Theories of Everything with Curt Jaimungal - The (Simple) Theory That Explains Everything | Neil Turok

Episode Date: April 23, 2024

Neil Turok joins Curt Jaimungal and Theories of Everything to discuss his new hypothesis regarding the origins of the universe, building on Stephen Hawking's geometrical model to propose a theoretical approach that avoids the singularity at the Big Bang by suggesting a minimal, mirror universe scenario without requiring inflation. Please consider signing up for TOEmail at https://www.curtjaimungal.org  Support TOE: - Patreon: https://patreon.com/curtjaimungal (early access to ad-free audio episodes!) - Crypto: https://tinyurl.com/cryptoTOE - PayPal: https://tinyurl.com/paypalTOE - TOE Merch: https://tinyurl.com/TOEmerch  Follow TOE: - *NEW* Get my 'Top 10 TOEs' PDF + Weekly Personal Updates: https://www.curtjaimungal.org - Instagram: https://www.instagram.com/theoriesofeverythingpod - TikTok: https://www.tiktok.com/@theoriesofeverything_ - Twitter: https://twitter.com/TOEwithCurt - Discord Invite: https://discord.com/invite/kBcnfNVwqs - iTunes: https://podcasts.apple.com/ca/podcast/better-left-unsaid-with-curt-jaimungal/id1521758802 - Pandora: https://pdora.co/33b9lfP - Spotify: https://open.spotify.com/show/4gL14b92xAErofYQA7bU4e - Subreddit r/TheoriesOfEverything: https://reddit.com/r/theoriesofeverything  

Professor there's a quote from you the big bang is a mirror explain. So this is a new hypothesis we're exploring. It is i would say a development of an approach steven hawking proposed you know hawking was. Obviously wondering about how the universe could come out of a singularity. wondering about how the universe could come out of a singularity, and that's maybe the most fundamental mystery in cosmology and basic physics. How did everything we see come out of a single point? That's what the Einstein equations imply, and it's very mysterious indeed. So Hawking's picture was very geometrical.

He said, let's trace the Big Bang back to the singularity. Space is shrinking to a very small point. We can sort of think of this like a cone whose tip is sharp. And so if you like the cross-sections of the cone, as you go up the cone, that's time and the cross sections denote space. And so the cross sections are a circle which is shrinking to a point at the Big Bang. So Hawking's idea was to essentially round off that sharp tip by going to imaginary time instead of real time. So as long as you solve the Einstein equations in real time, the existence of a

singularity is unavoidable. One can show that you're just forced to hit a singularity at the Big Bang. This is Hawking's Singularity Theorem. But if you make time become, instead of going along the real axis of the complex plane towards t equals zero, if it makes a bend and goes up the imaginary axis, then the space becomes Euclidean, not Lorentzian. So the metric is plus dt squared plus dx squared. And if that's the case, then the Euclidean Einstein equations allow you to round off the space in a smooth nose of the cone rather than a sharp tip. So that was his sort of trick for avoiding the singularity. So I worked on this for many years. What's appealing about it is that you sort of avoid the chicken and the egg problem in cosmology.

The chicken and the egg problem is what came before. And if time is infinite into the past, there's always a before. And so you just end up endlessly asking what came before that and before that and before that. If instead you do have some theory of a boundary or a boundary condition, let's say, at the Big Bang singularity,

that sort of resolves the question of what there was before. So it's a much more minimal picture of the universe. It is the most minimal picture picture is that somehow what happened in the beginning is there's just a boundary condition. Hawking proposed a particularly simple one. His proposal is that there is no beginning boundary. If I imagine a rounded cone, as I go down the side of this cone,

well, there's no special singular point. No point is any different than any other really, near the beginning, it's just the surface of a sphere near the tip of the cone. That just avoids the question of what caused everything else. So I was very taken with this idea, but worked on it for several years and found it didn't work.

Hawking's proposal predicts that the universe is empty, not full of radiation. And it took me a while to see that the problem is really that Hawking tried to realize his idea in the context of inflation. Inflation is a very hypothetical picture of the early universe, which postulates that the universe was dominated by a strange form of energy called inflationary energy, and that causes the universe to expand exponentially. And the reason people like the idea

is that it seems to explain why the universe is so smooth and flat and isotropic today, because you essentially just sort of blow up a small patch and stretch it out into something much flatter and smoother. But I've never been a big fan of inflation because you sort of get out what you put in. What do you mean? You postulate a new form of energy and then you dial all of its properties so that the resulting universe fits the observations we see.

So literally you don't get any definite prediction, you just get out what you put in. So normally what people do is they assume there's an extra scalar field which has this type of potential energy which can drive inflation. And then you find all the predictions of the theory depend on the details of that potential energy, which is a free function. And so unfortunately, there are no really precise predictions of inflation. It's just what we call a fit. You know, you just dial the shape of this potential to match what we see.

Now, for people who are listening, what would be the difference between that and say the standard model, which has some parameters that you then go and experimentally find out? The difference is that with inflation, the standard, the difference is the standard model does not give inflation. Okay. So none of the forms of energy in the standard model are of the right type to give inflation of the kind we need. What I meant to say is like, let's imagine that you have some formula and now you have to go and measure in order to fit the curve that you measure the experimental data. Right.

Right. But that's a characteristic of almost any scientific enterprise that's mathematically modeled. So what's the difference between inflation and say the standard model, which is similar in that regard? The standard model is built on some rules of consistency, theoretical consistency, which are very strong. And so that's the requirement that the theory is consistent with quantum mechanics and relativity.

That severely constrains the number of parameters you can include. For example, in the standard model, there's the idea of renormalizability. You have a certain number of parameters, then you calculate all the quantum corrections in the model, and all of those corrections are parameterized by a very small number of parameters. It's about 20 parameters in the Standard Model. That sounds like a large number, but in fact the number of different observations are millions or billions.

So it's actually a tiny number of parameters as compared to the number of physical phenomena you're predicting. So standard model is very highly constrained by requirements of theoretical consistency. Now the problem with inflation is you are trying to couple the standard model of quantum fields to gravity. And nobody quite knows how to do that. standard model of quantum fields to gravity. And nobody quite knows how to do that. So when people started building inflation models,

they essentially relaxed the rules to say, okay, well, we don't really know what's needed for consistency. So let's just allow scalar fields who are not consistent with renormalizability and all the other requirements in standard model physics. So they ended up with a sort of slew of models like tens of thousands of different inflationary models.

They all give different predictions. And unfortunately, the observations are not pointing to any one of them. The simplest inflation models were ruled out several years ago. There's one sort of smoking gun signal of inflation, and that's the prediction that this explosive phase of the early universe should have given rise to gravitational waves, very long wavelength gravitational waves, which is created by this sudden expansion of space. But the observations are now bearing down very strongly on gravitational waves. So whereas the simplest inflation model predicted they would be about 20% of the CMB

signal, you know, when we look at the cosmic micro background, we see these fluctuations, we can tell what fraction of those fluctuations were due to gravitational waves. The simplest inflation models predict about 20 percent. The slightly less simple models predict, well, at least about 10 percent. The observations are now at 3 percent, and in the next three years, they will fall to 0.3 percent. That's a prediction of yours? No. to 0.3%. That's a prediction of yours. No, this is everybody accepts that inflation predicts gravitational waves at some level.

I'm sorry, Professor. What I meant was, is it a prediction that it will fall from 3 to 0.3? Oh, yes. Sorry. Yes. That's not my prediction. It's the prediction of the experimentalists.

I see. The experimentalists are doing a fantastic job of measuring how much of the signal in the cosmic micro-vanisotropy is due to gravitational waves. And what they found is much less, there are much less gravitational waves than sort of simple inflation models predict.

And their upper limit is coming down and down and down. And as it comes down, it makes it more and more difficult to build a consistent inflation model. You can do it and you will always be able to do it, but the model becomes more and more contrived and less and less compelling. Now I would contrast that. So inflation, I just emphasize is a kind of phenomenological fit. That's what I would contrast that. So inflation, I just emphasize, is a kind of phenomenological fit, that's what I would say. You're just parameterizing some observations with some arbitrary functions. It's not a theory at the level

of Einstein's theory of gravity or Maxwell's theory of electromagnetism. I mean both of those are very clear theories, very highly principled theories that are not very adjustable. They predict what they predict and either they're right or wrong, and that's why they're interesting. In both cases, there are thousands or millions of observations which confirm the detailed predictions of

the theory without any need to adjust parameters. Maxwell's theory of electromagnetism and light has no free parameters in it, and it fits perfectly. All phenomena involving electromagnetism and light. Einstein's theory of gravity likewise fits perfectly. All the observations we have of black holes and so on. So I guess I've never been a fan of inflation because it always seemed somewhat ad hoc and more like a fit than a theory.

