The Timescape Illusion That Changes Everything! David Wiltshire

Time is important, and so let's call it the time scale. What if everything you've been told about the expanding universe is wrong? What if the acceleration we see in the cosmos, that was awarded with the Nobel Prize by two of my past guests, Adam Ree and Brian Schmidt, is nothing but a cosmic illusion? What if it's a trick of time itself?

We're used to thinking that there is a single age of the universe, and that's all there is. But actually, there is a relativity of cosmological time that is there in the structure of Einstein's theory. This isn't fringe pseudoscience. It's a real model. One of the most exciting models to come on the cosmic stage.

Today, we're going to confront the very physicist that has stood by this claim and made these claims for more than a decade now. What's the cost of believing in the wrong universe? David, your model suggests that time runs faster in cosmic voids, and that this differential clock rate explains the illusion of why we think the universe is accelerating. But voids don't just affect clocks, they affect photons as well. And my interest, being in Southern California, is not just from Hollywood movie stars who may want to move out of voids to slow the aging process down. But I want to know if this illusion is real, why doesn't it show up before? Why didn't it show up in the CMB data, or in Baryon acoustic data before now, or in gravitational lensing data which probe the same geometry of time? Have you really uncovered a new layer of relativity, or are we just misreading our own stopwatches?

Well, I think we've been misreading things for a long time. So, the thing is, you can interpret that same data in different ways. It's fitting a model to the data, and dark energy, etc., that is a stand-in prop for something that we don't understand. And my view is that we really have to understand the foundations. And that's why I've been going back to foundations to look at what we don't understand, because there are bits of Einstein's theory, getting Mach's principle in there in a proper, deep way that he never fully resolved, but which are actually there in the theory. I claim it's just that we have to understand things, that that means going back and looking at data, really the deep underlying physics.

Let's start there. Let's start with Mach's principle. M-A-C-H, not M-O-C-A-K, which a lot of people like to mock other people. Who is Mach? What did he do? And why was his 1800s era kind of thinking, and almost philosophy rather than hardcore quantitative physics, why was that so important? Why was that so influential to Einstein himself?

The thing with relativity is that space and time are a relational structure between things. And in looking at that relational structure, we've got to look at, well, what is the relational structure between us and the whole universe? Newton thought about Mach's principle in the sense that he imagined, well, if I have a rotating bucket of water, then the water will creep up the sides of the bucket. So there is an absolute frame of rest. Mach, in the 19th century, said, well, actually, it's really a relation between the fixed stars and the buckets. So if I could rotate the whole universe, then I would get the same thing. So the thing is that there is a relationship between inertial frames. How do we define the distant parts of our universe, infinity, and trying to understand what is the relationship between us and the whole universe? What are the averages?

So Einstein thought that he, well, he was hoping to find that relational structure in general relativity. But there are solutions of his theory, such as Gödell's universe, which rotates about every point, which are really unphysical, which should be outlawed by some deeper principle. And that's what I'm claiming to do with what I call the cosmological equivalence principle. There are certain solutions of Einstein's theory that should not be allowed by its fundamental principles if we deepen those principles and try and understand things better. That's Mach's principle, and why I'm trying to do things. And I believe it's there in the relativity. Einstein just didn't go quite deep enough into all of the parts of his theory.

Right. And that's what makes us so fascinating, because among the many things that Einstein did, he certainly created many, many ingenious inventions and discoveries in physics, but he also had a share of blunders and missteps and whoppers. And I always say, it's too bad, because he could have had a good career. You know, he would have been famous. Uh, but one of the things that he was sort of least comfortable with, although it's sort of apocryphal story that Gamow, I think, made up, which was that he called the cosmological constant his greatest blunder. Talk about the cosmological constant. Is it the cosmological constant that you're against, or is it the whole notion of dark energy that I shouldn't say you, but I should say that data are leading us to believe may not be part of the cosmic reality?

Well, the cosmological constant, that's what it actually is, because I think we can actually try and understand why we put in a cosmological constant. It's a hint about something deeper. So, it's not a, I'm for or against this. I'm trying to understand the theory in its essence. And understanding the theory in its essence, I haven't quite got there to understanding the full import of the cosmological constant in quantum field theory. But I believe there are certain questions one has to answer first before answering those other questions. So there is no need for a cosmological constant. It's something that we can add as a counter term in our averages. And but it doesn't evolve as a constant. So the thing is trying to understand it. I believe there are deeper things to come out. And what I've got is a phenomenological theory trying to probe those questions and therefore lay the foundations for something better and bigger. So that's what I've been trying to do in going back to the foundations, because I, I think about foundations. I have done so for decades. And, you know, and going into things more and more. You know, so I started out in higher dimensional gravity, string theory, etc. But and I'm trying to understand what higher dimensions are. And I decided at the end of my PhD in the early 90s that, well, I wasn't clever enough for that. But there's these other problems, and there's so much data that's coming out of cosmology. And so it's important to try and understand those things, really to go back to the first principles. And that's what I'm trying to do.

So Einstein knew about gravitational time dilation. And if you could summarize the basic facts about gravitational time dilation, and in fact, how time can run differently according to different observers, compared to some global cosmic or core or proper cosmic time, can you explain the essence of that notion that time is gravitationally dependent, and perhaps dependent on matter distribution?

