Into the Impossible With Brian Keating - String Gas Cosmology: Challenging Inflation | Robert Brandenberger (#336)

Episode Date: August 9, 2023

Watch this episode on YouTube to see the slides: https://youtu.be/G3xy-bEDJCY "I view string theory as the most promising way to quantize matter and gravity in a unified way. We need both quantum gravity and we need unification and a quantization of gravity. One of the reasons why string theory is promising is that there are no singularities associated with those singularities are the same type that they offer point particles." — Robert Brandenberger In this thought-provoking conversation, my grad school mentor, Robert Brandenberger shares his unique perspective on various cosmological concepts. He challenges the notion of the fundamental nature of the Planck length, questioning its significance and delving into intriguing debates surrounding its importance in our understanding of the universe. He also addresses some eyebrow-raising claims made by Elon Musk about the limitations imposed by the Planck scale on the number of digits of pi. Moving on to the topic of inflation and its potential detectability, Robert sheds light on the elusive B mode fluctuations and the role they play in understanding the flaws of general relativity. He explains why detecting these perturbations at the required scale may be beyond our current technological capabilities. The discussion further explores the motivations behind the search for cosmic strings in the microwave sky and the implications they hold for particle physics models beyond the standard model. With his expertise in gravity and the quantization of mass, Robert Brandenberger emphasizes the need for a quantum mechanical approach to gravity. He discusses the emergence of time, space, and a metric from matrix models, offering new insights into the foundations of our understanding of the universe. The speaker's work challenges conventional notions of inflation and proposes alternative models, such as string gas cosmology, as potential solutions. Beyond the scientific aspects, Robert Brandenberger reflects on his role as a scientist and educator. He expresses his gratitude to a mentor and shares advice he received about navigating the academic world. Additionally, he discusses the evolution of being a professor over the past three decades and shares his thoughts on the profession as a whole. Please join my mailing list 👉 briankeating.com/list for your chance to win a real meteorite 💥! Join me and ⁦Lawrence Krauss for an Onstage Dialogue ⁦at the San Diego Air & Space Museum Tuesday, Oct 17, 2023 at 7:00 PM: https://www.eventbrite.com/e/live-onstage-dialogue-brian-keating-lawrence-m-krauss-tickets-699430514497 Support The INTO THE IMPOSSIBLE Podcast by supporting our sponsors: Post your free listing at LinkedIn Jobs https://www.linkedin.com/impossible Thanks HelloFresh! Go to https://www.hellofresh.com/impossible and use code 50impossible for 50% off plus free shipping! As an Into The Impossible listener, you can get 15% off a MASTERCLASS annual membership masterclass.com/impossible Subscribe to the Jordan Harbinger Show for amazing content from Apple’s best podcast of 2018! https://www.jordanharbinger.com/podcasts  Please leave a rating and review: On Apple devices, click here, https://apple.co/39UaHlB On Spotify it’s here: https://spoti.fi/3vpfXok On Audible it’s here https://tinyurl.com/wtpvej9v  Find other ways to rate here: https://briankeating.com/podcast Support the podcast on Patreon https://www.patreon.com/drbriankeating  Become a Member on YouTube- https://www.youtube.com/channel/UCmXH_moPhfkqCk6S3b9RWuw/join Learn more about your ad choices. Visit megaphone.fm/adchoices

Cosmology is the area that I'm really fascinated about because it's an area that connects deep philosophical questions with hard data. And the philosophical questions they concern the origin of the universe. And that also means the origin of space and time. If you would have asked me three years ago how I would judge the chance of inflation being part of the story, I would have said, well, more than 50%, but it's worthwhile exploring alternatives because Aethera grows by being challenged with alternative. Any sufficiently advanced technology is indistinguishable from magic. Open the pod bay doors, please help. All right. So we'll get started right now with my good friend, my mentor from way back when one of my thesis committee members.

one of my favorite members, the second one to appear on the podcast, Professor Robert Brandenberger, second only to Peter Timby, who was my actual thesis advisor, who did appear on the podcast many years ago on Father's Day, because as you know, Robert, there's sort of a fatherly, motherly connection between a student and their mentor, and I certainly feel that way about you, although you're not old enough to be my father, but sort of like a cool, rich uncle. Anyway, Robert, how are you today? I'm quite well. It's my sabbatical year. Oh, that's great. And you're in McGill now? You're in Montreal? Yeah, I'm in Canada, but on Sunday I'm heading back to Europe.