But obviously, it's very challenging to try and make a more compelling theoretical framework, which is much more rigid, doesn't involve all these arbitrary functions and parameters, and is consistent with everything we see. Essentially, what we've done recently with the mirror universe proposal is modify Hawking's initial idea to be an idea about the beginning of the universe, the boundary condition at

the beginning, which does not involve inflation. Inflation is not needed in our proposal. Nevertheless, we're close, I would say, to having a complete description and understanding of exactly what the Big Bang singularity is. That's what motivates me. You see, another way of saying it is that particle physicists for the last 50 years or more, preceded by every time a new phenomenon was

discovered, they added a new field or particle, right? So there was electrons and protons were known and then they couldn't really understand the structure of the nucleons so they added quarks and then there were gluons and that all worked very well but then new accelerators came along. They found new particles. They kept adding more generations of fermions. So basically the mode of operation of the field was you build a bigger accelerator, discover a new particle, add some more stuff to the Standard Model. That stopped working around 1980. in the 70s, the current framework of the standard model was all in place, and no accelerator

since that time has discovered anything extra. All the major theoretical ideas were in place in the late 70s. So far, the bigger accelerators we've built, we've not found any new particles that weren't already predicted. And so this is kind of shocking. The Large Hadron Collider, you know, was built to find the Higgs boson.

It did, but that was predicted in the 60s. Most theorists were predicting there would be a slew of new particles, right? Instead, we find nothing. And so I am very interested in the idea that perhaps we do know all the laws of physics. They're sitting in front of us. The Einstein's theory of gravity, we've got the standard model. The challenge for cosmology is

understanding how these things work together. It's not so much adding new ingredients. I believe it may be true that we don't need any new ingredients. All we need is to understand how the ingredients we already know fit together. So my philosophy has become one of extreme minimalism. Right. Let's try to explain everything we see with the minimum number of theoretical principles.

Now what's interesting is that this is a hallmark of simplicity and beauty and physicists as well as mathematicians, but physicists are motivated by in large part beauty and simplicity. Yes. So why is this such a controversial view? It's a good question. I think frankly it's people got into bad habits. Such as not which people, although you can talk about that, but the bad habits in particular. All Not which people, although you can talk about that, but the bad habits in particular. All the people like me, okay? Everyone like me. And I was in these bad habits too.

You know, I entered the field in the early 80s where the Standard Model was in place and people invented the idea of a grand unified theory. Okay, so grand unified theory was supposed to unify all the forces, strong, weak and electromagnetic forces, unify all the particles, electrons, quarks, neutrinos and so on. But the idea was the way you unify them is by adding, putting them all into a bigger

framework called the grand unified theory. So the hope was that you would get a greater degree of simplicity and beauty by adding more stuff. So as well as the forces we already know, there would be other forces. I mean in the standard model, in a certain sense, there are 12 force carrying particles. There are eight gluons, three weak bosons, and one photon. Okay, so 12 force carrying particles. In the simplest grand unified theory called SU5, there were 24.

So you added 12 more, okay, in the hope that the complicated group structure of the standard model, which is SU3 times SU2 times U1, that would all be included in SU5, okay, which sounds simpler and more beautiful and more elegant. Right. But the way in which this was done was extremely naive. It was to say, look, we know a certain number of the ingredients. Let's imagine that there are more particles which are heavier and so haven't been found in accelerators, when we add in those more additional particles,

everything will simplify and become more beautiful. It never really worked because when you added more of these force-carrying particles, you also had to add more of another kind of particle called a Higgs boson, which breaks the symmetry, which would break the symmetry from SU5 to SU3 times SU2 times U1. So you kind of unified it in a sense, but then you had to add more stuff with more parameters and more arbitrariness in order to sort of unbreak the, or to break that unifying symmetry. So, and then people went further. They said, well, maybe SU5 isn't the whole story.

So, you know, let's add strings. Right. So now you had strings with all kinds of extra particles, in fact, infinity of extra particles, and then string theory didn't work. So in four dimensions, so you add six extra dimensions of space. And then string theory didn't work, so in four dimensions, so you add six extra dimensions of space. And then string theory didn't really work. There were too many string theories.

So then people came up with M theory, which is now seven dimensions of space and has membranes in it as well as strings. And this sort of just kept escalating. it as well as strings. And this sort of just kept escalating. Editors note here, Superstring Theory has nine plus one dimensions, so nine dimensions of space, one dimension of time, and M Theory has ten dimensions of space, one dimension of time, so 11 dimensions in total. There's a string theory iceberg video where I break down the math of string theory in three hours and the link is in the description. Correct. Yeah. So M theory, you added another dimension. But it's a bit of a peculiar dimension,

which has strange ends to it. So yeah, initially I was very taken with all these ideas, and I pursued them very vigorously. What has always distinguished me from other cosmologists, I think, is my focus on observational tests. I think all of these theories are nothing unless they make clear predictions. Right.

And we tried to use M theory to explain the Big Bang itself and then to get predictions. And we kind of showed that in a similar manner to inflation, we could fit what we see in the sky. But you know the number of parameters in the theory was way in excess of the number of observable parameters. And so I was never very happy with that. It's not a real theory. It's not really predicting anything. It's only fitting things. So I've become much more demanding. I want a

theory in which we take the forces and particles we know, and we don't add anything else. And we nevertheless, explain how the Big Bang worked, and how quantum gravity works within this minimal framework. This is, if you like, the extreme optimist view that I think maybe we've discovered all the particles we're ever going to discover or almost all of them. The real task is figuring out how they work together consistently. Now why am I optimistic?

I'm optimistic because of this point of view. One the Large Hadron Collider hasn't seen anything else, so that confirms this point of view. Secondly, observations of the cosmos are pointing to extreme minimalism. So if you ask how many numbers do I need to describe all cosmological phenomena on large scales? How many parameters do I have to add to the standard model? And the answer is five, just five numbers.

And they're all very fundamental numbers. So one is the cosmological constant, sometimes called the dark energy. This is a very, very basic number telling you how much energy is in empty space. Two is the amount of dark matter compared to ordinary matter. Again again a very fundamental number. Three is the number of baryons, which are protons and neutrons, the nuclear particles we're

made of, compared to the number of photons, again a very fundamental number in physics. So there are three numbers for the matter content of the universe, and then just two numbers that describe the fluctuations we see in the universe. What came out of the Big Bang wasn't perfectly uniform. It has some slight density variations from place to place, and those gave rise to galaxies,

and stars, and all the interesting structure. So the amazing thing is today, by looking back to the early universe and mapping the cosmic micro background, we can see these fluctuations and measure their statistical properties. And they turn out to be unbelievably simple. It's basically what's called Gaussian random noise. It's the simplest possible random noise pattern you can imagine with a scale invariant spectrum, meaning that the variations have the same strength on all scales.

And so that's one parameter, the strength of these fluctuations. It's about one part in 10,000. And secondly, there's a slight tilt, what we call a spectral tilt, that the fluctuations get ever so slightly stronger on large scales. So it's not exactly a scale invariant, it's just close to it? It's not exactly. It's scale invariant with the tilt of 4%. Okay. So if I go, if I change the scale, yeah, what's the way to say it? Yeah, basically it's saying that if I...

If you have waves of a certain frequency that they're more diverse or more varied than the others? The longer wavelength waves are ever so slightly stronger, but only by 4%. So if I, yeah, so basically if I double the wavelength, then the amplitude, it's actually the power spectrum, so it's the amplitude squared, goes up by two to the power 0.04, that's 4%. Right, right, right, okay. Now it's a very, very tiny amount,

but it's also a very beautiful thing, that it seems to be a perfect power law. Over all the scales we can see, it's what's called in physics, we see this in more mundane phenomena. It's called a critical exponent. It looks like that's what the universe has. It has scale and very power spectrum

with a small critical exponent. So basically, they're two extra numbers. So altogether, you get five numbers specifying everything about the universe on large scales. Now, the simplest inflation model would add a whole slew more numbers, okay, on top of these five and enable you to fit them, but you're not really explaining them.

What we've claimed we've been able to do is explain and enable you to fit them, but you're not really explaining them. What we've claimed we've been able to do is explain all of these five numbers without introducing any new particles or forces into the standard model of physics that we know. So it's a extremely minimalist program. Now I have to confess this, some of them we are actually just fitting. Okay. The energy in the vacuum, we have an explanation why it has to be small and positive, but we don't predict the value yet. So we

just adjust this value. The dark matter density, again, we have a free parameter which we adjust to fit that value. It's actually the mass of a right-handed neutrino. We dial and it fits the value. And then finally, the number of baryons to photons is a parameter which exists in the standard model if the standard model has right-handed neutrinos, as it has to have to explain neutrino masses. So, essentially, in a pretty minimal way, we fit those three numbers. The other two numbers, the strength of the fluctuations and the tilt, we claim we can explain using standard model physics alone, okay?

