Theories of Everything with Curt Jaimungal - The Theory of Gravity That Shouldn't Exist

Episode Date: April 9, 2025

Head on over to https://ver.so and use coupon code TOE at checkout to save 15% on your first order. As a listener of TOE you can get a special 20% off discount to The Economist and all it has to offer! Visit https://www.economist.com/toe Today we are joined by theoretical physicist Claudia de Rham for her return appearance on Theories of Everything with Curt Jaimungal to discuss the possibility that gravity itself has mass. In this mind-bending conversation, she explores how this idea challenges long-held assumptions in general relativity and opens the door to a new understanding of dark energy and the structure of the universe. We also dive into the frontiers of cosmology, quantum gravity, and what it means to question the foundations of physics. Join My New Substack (Personal Writings): https://curtjaimungal.substack.com Listen on Spotify: https://tinyurl.com/SpotifyTOE Become a YouTube Member (Early Access Videos): https://www.youtube.com/channel/UCdWIQh9DGG6uhJk8eyIFl1w/join Links Mentioned: •⁠ ⁠The Beauty of Falling (Claudia’s book): https://amzn.to/4i4Z9cx •⁠ ⁠Claudia’s published papers: https://profiles.imperial.ac.uk/c.de-rham/publications •⁠ ⁠Claudia’s first appearance on TOE: https://www.youtube.com/watch?v=Ve_Mpd6dGv8&t=83s&ab_channel=CurtJaimungal •⁠ ⁠Carlo Rovelli on TOE: https://www.youtube.com/watch?v=hF4SAketEHY •⁠ ⁠Curt’s Substack article on energy: https://curtjaimungal.substack.com/p/what-is-energy-actually •⁠ ⁠Neil Turok on TOE: https://www.youtube.com/watch?v=ZUp9x44N3uE •⁠ ⁠Tim Palmer on TOE: https://www.youtube.com/watch?v=vlklA6jsS8A •⁠ ⁠DESI article on The Economist: https://www.economist.com/science-and-technology/2024/06/19/the-dominant-model-of-the-universe-is-creaking •⁠ ⁠String Theory Iceberg on TOE: https://www.youtube.com/watch?v=X4PdPnQuwjY •⁠ ⁠Leonard Susskind on TOE: https://www.youtube.com/watch?v=2p_Hlm6aCok •⁠ ⁠Chiara Marletto and Vlatko Vedral on TOE: https://www.youtube.com/watch?v=Uey_mUy1vN0 •⁠ ⁠TOE’s telling of “The Dark History of Anti-Gravity”: https://www.youtube.com/watch?v=eBA3RUxkZdc •⁠ ⁠Positive Signs in Massive Gravity (paper): https://arxiv.org/pdf/1601.04068 Timestamps: 00:00 - Introduction 01:20 - Claudia's Approach 09:11 - Claudia's Motivation 14:45 - Dark Energy 23:35 - Causality 27:19 - Other Approaches 45:10 - New Physics 50:47 - Dark Energy (continued) 57:36 - Quantum Gravity / String Theory 01:14:10 - Gravitons & Photons 01:21:44 - Symmetry 01:30:25 - Double Slit Experiment 01:50:15 - Cosmology 01:54:45 - Massive Graviton 02:00:10 - Conclusion Support TOE on Patreon: https://patreon.com/curtjaimungal Twitter: https://twitter.com/TOEwithCurt Discord Invite: https://discord.com/invite/kBcnfNVwqs #science Learn more about your ad choices. Visit megaphone.fm/adchoices

When I was doing my PhD, I had just bought into all of these theorems. They were written by very famous people, but we realized that we were able to violate these NERGO theorems. General relativity can't be the final answer. What if gravity itself has mass? This seemingly simple question challenges decades of foundational physics. In this second conversation with Professor Claudia de Rham of Imperial College London, we venture even deeper into her revolutionary theory. De Rham didn't set out to overturn any established physics, she was searching for an explanation

for the cosmos' accelerating expansion. However, in doing so, she discovered that the impossible may indeed be possible. Gravity itself may have mass. This is known as massive gravity. This potentially solves the so-called cosmological constant problem that has puzzled physicists for nearly a century. As we explore the implications of this massive gravity, we talk about, well, what does that even mean?

We'll also discover how symmetries emerge from chaos, why energy may be a concept that we need to abandon in dynamically curved space-time, and what recent cosmic observations tell us about the fate of our universe. Tell me about a time where there was some established physics theorem and you found a way around it. What was that theorem or folklore or concept and how? How did you find a way to circumvent it? So one thing I've done is related to a no-go theorem related to massive gravity.

So maybe I need to unfold this a little bit, what massive gravity is and what the no-go theorem is. So we understand gravity thanks to Einstein's theory of general relativity and there's a little bit of this tale that tells us that we don't know how to reconciliation gravity with quantum field theory. Actually that's not quite true. In Einstein's theory of general relativity we do understand how we can describe gravity as a particle. We can call this particle the graviton, that doesn't matter too much. But we do understand that very well, so we can embed gravity as in Einstein's theory of general relativity into a standard field theory framework and represent the force of gravity a little bit like the other forces of the

standard model of particle physics, like the electromagnetic force. So for instance, we know how gravitational waves are a little bit the analog of electromagnetic waves. And we can ask ourselves in principle the question as to the gravitational waves, which are carried by light. We can in principle ask ourselves the question as to light, which are electromagnetic waves, whether the particle that carries them may be a massive particle. So in the standard model, as we understand it at the moment,

we think of light, we think of electromagnetic waves as being a massless phenomenon carried by a massless particle. But in principle we can think of it as a massive particle and we can put a bound on how massive the photon, the particle carrier of light, would be. And there's no issue with that. We have bounds from observations on how heavy, if it were, electromagnetism or light would be. And so we can ask ourselves the same question, in fact, for gravity.

This is a very sensible question to ask ourselves. In fact, it's the first question we should really ask ourselves when we think of gravity as being carried by a fundamental particle like the graviton. You may ask yourself, what is the mass of this particle? Is it massless or could in principle have a mass? And if so, what is the constraints from observations on that mass?

And this is where the hiccup comes in. This question was already been addressed or tried to be addressed almost now a hundred years ago, already since Fiat St. Pauli in 1939. They already tried to establish whether it would be possible for the graviton or a field that would behave like the graviton to be a massive particle. And it comes up with all sorts of different luggage along the way. And they realize that it is in principle if you just wanted it to be completely independent, completely isolated from anything else.

But we don't want the graviton to be completely isolated from anything else. We like it to be interacting. We want it to be the structure of space-time. We like it to be realizing the reality in which we live in. And therefore, we can't just think of the graviton as being an isolated particle not interacting with anything else. In fact, this is a virtue of gravity that it interacts with everything. This is based in universality, the equivalence principle of general relativity, which tells us that everything and anyone interacts with gravity and gravity interacts with everything and everyone. So as soon as you want to think of gravity, you also need to think

of it as interacting with everything else. And so this is where the issue came in. People were able to give a mass to the graviton or to People were able to give a mass to the graviton or to think of how to give a mass to the graviton. But as soon as this graviton started interacting with other particles or even with itself, there seemed to be a no-go theorem. So a challenge which was impossible to overcome to the point where people came up with theorems

that told you exactly what would go wrong if you were trying to think of, even in theory, of having a mass for the graviton. And the no-go theorem came under different names, but they were always boiling down to the same aspect, which is that as soon as you think of the graviton having a mass, then you start exciting some modes for gravitational waves, which would carry negative energy. And so maybe we can go to the notion of energy in a bit, but for now we can just think of having some modes, some modes for polarizations of gravitation waves, which would have negative energy. And so in principle, as soon as you think of the graviton being massive and interacting

with the rest of the world, you could have some processes getting energy and taking this energy with an infinite negative pool of energy of the massive mode of the graviton. And that would lead to a complete instability, in fact, an instantaneous instability of even the fabric of space-time as we know it. So that's the curse of the matter for why we can't in principle, or there was no-go theorems as to why we couldn't give a mass to the graviton. So there was no-go on massive gravity. And this came up in different formulations.

But? Yes. This came up in various different formulations throughout the decades, particularly in the 70s, again in the 80s and in 2000. And in fact, when I was doing my PhD, when I was doing my postdocs, I had just bought in into all of these theorems. They were written by very famous people. Then I'm going to name them, but I was certainly not going to go and contradict them in any

way. But we realized that we were able to build a model based originally from extradimension, which in fact was violating these NERGO theorems. It was based on extra dimensions and so that's why we thought we could get some leverage from that. But in fact we could in principle just represent it from a four-dimensional point of view. When we look at it from a four-dimensional point of view, we saw that the no-go theorems should be that I would tell us that something could go wrong, wasn't going wrong at the order that was predicted.

So this really motivated to better understand what were the assumptions behind those no-go theorems and what were the real implications. And we realized that, in fact, it was way too quick. The assumptions were good, but the realization of those assumption into no-go theorems were always using some shortcuts, which in fact could be overcome. And so there was many different realizations

of those theorems in different languages, but we got the motivation to really look into each thing, each and every single one of them when we realized that in fact there was much more to it. And so then realizing that there was a way to bypass this no-go theorem, we then realized how to in fact completely formulate a theory of massive gravity, which was free from all of the pathologies that people thought should exist before that. So you weren't looking to evade the theorem initially, or outwit the people who formulated it. What was it that motivated you then in that direction? What was the spark that let you think, okay, maybe grass, sorry, grass is massive, maybe gravity is massive?