Very nice. I'm originally from Switzerland. So it's like going home. That's right. That's right. I can spend some time at the beach or walking the mountains and thinking about things. Yes, and I remember you walking around the corridor. of Barris and Holly, you were an inspiration to me and many time past guests, Stefan Alexander. I just had the pleasure of spending some time doing some thought calculations with Stefan this past weekend for Mother's Day. He visited here. And so, Robert, we've connected again because of a very, very interesting scenario, which was that on the website Reddit, which has a lot of crazy stuff, but some interesting stuff about physics. There was a paper about your work. One of your

papers was the trending topic. That means it was the most viewed, most talked about topic and all of physics. And I thought that was pretty much a sign that I was overdue to have you on the podcast. I've actually had a note in my calendar. I checked it from November 2020. So I beg your forbearance and forgiveness for not having you on sooner. But we're not going to talk about that paper, which is about converting gravity to light or maybe the other way around. But we're going to talk about very, very interesting topics. And that has to do with alternatives, perhaps alternatives, to the standard paradigm.

And I remember you as a mentor that you taught me many things. And one of them was to not be afraid and to take risks, but take prudent, prudent risks. and pursue avenues, even when people didn't really think they would bear fruit. I've had a lot of people on this podcast who are very negative about string theory, a lot of people that are negative about inflation, but I've also had more people that are positive about those things, including your collaborator, Kamran Vafa, who I had on many years ago as well.

And so I want to ask you, what is the most fascinating area of physics that you're currently researching right now? So as you know, I work on a wide range of topics, all theoretical cosmology. So I'm a little bit handicapped because I don't do computer work. So I have to do work with pencil, paper, and most importantly, an eraser. Because often the ideas don't pan out or I make calculation mistakes. But I'm, so cosmology is the area that I'm really fascinated about, because it's an area that connects deep philosophical questions with hard data.

And your group is one of the groups providing the hard data. And the philosophical questions, they concern the origin of the universe. And that also means the origin of space and time. Now, so you mentioned two things. You mentioned string theory and inflation. So let me focus first on inflation. So over the past 30 years, inflation has become the paradigm of early universe cosmology. In fact, it's made it into astronomy textbooks.

You read an astronomy textbook and this section on cosmology starts with saying that the universe began with a big bang and then followed the period of inflation, which is an excellent. exponentially growing space, like exponentially growing prices. So now, there's a sort of a problem with this scenario. And if you would have asked me three years ago how I would judge the chance of inflation being part of the story, I would have said, well, more than 50%, but it's worthwhile exploring. alternatives because A theory grows by being challenged with alternatives. And if you work out good alternatives, and then you can basically challenge people who work on the standard paradigm to do better.

So my view has changed, and my view has changed because of something which we call the Transplankian censorship conjecture. So the TCC And this is a paper which Bedroia and Vafa wrote now almost four years ago, 2019. There was a follow-up paper which I co-authored with Emma

and with Mariana Loverd. So inflation is the idea that space expands exponentially. And that means that if we have little waves on this space, then the wavelength of these little waves

also expands exponentially. So in our models of inflation, if we look at the wavelengths of small density perturbations, the density perturbations that you experiments are measuring, if we trace them back to the early universe, then in the standard inflationary models, we find that they emerge with a wavelength,

which is smaller than the plunk length. And maybe not all of it. your listeners know what the Plunk Length is, but it is the boundary of our knowledge. We know that on length scale, smaller than the Plunk Length, we don't understand the physics. So the problem for inflation is that everything that we measure today, according to an inflationary scenario, starts out in this window where we don't understand the physics. And so based on this argument, Wafinbred Varya, postulated that there's a new fundamental principle of physics that says that this situation never should happen.

Little density perturbations on length scales smaller than a plump length should never be able to become larger than a particular length scale, which is called the hubboregias. which is the inverse expansion rate. And this is sort of the length scale above which these little waves, if they start from quantum mechanics, they kind of become classical. And we all measure classical things, distribution of galaxies, migrave anisotropies. So this transplankian censorship conjecture says that things that are now classical never come

from this transplanckian medium. Is this related to like a cosmic censorship or a, okay. Yes. And so after this initial work, I was asking the question, where does this come from? How can we actually argue for this? And I know that Roger Penrose is a frequent guest on your program. That's right. And I guess you were referring to his censorship conjecture.