So there's different sorts of time dilation. And I'm, what I'm going to claim is that, in contrast, your show is called "Into the Impossible," but actually, I think "Timescape" might just be possible. Right. So to set the notion of time and to understand structure, then we're looking back into the deep past. Our telescopes are time machines, as you know. And of course, what you're most familiar with is, of course, the cosmic microwave background, because that's what you've been working on. And back then, the universe was essentially a featureless fluid. And we're looking at little fluctuations of parts and parts in a hundred, whatever is, 10 to the minus 5, right? So, but as we, as the universe evolves and those things form, those form the seeds of structures, and the traces evolve over time. But as things go on, then we're seeing more and more structure. And it's only deep in those structures that we have notions of what time is. So the thing is that if we look at the structure in the universe, then there's more and more of it as the universe evolves. We, if we squish things down onto a light cone, then, um, looking, you know, at some level, it looks as if there's some homogeneous distribution with Poisson statistics or whatever. But the closer we get to our own epoch, then there's more and more structure. And the thing is that that structure, by Einstein's equations, should, you know, Einstein's equations tell us that matter and geometry are related. But there is a scale to that, because it's a causal theory. So there are things which don't propagate the average density, and there are things which propagate the gravitational waves. But the whole point is that there should be some causal evolution. And if we look really close by, we, in general, the universe is dominated by voids. All structures are in thin filaments and sheets, which, so there's the cosmic web. And all the actual things that form structures are gravitationally bound. That's to say, they've overcome the initial expansion of the universe. So the universe was expanding really, really quickly early on. And the filaments and voids are still expanding, but they're, the point is, they can be expanding less quickly. So now we're talking about the voids. And in particular, this is a map of large-scale structure. It's an actual map of data, redshift versus distance, but really showing redshift on the axis and time on the right 45-degree axis. And then we see structure that's indicated by luminous dots. And then we see great many dots that are not luminous, or great many regions which are not illuminated. And we call those voids. So take it away, David.

We actually live in thin sheets which are called walls. So all structures which formed in situ were such that they overcame the initial, they broke away from the expansion of the universe and collapsed. And they form a tiny fraction of the volume of the universe today. So most of the universe today is in voids of a certain diameter. And that diameter is set by the primordial fluctuations. It's by the sound waves in the plasma. So that those sound waves amplify things and give rise to differences today. So that's what we have. And so we've got a universe with different structures. And if you look really close, then there is actually no statistical homogeneity and isotropy. So the thing is, then we want to think about what is going on. And is the Lambda CDM model a good model for looking at this sort of stuff, when actually Einstein's equations apply only on small scales? So the thing is, we've been using the Friedmann models for the global evolution of the universe as if they are a local geometry, when really they are a statistical thing. And there's a difference between what I'll call statistical geometry and local geometry. So that gets down to the question of time dilation and boosts. And you asked, what is gravitational time dilation? Well, we should think about just differences. So there are different sorts of time dilations. If I just have two frames which are close to each other, one whooshing by the other, then they can have arbitrarily large time dilation. That's the normal special relativistic time dilation. So if there are denser regions, then in general, and the distance between things is fixed, you know. So here on Earth, we have an acceleration because the floor, the ground is pushing us up relative to some GPS satellite. And but there is a difference in the gravitational potential. So even if the distance is fixed, then those in the denser region will experience that their clock would be effectively going slower than the other one. Now, the thing is, when all of our notions of understanding about time dilation, and when it's large and when it's small, are based on bound structures, we normalize our clocks relative to one at infinity, assuming that the universe is completely empty. But it is not empty. So we know that here on Earth, we are four and a half years younger than if we had been up on a GPS satellite, because it's parts in a billion. If we look at stars, then the difference is border parts in millions. And those are all small differences. So I'm talking about large differences. And it's a question of how do I keep two clocks synchronized if there is a difference in the relative volume deceleration? So we're talking about a collective degree of freedom of the background, not which is different. It's statistical, but it's there in Einstein's theory.

So if one of your respondents asked a question about cosmic coincidence, well, the cosmic coincidence in the standard cosmology is, well, we look back in time. So here, this is a logarithmic map of the universe. So it's Max Tegmark and others who published this back in 2005. And if you look back here at early times, then, well, you could say that structures, more or less as we saw in the other slides, they, you might say, well, that's just plus noise, and it's reasonably statistic, it's reasonably on average that they are the same everywhere. But as time goes by, then you get all these structures forming. And the thing is, in the standard cosmology, it appears that the universe is decelerating for most of its life and then starts accelerating in the recent past. And the thing is that that apparent acceleration also coincides with the structure becoming nonlinear in its growth. Now, which led a minority of people who look at the foundation, who look at general relativity and what's called the averaging problem, to say, well, maybe this is actually an effect of the structure that we're not doing things properly. So that's where I came up with the TimeScape cosmology. And so, a long paper called "Cosmic Clocks, Cosmic Averages, and Cosmic Variance" in 2007. And there's always been a solution to the cosmic coincidence problem, because it is determined by not just the fact that there are voids, etc., but there is a difference in clock rates. So, and you can boil it down. So this was in PRL in 2007. You can boil it down to something called, which I call the void fraction. And if you take an average observer by volume, then because the universe is dominated by voids in which expanding, in which there is all there is is protons, electrons, and helium nuclei, the primordial stuff, if you were just to keep the, as Einstein's equations tell us that matter sources geometry, and as long as we know exactly what the dust is, then the Friedmann equations are perfectly fine. So, and the thing is, here, a volume average observer is going to have a deceleration parameter which they'll always see the universe decelerating. But a wall observer, and the crucial thing is there's a difference in the clock rate and how we normalize things. The wall observer will, this polynomial down here, there's a cubic, and that cubic is initially negative. So that it is also the deceleration parameter is also a half early on. But as time goes by, when the void fraction reaches a crucial threshold, and it's about 59%, then there's going to be a change in the sign of this, so that it appears that the universe is accelerating, because suddenly the voids have taken over.