So what we wanted to do other time, and in fact, I still think it's a good idea, precisely how to realize it is challenging. But what we wanted to do other time is try to understand whether we could tackle the cosmological constant problem related to the late time acceleration of the universe with a better understanding of gravity at large distances. And at the time, there was all sorts of work based on extra dimensions because it was realized from string theory that you could have extra dimensions out there. And in fact, from M theory, one of these extra dimension could be large in the sense that it could be even millimeter size.

So there was all sorts of different ideas in trying to understand what is the representation of gravity from a four-dimensional point of view, and whether the leakage of gravity within the extra dimensions could in fact lead to modification of the behavior of gravity on large cosmological distances and this could help us understanding how to tackle the cosmological constant problem. The cosmological constant problem is very much as the interface between

quantum particle physics and gravity and it's coming from the fact that we would have expected to have all of the vacuum energy, the quantum vacuum energy of all the particles that we know of, to gravitate. And to gravitate with an amount that effectively the universe not only should be accelerating, but should be accelerating by many, many orders of magnitude larger as compared to what is being observed. And this in

fact, this cosmological constant problem or this quantum vacuum energy problem is also been known since almost a hundred years now since Pauli and even other people before him. At the start of quantum quantum field theory, very much so, people realized that if you consider the quantum vacuum energy of electrons, simply of electrons, they should populate space-time and lead to an accelerated expansion of the universe, which would mean that space between the Earth and the Moon would accelerate so fast that we shouldn't be able to see the Moon anymore.

And this is something that was postulated, that was written down, that was understood as a challenge already since Pauli at the very, very start of the formulation of quantum field theory, or even quantum mechanics in fact. And so faced with this problem, people thought that there was something one was missing in how a cosmological constant or how quantum vacuum energy was gravitating. And maybe for a symmetry reason or another reason that evades us as the moment, really the universe is not accelerating. And so that was the lure actually for almost 80 years until it was realized that the universe

is accelerating. The universe is not flat. It is expanding, but this expansion is also accelerating. And this is really the challenge because we would be happier if we would say, for a reason or another, I don't know what's happening, but there's no acceleration altogether. So all of this quantum vacuum energy, even though it should lead to an accelerated expansion of the universe, let's just forget about it and there may be some other phenomenon coming in the game. The issue is very much when all of a sudden we realize that the expansion of the universe is accelerating, but by really

just a ridiculously small amount. So what is it? Is this this quantum vacuum energy leading to an acceleration of the universe? Or it's not, and then we need to add something else, but no formulation is perfect. So what we were trying to do at the time is trying to understand whether it is this quantum vacuum energy that leads to an accelerated expansion of the universe, but not as much as one would have anticipated according to Einstein's theory of general relativity, because gravity is actually leaking in the extra dimension. And so this is something we don't see on short distances in the sense of we don't see that on solar system scales, on galactic scales, on cluster of galaxy scales, but it's something that we start seeing on very large cosmological distances, on the distances where we really see the accelerated expansion of the universe.

So that was the idea at the time. Um, not at all to go back into a theorem led by my great heroes, but much more into trying to tackle these issues. And we thought at the time we knew that it would be challenging to come up with a model, which was purely four dimensional, um, because of all those no-go theorems. So that's why we were basing ourselves on extra dimensions where the effect of the extra dimension may look like non-local from our four-dimensional perspective, so may look, may be expressed in a slightly different way, and yet could lead to effectively an accelerated

expansion of the universe. I have a variety of questions about energy, and we'll get to what is energy shortly, especially what is negative energy. But let's talk about dark energy. To be clear, dark energy is a placeholder for our ignorance regarding the cosmic acceleration. And then vacuum energy is seen as a natural candidate. But the problem is that it predicts these absurdly high acceleration rates. That's right.

So is there another reason other than that the vacuum energy is cancelled? So supersymmetry would say that the vacuum energy contributions are cancelled. Is there another reason that the vacuum energy shouldn't even factor in to the cosmological constant? Like it's a category error to think that we should be summing over bubbles and that should have bearing on the cosmological constant. I don't usually stop mid-conversation to talk about molecules, but this one's different. I've been taking something called cell being by Verso, and if you're into longevity science like David Sinclair, NAD+, that whole world, then this is exactly

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Verso also third-party tests every single batch and publishes the results. So you're not getting any mystery capsules here. If you're curious about aging well or want to feel better or think more clearly, then check it out. Go to verso.so.toe. And use the code TOE to get 15% off your first order. That's ver.so.toe. Thanks to verso for supporting this episode and supporting my health. And that should have bearing on the cosmological constant. So, the answer is we don't know. We don't know for sure. We don't really know.

So even for instance if we take supersymmetry as an example, it is an amazing symmetry that would cancel the contributions when the symmetry is being satisfied. So it is very possible that the realization at high energy is supersymmetric. So, if we discover new particles at the LHC or next particle collider or anything else, we will start seeing some signs of supersymmetry. That is still very much possible. And it is still very much possible that supersymmetry is being restored at a given scale. But the world that we experiencing at low energy is clearly not supersymmetric.

There's not a clear partner for each, for instance, Boson, there's not a clear famionic partner. So supersymmetry, the reality, it has to be broken below a given scale. This is observation. This is the reality of the has to be broken below a given scale. This is observation. This is the reality of the world that we live in. So even if there were supersymmetry that would cancel all of the high energy contributions, the contributions from the particles of the standard model, so the contribution from the particles that we know we are made out of, electrons, the top quarks, the Higgs, etc., they should in principle lead to a contribution to the quantum vacuum energy, which is not cancelled out by supersymmetry.

So there may be another symmetry out there, but supersymmetry is doing an amazing job at potentially cancelling out all of the contribution beyond, let's say, even TEB scale. But below that, we still need to face the fact that we have a leftover from the standard model which will not cancel by supersymmetry. Now it is a little tricky when we say the quantum vacuum energy of for instance loops of electrons lead to contribution to the interact with graviton and loop lead to quantum.

It is a little bit tricky when we say that loop of the particles of the standard model lead to a contribution to the quantum vacuum energy. In fact, what we're doing there is compute some loops, which technically add infinite. And so we need to do a renormalization procedure. And if we do the most conservative regularization, if I do for instance what I'll call dimension regularization, so I'm not putting a cutoff at high energy and not doing any of this, I'm just looking at how the contribution of these bubble diagrams, these loops flows with energy.

I see that for each massive particle, it leads to contribution which scales like the mass of this particle to the power of four. This is the most conservative way to do things. It is still possible that we don't understand everything in this regularization and renormalization procedure. That is very possible. However, we understand this renormalization procedure extremely well for all sorts of other loops, which we then go and compute and compare with scattering processes at the LHC and they give a flow and regularization

scales of all sorts of different things which we know, understand extremely, extremely well. So it is a little bit puzzling to think that we know so well how to compute those things when gravity is not part of the game and all of a sudden now all I do is I sandwich some gravity on external legs. I don't need really to deal with quantum gravity in the sense of looking at an ultimate high-energy completion of quantum gravity at or beyond the Planck scale. That's not at all what I'm doing. I'm just looking at a quantum effective field description of gravity, which we do on a daily basis,

I do it on the board, and we do look for observations of that in the sky. We think we know very well how to do that, and yet as soon as I start putting in some external legs which are gravitons, so I want to look at the effect of these loop diagrams of, let's say, electrons on external legs which are graviton, which in effect I'm wanting to see how this loop of electrons, loops of virtual electrons, for instance,

lead to an effect, to an interaction with space-time. That's really what we're doing. All of a sudden what we get as a result seems to be completely inconsistent with our observations. So probably it is true that something is going on there and we don't understand that so well, but it is very puzzling because everything else we understand it so well. Why is it the case that when I think of it in the case of graviton, that stops being so sensible? We don't know. The answer is we don't know.

You can go into string theory landscape and think of there being a landscape of different possibilities where the leftover cosmological possibilities where the leftover Cosmological constant the leftover Vacuum energy could take many different values and we just happen to be living in a realization where the leftover is just Just the right value because if it wasn't that right value, we wouldn't be here to ask ourselves that question. That is always a possibility, but then it's a little bit unsatisfying because we don't know how to probe that possibility. We don't know how to probe alternatives to that. We're sort of giving up on trying to find a more dynamical and more fundamental reason as to why the effect of all of the loops is

not leading to what we would have expected. Does philosophy inform your physics research? And by philosophy, you can count causality and thinking about lawfulness or the foundation of time into your answer? So those questions like causality, like unitarity, like the flow of time, that definitely informs all of our research, all of our results, all of the way we think about things. In fact, causality is really intrinsic to a lot of the questions that we're asking ourselves. So for instance, when we're looking at effective descriptions, effective quantum field theory

descriptions for some phenomenon around us, we always want to make sure that they satisfy some basic criteria of basic, I would call them basic physics, you can call them philosophy if you want to. We would like it to satisfy some notion of causality. This is essential for us. That manifests itself in many different ways. For instance, you can think of it, the notion of causality at zeroth order, you can think of it as saying, I want to end up with a phenomenology where I'm not able to go backwards in time and kill my grandfather so that I'm not there anymore. That's at the basic level. But in fact, when you represent that into a model where you think that Lorentz invariance is a fundamental symmetry,

then that tells you that you shouldn't be able to have processes that go faster than light. In fact, it's not really that. It's a bit more precise than that. But we can embed those concepts into much more formal, much more rigorous ways to clarify how to move forward. There's no notion of unitarity as well, which in some sense is a very simple concept for us to think about. It's really to say that if I think of the possibilities of a different outcome,

and so in quantum physics we know that things are not deterministic, I can do an experiment over and over again, for each time, for each realization, I won't know exactly what the outcome will be, but what I know is what the probability of a given outcome will be. And so we are thinking everything, the realization is really very much into probability or amplitude of probabilities of different outcomes. But we want the sum of all of these probabilities to sum up to one. And we want those probabilities, these individual probabilities, never to be negative. And I want it to be a real number. And so that seems to be trivial statements.