And we predict the tilt in terms of standard model parameters. One of the parameters in the standard model is the strength of the strong nuclear force. And we found that we could fit the strength of the fluctuations and the tilt in terms of that number. That we have a certain calculational framework in which the strength is determined by the strong interactions.

So that's quite amazing. We claim we have succeeded in unifying the particles and forces of the Standard Model with gravity and that when you impose the right conditions to unify them, you automatically explain the fluctuations that came out of the Big Bang. It's super ambitious. I would say rather few researchers today even understand what we're doing. They are getting more interested. I'm getting invited to give lots of talks. It's very, very ambitious physics. Maybe let me talk a little

bit about what's involved. Sure. And just as an aside, what is this theory called? So when you say the we, you mean Latham boil and yourself, what is this theory called for people who just want to search it? Like does it have a name string theory loop quantum gravity? No, no. Uh, I have been calling it in recent talks, I have been calling it a minimal SM slash

LCDM cosmology. Right. Okay. Okay. Now SM is standard model. LCDM is Lambda Cold Dark Matter. The SM is the theory which explains everything we know in particle experiments, right, the standard model. The LCDM is the dominant theory or description, not really a theory, it's the

highly successful description of the universe on large scales, Lambda Cold Dark Matter. And what I claim is the SM and the LCDM actually fit together very beautifully, right, within a certain theoretical framework. Yes. And that, and I claim that is the minimal framework. So you're not using SM to predict the values of the lambda CDM? We are. We are. So yeah. So we've combined them. Right. Well when you say combine, if it's derivable, then you

don't exactly combine it. It's more like you have it as an output. Explain it. Yes. Exactly. Exactly. Exactly. So no, we haven't given it a name yet. Um, maybe we need to. It's a good suggestion. Yeah. I would love that because I keep a catalog of different people's unifying theories. And so right now I'm calling it the Turok-Boyle theory. That's fine. There's also a minimal extension to the standard model. I was going to put the word minimal there because I heard you use that word. Yeah, yeah, yeah. And I didn't want to confuse it with minimal extension to the standard.

It's minimal supersymmetric extension. Yeah, exactly. So the minimal supersymmetric extension is now ruled out. You know, it's not, it's just wrong. But ours is way more minimal than that. Of course, of course, yeah. The supersymmetric standard model doubled the number of particles. For every particle in the standard model, they added a partner.

So it was the most prolific theory, you know, it just doubled the number of known particles. We are saying don't add any known particles Don't add any particles to what we already know. That's what we're saying We already know the full story. I'll include a lecture here for people to watch and also some of the papers They're on screen right now. It's being edited in and they're in the description and when you say that you don't add any particles There is 36 there are 36 fields, but these 36 fields, they don't have any particles. For some reason you say that there's not, sorry?

Yeah, they don't have any particles. Yeah, so why do you say that? Like what constitutes a particle? Is it that it doesn't have a mass spectrum or that you can't boost it or rotate it or what? Yeah, so there's a difference between a field and a particle. Um, a quantum field is the analog of, let's say electromagnetic fields. You know, these are the way they're initially conceived were initially

conceived as, as a function of space and time, which has some value everywhere in space and time, which has some value everywhere in space and time. Okay, that's a field. Like an electric field has some value at any particular point in space and at any moment of time. What was discovered by Einstein and others is that you can quantize these fields. And so the excitations of a field come in packets or quanta called photons or gluons or weak bosons.

So this idea of quantum field theory is a combination of quantum theory and classical theory of fields. And so traditionally what people have done is describe the quanta and their interactions. Now there is a sort of very fundamental problem lying at the root of coupling particle physics and the standard model to gravity. And the problem is so extreme that it's usually ignored. Okay. This problem was known about for at least 60 years. It's been well known about, probably 70 years,

but it was, it's so extreme that people have grown used to ignoring it. The problem is the following. When you have a field, right, some function that takes values everywhere in space, and you quantize it, so that it's, its excitations come in packets of energy, you find that the field when quantized is actually fluctuating in the vacuum.

So the vacuum is not empty at all. The vacuum is full of these, what are called zero point fluctuations of the field. And so people understood this, you know, going back to the 1940s, 1950s, that every possible excitation of the field is actually sitting there in the vacuum and sort of jangling away. The problem is that if you add up the energy of all these zero point fluctuations, it is infinite. And bosons, like the force carrying particles or the Higgs field, Higgs particle, bosons

contribute positively to the vacuum energy and fermions, like the electrons or neutrinos or quarks, contribute negatively. In each case, whatever field you add, you get an infinite contribution to the vacuum energy. Because there are more fermions than bosons in the standard model, actually you get negative infinity vacuum energy. Now, this is fine if you don't include gravity,

because the total energy in the vacuum, it doesn't matter. It's conserved, and when I do an experiment, I have some vacuum coming in and vacuum going out. So the energy is conserved. So all I see is the extra energy which I added in the difference. So you're not sensitive to the absolute value of the energy until you add gravity. When you add gravity, gravity responds to the total energy. And, uh, that's actually why cosmology was used to find the cosmological constant,

which is the energy in the vacuum. The way we found it is by looking at the total energy in the largest possible volume we can see so that it's as big as possible, and measuring its energy. What we found is that the energy is there and it's changing the expansion of the universe. That's how the vacuum energy has been measured is actually by using its influence on gravity. So, but the trouble is that the vacuum energy we measure or called a cosmological constant is really small, right? It's not zero, it's positive and small, but certainly not infinite.

If it were infinite, cosmology would make no sense at all. You try and write down Einstein's equations, you find the universe would re-collapse in a plank time. It's just ridiculous. So what have people done? There was this terrible problem staring us in the face ever since the 40s, that coupling quantum fields to gravity makes no sense. You're just trying to put an infinity into the Einstein equations, and not surprisingly, you'll get garbage. So what has been done is to invoke a technique called renormalization, which is basically a way to cancel infinities.

Using renormalization, you essentially could find a fancy mathematical way of ignoring this infinity. Unfortunately, this process leaves you with very little understanding of what's actually going on in the vacuum vacuum because you've just subtracted it away. There are other problems. The same renormalization process turns out to spoil the basic symmetries in the standard model. So one of the basic symmetries, say in Maxwell theory of electromagnetism, is scale symmetry. You know, in Maxwell's theory, an x-ray, a short wavelength wave,

is exactly the same as a light wave or a radio wave, which are longer and longer wavelength waves, because the whole theory is invariant under changing scale. And so in a sense, it's nothing really fundamental that distinguishes an X-ray from a light wave, from a radio wave. They're just scaled up and down versions of the same thing. That's a very profound symmetry, and which Maxwell's theory respects.

And turns out Dirac's theory of fermions has the same symmetry and these symmetries are really important for the sort of internal consistency of the theory. Well, Dirac's only if it's free and massless. Exactly, absolutely right. So Maxwell's theory does describe massless radiation. Dirac's theory, you insert a mass for the electron. But when you ask where does that mass come from, it actually is not allowed in the standard model if the full symmetry is realized, if the gauge symmetry is realized. Also doesn't allow mass terms. The way you get mass terms is by adding the Higgs boson,

which breaks the symmetry and introduces the scale. So these masses arise, as far as we understand, by breaking symmetries. So it seems that the way the laws of nature work is they have some underlying, very powerful, very fundamental symmetries, and then physics comes along on top of that and breaks those symmetries so that at low energies, we don't see all those symmetries so that at low energies, we don't see all those symmetries revealed. Now, the reason I'm so interested in the scale symmetry of Maxwell and Dirac for

massless particles is if you want to understand the Big Bang singularity, which I do, what happens there is that the size of the universe went to zero. That makes no sense. Unless all of the fields and particles in the universe actually do not care what the size is. Because if the photons actually do not are insensitive to the size, they don't even know if the universe expanding or contracting. And this is true in Maxwell's theory.

You can predict a photon without knowing anything about the expansion or contraction of the universe. You can predict how a Maxwell wave evolves. It doesn't care about the size of the universe. Likewise Dirac, if it's massless. So in the very early Big Bang, when everything was effectively massless, the natural way to make sense of the singularity, I think it's probably the only way, is if all the material in the universe actually is completely insensitive to the size of the universe. Then you say, well, it looks like space was shrinking to a point, but actually from the

point of view of all the material in the universe, it didn't see that. The universe is perfectly finite and the material in the universe is evolving smoothly all the way to what we call the singularity. So in other words, the singularity is just a result of a poor description being applied to a phenomenon that inherently doesn't care about the size. So a question that may be in the audience's mind is it's relatively straightforward to see the difference between something that's this size and this size and being scale invariant. Okay.