So we're doing an average. Let me just slow it down a tiny bit and explain it to my audience. The most brilliant in the known multiverse, but still, I do feel like this is a little advanced. I want to see if I understand it, and then I think that will maybe translate it into a way that my audience can get as much out of it as possible. So, in relativity, we know that mass distorts clocks and causes what's called gravitational redshift, but it also can slow down clocks. Newtonian potential is all you need. So any form of matter which distorts spacetime causes curvature, will manifestly cause a slowing down of clocks. Therefore, the absence of matter, or a deficit of matter, will cause the opposite effect, which will apparently cause clocks to run faster relative to clocks that would run slower, either in an empty universe or in a region of spacetime where there is more matter than the average. Now, in cosmology, it used to be called the search for two numbers: the Hubble constant, which is the rate of expansion, the first derivative of the scale factor with respect to time, how fast are distant galaxies moving away as a function of redshift in their distance? And the second number that Sandage used to make fun of cosmologists over obsessing with is the deceleration parameter. Now, for most of cosmological history, we believed, until David Wiltshire came along, but really for many, many decades, we believed there was only matter in the universe, and therefore the universe should be decelerating, because there should be enough gravitational force that should overcome the expansion force and eventually cause the universe to decelerate. And that's why it was called the deceleration parameter. Now, in the late 1990s, friends and past guests on the show, like Brian Schmidt and Saul Perlmutter and Adam Riess, discovered from distant Type Ia supernovae that the deceleration parameter was negative. And that seemed to imply there was not only some strange form of matter which wasn't gravitationally attractive, wasn't pulling and decelerating the expansion, it was accelerating it. And that came along at later times. Now, when David talks about filaments and walls, he's talking about the boundaries, like a sponge or a sourdough bread loaf or something like that. There are pockets or voids, and then there are walls of very high density compared to the voids. And what David's saying is that in the regions near the walls, you're going to have behavior much like you would have in a uniform matter density-filled universe. I should say one last thing. We have long believed that the universe is subject to what's called the cosmological principle, which is really an extension of the Copernican principle, which I always call the ultimate "Big Brother" statement, which is that you're not very special. You know, there's no special place in the universe. There's no special direction in the universe. And it goes along with something called Lorentz invariance violation. The last thing I want to say is that when you extend that beyond what Copernicus did in our solar system, you extend it to the whole universe, you have to go beyond a certain radius over which, obviously, the universe will be inhomogeneous and anisotropic on small scales. But David's even saying something more strong, that the cosmological principle must incorporate and must be possible to be tested on scales of varying length scales. And what you, I believe, are saying, just to finish my summary for breakdown for the audience, is that there are these regions of spacetime over which the volume average observer, where you're averaging over voids and walls, will see no acceleration. So if we see acceleration, it is obviously either attributable to some, you know, dark energy which we don't know much about, or it's an illusion caused by the differential rates of clocks. Did I get some of that right, most of that right, David?

Yes. It's an illusion from fitting a Friedmann-Lemaître-Robertson-Walker expansion to a universe when it's not exactly a Friedmann-Lemaître-Robertson-Walker expansion. So the thing is, and I've got a statistical Copernican principle, which I'll come to. So the thing is that we are an average observer for an observer in a galaxy, and there's, we have a mass-biased view of the universe. It's, you know, so the original problem with the Copernican principle was that we thought that the universe was expanding around, rotating around us, because we didn't take into account the fact that we're actually standing on a rotating planet. If we took an average position by volume in the solar system, we would have never made the mistake. And so this, that the same thing is true here, that we are making a mistake of thinking that the universe on every scale is exactly the same as the density in our own environment, because we're in a structure which broke away, which stopped the Hubble expansion, and actually all the stuff that we see is also, there are ways to test the difference. And so we might come to that. What I want to do is to describe a thought experiment. And this thought experiment is, what's the difference between motion and expansion? When are they equivalent? So there is a sense, if you cannot tell the difference between being at rest in an expanding space or moving in a non-expanding space, then those two things should be equivalent. So this thought experiment, a lot of people have done it. So I've discovered, so Nick Kaiser, for example, he interpreted things a lot differently, but he actually did the same thought experiment. So, but my answer is different to his, because I reinterpret the Kaiser rocket effect. Let's imagine that we have uniform expansion, but this is a collective degree of freedom of the background. And imagine that we're in Minkowski space, completely empty space, but we've defined what I call a semi-tethered lattice. So, a lattice of observers. We've got tethers attached at one end, but then we've also got wells. I've got my tethers attached here, but I've also got a well, an infinitely deep well, in which some tether is spooling out of this well. And it's infinite because we're allowed to do that in our thought experiments. And so, we, and we know about special relativity. We know how to synchronize clocks. And all these tethers are zooming out, spooling out really quickly. And then at some predefined time, we're going to apply brakes to each tether. And it doesn't matter what impulse I impart, just as long as we've all agreed that it's going to be the same impulse. So what happens? Well, so the important thing is, of course, things are going to keep on expanding. And so we're not bringing things to a complete halt, but I get heat. So I get friction heat in my brakes. And that heat can be, that's useful energy that can be transformed into other forms of energy. But as long as the force on this tether in one direction is the same as the one in the opposite direction, as long as the force in each direction is exactly balanced, then there is no net force. So this is an inertial deceleration, but it relates to a collective degree of freedom of the background. It is not a local transformation. It's not a local boost. And that's a critical thing. So the thing is that imagine that you have two lots of tethers, then two non-overlapping but not intersecting lattices. And one lot applies one impulse, and the other lot applies a different impulse. So one lot will decelerate more. And according to the rules of special relativity, the observers who applied the stronger impulse, they decelerate more, and so their clocks will be going at a different rate. So that their clocks will be going slower relative to the ones who didn't decelerate as much, because they applied a different impulse. So the thing is that that is there. It's in the structure of relativity. It's just that it is about a collective degree of freedom of the background. Now, in the actual universe, that, of course, it's rather than applying brakes to the tethers, it is gravitational instability, gravitational collapse, which is doing that. And the thing is, then, so the claim is that you can alter the way in which you do averages in general relativity to find what I call the uniform quasi-local Hubble expansion. So quasi-local means regional. It's about things which you have to integrate stuff over a region. So the thing with gravitational energy is that it is something which has never been completely understood, because of the equivalence principle, the strong equivalence principle can always get rid of gravity at a point. There is such a thing as dynamical gravitational energy. If you're heading towards a rotating black hole in Newton's theory and you come in with zero angular momentum, then you'll just go splat, right? So that, whereas in GR, if you're, you know, even if you haven't been drinking anything, you'll be dragged around by the rotational energy of the black hole. So the thing is that it is real. We measure it. It's just, you can't localize it as, you know, this is the gravitational energy at a point. It's in a region. And it's understanding the difference between local stuff, which we have with our boosts and our local frames, and regional things. That's the difference between local and quasi-local. And it's why it's the statistical side of Einstein's theory which is much harder, much stranger, much weirder, much deeper than what we're used to dealing with. We're used to dealing with a few-body systems, bound structures. I mean, even supermassive black holes, we can still treat them as, you know, effectively they're huge, but we can treat them with physics of bound stuff, and we're used to dealing with that. We're not used to dealing with this other problem, but it's there in the theory if we just, you know, it will require changes to understand the differences that are there, but it is there, and we can understand and make progress, is the claim.