And so the first justification that I give for the trans-blank incensorship conjecture is an analogy with Penrose's conjecture. So what Penrose says is following. Penrose notices that black holes with small charge. They have singularities in their center, but an observer who's outside of a black hole never measures anything. that comes from this singular region. So the observer is protected by a horizon. Now Einstein gravity allows for solutions where the charge is bigger than the mass.

And for such black holes with charge greater than a mass, the poor observer far away from the black hole is not protected from the singularity. And so Penrose posseated that in the theory that completes generativity, such pathological solutions cannot arise. So now if we translate penrose to cosmology with a very well-defined translation schema, then we get precisely the trans-blankian censorship conjecture. Now there are two other justifications

that I can give for the trans-blankan censorship conjecture, and they are both associated with words which are quite popular these days in the high-engine physics literature. One of them is unitarity, and the other one is entanglement entropy. So let me talk about unitarity of us.

So we would like to have a theory in which we can calculate how things evolve from the past to the future in a well-defined calculation way. The theory would satisfy that. is a unitary theory.

So the word unitary also comes from doing it at a quantum level. Now, you can show that in a model, okay, in an expanding universe, if we describe things using what's called effect of field theory, which is Einstein's classical theory coupled to what physicists learn in Rajatts go, you take gravitational waves, you take matter fields,

you expand them in Roria modes when you plane waves, you take each plane wave separately and you view each plane wave as a harmonic oscillator. So that's effective field theory. If we try to do that

in an expanded universe, then we have to continuously create new plane waves. That's non-unitarian. And if we try to do that, And if we want to protect classical observers from this problem, then we're going to get the Transblankian censorship projection. And the third justification is if we want the entanglement, if you want the entropy density at the end of inflation to be smaller than the entropy density that we need at the beginning of the standard Big Bang phase of cosmology, then inflation cannot last long.

too long, that again gives a transplank insensorship conjecture. And so based on this transplank insensorship conjecture, based on these unitarity and entropy considerations, I will make the provocative claim that the models of inflation that we have violate unitarity and violate the second law of thermodynamics. Can I pause you for one second, Robert? Because I'm sure people are asking, when I hear unitarity, I think back to my quantum mechanics class with Leon Cooper or Frank Levin, your former colleagues when you were at Brown.

And I think back to interpretations of quantum mechanics. I think back to the Copenhagen interpretation. I think back to things that respectable physicists should not enter into until much later in their career. Are these unitarity considerations? Are they in any way related to an interpretation? or do they have a direct, physical, falsifiable, observationally motivated a place in terms of their non-interpretative behavior? In other words, is it just a matter of interpretation?

And then we should shut up and calculate, as David Merman used to say, or are they real manifestations we can get access to physically? I claim that there are real manifestations that we can get access to. They have no relation with these measurement issues of quantum mechanics, the ones that you alluded to. So now, what way I can make this specific is, so I said that if you want to treat inflation the way, you usually treat it, you have to continuously create new waves. Yes. Yes. of different wavelengths.

Now you've given me a recipe for setting the initial amplitude of these waves if you create them. And this choice is going to affect observations. So I can give the standard choice which is not well justified, but if I give a modified choice and I will get completely different results for the spectrum of microRNA. out of this, which you measure. So different from the Harrison Zoldovich? Different from the Harrison Zoldovich. And different, not only in minor ways, but in major ways.

Interesting. Based on these problems that I change my mind, I actually think that alternatives to inflation probably are more promising at present state. Really? So when I've talked with my friend Paul Steinhard or Neil Turok and many others, Anna Eges, who's a brilliant young cosmologist in New York and also in Germany, and I tell them the following kind of complaint from an experimentalist point of view. I love alternatives, but better than an alternative would be a theory that doesn't invoke some of the aspects of inflation. In other words, it should be as radically different from inflation in my humble experimentalist perspective. In other words, it shouldn't have a multiverse.

It should not have different runaway chaotic behaviors. It should not have even a scalar field. And yet, and yet, correct me if I'm wrong, all of these, including Sir Rogers' conformal cyclic cosmology, which I've talked to him about specifically, and Enegis and Neil Turock. and Paul Sternhard. I've said, you all have the same feature that our good old friend, Sir Fred Hoyle, and my late colleague, Jeffrey Burbage, and Margaret Burbage had, which was a creation field. They called it the sea field in quasi-steady state cosmology. Nowadays, Paul and Anna, they call it just a, this is a scalar field. Andre Lindy, past guest, calls it the

inflaton field, and Sir Roger Penrose calls Arabonnes and other phenomenon. There are objects that we don't encounter other than the Higgs boson. And so I say to my theorist friends, can you give me a model that doesn't have a scalar field? Because at some level, you have to still posit, where did that darn scalar field come from in the first place? That's right. So I completely agree with what you said in everything. to even amplify on what you said. With scalar fields, you can get any cosmology you want.

