This Physicist May Have Just Solved Quantum Gravity

What happened at the Big Bang? Uh, what goes on in black holes? These kinds of questions have not been solved by these very complex frameworks for quantum gravity.

"You don't believe this, and you have some recent results."

"I used to believe it that quantizing gravity required extra dimensions, strings, membranes."

"What are the assumptions that go into this theory?"

"One of them is that the theory lives in a Hilbert space. We have an example of a theory which doesn't require that assumption."

For some background, yeah, for the viewers, I was sent this paper last night. Professor Neil Turac is the inaugural Higgs chair at Edinburgh, former director of Perimeter, and a 2026 fellow of the Royal Society. States of negative norm are called ghosts. A state with negative norm corresponds to a negative probability. That's just not true. You can't observe the norm of a quantum state, provided the S-matrix or Hamiltonian of this theory has this symmetry. The answers you get are always positive, and the probabilities always add up to one. We claim we understand quantum gravity in a certain limit. The trick we used to make sense of it may or may not apply to the full thing.

On this channel, I, Kurt Jaungle, interview researchers regarding their theories of reality with rigor and technical depth.

"Sam says, 'I think I know how it works.' And all it took is a slight tweak of the Born rule."

Today, ghosts, the Born rule, why strings may not be forced in nature, and why simplicity still matters.

"Why is simplicity so important?"

"Simplicity leads to understanding. Quantum gravity in four dimensions is usually said to require strings or require some other extra structure."

"You have some new interesting results, right?"

"Which we're premiering today."

"Okay. So I used to believe it that quantizing gravity was this uh, you know, required this huge amount of extra paraphernalia, extra dimensions, strings, membranes. The whole story has become more and more complex uh as time progressed without actually solving any real problem. And what I mean by real problem is what happened at the Big Bang. uh, what goes on in black holes? Is there information loss? These kinds of questions have not been solved by these very complex frameworks for quantum gravity. So what we've recently realized is that there's rather a simple-minded approach to quantum quantum gravity uh which actually has been around since the 1970s. Uh, was begun by somebody called Kelly Stell, who unfortunately passed away recently. But he wrote a paper arguing that if you include square terms in the gravitational action, so you generalize Einstein's action to Einstein's action involves the curvature of spacetime and also a length scale which is called a Planck mass or Planck length or or Newton's constant. It's all the same thing. So there's a scale in Einstein's theory of gravity. If you include terms in the action which are the square of the curvature..."

"...in addition to the regular..."

"...in addition to the regular Einstein action and the cosmological constant, which is kind of has no derivatives, then you have Einstein's term, which has two derivatives because it's a curvature, and then you can include curvature squared terms, and that's makes gravity much more like a gauge theory because in a gauge theory, the action is an integral of the curvature, the field strength squared. Um, Maxwell's theory, QCD, they all work the same way. So, in gravity, you can put the curvature squared into the action. And then there's almost a trivial argument that tells you that that theory, which includes Einstein, but also these four derivative terms um is renormalizable. Uh, now, renormalizable means that when you do quantum field theory and you calculate things, it is possible to um, although you get infinities in various calculations, you can absorb these into redefinitions of the coupling constants. Um, and so basically you you you're led to a sensible theory with what we call a continuum limit. Namely, at short distances, the theory is completely under control. So there is a renormalizable theory of quantum gravity which has been known since the 1970s, and as I say, this is the simple-minded approach. Now, there are reasons why uh people have more or less abandoned it, though they keep coming back to it. It's called quadratic gravity because it's quadratic in the curvature. The action is quadratic in the curvature. So um, yeah, there there's actually more and more interest in this possibility, which certainly is the simplest possible theory of quantum gravity. So it's renormalizable, and then in the 1980s uh Abradian Bavinsky showed it's asymptotically free. So just like QCD, uh, the theory of the strong interactions, when you go to short distances, the coupling constant goes to zero, and it becomes a trivial theory of just waves which don't interact. So you can imagine at very short distances, this theory is really extremely simple. So what's wrong with the theory? All those statements I made about renormalizability, asymptotic freedom, they are the Euclidean theory. That is how we do computations of the strong interactions, QCD. You can put it on a lattice and study um, you know, this the theory. But the only way we know how to really know how to study non-perturbative properties of of any field theory um is to work in imaginary time. Okay. The reason is that if you work in real time um, then the quantum mechanical path integral is very oscillatory. It involves the imaginary number, exponentially imaginary number. It's oscillating like crazy, and if you try to integrate anything, these oscillations are just impossible to control um if you do it directly. So you have to do some trick to control those oscillations. And going to imaginary time is a beautiful mathematical trick which converts an oscillatory integral into a uh perfectly damped, convergent integral. So there's this mathematical trick which people have used forever in quantum field theory and in QCD, and uh, but no, but not much in gravity. Um, it doesn't work with Einstein's theory of gravity. People have studied that. But if you include these squared curvature terms, they suppress the curvature on short distances. Um, and it looks like this theory is sensible in Euclidean time. So now, that's all very well. What I'm saying is that it looks like there's a sensible theory in imaginary time. But we don't live in imaginary time. We live in real time. So we have to do this procedure called the Wick rotation or or analytic continuation from this imaginary time to real time. Um, when you do that, they're two disasters strike, and this is why people sort of abandon this approach, although they keep coming back to it. What we've done recently is half understand how to deal with that. Okay. So the two problems, one of them is uh probably the oldest no-go theorem in physics. It's called the Ostrogradsky theorem. And so in 1850, Ostrogradsky, I think he was in St. Petersburg, um decided to generalize what Hamilton had done with Hamiltonian treatment of classical mechanics. And so Ostrogradsky asked, what if instead of F=ma, instead of a second derivative equation, what if we had three derivatives in the equation of motion, or four, or five, or any number of derivatives? What goes, does anything go wrong? And he found something very interesting, which is the Hamiltonian, or the energy of the system, if the equations of motion have more than two derivatives, then the energy or Hamiltonian is what we call unbounded below. You can have configurations of arbitrarily negative energy in this higher derivative system. Now, that on the face of it looks like a disaster, because if you brought such a system into the into contact with the real world, where generally the energy is positive um, this system could interact with the everything else, and its energy could go down, and the energy of everything else would go up. So it's an infinite source of energy, and we don't see such things in nature. Uh, and they might be wildly unstable. So um, this is called the Ostrogradsky instability, and in general, it's true if you try to write down a higher derivative system, you will find it's unstable in in general. There are exceptions, but in general, that's a problem. So people got very worried about this, and often uh, when people were building quantum field theories, and actually the first person, as far as I know, the first person to try to use a higher derivative quantum field theory was Homi Barber, who's an Indian um nuclear physicist, and people trying to understand nuclear forces, so they're trying all kinds of models and field theories, and they, Barber and Heisenberg and many other field theorists played with higher derivative theories. The reason they played with them is they thought it would make quantum field theory more convergent. It would it would reduce the infinities, and it's related to the fact that gravity with four derivatives is renormalizable. So it's a similar reason. Now, the disaster that happens in the quantum theory is slightly different than the classical. What you find is that the uh, space of quantum states does not have a positive inner product. It has what we call negative inner product, and states of negative norm are called ghosts. Traditionally in physics, what people have often said, and what we realized is wrong, is that a state with negative norm corresponds to a negative probability. Okay. And you'll find this argument everywhere in the lit, or many places in the literature, that whoops, we can't allow negative norms. They're unphysical. Um, they correspond to negative probabilities. That's just not true, because a quantum state is nothing but a label for a system. Its norm is neither here nor there. You can't observe the norm of a quantum state. Okay? So you've got these labels. Some of your vectors in this abstract space of states have positive length squared, let's say, and some have negative. So it's like in Minkowski spacetime, we have distances which are space-like or time-like, and one of them is negative, and the other is positive, and some are null. There are some null directions. So then the question we wanted to address is, can you live with a quantum theory in a space of states which has these three possibilities: positive, null, negative um, norm states? And what we found is, so mathematicians were studying this. This is called a Krein space. It's a generalization of Hilbert space. Um, and what we found is that provided there is a certain discrete symmetry in your theory, um, which we call ghost parity symmetry, and it basically, it's a very trivial thing. It's it's an operator which when you act on a negative norm state gives you minus one, and acting on a positive norm state gives you plus one. If you have a theory where that operator is a symmetry of the theory, um, you can now uh, define transition probabilities without ever normalizing the state. And the way you do it is with projection operators. Okay. So even if if I'm in Minkowski space, you know, it's a uh, non-degenerate. Every vector can be uniquely expressed as a linear combination of, let's say, space-like and time-like vectors. There's nothing singular about it. And the way you project, you can still project a vector onto its components, space-like or time-like. So you can do the same thing in this Hilbert space. But what you have to do is replace the Born rule. In quantum mechanics, the probability for an event is the inner product between an initial state and a final state squared. Okay. And now, if you were going to normalize this, the so normally we think of those states as being normalized. You know, integral of wave function squared is one. But imagine you can't normalize now because you're in this more general space. So what you do is you replace the Born formula. I then some kind of matrix transitioning you from I to F. This is some inter um, time evolution operator. So if S, that's called the S-matrix, is SF squared would be the normal procedure. So let's replace the initial state. So we've got two copies of the initial state because we have this thing squared. Replace the I I with dividing by its norm. Now you have a projection operator. So a completely equivalent formulation of the Born rule is to say, project onto initial state, evolve with the S-matrix, project onto the final state, evolve with the S dagger complex conjugate, and trace the answer. Trace means sum over all states. That'll give exactly the same answers in normal quantum mechanics. But the beauty is, because now it involves projection operators, it gives sensible answers even in a Krein space. And what we've shown is that provided the S-matrix or Hamiltonian of this theory has this symmetry, the one I mentioned, um, the answers you get are always positive, and the probabilities always add up to one. So we found that in dealing with theories like which have four derivatives, we have to very slightly generalize the framework of quantum mechanics, but essentially that's a, it's a trivial change, and then we find all the probabilities are positive. So we, so even though there are ghost states, you still trace over them. You trace over everything. Um, so this is very exciting because now I have to say that there's a caveat, which is that we haven't solved quantum gravity yet. Um, but we're halfway there. That's optimistic, of course, but that's a nice way of saying it. Um, so when you look at the quadratic gravity action there, there are two terms which are allowed. That's all. The symmetries of general relativity only allow two terms. What you, one is what's called the Ricci scalar squared, and the other one is the Weyl curvature squared, and this is the most general action. So there are two couplings you can play with. What we've shown is that if you take a limit where one of those couplings is zero, that basically decouples the graviton and everything associated with the Weyl curvature. You just decouple, you're left with the curvature scalar. That action is renormalizable, asymptotically free, and gives positive probabilities. So we claim we understand quantum gravity in a certain limit in which the only degrees of freedom are over the local scale of the metric. So this is fine for describing cosmology. Um, even there are black hole-like solutions to this theory. It's a kind of toy model for quantum gravity. The trick we used to make sense of it may or may not apply to the full thing. We will have to search in the in the full theory. Is there a similar discrete symmetry? This thing that gives plus one on positive norm, minus one. If there is, then uh, this will be a complete theory of quantum gravity.