So anyway, I have the cosmological equivalence principle. We don't need to go into the details of it. Usually, this geometry here is taken as the geometry of the whole universe. So the claim is that when you do the patching appropriately with the quasi-local Hubble expansion condition, then you are patching together regions on whose boundary the expansion looks like it's what we assume is the expansion of the whole universe. So if you integrate things on this boundary, the expansion, you get, you know, it's the kinetic energy of expansion. And the thing is that the kinetic energy of expansion has gradients. And when you look at it, it's not just Friedmann model plus local boosts everywhere. That's what we do normally. We assume it's Friedmann plus boosts. But this can be Friedmann plus some differential expansion which is not a boost. And it's, we're talking about the gradients and the kinetic energy of expansion of the expansion itself.

I see. Okay, good. So this cosmological inertial region would be the equivalent of an Einsteinian elevator, where, you know, previously we would have used a freely falling frame to cancel out gravitation locally. You're now expanding that to a volume instead of just a point.

Correct. So we're looking at regional backgrounds. If you look where structures form, it's what I would call a finite infinity region. So this is a notion of George Ellis, who first thought about the fitting problem back in 1984. And what I've tried to do is to go further with the fitting problem, defining finite infinity. So where you've got collapsing, so things vialize. So we're in a cluster of galaxies, and we're in the Local Group, and we are gravitationally bound to the Local Group. But then we assume that everything beyond that is just going to be, I mean, we see a CMB dipole, and we interpret that as not just the motions within the Local Group of galaxies, but the Local Group itself has to be moving at 620 km/s in the direction of Hydra in order to make the velocity vectors add up. So the claim here is actually there is very little motion of the Local Group. It is actually a differential expansion. And we, because we, when we're looking at structures below a scale of statistical homogeneity, then the differential expansion is going to show up. And we, it looks like a velocity, but it's a local boost, but it's not. And the thing is, so one can test that, etc. So the idea is, so there is a boundary which I'll call a finite infinity. And for us, it is a few megaparsecs, because we're on a thin filament in a void. If you're in a rich cluster of galaxies, you know, Coma Cluster or somewhere, it's going to be larger, tens of megaparsecs. If you're in, if you're actually a star which has been ejected into a void, and this would happen early on, this is, you know, then it's going to be different again. So the thing, does it hold in the opposite regime? Does it hold in the linear regime, when the CMB fluctuations are produced in the linear regime, when you don't have structures? Then it's difficult to define. So you can extrapolate what's going to become finite infinity regions. So, you know, I defined something called a void fraction and a fraction of walls. And you can, it's not precisely operationally defined at the CMB, but you can write down equations and put things into what is going, what's the earliest time then? Is it like the epoch of Baryon acoustic oscillations, or the higher redshift universe, or is it only in the local, you know, kind of Local Group scale of very low redshift? What's the highest redshift it would apply to?

Finite infinity well, emerges as all things emerge. So you could have some notion. It's not a cutoff. I, there is, it's an emergent phenomenon. And I would violate the Friedmann equation at one part in a million at the surface of last scattering. So there is a tiny, tiny thing. So linear perturbation theory is almost correct, but just there's a tiny, tiny difference. And that tiny, tiny difference is going to be important over time.

So what is dust? It's the most important thing, because at the present epoch. So once upon a time, you know, we're co-moving with the dust. And once upon a time, when Einstein was around, we thought that the density of the universe was the density of the inside of the galaxy. There was the great debate and all that stuff. And later on, people say, well, okay, galaxies are particles of dust. But actually, galaxies are not homogeneously distributed. We've got the cosmic web. So the thing is, you've got to actually coarse-grain over things, over effective fluid elements which are larger than the largest typical structures. And largest typical structures, because there's many atypical, a few atypical structures, are voids of a particular diameter. And I would claim that that is because the, it's the third peak, the third peak in the primordial spectrum. It's so rare inside a rare faction. So you've got Baryon acoustic oscillations, one, two, three, and a rare faction inside a rare faction is going to give rise to regions which are still expanding. And that is important in determining, so what's really important, the sound speed and a lot of things. But that is what is setting the scale. And so there's, and that's in the regime of what we would say is now nonlinear. So the Baryon acoustic oscillation itself, it determines the difference between the linear and nonlinear regimes. And this is the regime which is nonlinear. But the claim is there is a quasi-local uniform Hubble expansion condition in the regime which is nonlinear, and that gives us, that's giving rise to structure, and a way of understanding things. So, so there is a scale of statistical homogeneity. And in order to understand that, you've got to average over the largest typical structures. And we, because the universe is void-dominated, if we do certain observations and measurements on smaller scales, we're going to get differences because we are biased mass observers. But the local volume is dominated by voids, and actually we're on a thin filament in a void. And this is contributing a lot to things. So the Hubble tension, all that sort of stuff, is because of that. So we've got to account. So if you take some statistically average. So the thing is, if you take different cells and line them up and say, well, on average, is the structure in this cell the same as the structure in that cell? That's what I'll call the statistical homogeneity scale. It's not a scale above which the Friedmann equation holds. You don't have to have the Friedmann equation holding. The thing is, you can average the small-scale Einstein equations, in which matter and geometry are coupled. But then you're also averaging over the nonlinear degrees of freedom that make up the Einstein equations. You can't tell when you take your average, it's going to mix up the left-hand side and the right-hand side of Einstein's equations. When we average matter, we know how to average matter. As long as we're averaging non-gravitational degrees of freedom, then averaging is a reasonable business. But when we're averaging gravitational interactions of something which is nonlinear, in which the gravitational energy content is quasi-local, then we've got to do things differently. So the claim is that it's gradients in these cells that you have to take account of. And it's, so I retain a statistical Copernican principle. We are average observers for observers in a galaxy, but we're not at an average point by volume, which is always going to be in freely expanding space. So by Copernican principle, other average observers should also see an isotropic CMB, because we, the CMB is almost isotropic, you know, it's practically isotropic. But there's nothing in theory, principle, observation which demands that they will say the same. That any other canonical observer is going to have the same CMB temperature or the same angular scale. It's those differences which can lead to big differences. And it's those differences which lead to ideas which we can test.