And so now, my friend Slava Mukanov, who's one of this foundational work on inflation, how inflation gives rise to a mechanism of forming structure, he would agree with the following statement that I make. If the simplest scalar field model does not give something interesting, so if in your theoretical model you have to tweak the scalar field, then it is no longer a good model. But now you ask another question. So are there models of early universe cosmology which do not involve scalar fields? Yes.

And the answer is yes. And so I've been working on, I proposed together with your guest, the Komun Wafa, a model of early universe cosmology based on super string theory called string gas cosmology. This was back in 1989. And we have a improved version of that recently called Matrix Cosmology. So the answer to your question is yes. I'm very keen on working on cosmological models which do not involve a scalar field. And I'm going to make a prediction for your observations.

Okay. And that prediction is going to be a consistency relation between the tilt of the B-mode polarization that you're going to measure, the gravitational wave spectrum, and the tilt of the density perturbations. It's a specific definition. And for people who know the nomenclature, it's nt equals 1 minus ns. And this comes from a model based on super string theory. Now, can I make a side comment? Of course. Okay. Now, I'm critical to a, about inflation as you gathered. But I'm actually,

I like string theory. I think string theory is a good starting point to try to understand the universe. And I know that this among many people is an unpopular opinion. Anyway, so in our models of our universe cosmology, indeed, we start with super-string theory. However, we have to start not with a toy model, not with an effect of field theory based on super string theory, but with something truly stringing.

And so on our old work with Kuhnwaffe, we sort of said, well, what's the difference between a theory based on strings and a theory based on polyparticles? Well, all of your listeners can see the difference. If you have a string, you can stretch it, and you can tweak it, a string can vibrate. And if you have a string on a donut, the string can wrap the donut. Point particles can move on the donut, but he cannot wrap the donut. And they also know no vibrational modes of a point particle. So, Kuman Waffe and myself, we were asking the question, if you start with the same idea of a background space-time that we usually use in cosmology, and instead of having point particles on this space-time, but instead we have strings, the basic entities mean strings, will we get a difference? and we realize that there's a big difference.

And to illustrate this difference is a following. I can say the following. You take a box of strings and you compress it. You take a box of point particles and you compress it. Now, if you take the box of point particles and you compress it to smaller and smaller and smaller sizes, the temperature becomes high and high and higher without a limit. and eventually the temperature reaches infinity.

Yes. But you take a box of strings, you compress it. Initially the temperature rises, but then the temperature approaches a limiting value, and the increase in temperature slows down. Instead of... A singularity. There's no more singularity. You start producing the oscillator modes of strings,

and if the box becomes small enough, then all of the energy goes into springs that wind the box, whose energy becomes small. And the temperature goes down to zero. And that's this hexador. Maybe... That's this phase in which the temperature is close to this maximal temperature. This is the phase that we call the Hagadon phase. Haggadon phase. It's named after Haggadon, who first worked out the...

statistical mechanics of closed strings. So these strings are... You said this place was steps from the water. We just haven't found the steps yet. How much did we save? Enough. Enough to get lost! Or you could book a stay with Hilton.

Welcome to your ocean front room. Just steps from the water. The Hilton sale is on now. Book on Hilton.com or the Hilton app and save up to 20% to get the stay you expected. When you want savings, not surprises. It matters where you stay.

Hilton, for the stay. Sort of behaving like degenerate matter. They have a, and that's not to say there's anything wrong with that, but they have a different equation of state than a shoestring or a particle of dust or even dark energy, if I'm understanding it correctly. Because they must behave in a degenerate fashion such that you cool once you exceed in the approaching from high to low temperatures,

because then they cool down again, the network, the string network, which is also another phenomenon. So if I'm wrong, correct me, but point particles, well, as you said, point you can't, you can interact point particles, but they don't entangle. But if I'm not mistaken, the strings can actually interact, they can entangle, they can do more than, they can also scatter, but that's not all they can do, correct? That's correct. But then we go back to this equation of state, which you mentioned.