"Okay. What are the assumptions that go into this theory?"

"Well, let me first say what the assumptions were behind the claim that you need strings and 10 dimensions to do quantum gravity. The assumptions underlying that claim were um, were that um, essentially the only allowed theories had uh two derivatives in the action. Okay. Okay. So when people quantize strings um, they were not considering theories even of strings which had four derivatives. Okay. So that was one assumption. There are plenty of other assumptions. Probably the most, the strongest assumption was that you have to, you have to to construct the theory only in perturbation theory. Okay. So the thing that's always bothered me about string theory is it has no full formulation. There's nothing like general relativity where there's a principle that gives you the full nonlinear theory. String theory is kind of um, constructed with certain, trying to respect certain principles like Lorentz invariance and um, the unitarity, positive probabilities, and so on. But string theories, the assumptions are really rigid, and one of them is that the theory lives in a Hilbert space, which means that the norms of all quantum states are positive. And now that we've seen that you don't need that assumption, you know, the whole, the whole thing has no basis. Uh, I mean, if it's true, we think it's true. We have an example of a theory which doesn't require that assumption, and which is what we call UV complete. It's a, it has a full continuum formulation. This is a self-contained, complete theory, like QCD we believe is is such a theory um, and yet it doesn't have, it doesn't live in a Hilbert space. It lives in a state in a space with more like Minkowski space with positive norm states and negative norm states and null states. So just a tiny generalization of the orthodox principles means you don't need strings, you don't need extra dimensions to describe gravity. So that's quite shocking. And of course, it begs the question, what are the other assumptions that people were making which led them to conclude there's a multiverse? You know, I mean, you make one false move in theoretical physics and you're totally wrong. Okay. So that's the danger we all have to worry about, and I think people are not sufficiently worried about that. We should be examining very, very closely each one of our assumptions to say, is it really necessary? Uh, or is it just that we're traditionally used to making that assumption?"

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"Okay, let me see if I got this correct so far. And feel free to correct anything, including that I'm citing the wrong names, my pronunciation, anything. Okay, so in the 1970s, late 1970s, '77, someone named Kelly Stell came out with a theory called quadratic gravity."

"Exactly."

"That adds something to Einstein's Einstein-Hilbert's action. It adds R squared, actually, in its most general form, adds an R squared plus the the Weyl squared."

"Yeah, exactly."

"Well, firstly, why do we care about quantum gravity? Why is this such a difficult problem?"

"One of the problems is that it's non-renormalizable."

"Exactly."

"Okay, this theory is renormalizable. However, going back 150 years or so, there's another person, no-go theorem in sense, called Ostrogradsky's theorem, which says that if you have more derivatives in a certain class of theories, then you get instabilities."

"Exactly."

"These instabilities are of two forms. One is that you can be infinitely..."

"...negative."

"Yes. Sorry. Sorry. You can be unbounded. That's infinite automatically from below."

"Yes."

"Meaning that you'll just constantly decay, and it doesn't look like our universe is constantly decaying, as far as we can tell."

"Exactly."

"Now, maybe there's some direct sea argument for bosons or something like that. I don't know that could fill this, but whatever. That's right. That horn is not the horn you're going down."

"No."

"There's another horn."

"I'll tell you a little bit more about that horn, because there's this Ostrogradsky instability."

"Now, the fascinating thing about gravity is it has this character that gravitating system. Gravity has negative energy, right? The potential energy of a bound system has positive kinetic energy. The butt. With gravity, energy is negative. So already when we deal with gravity, we're somehow used to the fact that no, the energy isn't positive, right? The potential energy is not positive. Um, and it's more than that. Observations show us that the universe is expanding exponentially. Now, it doesn't sound like a very stable system, right? Gravity has this weird property, if we believe in the cosmological constant, that the universe is going to expand exponentially forever. That sounds awfully like an instability. When we've studied this four-derivative theory of gravity, we show that the Ostrogradsky instability is nothing but normal gravitational expansion. And if we analyze the expanding solution in just the same way that we do with Einstein's theory, we discover it's absolutely stable. Interesting. So the Ostrogradsky instability went away just by reinterpreting the theory as a gravitational theory."

"Okay. I didn't know that part. So for some background for the viewers, I was sent this paper last night, and maybe it's published now by the time we release this. I didn't see that part. Okay. So my understanding..."

"I see. Okay. Great. My understanding is that you looked at the other horn of the..."

"...of the Ostrogradsky instability, which says that you will have negative norms."

"Exactly. Negative norms are not wanted in a quantum theory. They're called ghosts."

"There are two kinds of ghosts people may have heard about. One is a friendly, like Casper the friendly ghost."

"Yes."

"Which is fine."

"Yes."

"Then there's another one, which is the the paranormal activity kind of yours."

"Yes. But what your innovation is, along with your partner Bateman, if I'm..."

"Sam Bateman."

"Great."

"...is to say, actually, see, there's no pseudo-Hilbert space. I was looking for that word. I thought it was called a pseudo-Hilbert space."

"It is. It's called a Krein space."

"Right, right. Okay. So Riemannian spaces are just plus plus. In the signature, pseudo-Riemannian, you allow a negative. And then..."

"Hilbert spaces are plus plus. And then I didn't know. I would have thought it would be called Hilbert."

"Hilbert, pseudo-Hilbert was called Krein."

"So very. So again, my student Sam Bateman um has this deep interest in the mathematical literature, mathematical physics literature, and he's just been exploring. And of course, the internet is very helpful, and even AI can find papers. And somehow Sam came across this notion of the Krein space, which is not generally known to physicists. Krein was interested in it because he was studying differential operators. He's a functional analyst. And so normally when you consider eigenvalues in the Schrödinger equation or whatever, you know, you very often make the assumption that you're that the space of functions is a Hilbert space. But Krein said, you know, let's drop that assumption. Let's allow uh, these negative norm state, negative norms in our functional analysis. And what he discovered is you can prove all kinds of additional things. Um, so this mathematical concept was sort of lying around in the literature, just waiting to be used, and as far as I know, nobody else ever used it. Uh, so indeed, it is a pseudo-Hilbert space. It's nothing but that."

"Then what you said is, well, maybe negative norms..."

"...are not a problem because they themselves are not observable."

"And physics is about what can you observe. And there's plenty of unobservable. You can have a red dancing unicorn in your theory, in the equations. If it's unobservable, it actually doesn't matter. Maybe there's another set of equations with the exact same observables without the red unicorn, but it doesn't make a difference. You don't see it in the lab."