Does TimeScape feature the same initial conditions? Does it have inflation, perhaps? What does it share with Lambda CDM? It certainly doesn't share Lambda, but what else does it share? Is there an initial condition similarity?

The initial conditions are the same, up to the Friedmann equation being violated at parts in a million. So we do simulations. So with Hayley McPherson, we're doing the full cosmological numerical relativity simulations. And so far, we're just doing the same initial conditions. But in the end, you would, if you want to see finer detail, you would change those initial conditions. So the question, so there are other questions about inflation, etc. Inflation is certainly phenomenologically correct. So we can have some other discussion about what actually goes on in the early universe. But the phenomenology of inflation is the same. So it shares almost the same everything. So yes.

So, we, I think you're on the next slide now, right? So, so I was just going to say that there are different, I'm not going to go into the math, but there are differences. So, all I want to say is that, you know, redshift, so, and I've left other slides out. There's a luminosity distance, there's angular diameter distance. As long as, as long as you're in a certain class of theories, and this is within those class of theories, but you're led to differences. So the Friedmann, the Friedmann equation has got certain expansion laws, and the TimeScape has a different one. And the thing is, you can write down in a certain limit, which is what I worked out in 2007, you can actually write down analytic expressions and get out results. And it's just that those different, so because they're different, then people won't study it, because it doesn't fit into the Friedmann framework. But, but I mean, a few people are now doing things. So Dez has done something. So anyway, that if we take different spatially flat Lambda CDM models, the Hubble expansion, because it is not really decelerating, it's only appears to be decelerating, it's always flatter than any particular Lambda CDM model. And so an important difference is in the, what's known as a comoving distance. So if you take three different Lambda CDM models, they all have a certain shape, and the TimeScape model will interpolate between different Lambda CDM models over different ranges of redshift. So the thing is, over a small range of redshifts, it's only going to differ from the Friedmann evolution by about 1 to 3%. You need a long lever to see big differences. So what best fits supernovae close by will, if you will, be different from what you would expect a Lambda CDM model that best fits the angular diameter distance of the sound horizon in the CMB. So the thing is, and of course, there is the Hubble tension, and there is no Hubble tension here, because it, and actually in many inhomogeneous models, you don't have a Hubble tension as a problem of the standard model. And what people ordinarily do, it's these smooth curves that we're really talking about, but people will do things in terms of an equation of state. So, the, all those previous curves, those concave in a certain way, with a certain shape, which depends on the derivatives. Before we get to the details of the, of those, you, on the previous slide, you say TimeScape. So that's a difference between distances as measured in Friedmann-Robertson-Walker, Lemaître-Robertson-Walker, and then you have the TimeScape prediction. So what is TimeScape? Can you give a concrete definition so we all have a frame of reference?

This is a particular phenomenological model in which I have an ensemble of voids and walls. So the walls are regions which are bounded by finite infinity, and they contain all the structure which formed, which broke away from the Hubble expansion. So the, so it's the walls and the voids. So I have extra slides where I've got detailed mathematical details. It is that statistical ensemble, and taking that statistical ensemble, I apply the quasi. So look at the expansion. There's a particular matching procedure to look at light rays and conformally. So in implying the uniform quasi-local Hubble expansion condition, there's a conformal matching between the average statistical light propagation and the local, within finite infinity region, propagation. So I'm assuming, as most people normally, so in the Friedmann model, you assume that the differences between our clock and the cosmic time are small, that they just relate to the gravitational potential within bound structures. The claim here is, okay, those are still going to be small. It's like the gravitational time dilation of parts in a million if you're near a star. So as long as you're not near a black hole and remaining static in some accretion disk, then those time differences are small. So the, the assumption here is, well, actually, those time differences are small. So what we're doing here is looking at a different phenomenological model, which is then fit to data. And so it's the overarching combination of a phenomenological model, and it's to be contrasted with the Friedmann-Lemaître-Robertson-Walker scenario, where you would also can have structure formation, you can have domain walls, you have walls, etc., but this manifestly separates out into different behaviors of geodesics. There's a similarity in the standard cosmological model where you can account for voids and you can account for domain walls or walls in structures, bound structures. But this says that you manifestly have to treat the behavior of geodesics differently in voids and for the average cosmological observer. When that's what led you to bring in these finite infinity and this notion of the cosmological equivalence principle, am I bringing all this together correctly?

I think so. I mean, it's your theory, so I don't want to, I don't want to bully a bit. Your statement was a little bit woolly there, Brian. But the issue I have is that, and I think the audience might be objecting to or concerned about, is that why can't this be taken into account in the standard cosmological framework of large-scale structure formation? What new features then are present in TimeScape that have such big ramifications that dark energy doesn't exist? And therefore, not only the cosmological constant, but experiments from the CMB alone, as you know, the CMB alone can measure the existence of dark energy. Type 1A supernovae can measure it. Baryon acoustic oscillations measure it, measure it. You infer it. The problem in cosmology is that measurement is an abused word, actually. We just see angles on the sky and fluxes of radiation. We have to put in a model in order to interpret it. And the problem is the experiment was done in a distant galaxy, a long, long time ago, in conditions that we can't control, you know, with thermonuclear explosions, which you're never going to be able to do in the lab, because it would mean, you know, controlled detonations of stars. We don't, you know, it'd be horrible to think that we could ever master the technology to that degree. So, and to look at that, we have to look at all, you know, all this mess in between and interpret. So that is the problem. But now, why does the standard model work? Well, it's because there is this infinite infinity scale back here. Because the geometry on this boundary is effectively Einstein-de Sitter. And as long as we're just looking at structure formation, then in the standard model, and just confining ourselves to thinking about these scales, then the standard models of structure formation, they're working pretty well. It's just a calibration. It's how we calibrate. So in the standard model, which is often done with Newton, you just put in the Friedmann equation to scale the box, right? And it's all done with Newtonian. So why does Newton work so well? It's because Newton will work pretty well on these scales, but it's just different differences are used to scale the box. So that's why things work.

So let's just say what equation of state is for the audience. We recently had Kyle Henson, the former spokesperson, past spokesperson of DESI, was here recently talking about the conflict between the DESI results and the equation of state that leads to a cosmological constant being the interpretation for observations and luminosity distances as the angular diameter distances determined from varying acoustic oscillations. He also brings in Pantheon and some of the same data that you bring in. So equation of state is basically a factor that accounts for the type of matter energy that we see in the universe. So you're going to show how the equation of state has an effective equation of state parameter W, and how that fits in or is not needed, really, in the TimeScape model. So please continue.