Right. But then that's for something non-zero. So as soon as you get zero, why doesn't it just yield a trivial equation like zero equals zero? So in physics, we are very used to the idea that the coordinates you use to describe something can be singular. So let's imagine I'm trying to describe the surface of a sphere, like make a map of the Earth.

So I can use polar angle, or we call this the polar angle or we call this, yeah, the polar angle sometimes called theta in 3D geometry and azimuthal angle called phi. Now, if I go to the North Pole, right, where theta is zero, the azimuthal angle is zero, the polar angle is zero, then the same point, the North Pole, is described by the azimuthal angle going from zero to two pi. So it's weird that you have many, it's multi-valued.

So basically this whole coordinate system is failing at the North and the South Pole. And we know that very well. When you make a map, if you try to make a map of the North and the South Pole. And we know that very well. When you make a map, if you try to make a map of the North Pole, you know, and you tried to tell somebody, you know, what latitude are you at, it's just ill-defined at the North Pole.

Right. So we're very familiar with the idea that in physics, your choice of coordinates can sometimes be singular. The way around that is to choose some new set of coordinates that are not singular. If I just put a square grid over the North Pole, I would have X and Y, and there would be no problem at all. I could tell you exactly which point had which value,

and for each choice of x and y, there would be one and only one point. Okay, there would be a non-singular coordinate system. So in physics, we're very used to the fact, and Einstein's theory of gravity, this is particularly true, that very frequently what looks singular in one coordinate system is actually completely non-singular in another coordinate system. In the first coordinates, people solved black holes in called Schwarzschild coordinates. When you fall into a black hole, as you cross the event horizon, the metric on space-time is infinite in short

child coordinates. But then much later, people discovered coordinates that are completely well behaved as you cross the event horizon. These are called Kruskal coordinates, for example. And so you realize that what looked singular was just an artifact of a poor choice of mathematical variables. In the case of the whole universe shrinking to a point, you see if your fundamental theory is actually insensitive to the size of the universe, then you are absolutely free

to blow up the size of the universe by any amount you like and it doesn't change any of the physics. So what you do is you design a blowing up so that when I'm shrinking towards zero, I'm actually also blowing up the scale in just such a way that when I hit the Big Bang Singularity, the sizes are all finite. And you can do that.

And actually that was our very first discovery is that if you solve the Einstein equations for a universe full of radiation, which is what we believe dominated the hot big bang, the solution is actually regular at time zero, at the so-called singularity. The Einstein equations do not see any problem at t equals zero. And this was a big surprise. So people had all assumed that this t equals zero, when the whole universe was zero,

that somehow the Einstein equations were singular. They didn't make any sense. Actually, we found you can just follow it right through t equals zero and the solution on the other side is unique. That's actually how we came up with the concept of a mirror. We just followed the generic solution of the Einstein equations back to T equals zero and out the other side. We found there is a generic class of solutions which are

completely well-defined and just evolve through that. Now we found a doubled universe in which before the Big Bang is classically identical to what's before the Big Bang is classically identical to what's after the Big Bang. What we found solving the equations is a mirror universe on the other side of the Big Bang. What we've ended is we elevated this into a principle. We said, okay, maybe the right way to describe the Big Bang

is to use what's called the method of images. All right, so imagine I'm trying to solve Maxwell's equations in the presence of a mirror. There are two ways to do it. One is I evolve these waves forward to the mirror and then at the mirror, I impose some special boundary condition, which forces the parallel electric field to be zero,

for example, and I will find those boundary conditions cause the wave to reflect. That's one way to do it. It's rather ugly. The elegant way to solve Maxwell's equations with a mirror is if I'm right-handed, I make a mirror image of myself which is left-handed and put it behind the mirror. So I literally mirror reflect myself, put my image behind the mirror, and then I just solve Maxwell's equations as if they were no mirror. And that's what I'll see. That's what i'll see so this is called the method of images you make a mirror image and you solve the equations so what we realize is we can do this in cosmology.

We can take the late universe. Make a mirror copy of it before the big bang. make a mirror copy of it before the Big Bang, and then we're able to solve the Einstein equations all the way through the so-called Big Bang singularity, and actually the solutions are completely well-behaved. The mirror image isn't real. The mirror image is just a trick for imposing a certain boundary condition at the Big Bang.

If you talk about this as a mirror universe, it's really legitimate to think about this as a one-sided universe with a mirror at the beginning. But that mirror, the implementation of implementation of what that mirror does is most easily done by reflecting our universe before the Big Bang and then just solving the equations as if there were no mirror. Okay, several questions occur to me. And I'll just say them out loud and then you can choose whichever one you find most interesting.

So number one is that when I hear of a two world model, a two universal, I think about the Janus points by Barbara, by Julian Barber. Okay. So question number one could be, what's the relationship between your model and his? I don't know. That's an easy one to answer. That's an easy one. I would say the first person as far as I know to think of this idea was actually Boltzmann. So Boltzmann was asking, why is there an arrow of time at all?

Why do we have to travel into the future and we can't travel into the past? Why is time different than space? In space we can go backwards and forwards, but in the direction of time we seem to have to go always forwards in space. In space, we can go backwards and forwards, but in the direction of time, we seem to have to go always forwards in time. And why is there an arrow of time? And Boltzmann's tentative answer was to say that the big, he didn't even know about the Big Bang. I mean, he was way ahead of his time, but he drew a parallel with a room full of air. And he said, imagine that you follow all the molecules in the room for a while, a very long while,

very, very occasionally, just by chance, all of the molecules will fly into one corner. Right? They'll all end up in some very small neighborhood of the corner. And then what will happen is they all come out again. Now, if I look at the air, just as it's approaching the corner, everything is approaching a corner, that would look like something going backwards in time, because that's a very unlikely fluctuation,

that everything goes into a corner, followed by a very likely evolution. If I put all the molecules into a corner, they're all going to come out, that would be the most likely. Basically basically he was saying that the natural arrow of time somebody would conclude if they observed such a thing is that time is going backwards when everything is sort of assembling into this corner, but time is going forwards when everything comes out of the corner. So Boltzmann tried to sort to assume that the universe we see began in a very rare event.

That very rare event was created by things going backwards in time to create it. I think that's a very beautiful idea. It relates very strongly to what we're proposing. I'm wondering if I can describe this. So ask yourself the following, let's prescribe a given, I don't know if it's possible to picture this, but a three-dimensional

geometry, all right? So let's just picture it at some surface. This is the universe at some moment of time. It's some three-dimensional surface, right? And so what I'm saying is we take that surface and we reflect it through the Big Bang. So now I've got an identical surface on the other side. Now I try to join these two surfaces by an evolution, some kind of evolution between them.

So it turns out that if you identify these surfaces without performing any symmetry operation in particle physics. You see, so in particle physics, we have something called CPT, which is a very profound symmetry of all the laws of nature. It says C takes particles to antiparticles, P invert space, so X goes to minus X,

and T reverses time. Under CPT, all the laws of particle physics are invariant. Now, CPT can either do nothing, if you don't do anything, C and P and T are all one, then this set of particles and forces would just go to the identical mirror image. You can ask, what does such a universe look like? What interpolating geometry is there

between those two surfaces? And the answer is very dramatic. It's that the two coincide, you see? They're identical, and you can just put one on top of the other. You don't get an interesting universe at all. That's a universe which you're just viewing at the same moment of time. It's really simultaneous. On the other hand, if If you do a CPT which is not trivial, in which P and T in particular are minus 1, you invert space. So basically this surface is not identical to that one.

Then it turns out you're forced to go through a singularity, just if you're going to interpret, interpolate between them. And so in our picture, there is a topological reason why there has to be a Big Bang singularity. And so this is like- Interesting. Yeah, there's a constraint in the Boltzmann picture.

There's a constraint which kind of forces you to go through an evolution in which the molecules of air in the room actually went into the corner and came back. And so in our picture, we claim we have a topological explanation for why there had to have been a Big Bang singularity. But as I say, it is much less singular than people have thought because the Einstein equations are obeyed all the way through. So what do you call this non-singularity?

Do you call it a smoothness or what do you call it? Different people call it, I refer to it by analyticity. Okay. Are you of the mind that all singularities are analytic or is it just black hole singularities? No, no, no, it's absolutely fascinating. So great question. What distinguishes the Big Bang singularity from the one inside black holes is that at least if the Big Bang was dominated by radiation, the fields which have the special local symmetry, if that is what dominates the Big Bang as observations seem to indicate, then the Big Bang singularity was analytic. It was smooth. When you say something is an analytic function, you can extrapolate it, you see.

So if you have, say, a linear function hitting zero, you know, just y equals x, and you tell me y is an analytic function of x, well, it's no problem to extrapolate it. You know, y is x, and that applies when x is negative as well. Analytic functions have this property of being able to be extrapolated in a completely unique way.