"Right."

"Okay. So, the negative probabilities are not, sorry, the negative norms are not..."

"...in and of themselves a problem."

"Correct."

"What is observable are the probability transitions."

"Exactly."

"And then those are fine."

"Exactly. Yes. So you, you mentioned BRST and F.I. Popov. So that's very good because physicists are actually very used to working in pseudo-Hilbert spaces. That's what these mathematical ghosts live in. But the usual prescription is you, you think you're in this big space which has both positive and negative and null states, and then you perform a projection and you say there's a physical subspace where everything is positive. Okay. And you use this bigger space to prove certain things. It's very, you basically respect more symmetry by working in this big space, but ultimately you project onto a physical subspace, and and that's a Hilbert space. So people construct transition amplitudes. They actually sum over all these unphysical directions, but at the end of the day, they do a projection onto the physical subspace. What our construction does is a generalization of that, which is actually more economical, because we live in this big space and we don't treat the amplitude as a physical quantity either. It's not in quantum mechanics. You've got to square it. Okay."

"We don't do that. We construct the probability directly as a so you've got some operator A which describes the full physical process. It's a projection onto the initial state, scattering matrix, projection onto the final state. And what we show is that probabilities are the trace of A dagger A, and you're just not allowed to think about A. A is not a physical thing, but the trace of A dagger A is. When we trace, that means summing over all states, including the ghosts. So in our construction, there's no need to do any projection. You sum over these states, even the ones with negative norm. You never project anything. You just directly construct the probability, and it turns out it's positive, providing you have this symmetry in your theory. So we've broadened the class of quantum field theories to ones which don't satisfy the usual axioms. They don't live in a Hilbert space, but they have all the other good properties. They're causal. They're unitary. They satisfy everything else you could want."

"Now, the paper is out by the time this comes out, hopefully."

"Yes."

"And people may have the question of, well, you're talking about quantum gravity initially, and then I look at the action, and it's this perfect square, which we're going to talk about why it has to be a perfect square. Right. But the quantity in it is a field, just a scalar field."

"Just a scalar."

"So what's its relationship to quantum gravity?"

"It is a sub, it's a particular limit of this quadratic gravity. So quadratic gravity has a bunch of different types of excitations. It has a graviton-like excitation which has spin two. It has a vector excitation, more like a Maxwell vector. It has a spin-two ghost, a guy that creates negative norm states. Those are all coming from the Weyl curvature term. The Ricci curvature is uh, telling you about the scalar mode, which is the local scale of the metric. Okay. So by going to the four-derivative theory, you have more degrees of freedom than you had in Einstein's gravity. Um, you've got all these ones I described, the the graviton, the the graviton, the ghost graviton, the vector mode, and the scalar mode. Um, and what we've been able to do so far is study a limit of the theory in which the tensor-like modes, the gravitons and the vectors decouple and they become trivial. So all we study is a scalar mode, and that scalar mode, we're claiming, is a sensible quantum theory. So if you like, it's a, yeah, it's a special limit of quantum gravity. Doesn't have gravitons, won't have gravitational waves. Okay. So it's not the real world. It's not the right theory of gravity, but it's a limit of something which might be the right theory of gravity."

"And you mentioned that it's UV complete."

"Yes."

"Okay. What about IR complete?"

"Okay. So it is very similar to QCD. Now, QCD is a, as we believe, a complete quantum field theory. It has a continuum limit. It's completely well-defined. As you know, it has very strange consequences in the IR, in large distances. It confines. You're not allowed to have free charged particles in QCD. Um, they have, you have to have glueballs or, you know, protons, whatever. So QCD is confining. That means that it's called asymptotic freedom and infrared slavery. Okay. So in the infrared, things get strongly coupled, and you just can't pull out the individual gluons. They they're too uh, strongly interacting. Instead, the only kind of real physical excitation in QCD is a glueball, just made out of many glue gluons. Um, that's what people study in lattice, uh, lattice gauge theory. Um, so this theory is similar. It's very weakly coupled at short distances in the UV, but at large distances, strongly coupled, still completely well-defined. You can put this thing on a computer and you could try to find what are the excitations. What's the analog of a glueball in this theory? Um, we haven't yet done that, but actually have a student doing it. It'll be interesting to find out what happens. It's like a, it's also like a toy model of QCD. It has the same properties. It's completely well-defined on the lattice, and then you can, you can study what happens. Now, this is very, this in itself has a lot of potential. Uh, but we're just beginning to scratch the surface. So there is a puzzle in basic physics, which is the separation of mass scales. We've got the Planck mass, which is 10 to the 19 GeV, huge number. Then we have the weak scale, which is uh, 100 GeV. That's the scale of weak physics. We have strong interaction physics, a fraction of a GeV, around a GeV. So that's kind of particle physics scales. So GeV scales. And then we have the cosmological constant, which is, you know, down at a millielectron volt. So essentially, there are three widely disparate scales, and this is called the hierarchy problem. Why does the law, why do the laws of nature have this ridiculous separation of scales? Okay. Now, imagine you have this theory which is asymptotically free. So in the ultraviolet, the coupling is weak. I then ask my, and let's say we, we define the theory at very high energies, where the coupling's, let's say, one-tenth. Okay. And then I think I know what I'm doing. Uh, uh, it's, it's a perturbative theory. That's weakly coupled. Now we go down to lower energies. Imagine this high energy is the Planck scale, just for, you know, as an example. You can then ask yourself, what would happen? You can ask at what scale would this coupling become strong as I come down in energy. When couplings run with energy, it's only logarithmic. And that's what happens in this theory. It's very, very slow change with energy scale. So as you come down in energy scale, it is absolutely natural and almost unavoidable that the scale where it becomes strong is exponentially smaller than the scale you initially defined it. And in fact, that's the case with QCD, right? QCD predicts a mass scale of around a GeV, but we have Planck mass in our theory. No one regards that as fine-tuning. Why? Because the QCD coupling is something like a 30th at the Planck scale, and then we come down in energy and become strong at about 1 GeV. Not a surprise, because it runs so slowly with energy, and it's exactly the same with this theory. So we hope, so there's a kind of puzzle in particle physics and gravity. Why is the Higgs mass so much less than the Planck mass? And within the normal Standard Model, that's just tuned. We just pick these two numbers, right, to fit the the real one. But now let's ask, why are those numbers so different? Well, if the Higgs is made out of this scalar, which is connecting the Higgs mechanism with gravity, it's pretty exciting. Then it's totally natural for the Higgs mass to be exponentially smaller than the Planck mass. So there's a hope that this picture will solve the hierarchy puzzle."

"Let me ask you something."

"The Higgs is not fundamental in your picture."

"No."

"Why do they still give you the Higgs chair?"

"Well, that's to do with Peter Higgs. Okay. So Peter Higgs um, I mean, he was a much more shy and withdrawn person than me, notoriously shy, and probably a lot more humble than me. Peter um, came up with the idea of the Higgs boson in the early 1960s um, when there's no experimental evidence, right? So, it was a pure theoretical uh concept, but it was absolutely radical at the time. Uh, Peter Higgs really thought about, well, he was inspired by superconductivity, which is a real phenomenon, and somebody called Anderson made a field theory model of superconductivity and realized that this is the way to essentially, well, the, you know, magnetic fields are expelled from superconductors, and Anderson understood that could happen if a particular kind of scalar field condensed, and and it's a composite field in the superconductor. It's made out of electron pairs. It's called a Cooper condensate. Um, so Anderson had realized there's this amazing mechanism which has the effect of giving the um, electromagnetic, the photon, a mass inside a superconductor. And Higgs said, 'Oh, wait a second. We could use this in particle physics.' So he generalized this method to a field, relativistic field theory. At the time, everybody told him this was nonsense. Okay. They said, 'You're in, you're using classical notions in a quantum field theory,' and um, 'it violates various assumptions.' You know, one of the basic assumptions people had made in quantum field theory is um, is called cluster decomposition. It's basically that things which are at a distance are uncorrelated. Okay. So it's kind of intuitive. Why should this thing know about that? Higgs's model absolutely violates this. It says the vacuum is full of a condensate such that if I measure the value of the Higgs field over here, it's exactly the same as the value over there. It's utterly correlated. So people were shocked. It violated the basic assumptions, but you know, ultimately turned out to be true. So Peter was a radical um, in his way um, and um, Peter would be the last person to defend the Higgs boson as being fundamental. I mean, the thing that's stimulated is not fundamental. The, the superconductor, the analog Higgs boson in a superconductor is not fundamental. It's made out of electrons. Okay. So um, now, why would you question uh, well, yeah, so the fact is that the Higgs theory he invented is not UV complete. If you, it has a coupling in it, and if you go to high energies, it has all the wrong behavior. It blows up at a finite energy scale. Okay, it's called the Landau pole. So we know the Higgs theory is not UV complete. So now we have a scalar theory which is UV complete. It's highly suggestive that actually the Higgs boson is in some way a composite of this other scalar that is complete, or at least it's, it's very worth exploring. I remember the doubt before launching this podcast. What if no one listens? What if I'm wasting my time? If you've ever felt that way about starting a business, Shopify is the partner that turns uncertainty into momentum. They power millions of businesses and 10% of all US e-commerce. From Allbirds to Gymshark to brands just getting started, no straggler left behind. Shopify's AI tool writes your product descriptions for you. It enhances your photography. It builds you a stunning store from hundreds of templates. Forget about the dormative haze of bouncing between separate platforms. Shopify puts inventory, payments, and analytics under one roof with the propriety of a true commerce expert. Their award-winning 24/7 support means you're never alone. And that iconic purple Shop Pay button, it's the backbone of their checkout, the best converting on the planet. Turning abandoned carts into actual sales. It's time to turn those what-ifs into with Shopify today. Sign up for your $1 per month trial at shopify.com/to. That's shopify.com."