Equation of state, so if you just have clumps of matter, cold matter, that has zero pressure. If you have the radiation, the microwave background radiation, has positive pressure. Now, if you have a gas of strings, what happens is that depending on the density of the strings, this equation of state changes. It starts out like radiation, and then becomes, something like cold matter and eventually comes something which has negative pressure. What does negative this? Wow. So it's it actually goes from for the this is for my cosmology students that are studying this right now. It goes from an equation of state of one-third to an equation of state of

zero, w equals zero, to an equation of state of less than minus one-third, correct? That's right. It goes to minus one-third. Now again, in your cosmology class, you, So you'll be studying equations based on Einstein's theory. That's right. And then if you just couple strings to that, you will still, even when the box is small, the Einstein equations will say it will still expand. That's right. So you take your box of strings,

and although the temperature is decreasing, the box will still decrease. So now there's a second aspect of strings, namely what that makes strings different from point particles is the following. What do you actually mean by position? So how do you measure position? So in usual physics, you take particles and you see where they land. You shoot particles, you look at their momentum and they land somewhere. they scatter off a point and that's how you can determine the position. But now for strings, you actually have these windings.

And there's actually a second way of defining position. So if you have a gas of strings, you actually have two ways of defining position. There's like a position and a dual position. And if the box becomes small, if it becomes small, smaller than the string scale, then any experimentalist will be using the dual description of defining space. And in terms of that, space will be growing up. And you will have a bouncing cosmology with no singularity. So you'll start off, and what will be the spatial geometry in the three different phases?

This is now the point. So the Achilles here of our early work, 1880, is that we just postulated that we would always set space was going to be a torus, either small torus or large torus. So a nine-dimensional donut. Because in string theory, you have nine dimensions of space. Now you can ask me why this is not a problem. This is actually a very nice feature.

Really? It's a very nice feature, yes. Why is that? Okay, so this is now a digression. And again, so the way that I will answer it, I will give you a defense of string theory against some of the popular criticisms. And one popular criticism is that with string theory, you can get anything you want. You have this landscape of possibilities. So I'm sure many of the guests.

Yeah, I've actually said that I have to confess to you as my father in a certain sense, Robert. I have used that complaint. I have used that attack against none other than one of the people who founded string field theory. And that's Michio Kaku, who came on for his book last year, The God Equation, in which he claimed, I said to him, well, you know, Michio, I don't have to. He said, well, string theory is often accused of predicting anything, as you just alluded to. but that's just like saying in Maxwell's equations,

you have to tell me what the ground state is. I said, but Michio, once I tell you the ground state, everything is determined. And furthermore, from just the field strength Maxwell tensor, I can get all the equations of all the behavior of every dynamical object in space time, at least in that simplified version, whereas you need to specify it for each one of these models, And furthermore, it could change as the landscape and the swamp land conjecture sort of highlight.

So anyway, I'm just confessing to you, Robert, that I have used that attack. But the first person, the only person so far, maybe you'll be the second person. But the only person to say that string theory makes a prediction that's experimentally verifiable is your colleague, Kamran. But it wasn't all that satisfying because he basically said that string theory, predicts the mass of the electron can vary from, you know, 10 to the 16th plank masses to 10 to the minus two plank masses. So in other words, there's a lower limit and upper limit, but he didn't, you're not predicting it to with precision that any high school chemistry, you know, student would be satisfied with. Anyway, sorry for the digression on top of the digression, but you're right. People do

criticize string theory for the lack, the infinitude of possible. ground states essentially. But now let's go back and throw out the strings and go back to point particles. If we do that, we can have any number of dimensions of space and time.

No one tells us why there should be three dimensions of space. Yes. We can have arbitrary number of fields. We can have one electromagnetic field, two electromagnetic fields, two electromagnetic fields, three electromagnetic fields.

We can have one scalar field, two scalar fields, three scalar fields. We can have any kind of potential we want for any of these scalar fields, and these fields can have any range. So it's a huge swamp land of theories if we forget about strings. Now comes string theory, and string theory says that we can only, string theory is only consistent in nine plus one dimensions of space and time. So nine dimensions of space and one dimension. So it's restrictive.

Now, it's, so I haven't worked out the detailed connections between string theory and particle physics models. So I can't tell you at low energy how many particle string theory predicts. But someone who has good mathematical talents will eventually be able to tell that. So all scalar fields that emerge from string theory have a geometrical origin. Their potentials are constrained. So among all possible effect of field theories, theories that you can get from point particles, this huge swamp land, they're only small islands that stick out, habitable islands. Unfortunately, it's not just one island.

