[00:00:00] The loophole is if you have integers rather than irrational numbers, you can avoid Boltzman brains by making everything happen much more quickly. The consequence of that is you have to live with an exact repeat of the universe an infinite number of times in the past and future. >> The philosopher Friedri Nature imagined that time and everything within it might repeat eternally into both the future and the past. It’s an idea we explored

[00:00:24] in our book battle of the big bang. But now there’s a new paper that suggests that exact cosmic repetition could be realized within quantum mechanics and might offer a way around one of cosmology’s strangest problems, the threat of boltsman brains. So to help us unpack this, I’m super excited by the fact I’m joined by the papers lead author Sha Carol. Welcome Shan. How are you doing? >> Great. Thanks very much for having me

[00:00:50] here, Phil. >> Yeah, I’m super excited about this. Let’s begin with the mystery of the the big bang’s low entropy condition. If if entropy has been increasing like for the past 14 billion years, wouldn’t we naturally expect it to be really low in the past? What precisely is so surprising about this low entropy of the early universe? >> Sure, that’s a great question. You know, entropy is this idea we all have disorderly randomness, disorganization.

[00:01:16] It increases with time. It seems very natural. You’re completely correct that if entropy has been increasing then it must have been lower in the past. The problem is we usually think about cosmology in terms of setting up initial conditions right you know there was it’s all very vague a little bit illdefined but there’s this feeling from our everyday experience that the way we think about physics is we set something up in a certain state and then let it go

[00:01:44] as a function of time. So if you wanted to say well the low early low entropy of the early universe is natural because entropy is increasing then you have to explain to me why entropy is increasing why aren’t we just in thermal equilibrium why aren’t we at high entropy already or you can think in a slightly more natural way as a cosmologist and say why was the entropy low of the early universe to begin with and that’s something we don’t really

[00:02:08] know the answer to. >> Right. Right. So what solution did Boltzman propose to this problem? It’s a great question also because Boltzman was really the first to put forward this sort of statistical explanation of what entropy is and he was trying to reconcile the second law of thermodynamics which says entropy increases which has a direction of time the direction in which entropy is increasing with the laws of Newtonian

[00:02:36] mechanics which don’t have a direction of time classical Newtonian mechanics works equally well forward or backward so he thought and many people had the idea that maybe you could reconcile these just using probability and statistics and he failed. It was pointed out including by one of his old professors Ysef Loid that he had made a little mathematical cheat in his uh assumptions. So later when he sort of returned to this problem and was

[00:03:03] thinking about it, he put forward several different possible explanations for why the entropy might have been low in the past. One is the one that we think is right. basically that there was a cosmological initial condition for some reason that set the entropy to be very very low. But another possibility he put forward was to invent the multiverse which is kind of a cool idea. You know the whole idea of the multiverse and the anthropic principle.

[00:03:31] It all goes back to Boltzman in 1895. He said you know what if the universe is just really really big and eternally old and it’s a box of gas and I know how to deal with boxes of gas. I’m I’m Ludvig Boltzman, right? And usually that universal box of gas would be in thermal equilibrium. And Boltzman was smart enough to know that that means life cannot exist. Life requires energy and food and fuel in the form of low entropy

[00:04:01] sources. But he said if if the universe lasts forever, there will be in certain parts of the universe rare but inevitable fluctuations into regions of lower entropy. And he literally says if you wait long enough, you’ll get a fluctuation the size of our galaxy. And so he suggests maybe you and I and the rest of the universe that we see around us is just the aftermath of a random fluctuation into a very very low entropy state in some local region of

[00:04:34] space where we can live >> right now. What is the problem with that? Was it I mean was it is it Edington that pointed out what the uh what the issue was going to be? >> It was Edington. As far as I know, Edington was the first. You know, you have to understand that this was not for whatever reason a very hot topic at the time and certainly in the 1890s. The idea of thinking seriously about cosmology was just not really current,

[00:05:01] right? Um when we finally had the discoveries by Hubble in the 1920s, then we could say, “Oh, the universe is expanding. There’s a big bang. There’s lots of different galaxies.” You know, the whole picture changed by a lot. But in 1895, no one was thinking about any of those things. They thought the universe was the galaxy. They thought it was more or less fixed forever. So there just wasn’t a lot of followup on Boltzman’s original idea. As far as I

[00:05:27] know, the first person to really point out the problem was Arthur Edington, who was, you know, a great astrophysicist, one of the people who tested Einstein’s theory of general relativity by looking at gravitational deflection of light during a solar eclipse. and he wrote a wonderful book um on the direction of time. In fact, it was Edington who coined the term the arrow of time. And he thinks about Boltzman’s suggestion

[00:05:52] and he says, you know, sure, if you wait long enough, you will get a fluctuation the size of our galaxy in which we could live, but you don’t have to wait nearly that long if all you want is to get a single person to fluctuate into existence. And he says if you count the number of people who will be fluctuated into existence in a huge fluctuation that looks like the galaxy that’s a much smaller number than the number of people who just

[00:06:22] fluctuate individually out there in empty space. This seems very counterintuitive to us like it’s it’s this is doing work that you know none of our everyday experience has any right to give us intuition to think about. But when you run the numbers, what Boltzman scenario predicts is that the overwhelming majority of observers will be minimal deviations away from thermal equilibrium, >> right? And that’s the famous Boltzman

[00:06:51] brain like just a brain fluctuates into existence. And uh let me let me ask you a question about this. What if someone said to you, I’m just going to bite the bullet and say, yeah, okay, most observers are Bzman brains. Why? Why do I care? >> You know, it’s a contentious issue. People don’t agree. I think that I understand the reason why, but I’m trying I’m still trying to convince my fellow physicists to think about it uh

[00:07:16] in what I think is the right way. Um when Edington wrote his book, he said, you know, what you need to wait for to fluctuate into existence is a mathematical physicist. He was being a little bit tongue-in-cheek, but you know, you get the idea. The idea that in fact you don’t even need the body of a physicist. You might just need the brain, you know, uh a very minimal set of atoms and molecules organized in such a way as to be conscious and aware.

[00:07:43] That’s that’s the idea. Whatever you think and it doesn’t matter what you think, but tell me what you think is required to make an observer and the minimal version of that will dominate by a huge amount over any more complicated version of that. So it was actually 2004 I believe that uh Andy Alrech and Lorenzo Sorbo coined the term Boltzman brains for these very very minimal fluctuations and the reason why they did that is because in 1998 we discovered

[00:08:17] the universe is accelerating and that led us to believe in the cosmological constant and and we’ll talk about it later but maybe Boltzman brains are a real problem you know they sort of be they had a renaissance in uh the turn of the most recent century around the year 2000. Now what you were asking is like how would we know like why why do we care? And I think that most physicists get it wrong for the following reason.