If I play the lottery, I shouldn't have more than 100% chances to win, and I shouldn't be able to have a negative chance to win because I can't quite make sense of that. This seems like completely trivial statements that guide our everyday life, in fact, is structural in the way we live our lives. If we didn't have this notion, then all hell will break loose. We'll be able to play the lottery over and over and over again and just take advantage of this. So it sort of sets up the structure of the reality in which we live in. And in the same way, this notion of unitarity sets up the reality of the physics with which we work.

And so the models with which we work. So to put up a counterpoint, last time we touched on ghosts and there were these good ghosts, which are the Fidei of Popov ghosts, and then the more problematic one like Desser, and I don't know how to pronounce Balware. I would say Bolwar Desser Ghost. Bolwar, okay, yeah, Bolwar Desser Ghost, great. Okay. And then there's also the polytype ghosts. So those are the ones you don't want. And they produce, say, negative probabilities. Now the Klein-Gordon equation initially faced rejection over negative probabilities, and I believe Schrodinger came up with it first, and just didn't even publish about it because of that reason. But then there was another switch in point of view where,

okay, the Klein-Gordon equation is not only okay, it's requisite, we use it in the standard model. So do you see that there's some other point of view where, okay, the Klein-Gordon equation is not only okay, it's requisite, we use it in the standard model. So do you see that there's some other point of view where what's seen as a fatal flaw here is no longer for negative probabilities or unitarity or even locality conditions? So as you say, we certainly use ghosts in some formulation, like for the father of pop of ghosts, we use those ghosts in some formulation, like for the Fadef Popov ghosts, we use those ghosts almost as a trick. When we have some symmetries, for instance, it's easier for us to work with our formalism where we take too much into account and then we

use those Fadef Popov ghosts or related ghosts to cancel out contribution that we know shouldn't have been there in the first place. And we do that a lot in many different things, but they are under control and you have to think of them as a mathematical trick. You have to think of this as a formulation. We give too much away and then we know how to control what we've given too much away and we know how to remove those things. So in that sense, it's a negative, it violates unitarity in the sense that it has a negative contribution and

negative energy, but of just the right amount to remove the positive contribution that that we had added on. And so in that sense, that is completely under control. Now, there are other situations like the ball word as a ghost, where this is not something which has been added to remove another contribution. It's just something that comes in, in its own accord. And you can see in the case of the ball word as a ghost, why it starts becoming problematic. And it's particularly problematic because you're dealing with modes related to space-time. And so let's just imagine a little bit what you mean by gravitational waves. We have observed gravitational waves and the way we have observed them is them distorting space within our interferometer, distorting the space between two mirrors in our

interferometer. And so they make the space between the interferometer evolve in time. But you can in principle, we are dealing with a theory of space-time, you can in principle think of having the same thing with time. And then if you start having a mode for gravitational waves, which allows you to jiggle things in time as well, then this is also related to some level of causality violation. And so this notion of breaking unitarity with some of those ghosts can be linked directly to a violation of causality. And as soon as you enable for that possibility to happen, then you're opening a whole Pandora box of pathologies which are not under control. Because this is not something that we engineered precisely so as to remove another contribution because we were lazy in some sense in the first place.

It's something that just populate your space time by its own accord. It's not that just populate your space-time by its own accord. It's not under control. So you may say, well, does it have its own way of thinking of it? I mean, in some sense, from the formalism, yes, you can analyze it. It is a pathology. And as a scientist, you can analyze it. You can try to understand it. You can look at its structure and it has a lot of interesting features in its own right, but at the same time you know that this mode, it is a pathology. You can't have it in your space-time as a fully dynamical degree of freedom in its own right that you can't have. And it is a little bit different as compared to saying

that you have an instability. So for instance the Higgs potential is unstable within some range and you may think that this instability may be the sign of a pathology but that is in fact just a time evolution and it's just a transition, a transitionary behavior from one point to another. And you can think, for instance, that the whole evolution of the universe is something that signals some level of instability because we are going into a different configuration. We are evolving in the evolution of the universe. Those are not pathologies. They are just the reality and we may not like that. It's never necessarily pleasant to be in an unstable configuration, but we can deal with it

and that may just be the reality. The issue with the ghost is that we know that that tells us there's no vacuum, there's no ground zero around which we can think about, about our theories. And so we can't even start looking at the model into how to represent anything. As soon as you have this actual negative kinetic energy mode, a genuine degree of freedom that has, who delivers energy when he moves, we know

that there's no ground zero in which we can start thinking of our whole quantum field theory framework. So in that sense, we can't even start doing anything. So speaking of energy, what is energy, especially in general relativity? What is gravitational energy? And what is this criteria or wish list that you would like a well-defined definition of energy to have, like locality or covariance or what have you? Yeah, okay.

So for me, I don't have so much about wish list for energy because I don't have the need of having this concept as being as fundamental as we may have otherwise have. I think we're very much driven by almost a Newtonian perspective of things being static in time. And this symmetry in time tells us that there's an associated conserved quantity, which we call energy. So it's almost a luxury to have energy as a conserved quantity and as a well-defined quantity that we can rely on.

And we can rely on to predict phenomena and to understand how you can borrow energy from one system, give it to another system, and that the whole energy within a box, let's say, should be conserved. Now, as you said yourself, when you have gravity in the game, things become much more complicated. There's no local conserved, ordinary conserved notion of energy in the same way that we would think we should have otherwise. And that in our everyday life, we follow the rules as if a notion of energy was conserved. This is related to the fact that gravity is in fact a spin to particles, so it behaves

slightly differently. And so the stress energy tensor is no longer conserved, ordinarily conserved. It's covariantly conserved, but that means that the conservation of the quantities related like energy, they're not absolutely conserved. There's a boring or there's a trade off between the energy of what we call matter, let's say, and the energy of space time. A system can borrow energy from the space time or just dwell energy into the space time, and that disturbs us a little bit. And we know this, maybe a simple example to think about, which helps us a little bit into making

the analogy into how we think of energy being conserved in normal system and how different things are with gravity. Let me just imagine that I have two stars. Let me imagine I can start having one star and that star is emitting light. It's emitting electromagnetic waves, and so that star is losing energy at one point, it will die and that's sad, but that's life. It's losing energy, but this energy is being carried by the electromagnetic waves, it's being carried by light, and so in principle, if I take that star and then I were to draw a sphere around that star, I can compute the amount of energy lost by that star,

but also the flux of energy carried by light, by electromagnetic waves within that sphere around, or that box, whatever, around that star. I have a complete trade-off between the amount of energy being lost by that star and the flux of light going through that surface. And so we have this very well understood notion of conservation or trade-off of energy in a normal system.

Now if I do the same thing with gravity, so let me just imagine instead of having one star, let me just imagine I have two stars, I can do that as well. And so they will lose energy through light, they radiate light, but they also radiate gravitational waves. We actually need two stars rather than one for gravitational waves to be radiated. And that we know. In fact, there are some systems where they lose more energy through gravitational waves than they lose energy through radiation of light. So it's not something which is simply innocent. It can be quite substantial.

So for some system, they lose most of their energy through the radiation of gravitational waves. You could in principle ask yourself if you could do the same thing. Let me just draw a sphere that encompasses those two stars and let me think of the energy lost by that system of two stars. So they're losing the chemical energy, they're losing some energy inside each of the stars, but they're also losing some of their potential energy because they're getting closer and closer together through the radiation of gravitational waves. And I can think I'm a little bit further away

from these two systems of stars, I drew a sphere around them, and I compute the flux of gravitational waves through that surface and the flux of light through that surface. And that doesn't work in the same way. There's no such a notion of local, at a given finite distance away from these two stars,

of energy which is conserved. For that system, I will really need to go to infinity, if it's asymptotically flat at infinity, if I recover flat space-time at infinity, then I'll be able to finally define a whole notion of energy which will be conserved, but only because in flat space-time asymptotically. And only in that case, I'm able to define a local standard notion of energy. And that's because the notion of energy is very much a consequence of is very much a consequence of some symmetries of the space time. You need to have a time-like killing vector to have a conserved charge, a conserved quantity related to that. All of this is actually, I should say, I want to say it because it's important, all of these concepts is actually thanks to Amy Noether that understood very much the, she pioneered

all of this fundamental connection between symmetries and conserved charges. And nowadays we understand, the whole world, we understand it through this notion of symmetries. They are the building blocks of everything that we, how we represent reality around us through classification of different symmetries and those different symmetries come in with as a consequence with conserved charges but only when we have what I'll call time translation invariance or that flat space time has or something related to a time like Keeling vector so this is the same thing a symmetry in time if you want, then I can have the luxury as a present to have a conserved charge associated with it, which

I can call the energy. But in a normal gravitational setup where I have space-time, this is not the case. And there's not going to be any local gauge environment quantity which is unobservable and that directly tells me that there's no such a thing as a local ordinary conserved notion of energy even if I integrated within a given volume that doesn't happen. So for those two stars you really need to go to infinity to define this notion of conserved energy. And that's if you're lucky and you're asymptotically flat.

