bound on the mass of the right-handed neutrino or is that like an actual prediction for it? It's an exact prediction, okay.

That has to be its mass. Now it's very hard to measure indirectly. I mean, you would have to literally have a little grab a meter and go through space and wait until the right-hand of the neutrino travel past you and measure the deflection due to its mass. One day that will be possible. It's not possible today.

But no, this is a very precise prediction of its mass. There are no free parameters in that prediction. So if it's stable, the lightest neutrino is massless. Why? Because to make it stable, I had to switch off this vertex. And if I switch off this vertex, I have to switch off that one. And that means this left-handed neutrino cannot acquire a mass by becoming a virtual right-handed neutrino for a little while. So the prediction is that the lightest neutrino, namely

one of these left-handed neutrinos, is exactly massless. And amazingly, this is now possible using the Euclid satellite telescope survey now underway. And basically what you do is measure the strength of clustering of galaxies on a certain scale, which corresponds to the... Well, yeah, let me start again. The way you measure neutrino masses using galaxy surveys, and it's quite extraordinary that you can do this, is by measuring the strength of the clustering of matter. Now, if the neutrinos are massless, they do not clump with the rest of the matter.

If they have a mass, then as the universe expands, they actually slow down relative to the expansion because the mass becomes important and they no longer are moving at speed of light. They slow down and they clump with the other matter. That effect turns out to be large enough that by measuring the clustering of galaxies, you can measure the mass of the neutrino.

They claim they will be able to check that the lightest neutrino is massless within about 5 sigma, quite accurately, using these forthcoming galaxy surveys within the next five years. So should this prediction be confirmed? My claim is that this will be easily the most compelling explanation for the dark matter. There are other predictions. We can predict the decay rate of atomic nuclei, a process called neutrino-less double beta decay, but that process is very, very slow and may take one or two decades to measure. It's a very, very tough experimental test,

but if this one works out, there will be very strong motivation for doing nuclear physics experiments to check this idea that the dark matter is the right-handed neutrino. So where do we get to? Well, the Big Bang was a special type of singularity. The size of the universe is governed by what we call the scale factor.

This comes into the metric on space-time. What happens is that as time goes to zero, this scale factor, the size of the universe, shrinks to zero in a very simple way, just linearly in time. When it hits zero, we call that a conformal zero, meaning that the scale shrinks to zero, the overall scale shrinks to zero, so colloquially the universe is at a point. But as I mentioned, you can always blow up the scale essentially by dividing by this quantity that goes to zero. You can blow it up and that becomes the mirror. So

this conformal zero in this picture of the Big Bang becomes in fact an extended three-dimensional mirror in what we call the conformal frame. One way of saying it is that the conformal four geometry is actually regular at the Big Bang. This is a resolution of the big bang singularity the big bang is not. The shrinking away i mean the big bang is in the sense of shrinking away of space but the thing is the particles of the four particles and forces do not. Do not not affected by that strength that shrinking. They still in a bay they still being equations as if they were in extended three-dimensional space. So this is a way of resolving the Big Bang singularity and turning it into a mirror.

So I was going to tell you about explaining the geometry of the universe, but I think that's too long. I want to talk a little bit about the most exciting and most recent development in this hypothesis. And so this is addressing the very fundamental dilemma which occurs in coupling quantum fields to gravity. Okay, so we know that in order to describe the laws of fundamental physics, we have to use quantum fields. This is an extremely successful technique, and it's the basis for the standard model. Everything is described by quantum fields in the standard model. However, these quantum fields look like the right-hand picture in the vacuum.

And this is just a consequence of the Heisenberg uncertainty principle. You might want to set a field to zero and just say there's no electric or magnetic field in space, but this is inconsistent with quantum mechanics. Why? Because the magnetic field is like a coordinate of a particle, x, and the electric field is like the velocity of a particle or its momentum. And the Heisenberg uncertainty principle says that either you measure x or you measure p, you can't measure both. You

can't set the position of particle to zero and its momentum to zero at the same time. You can do one or the other. And so what happens in the quantum vacuum, you might say, okay, let's have zero electric field, but then you've got infinite magnetic field. You might say, okay, zero magnetic field, but then you've got infinite electric field. So the compromise which happens in the vacuum is that neither the electric nor the magnetic fields are zero. They're both oscillating with what is called zero point fluctuations. So the vacuum is full of these fluctuations, which are pictured in the right-hand side. And these are all the fields in the standard model. The electron fields, the photon fields, the strong force, the weak force, everything is sort of going

crazy in the vacuum. I say going crazy advisedly because there's infinite energy in these oscillations. This is a very deep paradox about trying to couple quantum fields to gravity. Now not only do you get infinite energy in the vacuum, as I mentioned, gravity detects all energy, and in particular it's very hard to stop gravity feeling all this energy in the vacuum. You led to this immediate paradox that gravity is coupling to an infinity and cosmology doesn't really make any sense. People cheat in various ways.