[00:08:41] Most physicists say something like when you don’t know who you are in the universe when you live in a universe that potentially has many many different observers. You should reason as if you are a typical observer in that universe. And a typical observer in a Bullsman brain dominated universe would be a lonely little brain who looks around and sees nothing but empty space all around. And so the typical physicist says, I

[00:09:07] look around, I don’t see empty space. Therefore, I’ve ruled out the scenario by observation. The problem is most in the in that scenario most people who think that they’ve ruled out the scenario by observation have also just randomly fluctuated into existence. Right? So it is entirely consistent to think that I am a observer who sees the room around me etc. and I’ve also just randomly fluctuated into existence. So I don’t

[00:09:39] think that just appealing to the data is the right thing to do. There’s there’s a longer I mean you can get into it if you want. There’s a longer philosophical discussion about how to do anthropic reason properly. I would argue that you should not think of yourself as a typical observer in the universe. You’re not, you know, you’re not and that’s not the right way to think. The real problem is given who you are like who you

[00:10:04] actually uh what you see around you, your local situation, your memories, all that stuff. The real problem is that all of that just fluctuated randomly into existence if you live in one of these universes. And therefore, if you conclude that you’re a Boltzman brain by this sort of kind of reasoning, [snorts] you have no right to conclude you’re a Boltzman brain because all of the evidence and all of the thoughts you have about physics just randomly

[00:10:31] fluctuated into your brain. This is called cognitive instability. It’s impossible to both believe this and have a good reason to believe it at the same time. So my argument is that we should just exclude the possibility of being a randomly fluctuated Bzpin brain when we try to think about reasonable cosmological scenarios. >> Right? Okay. I want to go back to the discovery in 98 about the cosmological constant. You know, we found that the

[00:11:01] universe accelerated expansion. Uh, you know, one popular idea is that it’s driven by a cosmological constant. Why does that lead us to think that there will be Bolzman brains and and does it mean that even if there was only a single universe and it’s governed by this cosmological constant, if we wait long enough, we will have this Boltzman bane problem? What’s the connection between these two facts, the the dark energy and the Boltzman brains? Well,

[00:11:26] it’s a great question and before I actually answer it, let me just clarify the word multiverse in this context. Boltzman didn’t use the word multiverse. He was thinking of a single universe, but in his universe, different regions would become habitable now and again. And so there’s sort of different pockets within the larger universe. And that’s exactly what we can imagine have happening in our actual universe where we live. So you don’t need to think

[00:11:52] about inflation or quantum mechanics or any of these you know crazy ideas to let this happen. All you have to think about is the cosmological constant. So the cosmological constant is just the idea that empty space has energy. And the way that it works is there is a constant density of energy in empty space. A constant amount per cubic centimeter that doesn’t change as the universe expands. the density of matter or radiation dilutes away as the universe

[00:12:23] expands. But if you again run the math, the prediction of the cosmological constant is it’s a constant amount of energy per cubic centimeter. So what that means is the universe never really stops expanding and in fact it leads to what we call an accelerated expansion which is what we got the data for back in 1998. And there is a theorem which is sort of it’s not really a true theorem. It’s a theorem that is true under certain

[00:12:47] circumstances proven by Bob Wald who’s a famous general relativist back in the 1980s called the cosmic no hair theorem and it says that if you have a positive cosmological constant which the data says is very plausible then eventually the universe just empties out you just wait long enough all of the fluctuations all the galaxies all the perturbations whatever they disappear it’s exactly like the nohair theorem for a black hole

[00:13:13] which says black holes settle down into a featureless state. The universe settles down into a featureless state. But again, just like black holes, in the 1970s, Stephven Hawking pointed out to us that black holes, even though they’re very simple, classically, when you include quantum mechanics, they start radiating, right? They give off Hawking radiation and eventually they evaporate away. It turns out that a universe with

[00:13:39] a positive cosmological constant does exactly the same thing. When you include quantum mechanics, it has radiation that you would detect. I have to be very very careful about this because you wouldn’t detect it because you wouldn’t be there because you don’t live in empty space. Like the definition of empty space is there’s no one there to detect it. And that actually turns out to be super important. But technically again, if you

[00:14:02] just sort of imagine a thought experiment, a detector in this empty universe would detect a very very faint low temperature background of radiation just like with black holes. And even though it’s very faint, even though it’s very low temperature, etc. the naive interpretation, which again I’m going to disagree with at some point, but the naive interpretation is that means there are fluctuations that there’s sort of a

[00:14:29] random stream of particles that are created and even though most of them are very very low energy, some of them occasionally if you wait long enough will be high energy. And remember, you have infinitely long to wait, right? That that’s not a constraint. So, if you just keep waiting, not only will the occasional photon come along, but sometimes two photons will hit each other and make, you know, a proton anti-roton pair, or they’ll make other

[00:14:54] particles, and they will basically fluctuate into every single possible configuration of matter that you can have out there. Um, which means that it’s exactly like Boltzman’s scenario of an eternal universe with random thermal fluctuations. That’s what he was imagining. He was literally thinking about a box of gas. We thinking about an empty universe with a positive vacuum energy, but the upshot is basically the same. And so this is really the thing

[00:15:25] that I’m a little bit surprised physicists don’t think about more. I mean, the Boltzman brain idea gets a lot of PR. You know, they appeared on Star Trek, Strange New Worlds, things like that. Like, it’s a it’s a very compelling phrase and idea. But professional physicists don’t worry about it nearly as much as I think they should because our best current model of cosmology seems to give us the possibility that this thing happens and I just told you

[00:15:54] five minutes ago you should rule out any cosmology in which this thing happens. So that’s a problem for us. >> Right? So if we take this idea seriously, we’ve got this problem like LCDM, the standard cosmology says we should be dominated by BS and brains. It’s almost self-refuting. So we’ve got to find some kind of fix. U but yet the evidence is quite compelling that the standard molecology is pretty good. So something is going a miss. And you’ve

[00:16:22] suggested that a particular kind of cyclic universe, one that is exactly periodic might offer some kind of solution. Now before we get into the mechanisms and dive deep into how this proposal is going to work, I just want to clarify what is this difference between a cyclic universe and a periodic universe or a periodically cyclic universe. >> Yeah, good. So you know um there there’s a lot to say about this. Can I can I like just give an aside for

[00:16:50] one minute before I actually answer your question if that’s okay? >> Go for it. Um, I previously wrote a paper with two graduate students at Caltech back when I was at Caltech pointing out a loophole in the Boltzman brain argument. I ba we basically argue that under certain circumstances, you could empty out into the kind of universe that Wald predicted where there’s really nothing there but empty space, but you could avoid the thermal

[00:17:15] fluctuations. And there was a technical requirement for our mechanism to work which I’ll just state out loud and then we can talk about what it means. The Hilbert space of the quantum theory of everything has to be infinite dimensional. Okay. So this is a very fancy way of saying there need to be a literally infinite number of possible quantum states in the universe. And so we argued that if that was true you could get out of the Boltzman brain

[00:17:43] problem. But we didn’t argue that it was true. We said like if it’s true then you can get out and that leaves open the question of well what if it’s a finite dimensional system and so for years I was under the uh impression I would have told you that if the Hilbert space of the universe is finite dimensional which again is just a way of saying there’s only a finite number of distinguishable quantum states that the universe can