"I'd like to explore the relationship between this 4D gravity quantization paper set of papers that you have now and your Leam Boil simple TOE CPT symmetric universe, whatever its moniker is."

"Yes. CPT symmetric universe. Yeah. It's, this is all the same thing. Okay. So what we realized in proposing the CPT symmetric universe and then exploring it, and and I should just say the philosophy behind it was extreme minimalism. Right? What we've seen in the observations, both of the universe on large scales and in colliders on small scales, is surprising economy and simplicity. Uh, what we see is minimal. Okay. We see, we can use five parameters to describe everything on large scales, and then the Standard Model of particle physics is actually a very economical framework. Um, and there's, in both cases, there's no evidence for anything else. And the more we look, you know, the less we find. So that doesn't mean we should stop looking. Uh, if we find something, it will, something unexpected, it'll completely disprove our framework, which would be very welcome. But I think that it's a sensible first uh, starting point to see what's the minimal theory I can use and explain everything we see. You know, of course, that's the obvious thing to do, but strangely, that's not what people have been doing. So we decided to do that. Having decided to do that, all sorts of things started to fall into place. We could explain the dark matter in a simpler way than anywhere else anyone else. We could explain why the universe is smooth and spatially flat and the horizon puzzle. All these things dropped out without requiring all the bells and whistles that previous people had assumed. The one thing that didn't drop out was the fluctuations. So we look at the sky, the the plasma, hot plasma of the hot Big Bang which surrounds us, and we measure its temperature, and we see these fluctuations in the temperature, and they're very important because they gave rise to galaxies and, you know, they're our ancestors. So now we can see those things. What caused those fluctuations? So in the inflation models, they are caused by quantum fluctuations on microscopic scales which get exponentially stretched to large scales. Um, in our case, we don't have inflation. So we can't stretch these things. So how else could you get them? So the point of view we took is, look, let's just take it at face value. Imagine they look like the vacuum fluctuations in a quantum field. They have the statistical properties. It's called Gaussian random noise. But they have a spectrum, meaning the strength of the fluctuations as a function of scale or wavelength. Their spectrum doesn't look like a normal scalar field. It's more red. There's more power on large scales. What does it look like? It looks exactly like a four-derivative field. Okay? That's what we see in the sky. So if you just say, how would I interpret the sky as a quantum fluctuating field, it's a four-derivative field. There's no question. And now the, so that's what starts us on the path of thinking about high-derivative fields."

"And now this is closing because we see what you need for quantum gravity is a four-derivative field. It tells us what we're looking at in the sky is a signal of quantum gravity. Okay. So this is the, the more we pursue this simplicity um, the more unexpected unifications seem to be happening. And if we, you know, it's a wonderful thought that actually look at the sky, we're just seeing the birth of the universe, and those are precisely the quantum fluctuations in quantum gravity. What, what more could you ask for?"

"Interesting. So I recall if the CMB fluctuations were because of the 36 fields from..."

"Right."

"...people can watch the earlier episode to understand what those are."

"Same kind of fields. Yeah."

"There's a paper by Klein and Hell."

"Ah, good."

"About that they won't propagate."

"No, the paper by Klein and Hell. Uh, it's true. The papers come out criticizing us and saying we're making obvious errors. Okay. So I have uh responded in great detail to the journal and say it's not a secret. They asked me to referee it. Um, and yeah, it's hard to say something polite about it, but um, I will try."

"Uh, so they recapitulate various old arguments, one of which is Ostrogradsky. Um, they do something quite strange in their paper, which is, which is the following: that these four-derivative scalars of the type we introduced for cosmological reasons and to explain the micro background. These four-derivative theories uh, couple to gravity. Okay. But the way we used them was to say, given um, a curved space background, given a spacetime, put these scalar fields on and see how they quantum fluctuate. Klein and Hell don't do that. They put in the scalar fields which couple to gravity, and they treat their action as if it is the gravitational action. Okay? It's not."

"So can you explain the difference between those two approaches?"

"Yeah. So in the one approach, you treat, in in the approach we used, because at that time we weren't yet ready to study quantum gravity, right? So we said, okay, we'll do something simpler, which is to assume a curved background, but that's just fixed. And then we study quantum fields on that background. And actually, the question we were asking is um, what is the stress energy in quantum fields fluctuating on a fixed background? The puzzle we wanted to resolve is, does that stress energy make sense? You see, there's a terrible thing about quantum fields. Even in a fixed background, their energy is infinite. There's a what's called a UV divergence. Um, that uh, and and then you're going to sort of, so we were trying to study gravity in two steps. First of all, just take a curved background with fields on it. Then take those fluctuations, calculate the energy in them, and see what effect those would have on the gravity. Okay? So, it's not a full-blown theory. It's just an attempt to understand how can gravity possibly couple to quantum fields that have divergent energy. Right? This is a, a very fundamental problem. So we were studying these four-derivative fields on a fixed background. So Klein and Hell took the same model of these four-derivative fields and said, okay, let's study that as if that describes the dynamics of gravity."

"That's not what we were doing. Okay. And then they discovered that this is not a good theory of gravity. Well, you know, so what? It's not what it was invented to do. So we, we have to add other terms which describe gravity, and then we have to combine the whole thing. So yeah, their analysis seemed off the point. And then secondly..."

"So their analysis was correct, but it wasn't what you were saying."

"I'm not sure it was correct. The paper is not clearly enough written to tell. Okay. But either way, it's not what you were saying. Totally irrelevant to what we were saying. The other thing is they repeat the folklore that negative norm states are not uh, admissible. And uh, and and therefore they just completely missed the point, which is in our latest work, that to describe four-derivative theories, you have to be willing to include negative norm states. If you just rule them out from step one, you know, I agree with them. You can't do the, the normal procedures of quantum mechanics don't work, or quantum field theory don't work. But that's why you have to go beyond them. So yeah, I, I mean, there are lots of other issues with their paper. Uh, it's actually quite hard to figure out what they, what they really are saying. But um, uh, yeah, I'm not, I, I think a, they're off off point, and b, they don't know about our new stuff, and when they do, I will be delighted to go and explain and have them try to poke holes in it. But, you know, trying to poke holes is good. Uh, all criticism is welcome. Um, and and that's how we make progress. Is there anything about the way that you've solved negative norm states or reinterpreted it such that it also rescues other theories which were considered dead because they produce negative norm states?"

"Well, yeah, there is for sure an infinite class of higher derivative theories um, which will have the same property that when you take this broader picture of the Born rule, they will still be consistent. So yeah, there's an infinite class of theories waiting to be explored, and they will be renormalizable, and they could be asymptotically free. So all we've done is really the simplest one. We've shown that quantum gravity itself, this quadratic gravity theory, includes one of these fields. Now, as you know from our earlier work, we needed 36 of them to cancel all of the divergences in the Standard Model. So this, there was this kind of numerological miracle."

That if you take standard model fields and you compute its the the stress energy tensor in the vacuum, um, all of the infinities go away. The standard model cancels against these other fields only if there are 36 of them and only if there are three generations of elementary particles. So this is the simplest explanation for why there are three generations of elementary particles. Our explanation involves these fields, but 36 of them.

Now, what I've just told you about with this quadratic gravity only has one of them, and we don't yet know how to square that, how to, >> what is it called? Square the circle. >> Sure. >> We don't yet know how to do that. There are 36 in one argument, there's one in the other one. And how, but you know, at least, uh, these two things seem to be different sides of this or related. So when we get to study the tensor modes in gravity, this Vile squared term, if we resolve it in the same way, maybe that will tell us why there are 36 of them. And maybe the 36 come out of gravity. That's actually not would not be that surprising. There are formulations of gravity which very naturally have 36 objects in them. Uh, this is in in loop quantum gravity, people are very familiar with this. It's called BF theory, um, and naturally it has 36 of these fields. So, you know, the dream would be that that's somehow related, but we haven't made that work.