The equation of state is that you assume that there is a fluid with the dark energy, whatever it is, P is equal to W times rho, the density of the fluid. And for a cosmological constant, you'd have exactly minus 1. And actually, if it went less than minus 1, there are problems with causality. So an equation of state should really be between, to satisfy what's called the dominant energy condition, that you want the speed of sound to be less than or equal to the speed of light. Then you want the W parameter to be between 1 and minus 1. And if you cross that's in the standard cosmology with the Friedmann equation. Now, if you had W going less than minus 1, and it was fundamental, that would be saying that you get into problems with causality, with conservation of energy, with closed time-like loops, and so back in the 1990s, it would have been really difficult to publish things like this. And I believe that Robert Caldwell, I mean, had difficulty getting his paper about phantom dark energy published in the first place, because, you know, it's been known since the 1960s that models of Hoyle and Narlikar, that you have to violate energy conservation. And, you know, certainly we do that at the beginning of the universe. It's really important to understand, but you have to violate energy conservation in such a way that you could have closed time-like loops and all sorts of existential crises if you let this W parameter go below minus 1. But if it's not, if it's not the Friedmann equation, because it's really just smooth curves, it's not the Friedmann equation. This TimeScape has a different smooth curve as opposed to the others. So, but you can nonetheless go away and work out what you would interpret if you don't have the Friedmann equation. But make the mistake of interpreting it as a Friedmann equation. You get something, and you're dividing by something. And this something here, it goes through zero, and it means you have an artificial infinity, right? And so you get really results which really don't, which are not what you expect. And you would say that it is evolving with time. And in fact, so if you go back to a paper of mine in 2009, I came, I had the prediction that it was, that's old data, it's based on what was then supernovae, the Union, the Constitution. And the thing is that you go away and you parameterize dark energy in terms of some.

The evolving equation of state and what is now seen is of the form of what I expected with the time scale. So you've got all this stuff, and so these were 2024 results. There were other results this year, and there was big stuff in the popular media. "Oh, dark energy is evolving. We don't understand what it is." And because people don't want to read my papers, because it means doing it, it means going back and starting at the beginning. And people have a lot invested in decades of work, and you know, almost well, a century if you're right. I mean, literally three Nobel Prizes awarded for discovery of the cosmological concept. Well, they discovered it's something important. So I'm I'm perfectly happy that Brian and Adam got the Nobel Prize. The Swedish committee just forgot to put the word "apparent." So just add the site word "apparent" in the the citation, and you know, they discovered something really crucially important. So I've got no issue with their award. It's just that, and you know, they discovered something important. And the thing is that we have to understand what that important thing is, and it means not just tweaking our models. It means actually going back to the essence of the theory and redoing it from the bottom up. Mach's principle is not something that most cosmologists do, right? So that that's a challenge. And I think you're right. People don't want to do that because they're lazy. But what would it mean to to validate this model? I mean, you must have been quite pleased with the new results from DESI and and last year's DECam data releases. You must have been quite pleased. On the other hand, it must be quite frustrating for you to to see that, you know, there's this, there's still interpretations which aren't really considering timescape as a fundamental, perhaps more simplistic in the case of, in the sense of Occam's razor explanation for the observation. So, how do you, as a man, how do you react to that?

As a theoretical physicist, I want to think about things and I ask the right question. And in going, I've had the privilege of talking to every leading cosmologist about these ideas. A lot of them immediately get it and say, "Can't believe that Newton could be wrong on on these scales." Yeah, I mean, we might be able to guess who would do it. In 2009, I gave my stuff at a at a meeting, and I gave my talk, presented the cosmological principle. An elderly woman comes down, shakes my hand, says, "Congratulations. Congratulations. This is the true spirit of relativity." And it was Yvonne Shklovsky. And she was one of the few people that Einstein allowed into his office when she was a postdoc to talk physics. And if she, she was really enthusiastic. That's all you know, that's recognition. That's that's what you know. So to see that she was so enthusiastic about it, I just thought, well, okay, I've done something. Whether it's right or wrong, at least I can think so.

In the standard cosmology, you have an Omega Lambda. So there's a difference between bare parameters and dressed parameters in the in the redshift. So it is very much like, so this is including radiation, and up to this point in the evolution, things are very much like a standard cosmology with no Lambda. So the kinetic curvature, which is so spatial curvature, which I think is as kinetic energy of expansion, is not scaling in a particular way as it does in Friedmann. That's the difference. So the universe today is dominated by the kinetic energy of expansion of voids, and it scales in proportion to the void fraction. I mean, so volume fraction here, so it's a cube root. And and so that's the difference. So there's a term called back reaction, which a lot of people have argued about in different ways, and that remains small. And the thing is, you need the timescape interpretation in order to interpret this properly. That that's the claim. So there are differences in the variance. So, so, so the the ages of the universe that you get out are comparatively large. So that's, you know, is a timescape because the age, the volume average age of an observer who's not bound to any structures. So the observer who sees the most isotropic possible CMB. So you've got to talk about which observer, you know, you don't just have one clock at every point. You know, give somebody a local boost, and of course, you can have an infinite clock difference. The point is that there has to, there have to be canonical observers. There is a volume average observer, the the one who sees the closest to isotropic CMB as possible, and they will all have some dipole. And that is the volume average observer. And the thing is that a relative volume deceleration, which is small, it turns out to be the same order as so numerically, so it's less than angstrom per second squared at the present epoch. It's so tiny. And it comes out actually to be the Mond scale, better than the Mond scale people predict because they they put in an extra factor of pi. And anyway, so there are reasons for that. But one must remain skeptical about anything which you didn't put in, and I didn't expect that. But but anyway, a tiny difference in volume deceleration when you've got billions of years to integrate can make a difference. And so that's that's the the point is that because dark energy, I claim it's related to the kinetic energy of expansion and its gradients, then that can be much, it's very, it's qualitatively different. And it's the the fact that these numbers are so large, you're saying it's a big effect. That's why there is there is people will, you know, that's why most colleagues, you know, it's been the case of, well, that's an interesting idea. What does everybody else think?