[00:18:06] possibly have and some people believe that some people have argued that that’s a good way of thinking about cosmology then you would get mostly Boltzman brains, then you would get fluctuations, it would be ruled out by all the considerations we were just looking at. And the the way that you analyze such a thing, the great thing is quantum mechanics, despite all of the weirdness about measurement and interpretations and all that fun stuff, at the level of

[00:18:33] the equation of motion, the Schroinger equation is the equation of motion for quantum mechanics. It’s actually a much simpler, easier equation than Einstein’s equation for general relativity or Maxwell’s equation. Like the the quantum equation is much easier to solve than the classical equation. So you can solve it exactly. [snorts] And the difference between periodic and cyclic is in a cyclic universe, you repeat the features

[00:19:00] of the universe. So you imagine like, okay, right now we had a big bang 14 billion years ago. We’re expanding and cooling off and emptying out. Maybe in the future the universe will start to recolapse and it will undergo a big crunch, but it won’t just hit a singularity and stop. It will bounce and you get another big bang in the future. But what you’re and then that cycle can recur over and over again. But there’s two things going on. One is the actual

[00:19:30] relationship between the different cycles is only approximate, right? Like the gross features are basically the same. There was a bounce and then a bang and then you expanded and cooled and then you recolapsed and you do that infinite number of times, but the details don’t need to be exactly the same. There’s no reason that they would be exactly the same, right? The conditions that lead to one crunch might be a little bit different than the ones

[00:19:53] that led to the previous one. And the second thing even more importantly and and here’s the thing where cyclic universe afficionados usually won’t be honest with you to be perfectly honest. Um even in the gross features in almost all viable cyclic universe models it’s not really exactly the same thing happening. The universe doesn’t really collapse. Whether you call it collapsing or not depends on what coordinates you use. And

[00:20:22] there’s some fancy general relativity uh um tricks of the trade being applied here. But overall there is still an arrow of time in a typical cyclic model. The overall entropy of the universe is still changing. Generally if you have two particles and let them go and don’t let them dissolve or whatever as cycles go on they will not move apart and then come back closer together. They’re just going to move apart and move apart and

[00:20:48] move apart forever. In contrast with that, a truly periodic universe is one where whatever happens from one cycle to another repeats exactly down to the level of where every particle is or every quantum state of every part of the universe. So there’s literally a path of the universe through the space of possibilities that is a circle that comes back to exactly where it left. And that’s that’s kind of the loophole that we seized on to get rid of

[00:21:20] the Boltzman brains. >> Right. Okay. Actually, before we get into that, I just want to come back to one thing you said. You said that if if Hilbert Space was infinite dimensional, you can avoid the Boltzman brain problem. Can we just unpack how how would that work exactly? >> Yeah, good. So to be a little bit more specific about the story of why Boltzman brains are there in the first place, um because the cosmological constant makes

[00:21:45] the universe expand and accelerate in perpetuity. In a universe with a cosmological constant, there is a distance away from you that is so big that once someone gets that far away from you, you can never come back to it again or it can never come back to you because the space in between you and it is expanding too fast. So this is a cosmological horizon. Every observer in this universe is surrounded by a region that says outside

[00:22:15] here you cannot interact anymore. You cannot talk to them. they cannot talk to you. It’s exactly like a black hole horizon. So, um, now there’s two ways to think about it. The the that horizon is what gives the radiation, okay, in in the in Stephen Hawkings way of thinking about things, but what happens outside the horizon is the question. If the there’s a very good reason to believe that the number of quantum states inside

[00:22:45] the horizon really is finite, but naively classically outside there’s an infinite number of things that could happen. [snorts] And so what you can imagine, what you’re welcome to imagine, and we wrote this paper arguing that it’s true, is that whatever happens, whatever fluctuations happen inside our observable horizon, they go out. They go out to the void to the infinite region around us and they never come back. And

[00:23:11] so rather than truly fluctuating, our observable universe settles down into a truly constant nonfluctuating state. And there’s intricate arguments here about the nature of quantum mechanics because the state is thermal. Thermal is the word physicists use to describe something that looks like it has a temperature. And you think, well, if it has a temperature, then there’s fluctuations. But a thermal state in quantum mechanics is a different thing

[00:23:39] than in classical mechanics. It is true that if you measured it over and over again, you would see fluctuations. But that’s why I said 15 minutes ago, it’s crucially important there is no one there measuring it. Right? Measurements have this special role in quantum mechanics. And what the state is doing when no one is measuring it is different than what the state is doing when someone is. And in this empty universe, there’s no one measuring it. There’s no

[00:24:06] fluctuations. So we argued in that infinite dimensional Hbert space, there would be no Boltzman brains, >> right? Okay. So let’s go back to the the cyclic scenario. So generally we we point out in the book and lots of people have said it you know if we want to understand the big bang we’re probably going to need this fusion of general relativity or theory of gravity with quantum mechanics or theory of [snorts] the very small and and a conventional

[00:24:29] approach is like you you take this classical theory general relativity you try and quantize it but it looks like you’re trying to do something quite different like you’re trying to start with like the quantum and get the classical out. Can you unpack what’s going on here? Why take this approach? How is it supposed to work? >> Yeah, I mean this is a sort of a a big program, a bandwagon that I’ve been pursuing for, you know, over 10 years

[00:24:56] now. And here’s the basic idea. It actually came out of the fact that I became a hardcore Everettian when it comes to quantum mechanics. You know, thinking about the quantum state of the universe, how it branches into different possibilities. And on the popular level, when you’re talking to people who are not professional physicists, obviously what they care about when it comes to the many worlds interpretation of quantum mechanics is that there are many

[00:25:23] worlds. Like that’s kind of bizarre and and interesting. But to the professional quantum mechanic, really what it comes down to is all of quantum mechanics is a quantum state obeying the Schroinger equation. That’s all there is. When I teach quantum mechanics, I’m literally teaching undergraduate quantum mechanics uh right now at John’s Hopkins. Shout out to any of the students who are watching uh the video. Um I’m very

[00:25:49] conventional about it and I, you know, I explain there’s the Schroinger equation and the quantum state, but then separately there are these rules for what happens when you make a measurement. Okay? And in the conventional textbook version of quantum mechanics, that’s just two different sets of rules. and many worlds comes along and says no actually we can derive the appearance of measurement and collapse and things like that just

[00:26:14] assuming that you have quantum mechanics and obeys the Schroinger equation. So from that perspective, if you ask what the universe is, what is reality, right? The answer is not spacetime or fields or strings or loops or anything like that. It’s the wave function. It’s the quantum state of the universe moving in Hilbert space obeying the Schroinger equation. [snorts] And rather than doing what we always do, including in a quantum

[00:26:43] mechanics course such as my own of starting with a classical theory and quantizing it. So taking this classical model, you know, here’s an electron moving in the potential energy of a proton and making a hydrogen atom. There’s a classical version of that and we can turn the crank and turn it into a quantum mechanical theory that matches it. But we think that nature doesn’t do that, right? In fact, neo nature just starts quantum mechanical from the