>> Is there any relationship between your latest papers and then Mannheim's Bender's conformal gravity?

>> Yeah, we're we're all trying to do similar things. Um, Bender and Mannheim were also puzzled by these negative norm states. Okay. And, uh, Bender in particular has been very interested in studying quantum Hamiltonians which are superficially unbounded below. Okay. Uh, but nevertheless have positive spectra. Okay.

>> Bounded above.

>> No, unbounded above. >> So, so take a potential which is minus x to the fourth. Okay. >> And study it quantum mechanically. So Bender will tell you that when you study it correctly, the allowed energies are all positive and they go up to infinity. So it's it's very counterintuitive. And basically, he does it by deforming contours in the complex plane. It's a very elegant method, but there's a slight difference between what we're doing. So you can say it as following. Bender and Bender's method and Bender and Mannheim were interested in Vile squared gravity. You see, so actually most people have there these two terms in quadratic gravity. Most people are focused on the V squared gravity because it has more symmetry. Uh, there's there's no length scale. It is invariant under locally rescaling. It has no scalar. In in the language, the Richie squared term has a scalar. So we discovered that there's a limit where you can just ignore the Vile squared and everything is in the scalar. That's what we've been studying. Ben, um, Mannheim's focus was precisely on this Vile square and gravity, cuz he thinks maybe that's the fun, that's a kind of fundamental theory, has more symmetry. Um, but they still had to get rid of the negative norm states. They did it in a way which essentially does the following. I've got some states which have negative norm. Um, and so I just redefine my inner product to put a minus one in front of those when I have two negative norm states. What we've shown in our papers gets very interesting is doing that is not covariant. Okay. That is not consistent with, uh, space-time invariant. You, you pick a particular frame and you work in that frame. Um, and so their procedure, um, uh, I believe will not give a consistent quantum field theory. It'll break the basic symmetries in the in the theory. So far, they've only really applied it in quantum mechanics, which is a lot easier than field theory. Field theory, you've got to respect Lawrence symmetry, translation symmetry. Um, and, um, and if you sort of do a brute force change of the inner product, you will mess those up. Um, so, so yeah, they, we're all circling around the same problem. We claim that our resolution is, uh, is the only covariant one. It's the only one that fully respects the symmetries of the theory. So, it's definitely preferred, and we claim that if they did do more detailed calculations, they're going to discover problems. Um, wouldn't be surprising. They've only analyzed it at a very elementary level. But no, Mannheim and, uh, and Bender and us are often in discussion about these things. And, um, Mannheim even claims that this Vile squared gravity can solve the dark matter puzzle. Right? So he claims it reproduces galaxy rotation curves without the need for dark matter and things like that. So he's, he's super ambitious with this program, as we are. Uh, we think his framework doesn't quite work. He will undoubtedly think ours doesn't for some reason, but we discuss in a very collegial, um, manner, and we're all after the same thing, which is a simpler explanation for, you know, for the properties we see.

I was just interviewed by someone from New York magazine who was asking me about someone else's theory, not related to physics actually, but someone else's theory. And then she was asking me, well, what do you think of all the criticisms about the theory? Then I said, you have to be specific about which criticism, because the mere presence of criticism, >> that's every single theory. When you're a champion of theory A, you're going to criticize theory B for a variety of reasons. >> This is just how it works. >> And it's healthy, right? You, you welcome the criticism because often the critics will see something you've missed. And, you know, I'd, if the theory is wrong, I'd rather know today than tomorrow, right? Because I don't want to waste my time on it if it's wrong. So, so yeah, if somebody points out a a flaw, you've, you, you should welcome that. Um, but of course, you, you try to see if if it's real or or have they made a mistake. Um, so I think that, you know, in the in the early 20th century, you, 1910s, 1920s, when people were developing quantum mechanics and GR and all the foundations of modern physics, there was this very intense debate. You know, Einstein's theory of gravity wasn't the first one. There was Nordstrom, and there were very other people, there's Whitehead as well. Why the theory exactly? And they're all in, you know, in in turmoil, criticizing each other like mad, and the best theory survives. So I very much hope we will go into a phase like that. The field needs it desperately. The orthodoxy, string theory, has become an orthodoxy, which is which is terrible for the field, but it's an orthodoxy without any predictions. You know, that's really sad. If all the young people are working in a framework which doesn't make any testable predictions about the real world, um, the whole goal of the field becomes lost. So I think it's really important that people are pursuing different approaches. They should be as simple as possible and as testable as possible, and we should try to rule them out as quickly as we can.

But, you know, what we've discovered in our work is this loophole. It's a little loophole. People had all been assuming any sensible quantum field theory must live in a Hilbert space. And it turns out that assumption is not correct. You know, something as elementary as that, uh, there may be other things. >> And we need to know what they are, and we need to start pushing on those, uh, on those axioms to see if by varying them a little bit, we will, uh, we'll find the right answer. You know, what drives me is that the observations are so simple, um, that for reasons we don't understand, the universe seems to be extremely simple in its laws on very tiny scales and on very large scales. All the complexity is on human scales, right? I mean, stars are quite simple, and much simpler than people, right? So the complexity, certainly of, you know, go atoms are pretty simple, fully characterized an atom, then you get to, you know, materials, they're getting more complicated, and then you get to bacteria, which are very complicated, and you get to living things and people, we're incredibly complicated. But if you keep going to larger scales, things start simplifying again. I mean, the planet is pretty simple, the Earth, the sun. You go to the larger scale, you go to things get simpler and simpler. We see black holes, which are very big, but they're extremely simple. A black hole just has a mass, angular momentum, charge. You know, it's like an elementary particle. And then you get to the whole universe again, it's astonishingly simple on large scales. So, um, uh, you know, what I think of our job is to, as physicists, is to understand the simple things, the very small, the very large, and those seem to be incredibly well modeled by very precise mathematical formulas. Um, that doesn't explain everything at all. It only explains the extremes. And then we have to somehow understand how this interaction between the very large and the very small ends up producing complexity and life and consciousness and all these wonderful things, which physics is not ready to address yet, cuz it's just too difficult.

>> Is there a reason why the universe at the large scale should also be simple? I understand at the small.

>> I don't think there's a reason. Um, well, I would say the following. Um, I, you know, I was very privileged to know and work with Steven Hawking, who was probably the most profound thinker about gravity within a large group of very profound thinkers. I mean, Hawking was building on Dwit and other, uh, John Wheeler. So the field of sort of gravity and, uh, and quantum gravity attempts to do quantum gravity did attract some pretty amazing people, and Hawking was one of them. So Hawking introduced this concept of gravitational entropy, which is now entropy is a very profound principle in physics, which explains macroscopic properties. Right? So take air in a room. Why is it smoothly distributed in the room? That maximizes the entropy. That's just a typical state. Um, and, uh, so Hawking did the same. Hawking realized how to define entropy for a space-time in gravity. So he associated an entropy with a black hole. And what we did, uh, a few years ago, is generalize his arguments to cosmologies. You can associate an entropy with a different cosmology. And what we find using Hawking's definition of entropy, which is tremendously elegant mathematically, is that the most probable, or the universe with the greatest number of microstates, is smooth, is homogeneous and isotropic, and flat, spatially flat, just like ours, and has to have a small positive cosmological constant. This is a consequence of Hawking's formulation of entropy. So why is the universe so simple on large scales? Same reason that a a room full of air is almost uniform. It's just a typical state. Now, it's very interesting because in cosmology, people traditionally took the point of view that the problem was to understand the initial conditions. You know, for some reason we don't understand, somebody injected or or somebody set off a universe. And then the big puzzle is why did they start a universe in such a smooth state that when it got big, it would be as smooth as we see it. You know, that was very paradoxical. They would have to start the universe out in this incredibly special state for it to be end up so smooth. I mean, if it was lumpy initially, it would have just collapsed early on or fragmented or made black holes. It, it doesn't do that on large scales. It's incredibly simple. So, that was a big puzzle. So, they said, "We've got to start it." Uh, it, so they imagined somebody started the universe in a random state, and then they wanted a dynamics, inflation to smooth it out and make it big and smooth. Um, the same, you know, the room full of gas, which I mentioned, doesn't require anyone to smooth it out. It's just typical. But there are sort of two points of view. One point of view in thermodynamics is called the ergodicity, which is that, and the argument is, even if I put the molecules in the room in one corner and the rest was vacuum, if I let it go, they will bang around and smooth themselves out. And so that the argument is that if you let the system evolve, it's going to find the typical state itself. That's a traditional view of thermodynamics. But there's another, and this is the same as the the inflationist's view. They said, look, um, there's, they said there's basically no time for the universe to smooth itself out. You know, I can't, because the whole, it's only been 14 billion years. It's not in equilibrium. It came out of a big bang. There wasn't time. And, and this is where the horizon argument comes in. And they said, you know, two patches of space that were causally disconnected, >> right, >> couldn't interact. So, how could they smooth themselves out? It's impossible. >> Right? But that's is within the philosophy of ergodicity. Now, there's another philosophy which says no, ergodicity has nothing to do with thermodynamics. Okay? What you do is you put your molecules in a room, you quantize them. That's very important because that makes the states discrete. And then you, then you say, okay, what are the quantum states which are consistent with the macroscopic observables, the total energy in the room, the total number of atoms? That's a subset of the quantum states, and then I just pick one at random, okay? Because it's discrete, it provides a measure, right? There's a finite number of states, and they're all equally likely. So just pick one, and what you'll find is a typical state looks exactly like the room. It's smooth, homogeneous, because those are typical. You don't need any dynamics to get a typical configuration. Just pick it out of a hat. So with cosmology, that's, I believe, is the right way to look at the universe. You don't need dynamics to smooth it out. You just need a measure. You need a way of counting the different possible states of a space-time, right? That's kind of, you know, it's a bit mind-boggling that I have to think about the entire history of the universe and ask how many different histories are there. But in general relativity, that's what you have to do. The the basic object is a space-time, and you must count how many states are there for a space-time. But this is exactly what Hawking's formula does. So we just applied Hawking's formula. You see how many states there are, and then you see which macroscopic parameters correspond to more states, and you find that there are more states when the universe is smooth, for just the same reason that more states for gas in a room when it's smooth. It's very unlikely that all the molecules go in one corner. Um, and so, yeah, so the the point of view of simply counting states is, I believe, a much more profound view and much more appropriate for cosmology. And certainly nobody's started the universe. I, the uni, if the universe has some kind of self-contained existence, which is the most economical possibility, right? I mean, otherwise, we need some other thing than the universe to create the universe. You. So, and I'm always interested in the simplest possibility because I think it's likely to be the most testable. So, if the universe kind of defines itself, then, um, then all we need to do is to see which, so applying whatever condition we have, we have CPT symmetric, uh, condition which allows us to count the states using Hawking's method. Um, but other people may have other proposals for kind of the beginning of the universe or what is how how does the universe become self-contained. Count the number of possibilities and just pick the typical one. And if your theory says this is typical, then it's, it's a good theory.