That's what we discovered that the solution of Einstein's equations describing a radiation-dominated big bang, are analytic at t equals zero, and they have a unique extension to this pre-bang era. If you look at black holes, that is not true. So the singularity inside a black hole is totally different. It's what's called, it's very anisotropic. As you head towards a singularity inside a black hole, you get squished in one direction and stretched in the other two.

It's very anisotropic, and this actually means it's not analytic and you cannot forecast what comes out the other side. It's just impossible to forecast. Now in very recent work, which is not yet published, we have been trying to extend our notion of analytic solutions of the Einstein equations to black holes. And you can ask yourself, if a usual description

of a black hole is not an analytic solution of the Einstein equations, is there one which is? Is there some other description of black hole which does describe it as an analytic solution of the Einstein equations? And the answer is, I think this is still tentative. I think there is. And what happens is that as you head towards the event horizon, there's some matching process that basically when I fall into the event horizon,

I would come out of another event horizon, and it would never actually fall into the black hole. This is what we're studying now. So it means there's some other prescription for solving the Einstein equations, which does not mean that when you fall into a black hole, you fall in and hit the singularity. Because I believe that these singularities, you see the thing about this type of singularity, which is non-analytic,

it does not solve the Einstein equations. The equations fail there. So you cannot claim this as a solution. And if there's sort of any justice in the world, which I think there will be, this principle, the principle that the Big Bang singularity is analytic, that is telling us that we need to concentrate on solutions of the Einstein equations which are analytic. Okay, okay, wonderful, because my next question was going to be, if the universe is analytic at say the zero point of the Big Bang and analyticity implies that there's an analytic solution which can be extended from the origin arbitrarily, then why would it be that a black

hole isn't analytic given that it's presumably at some other space-time point? Yeah, so let me put this in another sort of framework. Our picture is that you take a big universe and its mirror image, and you ask yourself, is there any solution of the Einstein equations which joins the two? And I will only call it a solution if it's analytic, because then it really solves the equation.

If it's non-analytic, then it's ambiguous. It's inherently ambiguous. And why this is so important, it actually relates to path integrals and saddle point theory. You know, the classical solutions of the Einstein equations are called subtle points of the path integral for gravity. It means that basically they are a history in which the destructive interference is cancelling out. So classical physics arises through destructive interference from quantum physics. In quantum physics, you sort of add up all possible histories,

but they all come with different phases, and typically they all cancel out. If they, if all the phases, if there is, so destructive interference cancels out the contributions of all histories except classical ones. Classical ones are defined to be histories where there is no destructive interference. That all goes away. And basically something is only a legitimate saddle point if it is analytic. Okay. So we're claiming the Big Bang singularity is a legitimate saddle

point. In other words, it's not really singular. It's because it's analytic. When I go to a black hole, and if I believe that black holes form and then evaporate, which we believe based on Hawking's calculations of black hole evaporation, it must be that there is some analytic history solution of the Einstein equations, which interpolates between the stuff falling in to make the black hole and the stuff coming out as Hawking radiation when the black hole is gone away. Um, so there must be an analytic solution. No one has ever found this solution, but with our ideas of CPT symmetry, we now have some hints as to what that kind of solution might look like.

And if we do succeed in finding it, the physical interpretation of a black hole may be very different than the classical one based on the singular solution. The classical one says you just fall into the black hole and you're scrunched to zero and then that's the end of time, you know. So that's the conventional description of what happens in a black hole. If what we're saying is right, I suspect, and I don't have the maths for this yet, but I suspect that as you approach the event horizon of the black hole, everything becomes much more quantum. You'll go through some realm in which things are very quantum, and then you'll come out

in a region of space-time in which everything is sort of classical again. What do you mean you'll go through some realm? Well, okay. So the simple analog is quantum tunneling. So in quantum tunneling, so imagine I've got a particle in a potential, and the potential has a minimum followed by a barrier. And so imagine a potential which kind of comes down to a minimum goes up to a maximum and then goes down to. Arbitrary negative values so I put a particle in this potential well. And if it's got some energy it can rattle around in the well but it can't get out classically it can't get out. Classically, it can't get out. Quantum mechanically, it tunnels. Quantum mechanically, it can travel under the barrier and come out

the other side. And that's how atomic nuclei decay, right? The nucleons, the protons and neutrons are all stuck in a potential well, but occasionally one of them tunnels out. An alpha particle tunnels out of a radioactive nucleus like uranium and just flies off to infinity. So in quantum tunneling, what happens is that you do not solve the real equations of motion. I'm using real in this sense of complex analysis. If you put a particle in

a potential well with a certain energy and just leave it in there, it will stay there forever classically. Quantum mechanically doesn't stay there forever, it tunnels out. The way it tunnels out is because it follows a complex solution of the same equations, which so for example, under the barrier, the wave function is falling exponentially. And that's described by saying that the momentum is imaginary. The particle has imaginary moment, so e to the ipx is actually e to the minus kappa x, where kappa is real. That only happens because p is i times kappa. So quantum

tunneling is mediated by complex classical solutions. And so if the right description of a black hole is that it has these two sort of very classical regions in the far past, far future, but in the middle you have this much more sort of quantum object, it's quite plausible that that is described by a complex space time, whatever that means. Nobody has ever found this. It's a very hard calculation to do, but I think my guess is it will exist. My guess is there will exist an accurate description of the formation and evaporation of black holes, but it's one where the real classical solution of stuff falling in and then hitting a singularity, that's, in my view, that will be irrelevant. That's not a real black hole

because it doesn't solve the Einstein equation. It's not the saddle point of any path integral. It doesn't make sense quantum mechanically. I mean, quantum mechanically makes no sense for time to end. Principle in quantum mechanics is that evolution is unitary. You just see everything evolves with a phase, but everything, if you hit a singularity, time stops. That doesn't make any sense. So now if this picture is true, it of course will be very exciting because it'll mean that

there are, there should be real predictions for the behavior of black holes on scales of their event horizon. And we're now seeing these, right, with telescopes for the first time, we can actually see the event horizon. So, yeah, I think we have to come up with a consistent picture of what's going on in black holes. And if we do, it will make definite predictions. Hopefully that can be tested. But as you can tell, the whole program we're pursuing is kind of extremely minimal and ambitious.

We're taking only the laws that we know and the particles we're confident exist, and we're trying to describe everything we see using those laws. You see, to put it differently, why would you ever do anything else? I mean, minimalism is a very profound principle in science. And in decorating. And in everything. Occam's razor. You know, if you have a choice between a simple explanation or a complicated one,

go for the simple one. It's much more useful. As you make descriptions more and more complex, they become less and less predictive, and more and more arbitrary. This is exactly what's happened with string theory, supersymmetry, grand unified theories. They become more and more complicated.

So I'm taking the extreme opposite position. I'm saying just forget about all those frameworks. They never predicted anything anyway. Let's work with what we know and see what is the minimal resolution of these things. So you mentioned the 36. Yes, it doesn't seem minimal to most people. So explain why it is. It's a very amazing clue that we stumbled upon. So we started from the point of view that there's this awful contradiction staring us in the face, which is that quantum fields have infinite vacuum energy,

and Einstein gravity sees that energy. So what do you do about it? As I mentioned, there are more fermions than bosons in the standard model, so it's actually minus infinity. The standard model has infinite negative energy density. So how am I going to cure this? Well, the simple solution would be just to add the right number of bosons to bring it back to zero.

Okay. And it turns out that that number is actually 72, which is a multiple of 36. But that's not what got us excited. We also asked the question about this spoiling of local scale symmetry by renormalization. So this beautiful symmetry of Maxwell's theory and Dirac's theory, which potentially allow you to describe the Big Bang singularity, this beautiful symmetry which was there, got

spoiled by renormalization. So that is known in the jargon as trace anomalies, or sometimes called Weyl anomalies, after Hermann Weyl, W-E-Y-L. So there are these anomalies, which tell you that the symmetries which you had in the original theory are spoiled by these infinities in the vacuum. So we said, how can we fix, so it turns out there are two of these anomalies,

which spoil the symmetries and there's the vacuum energy. So basically there's three quantities and we wanted to set all three quantities zero. What is the minimal thing you could do to the standard model to cancel all these problems, all three problems, all three problems. We discovered that if you added 36 of a very particular kind of field, they all went away, they all cancel. So it's numerology. Now, what kind of field?

So this is a strange kind of field, which actually was originally postulated by Heisenberg, Werner Heisenberg in the 50s, as a model for the strong interactions in atomic nuclei. And so people have been playing with this type of field. It's a rather bizarre kind of field in that although it is a field, it has a value at every point in space, there's a huge degree of symmetry in this theory. So much symmetry that actually you're not allowed to have particles at all.