[00:27:11] beginning. And if you look carefully at this quantization business, you become less and less confident that it’s on the right track. You can start with one classical theory and make many different quantum theories from it. You can start with one quantum theory and have many different classical theories that give you that quantum theory upon quantization. There are some classical theories that have no quantum counterpart and vice versa. So the

[00:27:35] relationship between them is very very messy. [snorts] So therefore the attitude that we’ve been taking is let’s just start with quantum mechanics. Let’s start with wave functions or vectors whatever you want to call them in Hilbert space and let’s imagine that what you should do is try to take a classical limit of this quantum mechanical system rather than just starting with a classical theory and trying to quantize it. Now if you’re

[00:27:59] a working physicist you might very well say why should I bother? that sounds like work and I’ve had a lot of luck. I’ve had a lot of success starting with classical theories and quantizing them. And the response to that is well except for gravity. For gravity, you haven’t had that success. We’ve been trying to quantize gravity for 75 years now and it hasn’t really worked very well. So that’s a good motivation in my mind for

[00:28:25] just before we get to gravity even just thinking about quantum mechanics, thinking about what the possibilities are. And the very first question you should ask is is Hilbert space finite dimensional or infinite dimensional. And people never ask that question. So we’re uh that’s not exactly true. Most people don’t ask that question. Some people like I I need to shout out Tom Banks and Willie Fischler to uh physicists who

[00:28:47] have taken these problems very very seriously. And so they have they’ve uh blazed a trail for the rest of us. >> Right. And just to clarify, the Hilbert space is a space of all possible quantum states. Is that right? >> That’s exactly right. So, just like if you have, you know, a baseball, right? And you’re going to hit the baseball and it’s going to fly through the air and you’re an undergraduate physics major and you’re learning to calculate the

[00:29:10] trajectory of the baseball. [snorts] What is the input data you need? Right? You need the position of the baseball for sure, but you also need its velocity or its momentum. Either one. You can go back and forth, no problem. So it’s not just where the baseball is. It’s the state of the baseball which is its position and its momentum. [snorts] And the same exact thing in quantum mechanics. There is a quantum state which is literally the answer to the

[00:29:38] question what information do you have to give me to predict what’s going to happen next? And the quantum state rather than living in position and momentum space lives in this abstract thing we call Hilbert space. >> Right? So now then what is fundamental here? What’s emerging? I mean are we getting rid of space and particles and all the things that we’re familiar with? What’s what’s left? What is there that we sort of start with? It feels like

[00:30:05] saying a Hbert. It just seems very abstract and hard to get your [laughter] head right. >> It is 100% very abstract. Nothing um nothing mis uh that’s not a misimpression that you have. We’re basically getting rid of almost everything you’re used to except for time. Time is fundamental in this picture. Um I’m not wedded to that. Look, I’m not, you know, none of this I’m I’m exploring different options, right? So I’m exploring the option that

[00:30:33] Hilbert space is finite dimensional, that it’s infinite dimensional, that time is emergent, that time is fundamental. Like these are all on the table, but for the moment we’re saying that time is fundamental. It’s right there in the Schroinger equation, but nothing else is. Space is not fundamental. Particles are not fundamental. fields are not fundamental. We’re going to ask whether or not those can be found in some search in Hilbert

[00:30:59] space for sort of what emerges at a higher level. By emergence here, we don’t mean like climb out of a pit or anything like that. We just mean you know what are the approximately viable descriptions that we have for a system when we do some approximations when we ignore some information just like in the uh gas in the atmosphere in my room right now I can describe it using temperature and pressure and density without knowing all of the details of

[00:31:27] all the molecules underneath and you can derive that right you can actually start with kinetic theory or whatever you want to call it the theory of atoms molecules bumping into each other. You can derive what you mean by pressure and density and you can derive equations like the ideal gas law relating them to each other. [snorts] So that’s what we’re trying to do. We sort of know what it is we want to derive. We want to derive

[00:31:51] something looks like general relativity, like gravity, right? Like the standard model of particle physics in three dimensions of space and one dimension of time. And we want to do that starting from something very very abstract, a vector in Hilbert space. we have, you know, some tentative successes along those directions. Uh, but there’s a long way to go, >> right? I just want to push one one last bit on this that didn’t Einstein say

[00:32:17] time is what you measure on a clock and then don’t you need to then have a clock for there to be time? So, uh, how do you have time without any clocks? >> So, I don’t know what Einstein said. Um, there’s a lot of, you know, Einstein was a very quotable guy. He said a lot of things. >> It might be in this quote. It might be in this quote. Yeah, there’s a lot of things that get attributed to him. So, who knows? But I, you know, time is a

[00:32:41] thing that is measured by clocks. But just to say that time is what clocks measure is to miss a lot, I think. And this has nothing weird to do with quantum mechanics or anything. If you look at any attempt to write down the fundamental equations of physics, time appears there in the fundamental equations. They’re in Newton’s laws. They’re in Maxwell’s equations. They’re in all the different equations of fluid mechanics or what

[00:33:07] have you. Okay? Physics is very interested in the evolution of things through time. So the question of whether or not time is fundamental or emergent is super interesting. And there are good arguments that maybe it is emergent. But all of the actual theories that we have right now that work that are successful that describe some part of the universe have the property that time is fundamental in them. So I think we should at least be open to that

[00:33:38] possibility. That’s just because it is fundamental. >> Right. Right. So let’s let’s go back to this cyclic scheme that’s just coming out of this. Is it space from Hbert space? Is that the uh the manifesto here? One of the papers that we wrote, we got to use the title space from Hilbert Space. You know, I feel bad for people who are not professional physicists or mathematicians and who are trying to understand this stuff because we

[00:34:03] professionals are really bad at coming up with names for things and you say things like vector space and Hilbert space and then you say but it’s not like space and people are like ah why why are you calling it that? But yeah, it worked out for our title. So we really want to get an algorithm that would say [snorts] here’s a quantum mechanical system defined purely on its own terms. Okay, no reference to a pre-existing classical

[00:34:31] structure at all. But let’s see what kinds of classical structure can arise from it. And we’re able to show that under right circumstances, you know, space can emerge, even gravity can emerge. Um, we’re still working on things like particles and forces and stuff like that. >> Right now, in this scenario, then would I be right to say you in the cyclic model that you’re we’re going to talk about in a second, you’re we’re going to

[00:34:56] assume that Hbert space is finite dimensional. Um, is that right? And is there any reason to think that’s true? Couldn’t I just quote this old paper from Carol that says, “Hey, we can get out of it with infinite dimensional Hbert space.” >> The the the point is we don’t know. And you know I know that again this is something that I have to explain to people. I’m not advocating that my theory is perfect or right or even all

[00:35:20] that likely. You know what we do as professional physicists is we explore different possibilities. You know we all know there are plenty of people out there who have their favorite theory and want to tell you that it is the right theory. That’s not what I’m doing right now. I honestly don’t know whether Hilbert space is finite dimensional or infinite dimensional. If you had asked me a year ago, could space could Hilbert