>> Why is simplicity so important?

>> Um, because it leads to, well, why is it, why is simplicity important? It's important because it's what we see in nature. Okay. I honestly believe that for some reason, we do not understand, the universe is able to teach us about itself, its laws. Um, and, you know, that's very fruitful, because when we learn about its laws by observing it and even experimenting with it, um, that become, that knowledge becomes incredibly powerful, right? And so, yeah, it's a deep mystery why the universe is comprehensible. Part of that mystery is that, of course, we have evolved precisely by understanding the universe. So we have sort of crept along this path of understanding, but it's still a mystery. Why is that possible? Why is it possible to learn about the universe from within? Um, but it, but it's a wonderful mystery and very compelling. You know, if we can learn about it, let's do it, see where it leads us. So I believe in simplicity just because the universe has turned out to be astonishingly simple. I mean, this goes back to Pythagoras. Pythagoras, you know, who understood geometry, talked about the harmonies in the heavens, and realized music is nothing but, or how, how should I say, harmonies, uh, are mathematical in nature. Music sounds good because, you know, when things are sort of in the right ratios, and then he thought that geometry also would apply in the heavens. And so that was a sort of philosophy which led to people like Galileo trying to figure out what are these mathematical laws, and that worked. I mean, the inverse square law discovered by Newton, you know, incredibly powerful universal law. Why does it exist? We don't really know. But as physics has evolved, it's become more and more complete. Um, and my point of view is that maybe the physics we already know is 99.9% of the story. It has internal contradictions. But well, it may be just as fruitful to try to resolve those contradictions in a as minimal a manner as possible, right? That may be more fruitful than than going off down some, you know, diverging path which is driven by prejudices. Uh, so I think we've always got to keep an open mind. But, but what keeps us honest is this search for simple explanations. And for me, that's the most important thing in theoretical physics, theoretical physics, not to lose sight of that. It's not mathematics. I mean, mathematics is, you know, just, um, I shouldn't say just, because physics sort of feeds on mathematics, so mathematics is extremely important. But in mathematics, it's much less constrained. You just invent logical frameworks and try to see where they lead you. Um, whereas in physics, the focus is in which of those frameworks actually describe nature.

>> So what if a string theorist and a many-worlder said to you, Neil, we also care about simplicity.

>> Yeah. >> Actually, string theory is the simplest theory that comes out of extremely minimal assumptions, minimal zeros, ultra softness, and then the rest, and variance, and so forth. You agree with. >> Many-worlders. We, we actually care so much about the measurement problem. We can do away with the projection axiom. >> Right? >> So we actually minimal in that we're shaving, and as a consequence, you get some proliferations, but we're not looking, we're not seeking. >> To have so many children. We're not seeking. >> They are looking for a simple picture. They're certainly looking for a unified simple picture, but without. Yeah. So they would argue that inevitably, as a consequence of, um, their simplifications, they have made, they get enormous complexity in some respects. I mean, I think nobody could argue that a multiverse is the most complex thing you can imagine. Okay. So when they say that our prescription for simplicity leads to a multiverse, I definitely think they are obligated to go back and list very carefully what their assumptions were. And as I mentioned, one of them is that quantum mechanics requires a Hilbert space. Okay? And I think our work shows that's not true. Uh, and given that one of the assumptions which they didn't even make explicit has turned out to be possible to violate, the whole story about a multiverse being mandatory, I think is in doubt now. I never liked the multiverse anyway because I felt it, you know, if, if that's, if it really is true that that's the unique consistent theory, you know, physics is over. So I, but that's just a, you know, that's a prejudice on my part. Um, uh, so, yeah, but I think the important point is we really have to look at your assumptions very carefully if it leads you to crazy conclusions. I do regard many worlds as an equally crazy conclusion, um, which is the state, you know, it's just this enormous redundancy. You've got a theoretical framework in which you have all these universes branching and running in parallel, and the branches get bigger and bigger, and I strongly suspect this is completely ill-defined. I mean, I don't think anybody claims, you know, when spaces become too infinite, you just can't do math on them, right? That it's not in control, and it's always the same problem, is that there is no measure. Um, and so when I tell you a funny story, when when multiverse ideas first started getting popular in particle physics, I had a friend who knew, now what's his name? In A Beautiful Mind, the mathematician John Nash. >> John Nash. Okay. So, John Nash was obviously very brilliant, foundational thinker about mathematics, right? And and pretty crazy, as such people are. But a friend of, we started worrying about the multiverse, and a friend of mine went to ask John Nash, you know, what do you, now, actually, it wasn't even the multiverse. In inflation, you find that you find bubbles, uh, which are called, Alan Guth calls them pocket universes within the universe. You get a pocket universe which is infinite in extent, and now you kind of have to ask, where do I live? And so there's the measure problem. >> Right, right. >> Uh, inflation has this measure problem. Nobody's ever solved it. So a friend of mine went to Nash, and can you define a measure on an infinite space? And Nash says, no, it's ridiculous, no chance. Okay. So unless you have some special symmetries or, you know, something that really guides you, you are lost. If your theory makes a randomly infinite space, you know, goodbye, it's not going to be a predictive theory. And I suspect the many worlds picture is suffers from the same problem, that nobody's ever going to really be able to quantify probabilities or anything. It's, it's a, you know, it's a bad nightmare. So we'll see, maybe it'll turn out to be, maybe they will do well. But, but I, yeah, but I think it's, so for me, simplicity leads to predictivity. You know, it leads to understanding, and that's a kind of virtuous cycle, and we can never give up on that. Um, and, uh, it's very easy to go off pie, um, and convince yourself that, you know, what you, the, this crazy scenario is a logical consequence of your, of your theory, whereas in fact, you're blind, you, you're blind to your own assumptions. That's, that's the, the biggest gripe I had I have about, um, contemporary popularity. You know, the most popular orthodoxies, both in particle physics, cosmology, and so on. These orthodoxies are insufficiently self-critical, and especially they tell young people, it has to be this way. Okay. Uh, whereas I think it's much more valuable to tell young people, you know, we've reached this crazy conclusion. Can you figure out a way out of it? Um, and, and just be honest about the limitations and the unlikelihood of your framework actually actually being valid. I mean, uh, I'm, I'm always open to to and encourage young people to criticize my framework as much as everyone else's. Uh, and if there's a real flaw, we, we should want to know as soon as possible. But rather few people are thinking about the foundations. Rather few people. Too many people are just recycling orthodox ideas.

You're in a unique position. You used to be the head of Perimeter. >> How do you see the health of theoretical physics?