The world in which we live in now… Right. How reasonable is that assumption? No, that's not… You can make it mathematically, you can make it theoretically, but the world we live in is not like that. We know we're living in an accelerating, expanding universe, something which I'll call is close to De Seta, not Minkowski. It's a different topology. It's

different asymptotics. And so that we know there's not going to be such a thing as a conserved notion of energy. You know, for instance, that you can in an accelerated expanding universe, just in an expanding universe in fact, you can create out of the vacuum some physical particles. And so as time goes on, you have some particles being created, constantly being created. And you can think of this as being created with a finite amount of energy, is borrowed from this bath which is space time. You can just borrow energy from space time which if it's not flat and if it's curved as it would be the case in an accelerated expanding universe. That bothers us a little bit but it doesn't mean that it's not right. It just means that the rules of the games are in fact quite different in the presence of gravity. And this ability in fact to actually take in energy from the vacuum. So we can still make traction in defining

some quantities which are conserved ordinarily and then as you mentioned in your post as well. Actually, I have a popular article that I wrote on Substack called, What is Energy Actually? Which goes into technical detail into what general relativity conceptualizes as energy and why it's ill-defined. A link to that article will be in the description. I'm also recording a video version of that, so that link will be in the description as well. In your post as well, taking some pseudo-stress energy tensor to compensate that, but that

you really need to think of it as borrowing what is happening from space-time itself. And that has slightly different rules of the games. It doesn't make them wrong. But it's only in some very special limits that our standard notion of energy, as you want it to satisfy with being local, being gauge environment, being conserved, ordinary conserved, will be present. But typically, it's not.

Perhaps this is one of the reasons why, for instance, holography, ADS-CFT, has become so popular because you are living in ADS. Let's say the gravitational theory is in ADS, which is a curved space-time, but the boundary, it has a boundary, as you can think of its gravity in a box, which has a boundary. And on the boundary of ADS, where actually the CFD is living, on the boundary of ADS, you have a time like killing vector. So you have a symmetry associated with that along the time direction. And so then you have the luxury of having a conserved quantity which is energy related to this. So in the concept of holography in ADS CFT correspondence you have the CFT being described in flat space and then

themselves they have a notion of energy just like you have on the boundary of ADS you have a time-like Keeling vector and a notion of conserved energy as you would want it in there. Now, if you wanted to do the same thing for not AdS CFT correspondence, not in the same holographic description, if you wanted to do it in the Sitter CFT correspondence, because we live in something which is close to the SETA in the expanded accelerating universe. Then in fact the boundary of the SETA would not be a boundary which has a time like Keeling vector. So you wouldn't have a neutrality on that boundary and you wouldn't have

a conservation of energy on that boundary. So this is one of the reasons why it's actually quite the reality of the world we live in. The fact again, the fact that the universe has an accelerated expansion is quite problematic for even defining the very notion of energy in a way that the normal tools that we would like to use will not work. And that's just at the level of defining what we mean by energy. Firstly, you're an exceptional explainer. You're great at being a public science communicator. And I want to know how did you develop that skill

and has that translated to new physics for you? When I say has that translated to new physics for you? When I say has that translated to new physics, what I mean is have the insights that you've gleaned from simplifying for a general audience led to new research. So I don't know that I can answer the first question other than this. If this is something that you like doing, the more you do it, I think the easier it becomes. And you learn a lot from the questions that people ask. I think the key thing is being able to relate to the way people are thinking in the different challenges they may have in trying to address some of the concepts. So I think this is probably one of the essential things.

I don't know if it's easy to explain to others, but I think the listening part is the most essential part, I think. When you understand how people think about things and why some concept that you may have taken for granted and you may not have questioned them yourself because you don't think of it like that. You realize how other people think about it, how they address it and what are the stumbling blocks for them. I think it's very enriching for everybody.

It has been very enriching for me. I remember sometimes I was, you're in the bus and you talk with someone, just someone next to you on the bus. And first of all, being able to see that the things that we are studying, sometimes we go so deep in the research and it becomes so technical that you forget where everything comes in. And so being able just to explain those concepts to someone else who's not at all fluent in that language and go back to what actually was the original passion is really great. And seeing that this is something they can connect with because a lot of the questions we're asking ourselves, people connect with that. They want to know,

they want to know what is the original space time? What is a black hole? What is space time? What is gravity? Why are we here? What is going to happen to is the origin of space-time? What is a black hole? What is space-time? What is gravity? Why are we here? What is going to happen to us? All of those questions, we all have them and we're all excited about it. Everybody I think is excited about looking at the sky and trying to understand the world that surrounds us. But then in trying to connect with those people and seeing what that question means for them

and how they would go along addressing some of the questions that we all ask ourselves. I think it's very enriching for everybody. So I think this is very much something you can build on. Of course, it's not that the perspective necessarily helps me in designing whether it's a factor of two or pi in my equation, but putting things together in the bigger picture and understanding how things are connected with one another is very enriching. I think this is really where it comes in. To answer your question, I think yes, it does help a lot in making progress in the

research. I often describe it a little bit like a chess player where you see this. I don't play chess, my daughter plays chess, but you can see these people playing chess and they don't need the pieces anymore. They don't think about one step at a time, they think about the whole game as a whole. And so being able to embrace enough experience in understanding what is the long-term dynamics of a game, knowing how it has started and what are the different possibilities of outcome. I can think of this a little bit in physics as well, where the math and the logic and all of this formulation, they are the basis.

But if you're able to gain enough intuition, you can extrapolate yourself from that and use much more your creativity to understand where things are going without needing to go sit down and do every single step along the way. You'll do that eventually, but to get the bigger picture, you start with having embraced all of this intuition, which is coming from all sorts of different people you spoke with and all sorts of different backgrounds. And then from that, you understand where things are going. What does it mean? What does it mean if I have two electrons scattering and I have an interaction with a graviton there, but also when I push that to higher energy and I include a contribution from other things, you have a bigger picture of what will happen and from that what it means.

I think you want to understand what it means and how different things are connected with one another. And so I do think it does help and it does help to gain some intuition and just put aside a little bit all of the formulation if you can and use your creativity to free yourself a little bit and that's how you make progress. You need a bit of both, of course. You need to have built in from all of this formulation. You need to know how everything will fit in together at the end of the day. But at some point, you also want to be able to look

at the bigger picture. And so being able to talk with all sorts of different people does help a lot with being able to get the bigger picture. I should also state that you have a book called The Beauty of Falling, which will be on screen, and the link will be in the description. So while we're on the subject of dark energy, there are the DESI results that hint that dark energy may be dynamical. What does that mean? What do you make of it? And does it have any bearing on mass of gravity?

So it's really exciting. Any departure from a cosmological constant would be extremely exciting. Precisely what it means, I would say, is a little too early to tell. I think that there's a lot of signals which are sometimes below three sigma which come and go and so before it's actually very much there and has sufficient significance, it's going to be hard to tell whether it's going to survive or not. But it's true that it's going into more and more into this direction. So first of all, having some dynamical dark energy would be extremely exciting for many different reasons. Just the fact that it's not the vanilla model that one would have expected is telling you

that there's some signs from new physics and that is very much what we need. We need traction into something new that tells us where to go, where to look for more information on what is leading to the accelerated expansion of the universe. Anything which is dynamical is really fascinating because it tells us, it may uncover the reasoning as to why we have an accelerated expansion of the universe with precisely that amount of magnitude and not a little bit more or not a little bit less. If it is dynamical, then you can understand that much more dynamically. Having dynamical dark energy would tell you that there's actually other degrees of freedom out there. And so there may even be a particle, a field related to that. That would be really fascinating because it tells us that there's something else to discover

there. So, having dynamical dark energy to me would be fascinating because it tells you that it's not just a cosmological constant, which is kind of boring and we're stuck with that problem as to why it has that particular value. Having dynamical dark energy could tell us that it didn't always have this value. It's something that evolves in time and so it gives us really different new clues to the problem. One thing though is that we call it dynamical dark energy.

Really what it is, is an equation of state parameter which is not constant in time. This is based on the observations. But it could be due to many different things. It could either be that the actual source for the accelerated expansion of the universe evolves in time, or it could be that the dictionary between this source, between this dark energy or cosmological constant,

and its effect on the evolution of the universe is what evolves in time. And that would lead to, for instance, a modification of gravity. So if it's true that there is dynamical dark energy, what it tells us is that there's something new out there. Precisely where it is, if it's in the source, if it's in the gravitational side, if it's in between, that will have to be uncovered. What do you mean by the source?

So the source would be dark energy itself, being not just a cosmetical constant, but being something that evolves in time. So that's possibly the simplest possible. This could be the simplest possibility, although you need to understand what this field is and why it evolves in time. Or what we know is that this is what we observe. And if we observe something that appears to be evolving in time, it could still be the case that we have a cosmological constant, but the effect of this cosmological constant on the evolution of the universe is what evolves in time.

And so it's in the translation between what is present and its effect on the evolution of the universe. That's where the time dependence comes in. And if that were the case, then that would hint towards a model of modified gravity where as time goes on, or when the scales change, then the effect of a particular source, for instance a cosmological constant, is different and so leads to a slightly different rate of acceleration of the universe. And that would really be so incredibly fascinating.