[00:35:43] space be finite dimensional? I would have said I don’t think it can because of the Boltzman brain problem. And so we we found a loophole in that argument which I think is very important. >> Right. So let’s let’s get to the loophole then. How can you get out of us going back to Boltzman brains if you have a finite dimensional Hbert state? So a very good analogy here is to think about the planets moving around in the solar system. Okay? And even for this

[00:36:13] for purposes of the analogy, forget about the real world where the planets pull on each other. Okay? Think about you know Kepler’s laws where the planets are moving on perfect ellipses and doing everything right. Um, Pankare, Henri Pankare, the famous mathematical physicist circa the year 1900 proved a theorem called the recurrence theorem. And basically he said if you just let the planets move around in circles, if you start in any

[00:36:40] configuration whatsoever, if you wait long enough, they will line up again in the same configuration. [snorts] And that makes perfect sense because if you think about every planet going around, there’s only so many places it can be, right? Like it’s it’s just an ellipse. It’s going to every planet is certainly doing the same exact thing over and over again. Now, the periods with which they do things might be unrelated. So when Panker says it’s

[00:37:08] going to line up exactly where it started, he doesn’t really mean exactly. He means you tell me what error you will tolerate, right? what imprecision you will tolerate and the planets will line up to that precision exactly. But if uh and that’s by the way that’s a really good analogy for Hilbert space. A finite dimensional Hilbert space is one with a finite number of planets. [laughter] An infinite dimensional Hbert space is

[00:37:33] with an infinite number of planets whose periods get longer and longer. And there the the recurrence theorem fails, right? Because the the periods might just get longer and longer and longer without bound. But in a finite dimensional Hilbert space you have a recurrence theorem. You have a quantum version of the recurrence theorem just like poner had in the classical version. And so now this fiddly little mathematical detail

[00:37:56] suddenly matters. Imagine you just have two planets. Okay just just pick two and ask will they ever line up exactly where they started. You know if the if the period if the year for one planet to go around the sun is exactly twice the period of the other one, then they will line up exactly like that’s not too surprising, right? You know, one year for the big planet, uh, two years for the small planet, right? Back where you

[00:38:23] started. But if the period of the long of the of the further planet is some irrational multiple of the period of the of the faster planet, then they will never exactly line up ever again. If it’s pi times the period of the younger planet, then they’ll get very very close, but they won’t exactly line up ever again. Okay? So, not so so that’s one fact. The whether or not the periods are rational multiples of each other or

[00:38:57] irrational multiples of each other depend uh fixes whether or not they will line up exactly or only approximately. The other thing is you notice that when the period is just twice what the uh the period of the slower planet is twice the period of the shorter planet it doesn’t take that long for them to line up right like you know okay just wait one year for the longer planet whereas if it’s pi it’s going to take you know not just

[00:39:24] three years but like a lot of years until they just happen to come really really close and when you have many many many planets or many many many dimensions of Hilbertra space the same thing happens When you have this rational or integer multiples of the time scales, not only will they line up exactly, but they will line up quickly. And when they’re all sort of irrationally not really related to each other, it will take a very very long

[00:39:49] time for the same um thing to happen again. So all of this translates exactly into the quantum mechanics of Hilbert space. That’s why the quantum mechanical equations are so easy. It’s just like everything is moving in a circle and it just takes out a certain amount of time. That’s all that really ever happens in Hilbert space. It’s the combination. It’s the comparing the different circles that really matters. And so, of course,

[00:40:13] generically, like if you didn’t work very hard, there’s no reason at all for the period of one planet to be twice the period of another one. Like in our real solar system, that’s not what happens, right? There’s some arbitrary number that you have to go out there and measure. So the expectation and the expectation that I would have had before a year ago is look the generic case is there’s a recurrence time given some precision that you care about but that

[00:40:40] recurrence time is very very long and what that means is if you just have the quantum mechanical state of the universe it will be very much like what Boltzman said it will be most of its time in thermal equilibrium there will be small fluctuations downward if you wait really really long, you will get something that maybe looks like a big fluctuation downward in entropy. And we can interpret that under the assumption that someday we’ll be

[00:41:08] able to derive space and particles from Hilbert space as a big bounce, right? As a collapse and a crunch and then a bang again and then that maybe that’s where we live. But it has all the problems that Boltzman’s scenario had, namely that most of the time you’re in thermal equilibrium. There’s a lot more small fluctuations than big ones. You’re going to be dominated by Boltzman brains. The loophole that we discovered and by we I

[00:41:34] mean uh my collaborators Nadia Diachenko who’s a student and Sakshi Delani who’s a postoc we found that well what if despite the fact that it’s not generic what if you just say all of these numbers are integer multiples of each other or rational multiples of each other right what then? Well, then if you interpret that periodicity, then it’s an exactly periodic evolution, right? Just like the two-year versus one-year planet, it

[00:42:04] comes back to exactly where it started. [snorts] And it comes back quite quickly to where it started compared to the generic case where there’s all sorts of planets doing crazy things. And it we showed that if you just pick your numbers correctly, it will come back quickly enough that there’s not enough time to make any Boltzman brains. In other words, you can interpret the whole evolution of the quantum state as something much like our universe but

[00:42:31] played in cycles. So we expand, we empty out, it’s empty space for a long time, then it looks like we start to collapse again. We have a crunch that just looks like the time reversal of a bang. The crunch goes to a bounce and you get a bang on the other side. And it’s an exact replay of where you started, not just pretty close. So that’s sort of the consequence of finding this loophole. The loophole is if you have integers

[00:42:58] rather than irrational numbers, you can avoid Boltzman brains by making everything happen much more quickly. The consequence of that is you have to live with an exact repeat of the universe an infinite number of times in the past and future. >> All right. I think um didn’t Nietze have it as a test like if you were happy with your life, you’d want this scenario and if you weren’t, you wouldn’t. Well, Nietze was trying to derive moral

[00:43:22] implications from this, right? He he was suggesting that you should act in such a way that if whatever you were doing right now, you were going to do a million times in the future in the past, you wouldn’t be sad, right? You know, which is that’s pretty good advice whether or not it’s an actual viable cosmological model or not. >> Right. Right. So I guess the analogy here is if we started in this low entropy state and we have this

[00:43:45] particular scheme, we’re going to get back to it before we get to the production of Boltzman brains. Is that like the short summary? >> That’s exactly right. Yeah. So I want to be super duper honest about how much we don’t know about this, right? Like we can solve the quantum mechanical equations very well. We’re not very good at mapping them onto an interpretation in terms of a classical spacetime with particles and fields and things,

[00:44:12] >> but we know what it must look like if it exists, right? So that’s the story that we tell. Yes, there’s a crunch, a bounce, a bang, and it’s all, you know, the quantum mechanical equations can be solved perfectly, and it’s all within, by the way, the many worlds interpretation of quantum mechanics. So the branching of the universe into different worlds when some people measure spin up and some people measure spin down or the cat’s awake and the