>> It's, it's a, it's a wonderful field. Uh, it's a miraculous field. I mean, our predecessors did unbelievable things. Uh, Dak and Maxwell and Einstein and Newton, you know, these are, what they achieved is just, is still, the more we understand, the more miraculous it it seems. I think the field has been very poor about strategizing its own future. Theorists like me are so fascinated with what they're doing, they don't actually spend the time to think, how do we keep the field healthy? And especially all about young people and about encouraging diversity of cultures, of outlooks, of origins, of, you know, points of view. Uh, too often the older people encourage orthodoxy, which is very unhealthy. So, yeah, I think it's rather poor at, um, looking after itself and keeping healthy. Perimeter was an incredible opportunity because it had very good support from a donor. The government matched it, and we had amazing freedom. Uh, so I enjoyed it like crazy. It's doing very well now. But to be honest, I feel that in my role as director who built it substantially, uh, I was probably too conservative. And to, you know, the, the whole challenge is to persuade government to keep funding you. Um, and it's easiest to make the case if you're getting high citations and you're, you know, stealing people from, uh, Harvard or whatever well-known places. So the temptation is to is to evaluate yourself by, uh, the standards, you know, of the majority or the orthodoxy. Um, and I think that's unfortunate because it's really crucial to the health of the field to promote, uh, people doing unorthodox directions. There's not enough of that happening. So my worry about Perimeter is that it must continue to promote, uh, foundational thinking, and especially young people who are questioning the orthodoxy. That's tough to do in today's, uh, climate where people are worried about getting jobs and next grant and everything seems insecure. But I think the very instability of the world today, although it's awful and frightening and worrying, we're all, who knows what'll happen with AI, there are all kinds of wars going on, the global order is breaking down, maybe. So terribly worrying things, as bad as they are, I'm not in favor of them, but that in itself is incredibly stimulating of people who are questioning. You know, if the world is totally stable, um, then there's no real incentive, uh, to question things. So the very instability of the world, >> Interesting. >> tends to promote unorthodox thinking. Uh, you know, people, people say, look, the world's crazy, okay? So I'm going to focus on this little corner of intellectual thought, and, you know, it's very rewarding. I mean, you must find this running your podcast, you're, it, it takes you out of the real world and all of its problems because, and you're looking for beauty and simplicity and, and, and inner fulfillment, right? And that's great for foundational thinking. So, so I do think we're entering a phase where I am expecting revolutionary ideas to come out. Uh, and that's very exciting. And, you know, it's, it's not that hard to be a researcher, certainly in theoretical physics these days. You can go to a coffee shop, you, you got a laptop, you know, laptop's very powerful, even if you want to do some math computations or whatever. So it is becoming much more accessible. And your podcast, somebody wants to know what's, you know, important in physics. They can learn much faster than they could 10 years ago, thanks to your podcast and other things. So I think that's very interesting. A lot of people, I get email all the time from people saying, my, I've got a much better theory than yours. You know, help. But, you know, that's good. It's healthy that people are trying these things. What you have to do is try to see how to put, I mean, obviously you need some kind of filter. Not every, a lot of cranks out there too, but, um, we have to strategize the field. So somebody very bright, very original can very quickly get to a place where their ideas can be critiqued by experts who can tell them, you know, you're wasting your time, or you've, you're really on to something. So I, I really hope people who are influential in, um, science funding and in government will think about this. How do we create roots? And by the way, Canada is an exceptionally sort of welcoming country, has been, and it's the perfect place. So I, I sort of hope Perimeter can play some of that role, Canada more generally.

>> Well, thank you for coming to Canada for to Toronto to come.

>> It's such a pleasure to meet you in person and congratulations on everything you're doing. I think it's awesome.

>> Thank you. And well, to the extent people like the podcast, it's for the guests. So, thank you.

>> No, no problem. Anytime. Anytime. Um, no, I would, uh, you know, if you're interested in in talking to my student Sam, this guy Sam Bateman. Interesting example because he came to Edinburgh. He's from Ireland, where they teach a very mathematical oriented physics course in in Dublin, uh, in Trinity College. And he came to Edinburgh for a year to do masters, just saying, I'm not sure I want to do this, but, you know, let me just have a look, which is the best attitude. And so he did a little project with me, it didn't particularly work out, but, you know, he sort of enjoyed it. So the end of the year, he said, I'm, I'm not sure I want to do a PhD, but yeah, let me, let me try. So unlucky for him, he started doing a PhD with, and I gave him this impossible problem. >> Yeah. >> You know, because I thought the sky could be interpreted as a four-derivative theory. Let's try to quantize four-derivative theories. Seriously. Now, anybody else would tell you this is impossible. You know, you, you're just killing this guy's career. And sure enough, sure enough, after four years, >> we had made very modest progress, right? We, we'd looked at Bender and Mannheim, and there's actually a whole literature, lots of people trying different directions, none of which really worked. And then last September, when his funding had run out, okay, Sam says, "I think I know how it works." You know, and indeed, and all it took is a slight tweak of the Born rule, you know, which >> and financial insecurity. >> And financial insecurity, right? He's relieved of that, and the conviction that he's not going to get a job. Okay. So don't worry about it. And suddenly it all clicks together. Okay. So then what happens is now, so this is a PhD student with no papers, right? And that's my fault, cuz I said undoable problem. But then somebody comes to visit Edinburgh, guy called Raju Benug, Benugopolan, who's probably the world-leading expert in nonlinear quantum field theory effects like QCD. He's now director of the only funded accelerator in the world at Brookhaven. So Raju comes, and he's a very, very good quantum field theorist, and he meets Sam, and Sam is giving informal talks, and Raju realizes, oh my god, there's something here, right? And so next thing, Sam got offered a postdoc at the Simons Center in Stony Brook. >> Wow. >> With zero papers. >> Holy moly. So that's where Sam's going. But actually, Raju is having so much fun in Edinburgh. He's extended his visit to December, and so the three of us can work together. But, you know, that's the way it should work. All this chasing papers and, um, and Sam is this unworldly guy who's only doing it, you know, because he likes he likes doing it. And in the process of, you know, it's kind of miraculous, you discover a little thing, you can do it. It's not so little. He had to master covariant quantization of field theory, the textbook of this was written by Bogoliubov, um, the most recent one in the '80s, huge textbook, rigorous algebraic quantum field theory. Okay. I guarantee you, you know, 99.99999% of all practicing theorists have never even opened this book. It's too heavy. Sam learned how to quantize this four-derivative theory from this and other books. Um, and for me, this is not my specialty. I mean, I was much more applied in calculating cos, you know, CMBB and isotropy and things like in the cosmology. I mean, I did work with Hawking, but I'm not, I'm not a very sophisticated mathematician in any way. So, you know, Sam brought that, and then we worked together. It's very, very exciting. So now Sam is absolutely determined to to, you know, continue in quantum field theory. Um, and, uh, yeah, it might be interesting for you to do a podcast with him or other students. See what do they make of it? What do they make of the current >> Um, situation? They're terribly confused. I mean, imagine you go into theoretical physics today, and there's string theory, which isn't really working. There's Lenny Susskind telling you, I know the answer, it's holography, right? But I don't know how to do it. And, you know, I encourage a student to do it. I mean, would you go and do it with him? You know, its track record isn't, I mean, it's a brilliant guy, but the track record isn't that great. He's been advocating string theory for 50 years. Hasn't panned out. Um, so, yeah, it's a really confusing time. Um, you know, or you just go into astrophysics and and deal with data and observations and so on. But, you know, the stuff you're interested in, and I'm interested in, is the is the deeper theoretical questions. And there's some students who really want to do that. Um, but there's not really good environments for them. Um, even Perimeter, like I said, it's sort of too dominated by orthodoxy. Um,

>> What do you mean? You keep saying orthodoxy and conservatism specifically. What are you referring to?

>> Well, you encounter it all the time. I mean, um, people, I mean, most often in referee reports. So you submit a paper, and because the sheer volume of papers now being published, um, means that any one paper can't get more than sort of five or 10 minutes of a referee's time, you're just drowning in it, and so they have a quick look and they say, "Hey, I don't think this is consistent with B," and they, you know, send it back and reject it. So they're not really, I mean, there are some good referees, but by and large, and grants decided in similar way, very rapidly, very superficial arguments. Um, and, and jobs, the worst thing. I mean, you just ask any young person, any postdoc who's getting offers, and the one getting the offer will be the one working on a popular paradigm. Uh, and most of these paradigms have in the end not been successful. So why, why are all the jobs in paradigms which haven't worked? So then another side effect is that, um, string theory has had big spin-offs into math departments. So lots of math departments have hired people to do string theory, and those people in general don't care about observational predictions, right? They're just interested in the formalism. And so I, I'm happy for them that they've got jobs, but, you know, it's, it's tended to sort of dilute the field. Now the field becomes about mathematical issues which are not related. Like supersymmetry, supersymmetry is a huge thing in math departments. Why? You know, because it's mathematics, it's re, I don't think it's particularly exciting mathematics, but it is, it can be good mathematics. It's not earth-shattering. Um, and, uh, and but it, you know, it's not physics. Um, and so for a young person, they tend to get steered in the direction where there are jobs. They st get into mathematical formalisms, conformal field theories, and other. This is a great subject, but, you know, by and large, it's nothing to do with reality. Um, and that's where the jobs are. And so there are the few people thinking about the foundations of physics as they relate to actuality.