One thing which is very interesting, it's a little early still, but one thing which is very interesting is that at the moment observations seem to be suggest that it's going towards even smaller than minus one equation of state parameter. That is quite puzzling because normal matter, normal energy doesn't even need to be matter, normal energy as we know it, even quantum vacuum energy, typically is behaving with the opposite behavior, with an equation of state parameter which is slightly larger than minus one. Having an equation of state parameter, W, as it's called, being smaller than minus one would mean that the accelerated expansion of the universe would even go faster and faster. So the Hubble rate would go even faster and faster in time. And so that could lead to

a big rip. The universe is not only accelerating, but this acceleration is going faster and faster to the point where even if you consider the space between in cosmic voids, the space between two clusters of galaxies will be ripped apart. So we don't know. It's too early to tell, but definitely how dynamical dark energy goes would have incredible consequences for the future of our universe. What is the destiny, what is the fate of our universe depends on the precise behavior of dark energy. So it's amazing, I think, to us being able to look in the sky and see those results

from DAISY and then from that determine what is the fate not of us on Earth, but the fate of the very structure of space-time in the universe is incredible, really. We don't know for sure right now, but either way is going to be fascinating. I'll put a link on screen to the new DESI results. There's an article from The Economist on this topic, and so it's on screen right now if you want to learn more about this incredible result. I know you said that your approach is agnostic to whatever the final quantum gravity theory may be. However, one of the initial motivating reasons to go into string theory was that,

as a side effect, it produced a massless spin two field. So it didn't produce a massive one. I don't know if the fervor would have initially been as intense had it produced a massive one. So how do you make sense of the disparity between the string approaches to quantum gravity, which predominantly have massless spin-to fields, and then yours, and if massiveness is up for grabs, then is spin-to-ness up for grabs? Like maybe Graviton. Like, what is up for grabs? Just a moment. Don't go anywhere.

Hey, I see you inching away. Don't be like the economy. Instead, read The Economist. I thought All the Economist was was something that CEOs read to stay up to date on world trends. And that's true, but that's not only true. What I found more than useful for myself, personally, is their coverage of math, physics, philosophy, and AI, especially how something is perceived by other countries and how it

may impact markets. For instance, the Economist had an interview with some of the people behind DeepSeek the week DeepSe seek was launched No one else had that another example is the economist has this fantastic article on the recent dark energy data Which surpasses even scientific Americans coverage in my opinion. They also have the chart of everything It's like the chart version of this channel It's something which is a pleasure to scroll through and learn from links to all of these will be in the description of course. Now, the economist's commitment to rigorous journalism means that you get a clear picture

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Thanks for tuning in. And now let's get back to the exploration of the mysteries of our universe. Again, that's economist.com slash toe. Maybe grab a tongue. What is up for grabs? Yeah. Good. Amazing question. Let me just start by telling you that in fact, the first model of string theory, bosonic string theory,

actually came in with a massive spin-to-field. It was unstable and that was a mass supersymmetric version and there was all sorts of different problems. But in fact, the first model of string theory came up with a massive spin-to particle. That doesn't mean that I do believe that a massive spin-to graviton would come from string theory.

I don't think so. At the moment, the indications seem to suggest quite the opposite. But this is just to say, in fact, we have many different realizations and we never know for sure what is going to be the final outcome. Now, we have learned a lot from understanding what is possible to come from string theory, in fact, and what are potential high-energy completion of massive gravitons. So I think I like the approach of remaining quite agnostic in precisely what the high-energy completion is, so long as it satisfies some basic rules that we discussed about earlier, like causality, like unitarity. And it doesn't need to be string theory per se, but we want, however physics manifests itself at very high energy,

we want it to be so that it satisfies these very simple rules, without which I don't think we can even make sense of reality anymore. And we don't even need to have a notion of graviton. We don't even need to have a notion of quantum field. It can be something quite different, but some of those fundamental concepts like unitarity in the sense that if I have some probability of given outcomes, I want the sum of those probabilities to sum up to one and to be positive. I want causality to be satisfied. These are very much the ground rules for what we want to base ourselves on. And then it can be string theory or then it can be something

quite different. It doesn't matter. From that, you can actually make contact with how physics manifests itself at low energy. And we know that there are some models that I can come up with. There are some models that I can write down. And that seems quite consistent at low energy. And I can even convince myself that there could be good representations for what happens in the world that I observe, in the experiments that we make. They seem to be self-consistent within the remit in which we want to probe them. Yet, those models, in fact, we know they will never be embeddable.

They will never have a representation at high energy, or they will never come from a high energy representation of physics, which is consistent, which is unitarian, which is causal, for instance. And so these are good outcomes because then we can carve out a whole region of models. We have carved out all sorts of different ways to represent the world, which otherwise would have seemed consistent, but we know it's not consistent with having high energy completion, which is unitary or causal, or those kind of base rules.

Now for massive gravity, at zeroth order, it is already challenging because of all the modes that come in to be embeddable in a standard high energy completion. If in addition I want the high energy completion to be weakly coupled in the sense that I have a standard perturbative approach all the way up to high energy, then we know nowadays that this will not happen. Whether it is a disaster for massive gravity, some of my colleagues would say that's a disaster

for string theory. But in reality, even in string theory, it's not the case that it necessarily needs to be weakly coupled. We have to make a distinction between what is easier to keep traction on, what is easier to calculate, where we can actually make more predictions and make more progress, and the realm of all sorts of other possibilities. And this is where the distinction is. A lot of the time we go much further in directions which are easier to calculate, that's the truth of the matter.

When things are weakly coupled, when things are more perturbative, it's much easier to make traction in some directions. In those directions, we know that we're not going to be able to make contact with massive gravity. The graviton will have to be massless, and that's the end of the story. That is definitely true. In all of the string theory realizations that we have at the moment, we can't make space for a massive graviton.

It will have to be a massless graviton. So they can be massive spin-to-fields. And in fact, we do believe in string theory, there will be massive spin-to-field, but there's never such a case where you have what we call a gap, a separation of scales between a small remit where you have massive spin-to-fields, for instance, and a large gap and then nothing else so that we can treat those massive spin-to-fields as being a low energy effective description for the world in which we live in. It's always a continuum of states in between. So that is the nature of it. Does it mean that massive gravity is ruled out? Possibly. I don't know. It is in tension with the standard realization of strength theory. That is definitely true. I would say though that better understanding how you can have a realization which builds on this strong coupling, which is very challenging

to keep track of and very challenging to get predictable, observable from is actually interesting in its own right. I don't know whether this is going to be ultimately realized, but I still think that it is an interesting direction to study. It is possible that ultimately, even for our standard completion of the world in which we live in, we're going to need to rely on a strongly coupled high energy completion that may just be the reality. In that, if that's the case, then it will be much easier to understand how to make sense and strongly couple high energy completion. That may just be the reality. And in that, if that's the case, then it would be much easier to understand how to make sense of it in sort of a toy model,

as it is the case in massive gravity, as opposed to a fully fledged theory of quantum gravity. That is for the mass of the graviton. For the spin, so long as you follow a standard approach where you think of the spin first of all, that's also a consequence of a symmetry which is Lorentz invariance. So everything that a lot of the things I'm thinking about that people would be thinking about in string theory and in a lot of high energy completion are still within the remit that Lorentz environments is a fundamental symmetry. So the world in which we live in right now is not Lorentz environment, but that's a continuous breaking.

And if I were to zoom into a very small region of space-time, you'd see that you recover this Lorentz invariance. If you have Lorentz invariance, you have all sorts of related quantities associated with it. One of them, like the notion of mass, and another one is a notion of spin, which is discretized and you can have a spin zero like a scalar field. In fact, before general relativity, there were models for gravity which were based just

on a scalar field, a spin zero, graviton if you will. Now we know this is completely incompatible with observation. You can't have gravity being just a spin zero particle. You wouldn't get gravitational waves, but you wouldn't even get the right behavior in the solar system. Okay, so we can't have that. A spin-1 particle that corresponds in fact to the photon. The photon is a spin-1 particle. It's massless. You can have massive spin-1 particles like the W and the Z bosons. We also know that the graviton cannot be a spin-1 particle. It has to be at least a spin-2 particle. So really the question is, could it be the case that the graviton is not a spin-2 particle but it's

a higher spin particle and we're just seeing some subspace of the graviton, the spin-2 subspace of a higher spin particle. There are some models out there. There are some models out there with what it means to have a spin three particle and an even higher spin. In fact, it's quite challenging, we know, just to have a higher spin particle interacting just by itself without having an infinite tower of other higher spin without having an infinite tower of other higher spin particles being present as well, that window. And in fact, string theory is just that. It is a spin two and a whole higher spin tower of other particles that come in along the way.

That's what string theory is. So in that sense, part of string theory is having the spin two as one of the states, but a whole tower of higher spin. So we in fact embrace this spin-ness for grab in many of the models of quantum gravity. We know that we can't just stop at one given spin. The thing with spin two and higher spin is that as soon as you switch on, as soon as you have a spin two particle, and I'm not talking about a mass here, just in gravity itself, as soon as you have a spin two particle, we know that its behavior as you go to high and high energy, it grows too fast with energy to be consistent at high energy, it grows too fast with energy to be consistent at high energy.

And so you actually need to have an infinite tower of higher spin states where when you resum everything together, that's what's taming down the high energy behavior of, here I'm talking about amplitudes of probabilities and things like that. But we know already if you take general relativity, you have the spin-2 particle, you're going to need at some point to have an infinite tower of higher spin states that come in to lower down a little bit the behavior of gravity at high energy. That's the only way to have sensible high energy completion of the theory. And that's why we know that general relativity in its own right,

can't be the final answer. We need to have along the way all sorts of other particles that will help taming down the behavior of just the single graviton at high energy. Are you working on a theory that gives mass to the photon? What else are you trying to give mass to? In principle, you can give mass to anything you want. I am actually working in a theory. I can tell you one question I have.

It's related – well, it's lots of questions that I have every day. There are these, let's say, swampland conjectures or landscape conjectures. One of them is called the weak gravity conjecture. The weak gravity conjecture tells us that we would think for many different reasons, which are very well founded, that in fact gravity should be the weakest force there is. And we can think of this around a black hole, we can think of a black hole having a mass but also having a charge with respect to not necessarily electromagnetism, but it could be an electric charge, but also another kind of charge.