[00:44:39] cat’s asleep or whatever that branching and the whole set of worlds is what repeats over and over and over again >> right so when you get this branching does their entropy increase or does it stay the same when you get this of worlds in >> that is um going to depend on your definition of entropy this is [laughter] >> well that’s going to be the next question Actually you talk about this thing called the quantum bolts with

[00:45:04] energy. What why don’t we unpack all that? >> Well so it’s it’s a it’s a problematic issue because you know the second law of thermodynamics came along. Clausius Rudolph Clausius um was the first person to call it the second law. He invented the first law and the second law. But the basic idea predated him came from French engineer Saji Carnau. But Clausius was thinking thermodynamically. He didn’t know about atoms, right? He wasn’t thinking about

[00:45:33] probabilities or whatever. He was thinking about heat and temperature and and stuff like that. So, he defined entropy. And then people like Boltzman and Gibbs come along and they did believe in atoms. So, they suggested alternative definitions of the word entropy. Okay? And they weren’t even the same. Like even Boltzman had multiple definitions on his own. And then quantum mechanics comes along and there’s yet more definitions of entropy from people

[00:45:58] like John Fonoyman and others. So and and even physicists are very very bad about being clear about what definition of entropy they’re using at any one moment of time. So if what you care about is the arrow of time, why is the past different from the future? Why was I younger? You know, why do I remember the past? All that stuff. It’s not this fancy funimon quantum entanglement entropy that you care about. You kind of care about good

[00:46:29] oldfashioned classical Boltzman kind of entropy. And one one way we can say that is to say that’s the Boltzman entropy or the thermodynamic entropy. You know the universe just looks low entropy to us when we look at what the state of the early universe was. But obviously in our setup, we’re solving fundamental quantum mechanical equations. And so we’re going to need to have a version of Boltzman’s definition. It’s literally engraved on

[00:46:59] his tombstone in Vienna. Uh S= K log W. That’s his definition of entropy. So we want the quantum version of that. And we want something that, you know, is cosmological. So we’re not worried about what observers measure or anything like that. We want something that just applies to the whole universe. we can plot it very easily and when there is a classical interpretation of what’s going on it maps on to the ordinary classical

[00:47:25] Boltzman entropy and so we suggested a definition of that that we called the quantum Boltzman entropy is sadly we’re not the first people to invent a definition of something called the quantum Boltzman entropy and it’s not always the same definition so keep your wits about you anyone out there who’s reading these papers >> right and and then to get back to the question so when the when we get the splitting the many worlds

[00:47:46] What happens to the entropy? Does it increase? Like if you get the splitting of >> So by our definition, I had to had that long warm-up there, but in the definition we gave branching of the wave function does not increase the entropy of the universe. Um the entropy we which is what we wanted. That’s why we, you know, worked hard to make a definition that fit that criterion because what we want is a definition where entropy goes

[00:48:14] up when cream and coffee mix together, right? When cream and coffee mix together, there’s no quantum splitting of the universe. Everything is very classical, but entropy is going up. When I measure the spin of an electron, uh there is a branching of the universe. It spin up or spin down, but the entropy didn’t go up. I just measured a dot, right? And so we really wanted something that was fundamentally quantum mechanical but mapped onto the ordinary

[00:48:43] classical idea of order and disorder. And so that’s what we got. And so branching has nothing to do with it because branching is happening all the time. Right. You don’t even notice that that is not what we mean by the arrow of time. >> Right. Right. Right. So coming back to this this cyclic perspective, do we have any idea how long these cycles actually are? I mean I guess all you need is it’s it’s shorter than the time for box brain

[00:49:05] production but is there like a minimum maximum? Do we have any kind of ideas? We have very little idea. So and again um just I I don’t think I’ve said this out loud yet but I should. Our model is super fine-tuned. It is not in any way generic, right? Like you wouldn’t stumble across it. we we found a loophole and it’s a very tiny loophole and we honed in on it. Okay. So even within our model if you didn’t work hard at getting the

[00:49:39] periodicity of the universe to be sufficiently short you could still have a Bzman brain problem [laughter] right I mean you could have almost as long in our model as you would have in a model without all of the uh integer relationships between between all the cycles. So we have an upper limit on how long the period needs to be basically given by you don’t want the period to be so long you have too many bolts brains okay and we have a lower limit on the

[00:50:06] universe is already 14 billion years old so you don’t want the cycle to start after 15 billion years right [laughter] you don’t want it to be that noticeable >> but other than that that’s a very long range there’s a lot of room inside there to play and so um we do have requirements irements, but those requirements are not too ownorous. >> Right. Right. Okay. So, the actually the reason I ask is because I just saw a paper by Henry Tai and collaborators.

[00:50:32] And for those that don’t know, Henry Tai was very instrumental in the development of inflation. And he’s looking at these results from Desi, the the dark energy spectroscopic instrument that are claiming that the cosmos response actually changes over time. And then the suggestion was, well, if that’s right, and of course, we will wait and see if it’s right or not. Uh but then that the they will have a cyclic universe and it

[00:50:55] will last about 33 billion years. Is that too short for you? Cuz presumably you need things to sort of do you need it all to empty out. It’s like it seems very very quick. The stars will still be around. >> Well, here’s this is a big subtlety and actually this was the part of the paper where Nadia and Sakshi and I had to really think for the longest. In a typical cyclic universe, the story you tell is something like this. Right now,

[00:51:21] our universe is expanding. The dark energy, the cosmological constant makes it accelerate. It makes it expand faster and faster. We want it to eventually recolapse. So, we got to get rid of that dark energy somehow. It has to be time dependent or there’s a phase transition or something like that. And and people have various different ways of doing that depending on their favorite model. Our picture is very different than that.

[00:51:45] We have a story where the dark energy is a constant cosmological constant. It does not go away. Okay? It remains a constant energy density in empty space. And then the question is, well, how do you get the universe to recolapse if the is always being pushed apart by this dark energy? Well, I mean, the answer is that in it’s a yeah, what can I say? It’s a very complicated technical answer. I haven’t quite get figured out a way to

[00:52:15] to explain it. Once you’re in the empty phase of the universe, so if you go to the future, okay, um then there’s no way to slice spacetime uniquely. So [snorts] you know that in relativity, part of the whole point of relativity is no standard of rest is special, right? No observer is at rest with respect to the universe. That’s what relativity says. But cosmology says okay but the stuff in the universe the galaxies the microwave background

[00:52:50] etc that defines a standard of rest. Okay I mean spaceime itself doesn’t have one but if you look at the microwave background radiation left over from the big bang you can say whether you’re moving with respect to the rest frame of that radiation. And so we think of that as you know very natural like that’s the way we should slice spacetime into space and time what a way that respects that symmetry of the universe. But in the far

[00:53:15] future once everything evaporates away now you truly have no way of slicing spacetime in any special way. There is no microwave background to compare yourself to. There are no galaxies to compare yourself to. And so what happens is the universe does start recolapsing but in a different way of slicing the universe in a different coordinate system is the way that we would say it. And you know that’s possible without changing the cosmological constant