The question that I've had, and others have had, is that, you know, if Lambda CDM is wrong and timescape is right, the question is, what predictions does it make that aren't just the same as as saying that Lambda CDM is wrong? Are there new falsifiable predictions in the Popperian sense that time? Absolutely. Yeah. So let's go into that. So this is all, so it's what the Euclid satellite will measure. But I I haven't shown what we found with so the Euclid, so there's something called the Clack and Bassett L test. So maybe I can just show what we found in the P. All right. So if you're looking at, so the expansion history is different. It differs by one to 3%. And you can go away and you can quantify those differences. And so there's something called the Clack and Bassett Blue test, which can test the Friedmann equation, and it can test any alternative to the Friedmann equation. And for that test to be done, you needed you. So when projections, uh, I'll I'll I shouldn't have put this slide last, but uh, so when the projections were done in 2014 for the Euclid mission, people went away and said, "Okay, you're you're going to need more than a thousand supernovae, and you're going to need this amount of Baryon Acoustic Oscillation measurements." And you know, the last couple of we've been doing analyses with supernovae at various points, and recently with the Pantheon Plus, etc., there there are more supernovae of more than a thousand. So we said, "Okay, let's do it." And when we went and did that, then we first got that the timescape model was fitting better, and it has fit better. But the question was, this level of statistical significance? And the referee of the first paper said, "Okay, actually, you can do better than that because it's using this thing, the Tripp relation, etc. There's a lot of details, but there are two empirical parameters, the stretch and the color, and it turns out that you cannot assume that they are both independent Gaussian distributions, and they have non-Gaussian tails. You've got to do better." So the referee said, "You can do better than that." And so we went and did better. We went and did that, and then it suddenly the Bayes factor improved by a huge amount. But so log Bayes went up by two. So the the thing is, so in if I look at, so the Bayes factor, then the here go and show a plot. And if timescape fits better, then it's going to be up here, and if Lambda CDM fits better, down there. And beyond there's a statistical homogeneity scale and so on. So what we're going to do is chop out data and and refit everything as we go along. And timescape is designed to work on small scales where there is this quasi-uniform Hubble expansion condition. So if it timescape is fitting really well, then we we're going to expect it to be up there. And if Lambda, if the Friedmann equation works really well on the larger scale, so then we're going to expect things to be down there. And what happens is that you see, okay, that this is the result. And the Lambda CDM model almost goes to fitting better, but not quite. And then actually things change again. So how do you interpret that? Well, okay, so that is where timescape model is designed to work, and it is working as one expects. And this is the Hubble tension. If you cut out data and and your data is dominated by things at a certain distance, and you haven't accounted for other things, then that is the Hubble tension staring you in the face. And and but then the thing is that even on the largest scales, the timescape model is fitting. I mean, it it's never going to fit. You're not going to get a Bayes factor which is super large here because we're looking at a small lever arm and a small range of redshifts. And the timescape model, in order to fit, because the standard model is pretty good phenomenologically has been up until now, but now the cracks are showing. Once we've got data in more and more different sources of data, we got JWST, it's showing that there things aren't fitting, that the universe, there's a lot of structure and older stuff than we would expect naively. So all of that stuff that is not a direct prediction, but it's consistent. So the thing that we wanted to get to was this slide here, and this is the Euclid satellite. The Euclid mission tests the difference. So this is projections made back in 2014 by other people, not me. And I the only thing is I said, "Can you please put?" So if the Friedmann equation, so the Clack and Bassett Lou test is looking at it's a test of the Friedmann equation or of other expansion history. So there's some model called the TARDIS model. So the timescape model would come in here. And the thing is here, you've got there is a prediction here, and you can go away with this, and and so it's going to be decided.

Right. This is great, David. I didn't actually, I've done a lot of research into the model in the last few days, but I didn't know, I didn't realize this. This is a very high precision test in the sense that it's decisive. Again, Popper said that you can't prove something in science, but you can exclude things with what he called decisive experiments. And it seems to me this is exactly that. And your aim, and I always like to give a teachable lesson to my audience, who's a lot of them are students in the university. This is what a good scientist does. They don't just say, "I'm right, you know, please give me a Nobel Prize." They say, "What, how could I be wrong?" To know enough that they could be wrong, but actually welcome the challenge and hopefully be borne out in the end through the through the annealing process, the hardening process that occurs when you do things like this. So this is great. Anything else you want to say about this before we get to audience questions?

Well, if I'm wrong, I can retire and do something else, and my life will be a lot easier. No, you guys are new Kiwis, never retire. Roy Kerr is still going strong, right? I have to work crazy hours and and get very tired. It's the most interesting, exhilarating period in my career.

Okay, so I do have audience questions. I also have a couple of more questions of my own that I can't help but uh but ask the question of this uh this the model and how we can test it. We we do need more data. Obviously, there are results and there even theories that are coming in. As Eddington said, "Never trust, you know, an experiment until there's a theory that bears it out." So this is merely a statement of CL. I mean, I'm not trivializing it, but but it's really minimal ingredients, right? It's not adding some new field, chameleon fields, and and tracker fields, and and and landscape bosons or whatever. It's it's merely saying that you must account for the properties of time. It has the same number of free parameters as the spatially flat Lambda CDM model, which means you can test it with quite easily without adding extra stuff.

One question I had from the audience is, how did you choose the name Timescape? Initially, in my first papers, I called it the fractal bubble model, and I was told that um, you mustn't call anything fractal because there's all these uh debates, people won't like that. So then I thought, well, actually, the really important crucial ingredient here is the relative calibration of clocks in a universe with kinetic energy gradients, etc. So it's really time is important, and so let's call it the Timescape. I I then, of course, discovered that people have used this in science fiction, inevitably. But so anyway, I I started calling it Timescape from end of 2008, whereas the first, the first real paper was "Cosmic Clocks, Cosmic Averages, and Cosmic Variance," and that was in 2007, and I called it fractal wobble model.

So if you could change one thing about how cosmologists interpret time, what would it be? How how would you change the way that my colleagues and I, you know, simple experimentalists think about time?