And so we would want to be able for the black hole to evaporate its charge faster than it evaporates its mass, because as it evaporates, we don't want it to become too charged and become a critical black hole which would lead to a naked singularity. So this is a very very simplified way to explain the weak gravity conjecture in the sense that we would like to be able to evaporate into charge more rapidly than evaporate into the mass, if you want, or we would like the gravity to ultimately be the weakest force around. A lot of my work is trying to understand how to think of this weak gravity conjecture

and whether we know that from the high energy completion of quantum gravity, whatever it is, the ultimate completion of everything in fact, we can derive this weak gravity conjecture or slightly modified versions of this weak gravity conjecture. But something else I want to work about related to your question is the long gravity conjecture. So I told you that in, I don't know how much I want to go into that. Don't start working. Why? Is it because it's too new?

It's too new. Yeah. Now, let me just say, one question I have is if we know that, one question I have is if it were the case that the graviton could have a mass and the photon could have a mass in principle, I know that I can't embed that in a weakly coupled high energy completion. But let me allow for myself to have a strongly coupled high energy completion where some of the bounds that have been derived are not quite as rigid. So let me enable this possibility and think about whether it could be the case that the graviton could have a mass, in fact the photon could have a mass, in

fact every particles have a mass. It may be just very very small. And the bound we have on the photon mass, observationally, that's nothing to do with me, but observationally there's reason to believe that from the coherence of magnetic fields in galaxies, the bound on the photon mass is of the order of 10 to the minus 20 electron volt. I should say, in fact, there's some very nice papers by some colleagues of mine, Giyad Vali and Lasha, who've gone through this analysis again and I think they have some very nice results in showing that there's a little bit more leeway into that. Anyways, let me accept that in principle the photon could have a mass and if that were

the case, the bond is not so stringent. In fact, the bond is weaker as compared to the bound we have on the graviton mass just from observations. Now, I'd like to understand whether from being able to embed these theories in a consistent high energy completion, not necessarily weakly couple them, but it could be strongly coupled even, whether it is the case, whether it would be possible for the photon to be lighter than the graviton or not. I think that's an interesting question and it's on-ride because if we can come up with a way to understand as to why the graviton should always be lighter than the photon, it can be massless, but if you had a mass, it has to be lighter than the photon.

In fact, lighter than any of the other particles that exist, it would tell you that at long distances, gravity is always the force that survives. So it would be a long gravity phenomenon in some sense. All the other forces in nature will have to be switching off faster than gravity. So that's just one idea I've been trying to think about for breakfast, but there's lots of things that come up every day. So our audience largely comprises researchers in math, physics and philosophy, but there's also a substantial part, a portion that is lay, is not educated in physics at the university level. So I just want to distinguish something here. You said gravity could be lighter than the photon. Someone may think, well, the photon is light. The photon is light as in, so when you're saying it's lighter, you mean it has less mass.

Yes, yeah, yeah. Not that it's somehow more light-like. That's absolutely right. And in fact, the terminology is confusing, right? We call light light because it's light. Because it has very small mass or no mass at all. Yeah, yeah. Okay. I don't know if people know who are, again, who are not physicists, how difficult it was what you did in 2010 and how radical this approach is, because if I recall correctly

from our first conversation, you said diffeomorphism invariance in GR may be approximate, maybe something that emerges. Am I recalling correctly? Yes, so this is something that I think is quite interesting in that if you take a textbook on general relativity, on Einstein's theory of gravity, or if you teach it, or even historically, it always seems to be the case that you have these pillars there, you have the equivalence principle, you have these sort of even assumptions and we call them sometimes Einstein principles on which Einstein's Theoretical Relativity is being built. And if we phrase it like that, it may almost seem like these are for grab and I can just

remove them and I have a completely different theory which maybe would be consistent in its own right. It may be more historical or it may be because those are actually conceptually very important frameworks. For instance, the notion of covariance, the notion of the fact that every observer is equivalent and I can change my quoning system but you shouldn't change the notion of the fact that every observer is equivalent and I can change my quoning system but it shouldn't change the laws of physics and that's related to a symmetry which we call coordinated homomorphism invariance, diff invariance. Now you may think that this is

built in and general relativity emerges from that. And in fact, if you take that perspective, you can ask yourself whether you can get rid of this symmetry. Maybe it's not necessarily comfortable to do that, but you can ask yourself whether you can get rid of that symmetry and then you get up with a much more general theory of gravity, which is not based on this symmetry, but a lot get up with a much more general theory of gravity, which is not based on the symmetry, but a lot of other possibilities emerge. And in fact, you can go through this and realize that all other possibility for which they're not, they're breaking different variants, at least in the kinetic term, in the way the

dynamics of gravity is being built in, if you allow yourself, you enable yourself to include some potential correction, which would break that symmetry, you see that those potential correction automatically lead to pathologies, which are those goals like pathologies that completely rule out that theory. So I think this is quite interesting because it tells us that we don't need to base ourselves necessarily on these principles. We don't need to base ourselves necessarily on those notion of symmetries to build our theories.

We can start with, in principle, it will be much more complicated, but we can start with something which is much more messy, much more complicated, much more flexible. And then you realize that the only thing that makes sense is the substructure for which the symmetry just pops out. And so, in fact, it gives you a motivation as to why the symmetry has to be there. If the symmetry wasn't there, the theory would not be stable. And it's not, so it's not that we simply stubborn and we can't think things in a different way, or we just focus on particular framework where it has a given level of symmetry.

It's in fact that the symmetry is essential to protect the theory against all sorts of pathologies. And if it wasn't there, the world simply would be completely unstable to the point where there wouldn't be any structure of reality. So the only possibility is for this symmetry to emerge. Now if diphyomorphism invariance emerges, then, and diphyomorphism invariance is analogous in Yang-Mills to gauge automorphism invariance, then is gauge invariance approximate? Is there room for that? So I would say the same thing that in Yang-Mill, for instance, you know that the symmetry is there to preserve the stability of the theory. And that's the same thing in electromagnetism as well, where you have some notion of gauge invariance there as well. You can break that gauge invariance in electromagnetism by adding not a change in the kinetic structure,

because you know that this will lead to pathologies. You can break it for other terms, some other, what I call irrelevant operators, a mass term, so in principle you can add a mass to the photon. That breaks the gauge invariance that you have for electromagnetism. But even if you do break it softly at the level of the mass, you can't break it at the level of the kinetics. Even in models that consider the photon to be massive, the dynamics of the photon themselves through

the Maxwell structure has to be preserved exactly in the way it is. And so even if you enable yourself in the same way to start with something which even softly break the gauge invariance in electromagnetism, you'll restore this gauge invariance by stability for the standard kinetics of the photon. kinetics of the photon. So there's a conceptual clash between quantum theories, external and absolute time and then general relativity's dynamical space-time. You mentioned that massive gravity needs to be embedded in QFT. So does constructing a quantum theory of massive gravity give you some clue about time?

Like maybe it's due to the inherent scale introduced by the graviton mass. Do you have an answer to the problem of time? I don't have an answer to the problem of time, but it does give you a framework where indeed you, because you set up the scene much more clearly or you are forced to set up some parts of the scene from the outset. It's a curse, but also it's an ability to work with those things from the beginning. So there's a lot of things that where on the face of it, it's much more complicated in massive gravity, but possibly embracing those things and understanding how to make sense of those.

So the scale of the mass and indeed the breaking of the time different invariance may enable you to then understand how to make sense of it at the quantum level in a way that would otherwise have appeared much more challenging in a fully fledged theory of quantum gravity. Einstein had a whole argument, H-O-L-E argument, and that led him to say that diffeomorphism I believe that may be among some other factors, but that was one of the principal factors

that led him to diffeomorphism invariance because he wanted to retain determinism in GR. So does removing diffeomorphism invariance then at the fundamental scale reintroduce indeterminism into GR? I think it's hard to tell at this stage. I think we're not really there because I mean, perturbatively, we would get the same thing. That is okay. We understand how to, we can restore that symmetry if you want and you can think of

other degrees of freedom there that will restore that symmetry. I think really the question is what happens when you are in a regime where things are no longer perturbative and are so strongly coupled that the potential outcome of that is quite different as compared to what you had started with. But that is also very complicated to look into. So honestly I can't tell you at the moment, I don't know. What are gravitational rainbows? It's like rainbows, what are rainbows?

Rainbows are just the fact that light as it travels through a medium, let's say through water, through glass, will be affected by the medium slightly differently depending on its frequency. We understand that because as light goes through a medium, it will interact with whatever matter is in that medium in a way which is frequency dependent. If the wavelength of the light, the color of the light, is quite similar to the relevant scale in that medium, it will interact strongly with that and it will be slowed down by matter, by the atoms in that medium. And if it's very high frequency, it will just zoom through completely unaffected.

And so the speed of light in water is in fact dependent on its color. Because of that, as we shine light through water, through a droplet of water, when it just rains in the sky, we see that light comes out of this droplet of water in a way which is different depending on the different frequency, the different colors of light. So we see this pattern in the sky. Now you can do exactly the same thing for gravitational waves. Gravitational waves are traveling through the universe and most of the universe we think is empty,

but still we think that most of the universe is filled with dark energy. That's what leads to the accelerated expansion of the universe. What is dark energy precisely? I don't know. And we know more or less how it interacts roughly with gravity, but we don't know precisely how it interacts with gravity in a frequency-dependent way at very, very low frequencies. So it's possible that as gravitational waves are just traveling through the universe, they are interacting with dark energy in a way which is frequency dependent. And so if that's the case, we will see that gravitational waves with different colors

or different frequencies will have been affected ever so slightly by dark energy or other things along the way in a way which depends in their colors. Of course, we're not going to look in the sky and see a beautiful rainbow in the same way as we see it for light because we can't see gravitational waves with our eyes, so it's not going to look so pretty just like that. But in principle, the same type of phenomena can happen. And so we know, for instance, that there's different systems that emit gravitational waves and they do so within a range of frequencies.