It's a number of islands, and it's a landscape. So you see, this is why I argue that the criticism that string theory predicts anything you want is misplaced. It is not as predictive as we would like it to be. Maybe eventually it will be, but it is a step forward. to be. Interesting. And then I made a prediction for cosmology, a specific prediction, which is the one I just told you. Right.

So if we pivot back to the, you know, this notion of the predecessor, let me explain it like this, maybe they're prerequisites of these various frameworks for the early universe. There's Sir Roger Penrose conformal cyclic cosmology, which requires these ara bonds and this strange form of matter, as he calls it, that evolves and changes. And then it also emerges from a phase of black hole entropy with conformal dynamics that I still don't fully understand. But be that as it may, it involves a scalar field. Let's just say it like that, or it involves a new physical manifestation of field. Next, there is the creation field, the sea field of quasi-study state cosmology. There is the scalar field of the bouncing cosmological model of Paul Steinhart.

There are alternatives as well that have scalar field. And of course, the inflation inflaton scalar field. Now, I always point out, there's only one scalar field that we know for sure exists, and that's the Higgs boson, but that's a very different type of field than what the inflaton would be. So I guess the problem that I have with that is, you know, who put that there? You know, where did it come from? And so I would ask you the same thing. Is the minimum prerequisite for string gas cosmology, just the existence of space time? I mean, all these other fields have space time, plus they have a scalar field. So it would be,

in Occam's like simplification to only require space time. Am I getting that right? That's right. Absolutely right. So our input was space time and the gas of strings. But now, you see there was a problem with this scenario, because we don't just want to postulate a space time that behaves in some arbitrary way. We want to derive how it evolves in this early phase.

And in this early work of 1989, we had put it in by hand. So in my opinion, that was the Achillesquil of our early work. And so in our recent work, we've been trying to improve on this. Now, I completely share your view that we should not try to invent new scalar fields. So we're going to try to do something different. Now, at the beginning I was sort of arguing that if we have, if we want to describe the early universe using fields, then we are faced with this problem, potential unitarity problem.

Yes. We shouldn't just be using fields. We should be really using something fundamentally new. We should be using what physicists in my field call a non-perturbitant definition of string theory. So let's step back and analyze what I mean by that. If you go back to particles, then classically we know what particles do. Like on a billiard table, we know how particles move. Particles scatter. Classically, we can include quantum effects in the scattering of particles. These are the things that

you do an accelerate experiment. But if we want to describe the theory of particles, the theory of an arbitrary number of particles, we have to replace the notion of a particle by a field, like the electromagnetic field. Yes. And a particle will just be a little localized excitation of a field. Now, in string theory, we know how strings evolve classically,

and after a lot of work, we've also been able to study the quantum mechanical scattering of strings. But we don't have a theory of an arbitrary number of strings, the analog of the field theory of particles. But there is a proposal, and the proposal was made in 1996, 1997, by Banks, Fisler, Schenker, and Suskent. It is a matrix model.

And this was our starting point. So now, you see, I'm not, some people who you've interviewed are radical. They want to do things that are completely new. I'm actually, even though I've perceived as a radical, I'm actually fairly conservative. I just said, well, we need a non-protoperative definition of super string theory. What is the best thing on the market? And so we took that. So do you want me to say a few words about that?

Yeah, absolutely. And I want to make sure we have time to go over some of your slides at least, too. Okay. Good. So we are starting with a theory in which the basic ingredients are matrices and there is no space. It is a quantum mechanical model like a system of spins. but here it's a set of matrices. So it's a quantum mechanically well-defined system,

the very large matrices, n-by-n matrices where you let n go to infinity. But there are no singularities. It's a well-defined matrix model. There's time. And what we do is we consider this matrix model in a high-temperature state. Now there's no more evolution.