They subtract that infinity in certain ways. But there's a further problem, which is that these zero-point fluctuations in the vacuum spoil this beautiful local scale symmetry of the Maxwell and Dirac theory, which we needed in order to make sense of the Big Bang singularity. So these vacuum fluctuations seem to prevent us describing the Big Bang Singularity as a mirror. What we have done recently, very recently, is we discovered an entirely new mechanism, A, for canceling the energy in the vacuum, B for restoring the symmetry of Maxwell-Lindarach, the local scale symmetry. And we found we could do that in a very unique way. We call them dimension zero fields. They're rather peculiar fields, they do not have any particles, they merely exist, if you like, in the vacuum.

So all they do is sit there and cancel out these various diseases in the vacuum. Okay, so it's again extremely minimal addition to the standard model. It's very unique, their properties are uniquely defined. Then rather miraculously, these same extra ingredient, the same extra ingredient in the vacuum, turns out to explain the origin of the density variations. This is now rather technical. I'm going to leap to a formula which I'm not going to justify,

but this formula is a direct consequence of the assumptions I've laid out. It says that the power spectrum in the early universe, that's this curly p thing, as a function of wavelength is given by these numerical factors, which are just a consequence of relativity, quantum mechanics, quantum field theory, various numbers here, C beta, this alpha y, alpha 2, and alpha 3 are the strong weak and electromagnetic coupling constants as measured in the laboratory. Okay, so roughly speaking, you could say that this is given by defined structure constant, but it's for the strong, weak and electromagnetic forces. So these numbers are all a consequence of the standard model, right, all these funny fractions, a

direct consequence of the number of particles of various charges and types in the standard model. So these are all Standard Model. There's a number of effective degrees of freedom. This is basically the number of particles in the Standard Model. So these numbers are just inescapable consequences of the Standard Model. This is the red tilt.

You see this power of the fluctuations as a function of wavelength is growing with wavelength like lambda to this small power and this small power turns out to be 0.04 which is what we observe in the cosmic microwave sky. Okay so there is this rather magical formula that comes out of those assumptions. It turns out and this may a coincidence, but it's a very tempting one. Turns out that this formula matches both the amplitude and the red tilt. So this number gives you 10 to the roughly 10 to the minus five, uh, within a factor of two, it matches the observations, The red tilt it predicts is 0.042

using the CERN measurements of the strong coupling constant and the observed number from the Planck satellite is 0.041. So this is very tantalizing. All I would say at this point is that I think very few cosmologists are, except us, are convinced by this. Yet, I'm going around, Latham's going around giving talks, people are challenging us in various ways. If only you could do the calculation this way or that way or check this or check that, we might believe you. That's very important that we are checked and that we really present a full-blown calculation to satisfy everyone. There are various assumptions we've made. They are always the simplest conceivable assumption, but there are some assumptions in this result.

If this turns out to be theoretically safe, no one points out a problem with it. If the observations, as they improve, confirm this scaling, you know, extends to even smaller wavelengths, then this will be the explanation. OK. And cosmology will be unified. Just to close on this, what I've put forward here is the prospect, at least, of an extremely unified picture. There is just the standard model and gravity, perhaps with a few little additions in the vacuum but no extra particles no extra forces. I'm and maybe we are actually very close. Do you understand the physical all the physical laws governing the universe and how they describe the big bang itself. and how they describe the Bit Bang itself. If this is true, there are many, many other consequences.

It leads to a new picture of black holes, which resolves the black hole information paradox. It will lead to many other predictions because it's so constrained, this picture. And there's no wiggle room. I mean, either this picture is right or it's wrong. So we'll see. Here are some references of papers on this. There are other papers on the archive and then new papers in preparation. But thank you very much for listening and I welcome

any questions. Thank you so much, Professor. The question and answer session is on theories of everything. Check for it in the description or subscribe to get notified. It's a 90-minute Q&A about this lecture. Neil Turok was also interviewed solo for two hours here on TOW, and this is the most watched interview with Neil Turok ever. Check that out as well.

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