Now the system that we have observed for the merging of black holes or neutron stars that we have observed so far, the gravitational waves emitted a relatively high frequency within that spectrum. And so they zoomed through the universe completely unaffected by dark energy or anything else. But if we were looking at systems which are supermassive black holes starting their journey much further away, the frequency they emit to start with will be much lower, so more towards the red of the spectrum in comparison. And so they can start being much more affected by the medium of the universe, for instance

by dark energy. And then you could observe that the speed of very low frequency gravitational waves, we're talking very, very low of the order of 10 to the minus 30 electron volts, so 10, those orders of magnitude below what we have observed so far, but potentially we can observe that those would propagate at a speed ever so slightly smaller than those of very high frequency. So that would distort the signal that we observe. That would be a gravitational window. Whether they exist or not, I don't know.

That depends a little bit on what arc energy is. It depends how gravity interacts with arc energy. Depends on lots of different things. But it is something that we should keep our mind open for because this is a way to distinguish between different models. This is a new way to observe the universe. It's a new way to interrogate our environment and ask ourselves is this happening or not? Suppose we could do a double slit experiment in ideal conditions with gravitons. Would we expect an interference pattern? Yes, so we are dealing with gravitational waves.

So yes, in principle, you would expect the same thing for gravitational waves as you do for light. Yeah, there are waves, so you would expect that. So is there something different about gravity that acts as an observation or measurement in the measurement problem sense? So one thing which is different with gravity as compared to the other things is the fact that it's so weak. The strength of gravity is making it quite unique and that's possibly the reason why we actually can be here and ask ourselves that question. But gravity is much weaker

as a force as compared to everything else. So this has a direct impact in our ability to in fact detect the fundamental particle of gravity in the same way as we have been able to detect the fundamental particle of light. We know how to make sense of a single electron. We know how to make sense of a single photon. We can do experiments with that and we can look at the effect of a single photon. That we can do. But for gravity, because it's so, so weak, the effect of gravitational waves is already the way we observe on Earth. They've been so weak. Just think of just observing gravitational waves. We see light all the time. We're sensitive to light and it drops energy in our retina. We can see

light all the time. We interact with it quite strongly in some sense. With gravity, we interact with it very, very weakly. It's only when we have a coherent state on so many gravitons all together that the effect is sufficiently large to being able to observe a gravitation where it's passing through. If you were just to think of the effect of a single graviton in the same way as you think of the effect of a single photon, it's not only challenging at the moment to observe a single graviton with through our interferometers, a single one of those with a given momentum which is associated with the length of the

interferometer will lead to a displacement of space, an effective displacement of the mirrors in an interferometer which is too small to be observable. It's not just a technical engineering challenge. It goes below Heisenberg uncertainty principles. That is quite different as compared to everything else that we know. So we know that to prove the quantum nature of gravity, observationally, is going to be challenging. So there's one side of that. But then there's another side, which makes it even more problematic, is that if you try really to probe gravity in a way which becomes stronger and stronger,

you have this sort of protection mechanism where it creates a black hole. And so it sort of protects itself from even being able to being observed in stronger and stronger environments. So probing the quantum nature of gravity and being able to observe it in interesting regions, we do know is going to be very, very challenging. I'd like to get to some of your latest research. So you've been working on positivity bounds derived from the S matrix theory and how they constrain massive gravity. So can you please talk about that and explain what positive bounds are? Hi, everyone.

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Thank you and enjoy the show. Just so you know, if you're listening, it's C-U-R-T-J-A-I-M-U-N-G-A-L dot org, Kurtjaimungle dot org. Yeah, so positivity bounds are almost what... So positivity bounds are in fact something quite intuitive, I would say. If you think of having ultimate high energy completion of whatever it is, I don't know exactly what physics looks like at high energy. I may not have any fields there to describe reality. I may need to have use a different tool.

I may need to use strings. I may need to use something else yet I haven't even thought about. I don't know, but it doesn't matter too much because what I'm thinking about is amplitude of probabilities of given outcomes. And I don't really need to understand what are the fundamental blocks of nature at very high energy.

But what I do know is when I make a link between high energy and I go down to low and low energy, I can sum up probabilities. And so for instance, if I am at low energy and I take two electrons, let's say I take two particles and I scatter them together at a given energy, they're going to interact and lots of different things can happen. And what can happen depends a little bit on all of high energy physics, but all other additional contributions should adopt positively to some quantities related to the amplitude of probability. So whatever, if I have all the particles that come in there, that come and play along in

the game, all they can do is adopt for a new outcome, which will give an additional positive contribution to potential, to the realm of possibilities. So this is really what the positivity bounds are in some sense. It's embedded in this notion of unitarity, but you don't need to go into the details. It's very much into thinking that when I scatter things, so the scattering, this is what is encoded in this S-metrics, that's why we're talking about the S-metrics, I can look at the different possible outcomes. And if I have more and more physics coming in at high energy, that opens more and more possibilities or it opens up more and more possibilities or it

opens up more and more contributions to the potential outcomes, but they will bring in positive contribution. I don't want anything which may lead me to negative contributions because otherwise I could simply focus on this and end up with a probability, which is doesn't make sense, which is negative, let's say. So these are what the positivity bounds are. Conceptually, you can think they're quite simple. They're quite simple to understand that things should add up constructively and positively. Of course, it's a bit more mathematical than that. What I'm saying is a little bit

simplified. It's not entirely correct, I should say, but it's just to give you the gist of it, a little bit of the taste of it. But the beauty of this is that it enables you to make a connection between an unknown high energy completion. I don't know what it is. All I know is possibilities, contribution to an amplitude of probability at high energy, and then some potential outcome at low energy and some realization, some models at low energy. So I can form that,

have a model at low energy, which I'll call it an effective description. It's an effective quantum field description for the world at low energy. For instance, the standard model of particle physics, I can think of it as a low energy effective quantum field theory. It's valid up to a given energy scale. And even general relativity, I can think of it as an effective quantum field description. It's a quantum field theory, but an effective one which makes sense, makes complete sense. It's consistent, everything goes well, there's absolutely no problem, up to a given energy scale. And it's only when I start looking

at things at a high energy scale and I can think of doing scattering processes that involves gravity. When I start doing this at energy scales which are comparable to the Planck scale, then I start producing black holes and all sorts of funny things happen. If I were just to take general relativity with nothing else at high energy, I would seem to break this outcome of unitarity, break this notion that the probability should sum up to one. So this is really the issue and this is why we know that something else has to come up to compensate for that.

But now I can just take effective descriptions at low energy, the quantum field theories, and just consider amplitudes of probability at low energy and ask myself whether their behavior, and their behavior as a function of energy and different parameters which are related to some extent to energy, is consistent with what I would have expected had it come from a consistent high energy theory. And so, as I mentioned before, for some of those models, we already know that they will not be consistent. An interesting thing is that sometimes you can look at it at low energy and nothing wrong

seems to happen. In principle, there could be an okay description as an effective perturbative quantum field theory, they may be consistent. But then we know that in fact, they're never going to be linked to link them to a high energy completion, something bad has to happen somewhere along the way. contribution somewhere along the way and that can't happen otherwise we could just focus on this negative contribution and everything will be unstable, everything will be bad. So now you can do that for all sorts of theories that you have out there including for massive gravity. Now for massive gravity there's a very nice paper actually by Chang and Raman from 2015 or 2016, maybe it was 2016.

It's called Positive Science in Massive Gravity. So Massive Gravity comes up with different parameters for interactions. There's different parameters that come in. And then they show that there's an island of possibility among this parameter space where those positivity bounds are satisfied. So for the theory to be consistent and to be embeddable with a high energy completion, you need to be within a region of parameter space.

And that was quite nice because before, in fact, we anticipated that there would be no region of parameter space where it would ever be embeddable in a standard high-energy completion and you always needed something which is quite different. So, even the possibility for this to happen is quite interesting in its own right. And then there's been a series of other papers since then that show that if you make further assumptions and you push those bounds further and further. In particular, if you make some assumption which are stronger based on weakly coupled high energy completion, then you can't have the theory being embedded, massive gravity being embeddable in a standard high energy

completion. So that we know. So for massive gravity to have a high energy completion, it can't be just a weakly coupled high energy completion. It will have to be something quite different, which may be interesting, but makes it also quite challenging. So this is the statue of that. But in fact, just exploring those possibilities has enabled us to understand a whole other realm of different theories and how and when they can be potentially embeddable in a high energy completion. So one route of this is to explore much more deeply what the consequences of having more

strongly coupled high energy completion would be. I think to my mind this is really very interesting, but it's also very challenging. So what we know is that you have to redress some of the coupling constant that come in in the situation and the roles of the games become quite different but also very challenging to keep track of. So very little progress has been made in those directions for massive gravity. For other things, a lot of progress has been made but not for massive gravity. But another completely different direction is simply to use those positivity bounds not for massive gravity but all sorts of different effective descriptions

that we have out there. And for instance for particle physics we understand now that we have the standard model of particle physics that includes the Higgs, but if you were to ask the community 10 years ago, even 13 years ago, they would have told you that one would have hoped to observe something beyond the standard model, which is based on particular models coming from high-energy realizations. So either some signs of supersymmetry or some particular models that would have come in. And the reality is nothing has emerged. We haven't seen anything beyond the standard of particle physics, but we know that it will be hard for it to be just a standard of particle physics. We would have expected something else to come in. At the very least, we know that we have to couple it with gravity at some point, that the neutrinos have masses.