There's no more space, no more time. no evolution. And our goal was to try to see what we can get out of this well-defined starting point. In our recent work, we've been able to get a construction of emergent time, emergent space, an emergent metric. So metric is something that describes a distance in space and an early universe cosmology out of that. including things that you can measure in observations. Now, the time that emerges out of this construction, in the limit where you take the size of matrices to infinity,

this time is continuous, not just discrete ticks of time, but it is a continuous interval, like a string. And it ranges from minus infinity to plus infinity. So there's no big bank singularity. The space that emerges, that we had to work a little bit harder, also is continuous, and it does also infinite. So the space that emerges is infinite, but it is infinite only in three dimensions, not in nine dimensions. So even though the theory is the theory of nine-dimensional space and one-dimensional time,

What emerges is only a three-dimensional infinite space. And the other six dimensions are some structure which has not even a well-defined geometrical meaning. Okay, then we have it. Since now that we have space, we can give a definition of length. And once we have a definition of length, we have coordinates. We know what the metric is. and what emerges is that this metric is spatially flat. So we don't get the space that emerges is not like the surface of a sphere or the surface of saddle, but it is just flat.

It is something that evolves in time, but the space is flat. Okay, so we don't need inflation to reduce an infinite universe. We don't need inflation to produce something that's flat. the problems which inflation was initially designed to cure or automatically cured in this approach. And there are no scales in this approach. So there'd be no deviation from the Harrison-Zoldovych? Now comes the fluctuations. Since we have a thermal state, we have thermal fluctuations.

So we can compute the perturbations. and we find that we get something that is roughly consistent with observations. We get, to first order in the approximation, we get what you just called the Harrison Zerlobache spectrum. Something that's scaling variant. So if you take a box and you look at fluctuations in a fixed box, then independent of spatial scale, you get the same magnitude of fluctuations.

That's scaling there. So to first approximation, we get that. And if we now go back to our string gas cosmology toy model, then we automatically get the tilt, get the deviation, and we get this consistency relation, which I gave you. We also get gravitation waves. And there's no cosmological constant. So this is something that I'm really excited about. And obviously, this is a beginning of a research program. But I think I've answered your program.

this is an attempt to obtain an early universe cosmology which does not involve scalar fields. Indeed, I show you a criticism against these various other approaches which involve scalar fields. I think they're very interesting. In fact, I think if you like bouncing cosmologies, I think you have to pay close attention to this eq prerotic scenario, which was initially proposed by Kuri, Bofort, Steinhardt, and Turok. Because among balancing models, that's the most promising, in my opinion. Yes, and that's one of my, that was one of my questions from our friend, Stefan Alexander,

your former graduate student who's gone on to become a professor at our very own, my very own alma mater. I also had some questions from my colleague, Amit Yadav, who is working as a scientist for me for many, many years. And maybe while I'm getting those up, then we could get the slides that you have. We've actually covered a lot of the slides, but I want to get this slide.

If you could put up your slide, slide 17, because this is a terrifying slide to me. This is terrifying to me. You did mention there are gravitational waves. You did mention there'd be a consistency relationship between the gravitational wave power spectrum, the tilt of what's called the tensor power spectrum for the aficionados out there, N sub T, and the relationship between N sub T and N sub P.

I'm going to hold off because I think you are too scared of this. Okay, so go on. You take it away right. You see, this slide is in the context of inflation. It is saying that if you try to construct an inflationary model, which is consistent with a transplankan sensitive conjecture, then you need low-scale inflation, and then you get these negligible primary gravitational gravitational waves.

Yes, yes. I think that this is not the way to go because of all these problems. You should not be scared about that. But if you hear people say that a large R is a smoking gun of inflation, that's where you should object. A large R is not at all the smoking gun signal of inflation. alternative situations typically produce a fairly large R. Well, not the alternatives of conformal cyclic cosmology are best.

Maybe not that one. That one I haven't studied. But in our realization of Paul Steinertic scenario, we get a fairly large value of oil and in St.Gas cosmology as well. And we get a rough consistency relation, which I can tell you privately, which gives us a magnitude of R, but it's only a right. rough, so I prefer. I see. But maybe

you see, since this is bad news for standard models of inflation, let me go to another slide and name me the criteria. So if you are an inventive young

person, for example, a young listener to this show, and you want to construct your own model of the old universe, then what I'm going to give you is the criteria which you have to satisfy. So first of all, this is the data that you need to reproduce. So here the horizontal axis is angular scale, large angular scales, small angular scales on the right. And the vertical axis is amount of structure, amount of antisotabies.

and the black dots are the data, and it is the data that you have to fit. And this is actually old data. Now the error bars are smaller. And there's a red theory curve, which is not important, this context. Now, the red theory curve was actually predicted 10 years before inflation by Zeldowitz and Zunyaev, and people send you. And this is a graph which I took from the Zeldovich-Zeroyev page.

of 1970. So here, the horizontal axis is space, and the coordinates that I'm using are coordinates which are expanding as space is expanding. And the vertical axis is time, and this time here is the time when the microwave background is released. Now, Seldobich and Zuneyev assumed that there's some unknown mechanism that produces waves of density, density, waves at very early times on all wavelengths with a scaling environment spectrum. Now it is a fact that these waves are frozen in. They are standing waves until the wavelength becomes equal to this length,

this diagonal curve, which is actually the standard Big Bang horizon. And then they start to oscillate. So the wave that you catch here that enters the crosses the horizon will add the combination you catch it as a standing

wave with maximum amplitude. But this wave which has done five quarters of an oscillation, you catch it at a minimum.