[00:53:43] because you know that the universe expanded from the big bang to the cosmological constant, right? And so you just play that backwards. You know it’s a perfectly legitimate solution to the equations. And so we have a story that you know the universe expands it empties out. It spends some long time all empty and then you just stick on the time reversed version of that to the future in the right way and you get what looks

[00:54:08] like a collapsing universe. So we don’t have to play any games about changing the dark energy etc. We are not affected by any new wrinkles in the recent observational data. >> Right. Okay. Okay. And then what about the bounce part? I mean there have been a number of like people doing quantum cosmology like in loop quantum cosmology and some versions of string cosmology and various they’re all in our book you know where okay

[00:54:33] >> you wrote a book I’m sorry that our model didn’t come out early enough to be included in your book I do I do feel bad about that >> I wouldn’t know which chapter to put it in because we had one on periodicity and one on cyclic and anyway but are you are you do you have any thoughts on the bounce or would you just say well something like that will happen you know or is there anything specific Well, I think that, you know, the there’s the

[00:54:56] sort of very firm, rigorous, well understood parts of our story and then the much more handwavy parts, right? >> The rigorous and well understood parts are the equations and our solutions to them, right? Which is good. That’s what that’s what you like to have. The less well understood parts, like we said, is how to interpret that as spaceime. So there are theorems in general relativity that if you collapse to a big crunch,

[00:55:22] you’re going to hit a singularity and all the equations are going to go to infinity and blah blah blah blah. And everyone knows that there’s a little footnote to those theorems that say, well, these theorems involve classical general relativity and quantum mechanics might change everything. So we are quantum from the start. We never had those theorems. There’s never any obstacle in our picture to the universe bouncing in any way. The space-time

[00:55:49] interpretation of what is happening at the bounce is unclear. Uh but the fact that it bounces, the quantum state bounces, that’s 100% super duper clear. So, you know, I still have grad students. We’re still writing papers. We’re still thinking about this and we’re trying to think, you know, can we actually make some lemonade out of these lemons? Can we use our quantum mechanical understanding of where spaceime comes from to make predictions for like the

[00:56:18] cosmic microwave background or something like that? >> Right. Right. And it would there be any way in this scheme to get information across about or is it would it be tracked from one sort of cycle to the other? >> You know, it’s hard to say. Um the short answer is no. You can’t get information across because that bounce is a very very low entropy state. You can’t fit a lot of information into a low entropy state. But in you know a slightly more

[00:56:45] precise answer is the information contained in the wave function of the universe is conserved over time. It does not change. It’s the same at every moment. So in some very real sense it is being passed from uh before the bounce to after. >> Right. Okay. And and then what about the cosmological constant problem? Like we’ve got this issue that it seems to be that physics predicts the cosmological causes should be enormously bigger than

[00:57:14] what we observe and this is some people say it’s the biggest crisis in physics. Yeah. >> Does this outlook have anything to say about that or is that put to the side? >> It is part of a program that has something to say about that although we ourselves don’t have anything to say about it. So what do I mean by that mysterious statement? Um, the cosmological constant problem says that okay, you have something called the

[00:57:39] vacuum energy. Einstein pointed out you were allowed to have it. Now the cat’s out of the bag. Now you can say like, okay, what should it be? Right? One perfectly legitimate answer to that question is it should be whatever we measure it to be. You know, you don’t have any right to say what it what do you mean it should be? Who are you to say what it should be? But there is a for framework called effective field theory where we do kind of make

[00:58:05] statements about what magnitudes different quantities should have because in effective field theory we say look we don’t know what’s happening at very very high energies at very very short length scales. We only see the universe at relatively large distances and low energies compared to like atoms or the blank scale or whatever. Right? And so we invent a theory that works at low energies and that’s an effective theory.

[00:58:30] It bundles up everything that happens at high energies and just puts them into low energy observable parameters. When you do that, you get predictions for sort of natural values those low energy observable parameters should have. And one of them is the vacuum energy, the cosmological constant. And the prediction is hilariously larger than what we actually observe. That’s known as the cosmological constant problem. Now, this picture that we’re starting

[00:58:57] with, if you believe that Hilbert space is finite dimensional, then quantum field theory is not the right theory of the universe. In quantum field theory, Hilbert space is infinite dimensional, more or less full stop. There’s really no other way to do it. So, quantum field theory is a good approximation in certain regimes, but it’s not the fundamental theory of the universe. And so there’s sort of not a solution to the

[00:59:23] cosmologial constant problem. But again, Banks and Fisher had pointed this out. It changes the nature of the problem. The cosmos constant really becomes an input parameter. There’s a direct relationship between the dimensionality of Hilbert space and the cosmologial constant that you end up observing. And so no one thinks that the dimensionality of Hilbert space is fine-tuned, right? That’s just a number that nature gives

[00:59:47] you somehow and they’re related. So I don’t have an answer to why the vacuum energy is small but it’s a consistent story within this particular way of thinking about quantum gravity. >> Right. Right. Can we go back to one of your older uh ideas about you know explaining the arrow of time um which is this Carol Chen model. Can you maybe just unpack what what that model said and how are these two related or are they justly totally different ideas? How

[01:00:15] how can we think about these in relation to each other? >> Yeah. What you should do is imagine in your head a graph of the entropy of the universe as a function of time. Right? And what you know the data point you have is that right now it’s going up. So it used to be lower and now it’s going up. And what you want to do is say I would like a theory of the whole universe that naturally explains why the entropy of our observable part of the universe

[01:00:41] was lower in one direction and higher in the other direction. And that turns out to be hard to do because number one, if you just pick a random configuration of the universe, you’re probably in thermal equilibrium and the entropy is as high as it’s going to get and it’s going to stay constant in the past and future. And [snorts] number two, even if you say, “Oh, no. Okay, but I want to like conditionalize on some features of the

[01:01:05] universe right now like the existence of life or the galaxy or whatever. [snorts] Then you’re back to Edington’s story and you say, “Okay, then I’m probably at the minimum value of entropy of the local cosmological universe and it’s going to be higher to both the past and the future.” So that’s not what you want. That’s not what you want to try to explain. So um both the thing I did 20 years ago with Jennifer Chen and the

[01:01:31] more recent paper are attempts to explain how you can get a plot of entropy versus time where naturally it’s lower on one side and higher on the other. In the more recent one it’s because it’s periodic. It goes up and down a lot right? It doesn’t spend too much time at the top. It’s going to be going up and down near the bounce and we’re on one side of the bounce or the other. That’s the answer. In the earlier paper, we have an infinite dimensional

[01:01:57] Hilbert space and we say what that means is that there is no maximum to the entropy of the universe. The entropy of the universe can grow without bound forever. And in that case, you can imagine a curve that looks like what we call a U-shaped curve. It’s really like a parabola or something like that, but something that increases away from a minimum in both directions. And the point is we don’t live anywhere near the minimum. The minimum is not the