Maybe that's not really the big issue, but at some least before the planet scale, something has to come in. And we believe that something will have to come in even at a much lower energy scale than that. But before we were driven much more by beautiful, very well thought out, specific realizations at high energy, some specific models, which come up with their specific signatures at low energy. And unfortunately, nothing has been found along those realms. So nowadays, quite a different approach has been taken, where people are looking at what we call the SMEFT, the Standard Model Affective Field Theory, where instead of looking for specific model dependent signatures, they're looking

for all possibilities. So they parameterize the corrections that you can have beyond the standard model of particle physics. It's the SMEFT. So you're looking at corrections, which will become more and more important, the high energy, that go beyond the standard model of particle physics. But there's thousands of those. And so those positivity bounds can enable us to see where in this big region of parameter space, you have, you can be connected with a sensible high energy completion

and which regions you are not. And so that allows us to make tractions and focus in sensible regions in parameter space for physics beyond the standard model without being focused on specific model dependent, only focusing on a consistent high energy completion. And this consistency is just a notion of causality and unitarity. When people hear the terms high energy realization, UV completion, high energy completion, are those all synonyms? And then what would be a synonym for the viewer or listener so that they can understand it more? Is it final theory? Is it a more final theory? What does that mean?

Yeah, so it means slightly different things depending on the context. For this discussion when I talk about high-energy completion, I really mean something that in principle could be probed at infinitely high energy. You know that general relativity is an extremely good description of the world we live in up to some given energy scale. But we know that if I were to probe Einstein's theory of general relativity at too high energy, things go wrong. It's not longer consistent. It's no longer consistent as a quantum field theory. And so some new physics has to come in. It could be that there's never really going to be a finite end of the story.

It could be that we understand what is the next layer of physics beyond general relativity. We have, let's say say string theory and then things go on and then we realize there's something beyond that and there's something beyond that etc. But what we want to know is what at Le Verlet is what happens within a consistent quantum theory of gravity at energy scales beyond the Planck scale. But in some sense it doesn't matter too much whether it's the final word or whether it continues like a fractal realization because all we're asking ourselves is for physics, however, it manifests itself to be consistent in the sense that we want causality there and we want some notion of unitarity, the probabilities sum up to one.

So it doesn't matter if it's an infinite infinity of models that we need to go deeper and deeper and deeper, or if it stops and we'll get to a point where we understood everything and that's it, it's string theory, everything stops there and we have all the tools at our disposal to compute anything you want. I don't know, probably I will never know within my lifetime, and probably in the next generation we'll also find it quite challenging to know. And that's why we don't want to be too committed into there being a finiteness in our knowledge or whether we're going to keep pursuing our knowledge deeper and deeper levels to get more and more precise into what makes the structure of reality.

It doesn't matter. All that matters is that we know that what we have access to right now is not the final story. And there have to be something else out there for which we don't have direct contact with at the moment, because we don't have the tools to fully describe what's going on there. Now, the last time we spoke, you discussed longitudinal modes in the context of Weinstein screening, if I'm not mistaken, and how that overcomes the VDVZ issue. So does the presence of this mode in Massive Gravity leave imprints on the CMB that are different than standard cosmology? That's an excellent question and the answer is

Probably, although we don't know yet. What is quite likely is that the presence of this mode means that, depending on the scale you're looking at, you change every so slightly how easy or challenging it is for structures to form. For the structure we see in a universe, the clusters of galaxies and the filament of dark matter, they got seeded by original quantum fluctuations in the very beginning of universe, and then there's been gravitational collapse around them and things

being patched around those seeds, those structures. But if you change ever so slightly the strength of gravity because of this longitudinal mode, that will affect the spectrum of those structures. And it affects it ever so slightly differently depending on the size of the structure and depending as well on when they got formed in the evolution of the universe, whether it was early on or later on. So we would expect a slightly different realization of this. And in fact, there's some very nice work by Mark Wyman and Justin Currie where they're

looking at the different ways structure get formed depending on how strongly this longitudinal mode start kicking in through the hysterical universe. Now for the CMB, one would believe, one would think that at the time of the imprint on the CMB, this is coming from quantum fluctuations at the very beginning of the universe. The energy scales involved at that time are so high that the longitudinal mode would be completely screened because we're dealing with very high energy scale. So that probably is not where one would expect to see the best signatures for the longitudinal

mode. But really being able to come up with a precise calculation requires us to be able to follow the whole evolution of the universe in a theory of massive gravity, which is very challenging. But there's been some other work being done where just from the fact that not only you have a longitudinal mode, but just the standard tensor mode, the standard what you call gravitational waves are massive, that would change the spectrum of gravitational wave fluctuations at the beginning of the universe. And if we did observe primordial gravitational waves, which could be imprinted on the cosmic micro background

through polarization of the CMB, this would come in with a particular spectrum, which depends on the L, it depends on the angular, momentum and angular distance, depends on the frequency if you want. And that will be affected by the scale, the mass of the graviton.

In particular, if you observe primordial gravitational waves, so for instance, if you observe a polarization in the cosmic microwave background, that you can trace down directly to primordial gravitational waves as opposed to anything else like dust along the way or anything else. And if those came in at very, very large distances, let's say very, very large angular distances, then that would tell you that the graviton has to be effectively massless at the time of emission and therefore that could put a constraint on the graviton mass. So the spectrum of the polarization of the CMB

may enable us to put some constraints on the graviton mass. There's some very nice papers being done in the focus just on the effect of the mass on the standard tensor mode of gravitational waves. What about the spectrum of Hawking radiation or the temperature? Is there any introduction of decays into the mass of gravitons? Yeah, so that's an excellent question. In principle, yeah, you can start looking at those things.

In fact, yes, it's a very nice paper by Rachel Rosen, which has looked at the effect of the thermodynamics of the massive graviton and the correction. The reality is what happens is that you introduce a new scale, which is the graviton mass, in the spectrum. She has followed through the differences that comes in in the thermodynamics loads in a theory of massive gravity. In fact, in normal processes, the mass is so small as compared to the other scales in volume, it makes up very little difference. But it's still very interesting to see how you recover the standard, smooth, massless limit in the limit where the mass becomes very small. So Claudia, thank you for spending two hours with me.

I appreciate that. Yeah, thank you. Thanks. So it's great talking to you. I want to know before I talk about what is it that you're currently working on and where people can find out more about you. And by the way, there's the beauty of falling, which will be on screen and link in the description as well. What's your current assessment of emergent gravity proposals? You know, I really, I really like to stay agnostic. There's so many

good ideas out there. But at the moment, my work is very much making connection between those and low energy physics in terms of observables in a way where I don't want to commit too much into what is emerging gravity, what is the realization. Because to me, I mean, ideally, a lot of those ideas are dual to one another. And I would love it if in fact it's not just one realization or another, is if we see a correspondence between these different ways to think about it.

So I'm going to be speaking with Ted Jacobson soon and I'm curious if you have any questions for him. What do you think he's doing that's wrong? What questions come up to you? Don't put me on the spot for that. No, I don't want to go into that. I see him every so often, so I'll talk to him offline. You'll talk to him yourself. All right, great.

Okay, so what are you most excited about now that you're pursuing? You're going to be yourself. All right. All right. Great. Yeah. Okay. So what are you most excited about now that you're pursuing? Yeah. Every day I have a new idea and I like to pursue. So one thing I'm quite excited about is to try to understand whether, again, moving into this notion of symmetries where they emerge from more fundamental principle. So in a lot of the way we're thinking about things, we think of

symmetries as a guiding principle because it helps us to put an order into things and to keep things under control. But sometimes it's almost like a way to simplify our life. And in a lot of the work we're starting to see, we realize that it's not up for grab actually. They have to be there. Those symmetries are emerging from all sorts of different requirements which we thought were just there to make our life simpler. But in fact, it may be that high energy completion actually requires a level of symmetry, which from a low energy perspective, we didn't think we needed to.

But the high energy world is becoming more and more symmetric. So symmetries just emerge as you go to higher and higher energy. And that's just based not only on stability, if it were, but on even more fundamental principle, like again, unitarity. So that's one of the things I'm quite excited to look into into it. And what type of symmetries are actually emerging is an interesting question in itself. Are there any experiments that you're looking forward to? So I love the DESI experiment to be pushed further. But I mean, the next decade is just

going to be incredible in terms of observations from all sorts of cosmological observations. We're going to get much better with Euclid as well, beyond the DESI results. But then having space gravitational waves with LISA, the Simon's Observatory, Simon's Telescope, all of those things. It's really going to enable us to not only see the universe through the different structure, but also get a whole spectrum of gravitational waves, ideally going all the way up to nanohertz, all the way up to a hundred hertz, and connecting between these different frequencies of gravitational

waves is going to give us such a handle on gravity. To me, that's so exciting. It's incredible the wealth of data we're going to have. So it's a really, really good time to be in this field. Thank you, Professor. Thank you. Thanks. Thanks, it's always great to talk to you. I've received several messages, emails and comments from professors saying that they recommend theories of everything to their students. And that's fantastic. If you're a professor or lecturer, and there's a particular standout episode that your students can benefit from, please do share and as always feel free to contact me.

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