It's literally a theory. Explain. Right. Explain. Right. So there's certain basic principles you insist upon when building a quantum field theory. One is relativity, that the whole theory must be invariant under relativity.

Two, the theory must be consistent with quantum mechanics and quantum mechanics requires that you have a sensible definition of probabilities. Basically, in shorting a picture of quantum mechanics, you take the wave function, you square it, and that gives you the probability of finding any particle at that particular position. So you need a positive, a notion of what's called a positive metric on Hilbert space. The Hilbert space is the space on which quantum operators act. So when you quantize this funny theory, it's a funny theory in many ways. The field here is what we call the dimension zero field.

It's dimensionless, meaning it's more like an angle. You know, it's not a usual field, quantum field like the Higgs field or the Maxwell vector potential field, these have dimensions, they carry mass dimensions. This kind of field has no dimension. It's a dimensionless field like an angle. It doesn't have any mass dimension. Also an indication of very high degree of symmetry. You can change the definition of scale

and this field doesn't change at all. So the action for this, whereas for a Higgs field, the action is gradient of the field squared, integrated over space-time. The action of this field is what we call box of the field squared. So box is the Hempholz operator, it's a wave operator, the massless wave operator.

So you take the massless wave operator on the field, square it, integrate it over spacetime, that's the action. So there are actually four derivatives in this theory, not two. So you know, ever since Newton, we've liked equations of motion with only two derivatives, like f equals ma, you know, what is a acceleration is d two x dt squared. So most physical laws are formulated only with two derivatives. This theory has four, four derivatives. Now, one of the reasons that in QFT or when you have Lagrangians, you have at most two derivatives is because otherwise you have problems with

instabilities, Ostrogladsky instabilities, causality and renormalizability. Right. So people focus on theories with two derivatives for good reasons. So people focus on theories with two derivatives for good reasons. Ostrow-Gradsky in I think 1820 or 30 showed that any theory of classical mechanics with more than two derivatives has an energy which is unbounded below. And so that already suggests that such a system would be unstable. If I couple this theory with more than two derivatives with some other standard theory which has positive energy, I could feed energy from this system with unbounded below energy

into the positive energy system forever and create a perpetual motion machine or whatever. So Ostrowski argued you should never use more than two derivatives. So these are called runaway solutions or instabilities and so on. Now, this theory, the one with four derivatives, turns out that when you quantize it in quantum field theory, actually the states of the quantized theory are all positive energy. Okay, so there is no negative energy state. So that sounds okay.

Just saying that the problem Ostrich-Gransky was worrying about doesn't exist. There are only positive energy states. However, some of those states have negative norms or negative probabilities. If you take the inner product, it's not positive and can't be interpreted as a probability. So what you then say is, well,

I'm not interested in wave functions which have negative norms. I don't want them in the theory. It wouldn't be a sensible quantum theory. Okay. So what you have to do, now we're actually used to this engaged theory. Engaged theory, when you quantize them, what's called covariantly, you also get negative norm states.

And we're very used in that case to simply working on a subspace of states, which is positive. And we have to show that all the interactions leave you on that positive subspace. And so what we've shown is with these four derivative theories, the same is true. That you can pick a subspace, you have to pick a subspace, and on that subspace, all inner products are positive. The only problem is that that subspace only includes the vacuum Okay, that sounds like a huge problem No, I mean depends what you want to do with it. If you wanted to describe particles you would say it's a terrible problem

I can't describe particles because they all come along with these negative probabilities But if what I want to do is to describe the energy of the vacuum I'm completely happy. I say, okay, I throw in these dimension zero fields, they contribute to the energy of the vacuum, but they don't allow any particles. And what we found is if you add 36 of them, they fix the vacuum of the standard model, but you

do not have any extra particles. In fact, they do more than this because they give you a possible way of building the Higgs field out of these dimensions error fields. And that's very tantalizing, because that might end up solving the hierarchy problem. Oh, wow. Okay. So let's keep an accounting right now of all the problems that this solves.

So one is the vacuum catastrophe. Another is the hierarchy problem. Another is three generations of matter, which we haven't gotten to, but we will. Yes, we will. Another is the singularity problem of a big bang. Right. And the density perturbations on large scales. So we see the density.

And dark matter. And dark matter. So what we claim. And dark energy. Yeah. So what we claim is that everything can be fit into this framework. And the same. So what's left? The same. Well, this is possibly a unified theory of

everything without any new particles or forces. Okay, so that's why we're excited. It's a very radical alternative approach. In some ways it's not so radical, in some ways it's much less radical. Correct. That's exactly, that's how we feel about it. Because of the culture of physics today, it's now radical to be not radical. Exactly. You said it perfectly. So we're very surprised by this, but you know, there's a huge sociological issue, which is that people have been playing with supersymmetry and string theory and extra dimensions for decades, right? And inflation for decades.

And so there are multiple models. 99% of people in the field are publishing papers in these frameworks. As I say, there has not been a single, what drives me is there's not been a single precise observational prediction to be confirmed, which has been confirmed in any of these cases. That's what led me to profoundly doubt this methodology.

I said, okay, I'm going to adopt the opposite methodology. I'm just going to refuse to add anything extra and ask, what is the least I can add to the standard model, the very, very least which will allow me to address the primordial fluctuations, the vacuum energy, the number of generations. We stumbled on these 36 crazy fields which seem to cancel out the problems.

Now, I should say when we first introduced them, we just did, it was just a numerology. With 36 of these weird fields, we could cancel a vacuum energy and fix these symmetries. I should emphasize only it's very lowest order approximation in the calculation. It remains to be seen when you do it in more detail. That's challenging and we have to do it.

But it's a first hint. I can't claim it's done and dusted, far from it. It's a first hint. But with those very same fields, we then calculated what density perturbations should we see in the sky come out of the Big Bang. You know, what perturbations came out of the Big Bang, and that matches what we see numerically. So those same fields, these weird dimension zero fields explain why the fluctuations in the early universe were scale invariant, and they also explain quantitatively this small tilt.

So, we got much more than we bargained for. We never expected those numbers to come out. Again, I have to say we've made assumptions along the way. Always, we have always made what seemed to us the simplest assumptions, and those simplest assumptions led to the right numbers. Now we have to justify those assumptions and so on and so forth. But we are in the situation, I think, where we have a framework on our hands, which might just explain everything.

Now, let me ask you a sociological question. Do you think that theoretical physicists today, the majority of them, actually care about the nature of the universe, or do you feel like they more care that they uncover the theory? In other words, do they disagree with your theory or doesn't even get to that point because they're unwilling to listen, even though you say, look, I have the answers to the questions that you're searching for. It's a mixture. A large number of referees, for example, of our papers, clearly haven't read them. They look at the

paper, and this goes for grant applications too. I submitted a big grant application based on all this. The feedback I got was very disappointing because people were basically saying, where's the inflation? Where's the, you know, where's the stuff I'm used to? It doesn't seem to be there. Or they were just saying, you know, for derivative theory, clearly nonsense, and they weren't willing to engage. So that has been, I think most of the response

has been a bit like that, not really taking it seriously yet. I can't entirely blame them because what we've done is preliminary. We've made various assumptions and simplifying assumptions, it's very much a first step. Yeah, they can sit back and just wait. That's perfectly reasonable. I would say it's quite disappointing that string theorists who are using many of similar criteria to what we use are just so much embedded within 11 dimensions

or 10 dimensions that they won't engage with realistic cosmology. Most of them weren't, a few exceptions will. The very best string theorists in fact do engage. So for example, I was at a workshop recently with Ashok Sen who's a very, very original string theorist and has kind of had great insights from string theory, but is not at all sort of, you know, close-minded. And so he would certainly jump if he saw a framework

that was just as powerful as string theory, but involved much fewer assumptions. And he engaged very much and he was very interested and so on. So I've had, you know, we've had some positive responses, usually from the best people. There's a large number of people who more or less follow the fashion, and they have not engaged yet,

though I am getting lots of invitations to get talks. So I think it just behoves us to give lots of talks, explain, not to go away, and answer as many questions as we can answer. On the whole, I'm optimistic that eventually people will, you know, if this framework is right, people will definitely start to see it. One specific observation, you know, the most convincing thing in the end is an observational signature. If we have a signature which no one else has and it's seen, then I think people will start migrating to our theory.