>> I was speaking to Harvey Friedman, who's a mathematician who invented reverse mathematics. I don't know if you've heard of him. He's also the youngest professor ever, at least at the time, 18 years old.

>> I read about this, or maybe it was from your podcast. Okay. Thank you. No, pleasure. I, I think that is so important, and I wish for my own career, if only when I was, you know, 20 years old, if I had realized, if I could give myself advice, you know, back then, I would have said, work hard on the foundations. You know, instead, I got my PhD place, I listened to my advisor, he said, here's an interesting problem, go and work on it. You know, it took me a year to figure out it wasn't that interesting. Um, and I didn't question the orthodoxy enough. There, you know, what was in fashion was grand unified theories, and people worried about magnetic monopoles and cosmic strings, and there were all kinds of, you know, things people were worried about. And, um, I spent very little time worrying about the foundations of quantum mechanics, of gravity, and I wish I'd spent more. Um, and I would advise young people now, that's the most important stuff. If you actually want to discover something, the more time you can spend on foundations, the better.

>> Do you think the aversion to it is not only job prospects, the lack of them, but also there's the twin fear that that's where the crackpots tend to be, and I don't want to be that. Maybe that's also in line with the lack of jobs.

>> Absolutely. Absolutely. And it's not without foundation. >> And I put crackpots in quotations. I'm not to, I'm just saying these are quotes that I've. >> No, no, that's absolutely true. I mean, when I was a postdoc, I was in Santa Barbara, and a guy came, I think it was, I think it was, um, I can't remember his name, um, don't want to say it wrong, but a guy came to give a lecture about the foundations of quantum mechanics, and it was so woolly, it was sort of French philosophy at its worst. >> And, you know, rambled on and on about foundations of quantum mechanics, and we just thought this was the biggest joke. Um, and it probably was, okay. But then what happened is people started working on quantum foundations who actually were, um, yeah, more, uh, a little bit more mathematical. Had there was this prospect of quantum computing, which kind of focused the mind on what is really important. So there was an idea of actually testing these ideas and, and, and, uh, designing experiments to, like, um, you mentioned the guy at Toronto, um, you know. >> Oh, from Steinberg. >> Steinberg. Yeah. So, and his advisor was, uh, Yak Aronov. >> Oh, right. Right. >> So there were these ideas which were very much all about Gedanken experiments, and can we prove the weirdness of quantum mechanics in various contexts? And that was really fruitful. So that's foundations, but with a very strong focus on actually seeing stuff and testing stuff, and that's fruitful. So, yeah, I think foundations, when it becomes, if you like, I mean, I love philosophy, but it, when it becomes pure philosophy with no implications for anything else, then, you know, it's less interesting. Um, but, uh, yeah, I think the best philosophy is actually relevant philosophy in some way, uh, telling us how to live our lives, or or how we shouldn't live our lives, or what's, yeah, what the meaning of our lives are, why life is amazing and, uh, uh, challenging. Philosophy is very good at challenging physics and saying, you know, you're, you're, you're not making sense. Um,

>> Actually, Scott Aaronson said that he's never had to choose his words more carefully than philosophers. >> Right. >> Which sounds like the opposite of what most mathematicians, physicists, scientists tend to think. They think philosophers are those wishy-washy, unfalsifiable, ill-defined people.

>> It depends on the philosopher. There are people like that, but there are a lot of very rigorous thinkers, uh, in philosophy, and I think their skeptical turn of mind is extremely helpful, uh, because then they will press you, uh, to say, you know, are, is what you're saying actually meaningful? Um, so no, I think it's very fruitful interactions. But somehow, the people who do make advances in physics, I'm more concerned that kind of young people questioning the axioms of physics and trying to vary them and explore to what extent we've argued ourselves into a corner. Uh, and can we get out of the corner? You know, those are the young people. The, I think it's always true that the youngest people are going to be the most important for the future.

>> Jacob Barendes, who's a philosopher of physics. Yes. He said that if you have money and you're watching and you want to donate, the highest ROI comes from the philosophy of physics to actually produce fruitful new physics. Why? Because there's such a tiny amount of philosophers of physics.

>> That's true. >> And then if you actually look at what they produced, so David Deutsch with quantum computing, >> Right? >> Weak measurements. >> That's true. >> Entanglement, Bell's theorem. >> That's true. John Bell. Exactly. Yeah, I think that's true. Uh, funding should look at the underpopulated areas. And in fact, that was the secret of Perimeter's success is that when Perimeter started, nobody was supporting quantum foundations, and Perimeter, the first director, Howard Burton, decided to, that's an opportunity. So he recruited people working in quantum foundations like Lucien Hardy and, uh, Rob Spekkens, and Perimeter sort of cornered the, uh, it in quantum foundations, and people would come to visit, and it became a real hub for, which eventually turned out to be very fruitful. Um, so, yeah, so I would agree with him on on that. But, um, yeah, I would say more broadly, uh, it, quantum mechanics isn't the only game in mentality. You know, quantum mechanics is the non-relativistic version. When you bring in relativity and quantum field theory and gravity, that's where the power of physics really becomes extraordinary, and in cosmology, it's, it, it's more incredible than anywhere else. So I think the quantum, the philosophers of quantum mechanics are only looking at a very limited corner. Um, it, it's tough because to do cosmology, you've got to essentially know all of physics, right? All of physics is involved, and that's a big field. So, and it's scary, and you've got to deal with, um, and so I think there's a danger in philosophy is that you will end up just studying a little corner of some small aspect of physics, and whereas the, the big questions about physics are, are, are, yeah, ultimately involve cosmology.

There are surprisingly few philosophers of QFT and philosophers of GR. There's some, but there are surprisingly few. Then I don't think I've ever heard of a philosopher of cosmology, but if you're watching, please. >> I. >> I would like to know.

>> I think that's a very good point. If somebody started a course in philosophy of cosmology, it probably attracts vast numbers of students. Um, and, and yeah, it, it has so much to offer. You have, uh, all kinds of wild ideas like the steady state theory, and then there's inflation, and there's, you know, so, but most of all, we have these unbelievable observations. We're seeing black holes merge, and, you know, so we, we really are in a golden age for the field observationally, and we're very poor, uh, in terms of the theoretical range of ideas to make sense of it all. Uh, the universe is helping us because after all, it's really simple, and it's basically fitting, uh, extremely simple ideas. But, you know, why, where does that simplicity come from? What are the principles governing it? You know, in fact, I, I learned an interesting proposal which probably has some merit. You know, you can ask the question, why is the universe the way it is? Why the laws the way they are? And maybe it's the minimum you need to produce complexity at this level. So this can sound a little bit like the anthropic principle, but that's not what I'm saying. You know, something to do with human beings per se. It's self-organizing. The universe has this capacity to produce structures. So let me see if I got that correct. Yeah. >> So first, let's imagine we can quantify complexity. >> Right. >> So we can look at a variety of universes and say, this universe has complexity number 1,000. This one has 10,000. This one has 5,000. Yeah, there are. >> Then I ask, okay, what is the shortest program in a sense to produce this 10,001? >> Exactly. >> And then this one, and then this one. >> Exactly. >> And then I say, what is the ratio, the largest ratio between. >> Right. Right. >> Yeah. Yeah. >> Okay. That's interesting. >> It may well be that's correct. I think it's a very attractive idea that somehow the universe is is optimal at producing complexity out of simplicity, and it certainly seems that way because, you know, as I say, on small scales and large scales, unbelievably simple, it's really nothing interesting, uh, happening. But on the mi, in the middle, um, it's evolving in ways we can't predict now, and it's getting ever more complex, and, um, uh, capable, right? So. >> That sounds like a computer science question now. >> Yeah, it is. It is. Ultimately, physics is about information, for sure. And John Wheeler was the person who argued that. I was very lucky to know him personally, amazing character, such a kind, um, and absolutely visionary, person. Uh, we need more John Wheelers, that's for sure. So if there's a course on philosophy of cosmology, that's the target audience is the John Wheelers, cuz they can be incredibly, uh, helpful. I better go. >> Sir. >> No, it's very great pleasure. Thank you. Thank you. It's so much fun to meet in person. Thanks for coming. Yeah, I hope we meet again.

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