[01:02:24] big bang. The minimum is not anything special. What’s happening is that the universe is mostly empty and it’s spitting off little baby universes that start with low entropy expand increase in entropy. It looks like a big bang and then they enter their own sort of quiescent uh empty space periods. So it’s a completely different story than the recent paper. But in both cases they share the desire to explain why entropy was low in one direction of time and

[01:02:53] higher in the other one. >> And do they share this idea that if if you were at the bounce the other branches the arrow or time would point away from each other. >> Uh so I got like for the for the paper I wrote with Jennifer Chen there’s no bounce. There’s no bouncing. There’s it’s just not that it’s there’s a moment where the entropy is lowest but it’s not low in any sense. It could be really really high even at that moment. There’s

[01:03:20] just a it’s just a feature of every curve that has finite values but can increase forever. There’s going to be a minimum value somewhere. Okay. And yes, in that um model we were very explicit and sort of had fun with the fact that in one direction of time there’s a bunch of little baby universes and they all had their arrows lined up pointing toward the future. but they point in the opposite way from all the baby universes

[01:03:48] on the other side of this minimum. So there’s a double-headed arrow of time where in the far past and far future everything looks completely symmetric because the one is a time reverse of the other in the new paper. Now you’re bouncing and and cycling and things like that. But now you do have a balance. Now you do have a very finely tuned low entropy condition. So the paper with Jennifer Chen had the motivation of explaining the low entropy of our

[01:04:17] observed universe. Our new paper does not have that motivation. We’re just putting it in by hand and saying that it’s a lab. >> But it is absolutely true that in both directions from that low entropy point, you get something that looks like a big bang, something that looks like increasing entropy, something that looks like an arrow of time pointing away from the bounce. >> Right? So presumably some other principle would have to explain the low

[01:04:41] entropy state. But this paper is saying we’re not doing that. We’re doing can we get can we get away from the boltsman brains and have this infinite universe. That’s >> that’s we’re being very humble. >> Yeah. [laughter] Right right. So then if so I guess this is like it is a realization of nature’s like eternal recurrence theorem or or should I think my life is gonna live out infinitely or do I think of it as like one universe

[01:05:06] that’s on like a on a circle like my co-author Nia she and his student Beth call they had this model called periodic time cosmology where they they kind of stitch the universes together with like fromal rescaling trick of pen rows and they they have this big circle. So, do I think of yours as like, no, I’m going to live my life out forever over and over and over again, or do I think of it as like just one sort of circle? Well, we

[01:05:30] talk about that in the paper very briefly at the end and we say that’s up to you. [laughter] So, because we do, unlike almost everybody else, have an exactly periodic universe, you are absolutely allowed to think of it as being a circle rather than a line with an infinite number of cycles on it. Either way works perfectly well and there’s no difference between them honestly. So it’s the same universe either way. Whatever makes you feel

[01:05:58] better, you’re allowed to choose. >> Okay. Well, I enjoy life, so I’m going to say I’m going to endlessly repeat it over and over and over again. [laughter] >> Same mistakes will be made. Yes. >> Yeah. Right. So maybe we just summarize like what does the paper achieve? What does it not achieve? >> Right. So this paper is an example of trying to figure out how cosmology might work in a universe that was truly described by the ordinary rules of

[01:06:24] quantum mechanics. That is to say uh wave functions in Hilbert space evolving according to some version of the Schroinger equation. In particular, we were asking what if the Hilbert space was finite dimensional. So you’re going to have some kind of recurrence. Honor proved that a long time ago. you’re going to have some kind of cyclicness in any universe that obeys those rules. Schroinger evolution in a finite dimensional Hilbertra space. The worry

[01:06:50] about that is that you spend most of your time near thermal equilibrium with small fluctuations away from it and most of the observers or most of any kind of person you want to name are Boltzman brains actually not the observers that we know and love. So we found a loophole in that if the different cycles of the different parts of the wave function are related by rational numbers which is a highly non-generic condition then you

[01:07:16] can recur be periodic I should say much much faster on a much much shorter time scale than you otherwise would have and therefore of not give the universe enough time to have Boltzman brains and so it is a uh what we call a phenomenologically acceptable universe I I’ll say one more thing about that. Um, a year or two before we wrote this paper, I was uh thinking about finitism, which is an approach in the philosophy of mathematics that says, could there be

[01:07:50] a biggest number? You know, not an infinite number of numbers, just a finite number of numbers. And a lot of people in the math community who are f fond of either finitism or even ultra fininitism which is an extreme version say well look quantum mechanics says that the universe might be discreet at some fundamental level right and so why not and I never liked that because I said no quantum mechanics doesn’t say that it says the universe is a vector

[01:08:15] space and vector spaces have infinite numbers of vectors in them so but I forced myself to be careful about it and I said well okay could you pick out a finite number of states in Hilbert space and could the universe just live in those states rather than a smooth continuum which would be an infinite number of states and I came up with a little model in which that’s possible and it’s a finite dimensional Hilbert space with a with a little lattice of a

[01:08:42] finite number of points inside it where the universe chugs along along that lattice and in the paper I say the problem with this model is it has Boltzman brains and so it’s probably not acceptable phenomenologically So now we have solved that problem. And if I I would say if you’re the kind of person who really really really doesn’t like infinity, if you don’t want infinity to appear anywhere in your description of the

[01:09:08] physical world, this is the model for you. This is has a plausible chance of doing that >> while fitting the data. >> But then isn’t it cyclic over and over again? Isn’t that an infinity number of years? >> No, because you can just put it on a circle like you said, >> right? Okay. You could just pick that option and see your interpretation. Right. Right. Okay. All right. So, look, finishing up like this is obviously very

[01:09:29] stimulating. I guess it’s like a proof of principle. This is could be the way the university is. How do we make any progress? Like how do we actually ultimately you want a testable model that you can go and make some observations. What’s the next steps? >> Yeah, the is a very obvious set of next steps, but they’re hard and that’s why no one is really doing them right now. It’s easy for me to say um we’re looking for ways to start with a quantum

[01:09:55] mechanical state and extracting the classical emergent picture from that but we don’t really know how to do it. So figuring out how to do that is the obvious next step and you know we are thinking about that a little bit. Um in particular any good cosmological scenario the very first thing to predict is the density pertabbations right [snorts] both the spectrum of pertabbations are they um completely uncorrelated with each other

[01:10:22] statistically things like that and so right now we have no way of doing that and we’re trying to ask the question you know is there some way that we can go from very minimal assumptions about the finitness of the dimensionality of silver space etc to some kind of prediction for the microwave background anisotropies. Um I don’t know if we can or not. There’s other things you could try to look for violations of locality

[01:10:46] or Lorenson variance, things like that. Um but they’re all not very welldeveloped. It’s not that there are no predictions. It’s that we are not strong enough to make them quite yet. >> Right. Right. Right. Well, I can’t wait to hear more about this. Hopefully, we’ll we’ll get some more thoughts on that. And if you have any thoughts, do leave them in the comments. If you like this material, do like and subscribe. minutes just left for me to thank our

[01:11:11] guest Sean Carroll. Thank you so much Sean. It’s been absolutely fascinating.