There is one, which is very interesting. It's to do with neutrinos. There's pretty good evidence that right-handed neutrinos do exist. In the minimal standard model, and that's no supersymmetry, just as usually taught in quantum field theory courses, the minimal standard model has only left-handed neutrinos. But every other particle, electrons,

quarks have both left and right-handed. So all the fermions come in left and right-handed versions, but neutrinos don't in the minimal standard model. However, we know the minimal standard model is wrong because when we observe the light neutrinos, they have small masses. And so these mass differences have been measured in the light neutrinos. And the simplest explanation for those neutrino masses are that actually there are right-handed neutrinos which are very heavy. And so when a left-handed neutrino is traveling along, it can oscillate into a right-handed neutrino, a virtual right-handed neutrino, for a short interval of time. And then that right-handed guy decays back into a left-handed neutrino. So this neutrino mixing is called the seesaw mechanism

because the heavier you make the right-handed guy the smaller the effective mass of the left-handed guy. Yes. So this seesaw model was known since the 70s, it's very beautiful. If you say the right-handed ones are pretty heavy, bigger than about 10 to the 10 GEV, 10 billion GEV, so impossible to make in a particle accelerator, that's enough to explain the light neutrino masses. And indeed, in our framework with these 36 dimensions error fields,

we find we are forced to have three generations of particles exactly as we see in order for the vacuum energy and the anomalies in scale invariance to be true for to cancel. We have to also have three generations of particles just like we see and each generation must have a right-handed neutrino. Okay so we have three generations of particles each one has a right-handed neutrino that automatically gives the left-handed neutrinos a small mass. Now you can say what's the dark matter? How does the dark matter fit into this picture? And it turns out that one of these three right-handed neutrinos is the perfect dark matter candidate because

right-handed neutrinos are not allowed to couple to the force-carrying particles, the strong, weak, or electromagnetic forces. Right-handed neutrinos are completely neutral. And so one of them could easily be the dark matter. So in fact, this is the way we originally came to this whole idea, is we realized, hey, wait a minute, there's an obvious candidate for the dark matter. It's a right-handed neutrino. And then we asked, how do you predict the abundance of a particle which doesn't couple to any other particle in the standard model? Because you see, if a right-handed neutrino is the dark matter,

it must be stable, which means it cannot decay into other particles, which means that actually it couples to nothing in the standard model. It only couples to gravity. How do you predict its abundance? We found by considering this two-sided universe with the CPT symmetric boundary condition, we could then calculate the abundance of right-handed neutrinos, and we found that the number came out about right,

that we could get the right dark matter density from right-handed neutrinos by actually calculating how many of them are produced simply due to the expansion of the universe in this double-spectre. So that's sort of, now, if one of them is stable, right, it's easily the simplest candidate for the dark matter. I don't think anybody questions that.

And I would say therefore it's the first thing to go after. If it's stable, how do you go after it if it doesn't couple to any other particle in the standard model? Well, you go after it if it doesn't couple to any other particle in the standard model? Well, you go after it indirectly because you say the left-handed neutrinos are not allowed to couple to it either because if they did couple, then it would decay into them. So you've got to switch off that coupling of left-handed neutrino into right-handed neutrino for this one right-handed neutrino that's the dark matter. You must switch off that coupling.

That means that one of the left-handed neutrinos is exactly massless. So the signature of this dark matter candidate is that the lightest neutrino must be massless. And then the amazing thing is that in the next three to five years, we're going to have very precise measurements of the lightest neutrino mass. And that's coming from cosmology. So in fact, just last week there was a new galaxy survey, the results of a galaxy survey called DESI. Yes, yes.

The neutrino masses went up, or the sum of them. No, it was, they're setting a bound, okay? So basically, we know from other experiments, two mass differences between, say, the heaviest, the middle, and the lightest. So these two numbers are known. We don't know the absolute scale of the masses. So if the lightest one is mass less, then the sum of the masses is the smallest

it could possibly be to be consistent with these mass differences. So what they found, they're trying to set limits So, what they found, they're trying to set limits on the sum of the neutrino masses. So what they've succeeded in doing is setting a lower limit that the sum of the neutrino masses has to be at least as big as these two differences. Okay, roughly speaking, that's what you find. It means it's just consistent with what we already know from particle physics experiment from neutrino oscillation measurements. The sum of them has to be bigger than some number, and it

also has to be smaller than some number. But their current limit from this survey is not that constraining. I mean, it would allow the lightest neutrino mass to be, you know, well, significantly different from zero. However, in three to five years, the new measurements from Euclid will set the constraints on the sum of the neutrino masses to be so strong that you will force the lightest guy to be very close to massless. And that'll be something like a five sigma measurement, if it works, a five sigma measurement where you say that the allowed mass of the lightest neutrino has to be five times smaller than

the error bar in this experiment. Or you will constrain it to be within zero or close to zero at five sigma. It'll be a very strong bound on the mass of the lightest neutrino. So if that works out and if the lightest neutrino is consistent with mass less, then I think it makes this right-handed neutrino explanation of the dark matter easily the most economical, minimal, and plausible.

There are other ways to check it through measurements of what's called neutrino-less double beta decay. And basically you constrain the couplings of these right-handed neutrinos by laboratory experiments involving very large amounts of radioactive matter. Those experiments are being done now, but they will take about 10 or 20 years. We predict a rate of neutrino-less double beta decay. It's a very tiny rate and so it will take a long time for the experiments to actually detect it. So in your model, neutrinos are Majorana particles?

Yes, yes, that's right. I mean, that is the minimal setup. We have three generations of particles and the neutrinosome iron particles. Okay. Now going back to this dual universe, I know you said it's a mathematical trick, but the difference between a mathematical trick and physical reality is not always that easy to discern. So Minkowski thought that the metric was a reflection of actual reality and Einstein took it to be more serious and Dirac thought anti-particles maybe were just some mathematical

artifact. He didn't know what they meant. Absolutely. Absolutely true. So what conditions do you use to a priori say something's a mathematical trick versus maybe it's reflective of some underlying reality. I would say it more weakly than that. I would say, you know, this is a prescription. It's a mathematical prescription,

which makes it predictive. If the mathematical prescription you use to describe the Big Bang singularity, you know, is elegant, minimal, economical, consistent with all the other laws of physics that we know, then it makes it a good prescription. Now, what does it mean to say is it physically real? Is there a universe before the Big Bang?

Well, I would just take the example of, is there another person behind the mirror? No. The minimal picture of reality, it's only one person and at the middle. It's a good example. So I have become philosophically an extreme minimalist. And so I would apply that to everything.

So that's why I would say, what I liked about Hawking's picture, which he called the no boundary proposal is that it, the laws of physics described the beginning of the universe, you know, it wasn't that you, he was trying to get away from the idea that there was freedom in how the universe began. One picture is that a divine being came along and prescribed, this is how the universe started. And unfortunately, if that was true, then physicists wouldn't have much choice, wouldn't be able to describe that because presumably this is all in the mind of some

divine being and there may have been an arbitrary amount of choice involved and we could never figure that out. But if there was no choice in how you started the universe, if somehow the laws of physics themselves govern the beginning of time, that's a much more economical picture where the laws that describe the evolution of the universe also describe its beginning. That's what I really liked about Stephen's picture. He was trying to get a prediction about the beginning out of

the laws according to which the universe evolves. And so that you're tying together initial conditions with evolution. And so that's very appealing. Now the case, and this is the analogy he always drew, you see a situation where we don't need to describe initial conditions is thermal equilibrium. If I put gas in a room,

we know that it's pointless trying to prescribe initial conditions. I mean, there's so many molecules and so many initial conditions, then it just becomes ridiculous to write down equations for whatever 10 to the 30 or 10 to the 35 molecules. It's stupid. However, we have a really good description in terms of statistical mechanics. We just say the macroscopic variables like the energy, the total number of particles,

the total angular momentum of the particles, momentum of the gas in the room, the macroscopic variables are all prescribed, and then everything else we predict probabilistically. And that works extremely well. So in the same way, Stephen Hawking, I think, believed, I knew him very well, he wanted the cosmos to be a sort of maximum likelihood universe, where you put in certain macroscopic constraints,

like you might say, well, we don't really know what constraints to use, but plausible ones would be for a given value of the cosmological constant, for a given value of the curvature of space, quantities which are conserved in the evolution which do not change, what's the most likely universe? That's the most likely universe? That's the question he wanted to ask. And if you prescribe a boundary condition,

such as our mirror universe or Hawking's no boundary prescription, both of which are very elegant, you would take the same laws of physics and make different predictions. And hopefully one of them turns out to be correct. So that's the hope. And yeah, at the moment, it seems very plausible to me that is the way it's gonna work.

We're literally going to figure out what is the right way, well, why there was a Big Bang, what is the right way, well, why there was a big bang, what is the right way to describe it, and given the laws of physics we know, what's the most probable universe consistent with that picture of the big bang? And so, yeah, these are the lines I'm thinking along. There are many, many spin-offs to this.

If this works, it will explain the arrow of time. But will it explain it more than entropically or how does it explain it? Well, yeah, the basic point is that the boundary condition at the Big Bang, this mirror boundary, is different than the boundary condition at the Big Bang, this mirror boundary, is different than the boundary condition at future infinity. So we're going into this cosmological constant epoch.