Time is not like Newton. So we we're used to thinking about time. There is a single age of the universe, and that's all there is. But actually, there is a relativity of cosmological time. I claim that go that is that is there in the structure of Einstein's theory if we go deeper into that structure. And so we just, there are different different sorts of time. I've got volume average time and wall time. And as long as you can accept that, okay, we we have to recalibrate things and do some things different, then we know from just using GPS that it's there. So, so let's just take that a bit further and realize that, okay, bound structures are qualitatively different from other things.

Now, there are experiments you could do in future which, you know, so so in a moment, I'm going to ask you whether or not you've actually secretly smuggled in an absolute cosmic clock. But before then, I want to ask you a question that my audience is curious about, which is what you say to your critics. Um, what are their strongest arguments against Timescape?

In order to do the next level of tests, we have to calibrate the speed of sound in the primordial plasma, and that means the question of the ratio of dark matter to matter. We've got to do that properly. So within what I've done so far, the uncertainty is large. So if you look at our the paper from 2013 in Classical and Quantum Gravity, whether there is particulate dark matter or not, it has to recalibrate. So there are details to be worked out. I haven't come across critics with good arguments. There are people who say things without knowing what they're talking about. Like one certain Ethan Siegel on some channel will will refer to some paper that was written in 2005, before I ever did anything. And it's so it's setting up a straw man or some something else which is not related to my work and to shoot it down. Well, actually, that's not what I'm saying. He's known for that. He's uh, he's kind of a professional. We he's not, we call him the professional blogger around here. He's he's not an active astrophysicist anymore. It's just he's blogging.

Okay. So, question from an audience member named Elemental Element, which I considered giving one of my kids as his name. Some say that time is something fundamental, or some say uh, it doesn't exist at all, and some say that time is destined to disappear forever and get blended up into uh, some amalgam that we don't understand. But in Timescape, I think to summarize his question, what does Timescape say about the thermodynamic arrow of time, if anything?

It doesn't say anything directly about the thermodynamic arrow of time. That comes out of things which went on in the very early universe. So it it doesn't address those questions directly. So those are related to other questions about what goes on in the very early universe, about which I can speculate because I I love thinking about those things and have been doing so since my the time of my PhD uh back in the in the relativity group in Cambridge in the mid 1980s. So Timescape is it's talking about later things, and so there's symmetry breaking clearly, and it's it's understanding symmetry breaking, and it's understanding how symmetry breaking is related to to basic geometry.

Shall I get into a tangent about it?

Yeah, let's do a quick tangent before we wrap up with two more uh quick questions.

Yes. Go off on your tangent, please. Go off on your co-tangent.

Okay. So as far as I'm concerned, we've got to couple matter and geometry always. And the notion of spacetime is emergent. And the thing about Einstein's theory is that matter and geometry, it's a relational structure. And in the early universe, when the average relationship between things is purely like like there should be no notion of a fixed geometry. We're used to thinking about a fixed spacetime as string theorists and etc. We're used to thinking about these vacua, and somehow all of the the vacuum exists without the matter in it, right? And and so the problem with string theory is because it's thinking about classical vacua, thinking about quantum fields on a background, it's become a theory of nothing rather than a theory of everything. Right? And so what is quantum geometry? It's the internal degrees of freedom of particles. So Kaluza-Klein is a very interesting idea, but we interpret things in the wrong way. My background was, I worked on the Kaluza-Klein idea. I worked on brain worlds back in 1986-87, before they became fashionable, and I thought that was really rubbish idea. But the thing is that both of those ideas uh, they think too much in terms of classical manifolds, where actually it's really quantum geometry should be talking about the internal degrees of freedom of particles. It's different. And it's when and it's that when the initially the when the average relationship between things is light-like, then the notion of geometry should be different. And we, you know, whatever in inflation is a a phenomenology in search of a theory, and that theory is really going to involve quantum gravity, and it's going to and it's going to be different. Um, anyway, that's enough.

I want to uh end with a question about one of them my favorite people. We started off with some comments about about him and his blunders, and that's Einstein. So I want to ask you, you have five minutes with Professor Albert Einstein. What would you tell him about your theory and where it stands and where the future may head?

Well, I'd talk to him about gravitational energy because that's he spent a long time looking trying to understand the nature of gravitational energy. And I've learned a lot from looking at Einstein's mistake papers, the things that he did on the way to getting to the general relativity. So he did a number of things, and that was all about the nature of gravitational energy. So I would, and you can see the thought processes. And and and so I would talk to him that actually these ideas are here now, and actually Mach's principle is there in your theory. It's it's it's it's there in your theory, and we just have to, you know, ask these more basic questions that, you know, if if you had been able to, you know, back in in the 19 teens, then we didn't know that the universe was expanding. And you just have to go back and redo those, you know, redo those thought experiments. Can can we come up with a cool thought experiment together? Can we come up with some, you know, some new way of of testing things? That's what I talked to him about.

I told you last month I had Kyle Henson here from the DESI experiment spokesperson, past spokesperson, about the philosophical and maybe even psychological implications of living in a universe without a cosmological constant, still with dark energy, but with an evolving dark energy. I want to ask you a similar question. Let's imagine, not if you're wrong, but let's say you're right, David. Let's say it's eventually validated, maybe soon. You know, soon is a relative word. Dark energy is reinterpreted, and time is understood as regional. What does that mean for how we see ourselves in the universe philosophically? Einstein was not scared to ask these questions. What do you think about the philosophical and psychological aspects of your theory should it be proven right?

Let's say, well, it's it's just going along with Copernicus's idea to a new level. So uh, the Copernican revolution changed the way that society thinks, and this would be a further step in that process. That's all I can say.

David, this has been wonderful fun for me. I hope we get to meet in person someday and uh, have many more conversations. Uh, maybe on my next trip to the South Pole, I'll come through Canterbury. I've been. Yeah. Yeah, that's right. Come through. So yeah, we've got the South Pole operation. We we're the logistic base for the the South Pole operation here. So we do get visitors through. So yes, please, I would love it. My next trip uh, we'll schedule a visit to you. Thank you so much, David. Have a wonderful uh, rest of your day. It's almost evening here. Yeah. Okay. Thanks for getting up so early. Bye, David.