Universe will expand forever and become more and more vacuous. And there's a sort of mathematical notion of a spatial, space-like boundary and future infinity. And that's a boundary which is different than the Big Bang boundary. And the arrow of time is simply that these two boundaries are different. And so if I look in the extended picture, basically I would prescribe the future boundary,

which is this cosmological constant dominated universe boundary. I take the mirror image of it, I put in my CPT twist, and I'm forced to have a big bang singularity in the middle. And then I would say that the universe is completely symmetrical under turning the whole thing upside down, like an hourglass, there's no difference because the same boundary condition. But if I start in the middle,

it looks very different. The time going forward would appear to be this way here and this way there. I explained the local arrow of time in one half of the universe. Yeah, so that sounds plausible. I mean, be much more, I mean, there's actually another point I wanted to make, a sort of final point about, because what really matters to me

are observational predictions. I think a theory is useless if it makes no predictions. And so thinking about the Big Bang, you know, I claim we hope we may have a completely consistent description of the Big Bang singularity using only the known laws of physics. Now, if that is true, what's the prediction? And actually actually there's a very beautiful one, which is that at the Big Bang, the temperature was extremely high, gets up to what's called a Planck temperature. So 10 to the 19 GeV, really huge temperature at the Big Bang singularity itself. At that point, the gravitational degrees of freedom, gravity waves, are all excited.

So very naively, they would be in thermal equilibrium with the photons. Everything would be highly excited and thermal. And so if we now follow the universe forwards from the Big Bang to today, the photons have all stretched and become microwave photons which we detect with our microwave detectors like the map or Planck satellites, the gravitational waves would have stretched too, and they would be roughly millimeter wave, gravitational waves today. If you built a sufficiently sensitive gravitational wave detector,

and small enough that it could detect millimeter waves, you would literally be able to examine the Big Bang singularity itself. Because they are just emitted from the singularity by watching them. The early universe is transparent to them, and you would just be looking back to the hot phase when they were generated.

What it means is that we can in principle build a telescope, gravitational wave telescope, which will be able to look straight at the Big Bang singularity and check if our boundary condition is valid. Okay, this is a totally scientific question. Now the practical matter is that it's about a billion, you would need a gravitational wave detector about a billion times more sensitive than the best one we have today.

You would also have to make it millimeter sized instead of kilometer sized. But people are now working on that. They're real prospects for doing this. People have prototype millimeter wave, gravitational wave detectors, which work. They're not sensitive enough yet, but I think they will be. There's no roadblock.

I think this whole field of kind of speculating about the beginning of the universe, the boundary conditions, you know, what we would see if we were able to make observations has real mileage. I mean, this is a field that can ultimately be decided one way or the other, and that makes it really exciting. be decided one way or the other, and that makes it really exciting.

I do feel that much of our field has sort of wandered off piste. So string theory has become more like a branch of mathematics. It's very fruitful in mathematics. People are able to use string theory ideas to prove all sorts of, or it's stimulated all sorts of advances in pure mathematics. And I think that's, so, which is fine.

I mean, if that's its future, that's fine. But I'm obviously much more excited about describing the real world. And I strongly suspect that the correct description is going to be much simpler and much more elegant than string theory. What motivates you? Craziness. What motivates me is that I think life is a miracle, to be alive is a miracle and we

only live once. And so you better make the most of it. And so when you stumble across an opportunity to understand something, you know, nobody's ever understood before, um, you have to jump at it. Um, so that's what I've been doing all my life. Even though most of what I've done has been wrong, and I now believe has been wrong. I mean, I was part of the same family of people studying supersymmetry, grand unified theory, string theory.

My PhD advisor was the inventor of super string theory, David Olive. But right, right. A legend. Gliazzi, Olive and Schurck, yeah, was the first paper on superstrings. And so he kind of brainwashed me that string theory was it, but it took me a long while to sort of get some, become skeptical about that. But I don't regret, even the time I spent on wrong theories brought me into contact with similarly crazy people like Stephen Hawking and many, many others. And yeah, that interaction, I wouldn't trade for anything. Steven, I believe in particular, was just an amazing human being.

So much courage in one person is hard to conceive. Then I'm now pursuing ideas which I think Incorporated some of his insights but are much more ambitious than his Because he he wanted to latch on to inflation and kind of make that work Whereas I think Something even simpler is going to is going to work So yeah, it's it's an amazing going to work. So yeah, it's an amazing opportunity to work on this stuff.

Maybe it'll all come to naught. Could be proved wrong in an experiment. Could be we hit some mathematical roadblock and it's just clear. You know, we have these negative probabilities and we can't get rid of them. And, uh, there may be some intrinsic, uh, problem that, that kills the whole framework. There is something called GPTs. So not chat GPT, but generalized probability theory, which allows for negative probabilities. Absolutely.

Absolutely. So indeed that may also be, uh, a resolution, uh, in resolution in some areas of physics. Yeah, I think one of Wigner's formulations of quantum mechanics was a GPT. Exactly. That's absolutely true. Yes. He gave a general formulation of what's called a phase-based density, Louisville phase-based density in classical mechanics.

Wigner described the quantum version of that, and it works beautifully except that it has negative probabilities. But what you do is you just realize that when it gives a negative probability, you are using it in a region you shouldn't have been using it in. So yes, there can be situations like that, where negative probabilities kind of exist in the framework, but you just don't ask questions, which would lead to ridiculous answers. So maybe something like that. Now before we get going, while we're on the topic, I want to get your quick opinion on

the wave function of the universe and the measurement problem. Okay, good. The wave function of the universe. Yeah, I think it's, yeah. The original inventor was Bryce DeWitt. It's called the Wheeler-DeWitt equation. Bryce DeWitt, who was incredibly insightful and powerful theorist dealing with quantum gravity, one of the most sort of significant ever, he completely disowned the Wheeler-DeWitt equation. He said this is a meaningless equation.

Why? You see, the wave function of the universe satisfies the Wheeler-De a meaningless equation. Why? You see the wave function of the universe satisfies the Wheeler-Diwitt equation. What is the Wheeler-Diwitt equation? It is an infinite dimensional partial differential equation. Meaning, it has an infinite number of boundary conditions. The initial data for the wave function of the universe is so infinite dimensional, it's inconceivable. It doesn't really solve anything.

It's extremely arbitrary. Hawking implemented it within this no boundary framework, which was nice because it resolved these ambiguities. However, the answers it gave were completely wrong. It predicts an empty universe. His no boundary proposal predicts an empty universe. So yeah, I think the wave function of the universe, you've got to approach with extreme care. It's a very ill-defined and slippery notion.

It may be useful in some contexts, but you have to be very careful with it. I much prefer, and this is what DeWitt said, I much prefer the path integral formulation. Because the path integral, you're literally summing over geometries. You have some geometrical picture which guides your theory. So I think Bryce DeWitt said, basically, get away from the Schrodinger equation as applied

to cosmology. It's just too ill-defined to really make sense of. And his intuition was that the path integral, although that too is not very well defined, somehow you were using the right intuition to build on, which is summing over geometries. Yeah, so the first question was the wave function of the universe. Second was measurement problem. Oh, the measurement problem. We don't yet have anything to say about that.

I think it is definitely related to the arrow of time. The notion of a measurement. Why do you say that? Well, the whole notion of a measurement. Why do you say that? Well, the whole notion of a measurement is time asymmetric, right? Before the measurement, you don't know what state the system is, after it, you do. So there's a before and an after.

And so I suspect that if we solve the cosmological arrow of time, why the universe is going one way, which we may now see how to do, then it may also be clear why measurements only go one way in time, that you measure and then the wave function collapses. This maybe comes out of the formalism naturally. So I think solving the cosmological arrow of time is actually key to all of

these foundational questions of, um, how quantum mechanics makes sense. Professor, thank you for spending so long with me for people who just scrubbed all the way till the end for some reason. Professor Neil Turok is a legend in the field. You can even check the description to see all the awards that he's won. And you were also the director of the perimeter Institute at one point. Yes, just a legendary physicist and I'm lucky to have spoken to you for so long. Thank you. Well, thank you for taking the time. I really appreciate your interest

and that of your viewers. It's a great pleasure not just to work on this stuff, but to share it with others. Hopefully, my greatest hope is that one of the people who listens to my lectures or other lectures will go on and actually make the unified theory we're all looking for. If my only role is to encourage others, that's still a fantastic role to play. And I think all of us, all of us, all of us in the field really feel that way.

I'll leave your lectures in the description. All right. Enjoy the eclipse. Thank you. Thank you. Cheers. Firstly, thank you for watching. Thank you for listening. There's now a website, curtjymungle.org, and that has a mailing list. The reason being that large platforms like YouTube, like Patreon, they can disable you for whatever reason, whenever they like. That's just part of the terms of service.

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