So it is this evolution of density waves which explains these features. So the physics that case

rise to this was well understood 10 years before inflation. But you do need a mechanism that produces these initial waves.

And so these are the three criteria for successful early universe cosmology. First of all, the horizon, which is a distance that light can travel from the beginning, has to be much larger than what we think it is in standard big biocomology, because we have to produce a roughly isotropic universe. And then these, you have to have a mechanism that generally. generates fluctuations. And in order for this mechanism to be described by causal physics, physics obeying the Einstein's laws of special relativity, then the length scale that you produce the fluctuations on has to be smaller than the double radius at some early time. This is the second criterion. The third criterion is this gaining up. And so,

So inflation satisfies these three criteria. So time, space, physical length. This is a period of inflation where space expands exponentially. The horizon expands exponentially, it becomes exponentially larger than the Hubble radius. Wave lengths of fluctuations grow exponentially. And so if we trace back the waves that you are measuring, Brian, you trace them back. start out inside the Hubble radius. So here you have the two first criteria are satisfied.

But if you take a bouncing cosmology, so this is bounce point, expanding phase, contracting phase, no inflation. This is what the wavelength of the scales do. So time runs from minus infinity to plus infinity, just causality of all of space. Structuration start out smaller in a hubber radius. You have the possibility of a causal mechanism.

And in our stringer scenario, we basically have something that looks like quasi-static, and it can arise to a space time diagram that looks something like this. But now, let me give you the challenge to the young people, the young people who want to work in this field, who may be not even undergraduates yet, you have to come up with something better than the three things which I just briefly showed you would satisfy these three criteria.

And Brian, you don't have to be afraid at all about this previous slide number 17. Okay. Good to know. I'll be able to rest easier because I'm actually not afraid of it. Let me take a detour because that's what I love to do with you. So I think that most things in cosmology do not have a natural scale. In other words, as you show many times, inflation could occur. It could have occurred at a very low energy scale. It could have occurred at a very high energy scale. We actually don't know. There's no lower limit on the energy scale of inflation. On the other hand, there is a lower limit on the amount of B mode polarization. In other words, there is an amount of B mode polarization that's not necessarily primordial. And you hinted at it on a slide, but my colleague here, Raphael Flaugger, who you know undoubtedly very well, is one of the

Steven Weinberg's final students. Raphael and David Spurgel and others have looked at this, Paul Steinhardt as well. And this is that because of the what are called secondary perturbations, there is a lower limit. And I think my experimental colleagues, you have a lot of affection and appreciation, and you always did for people like Peter Timby, my advisor, and so forth. And you're always very connected to experiment. But sometimes I think you give experimentalists a little bit too much credit and praise because there is a sense of dishonesty, I believe, that we are attempting to measure certain things with very big projects, some of which I am very intimately involved with, as you know, the Simon's Observatory, the Simons Array, Bicep in the past, etc. And that is that we're basically assuming the conclusion that inflation took place because there's a preponderance of cosmologists that do support it. And furthermore, it is amenable.

It has a certain pleasing nature to it, even leads to things like the multiverse and other things, that some people find pleasurable, others find distasteful both to cosmology, but even to the scientific method. We'll leave that aside. So in terms of inflation predicting a multiverse, I would argue that this is not the case. my friend Slava Mukunov would agree with that. And let me maybe quote something from one of the other guests, Sabina Hosenvelder. She said sometimes people take their equations too seriously and don't think about the physics. And I think this argument that inflation predicts a multiverse where you treat inflation just in terms of your scalar field.

This is treating your equations in a domain where you can't trust them. Similarly, yes, I agree. In fact, people talk about things like the plank length as being some fundamental building block scale of nature. reality, if that were true, then the plank mass would also have to have some fundamental significance. But the plank mass is the mass of an egg of a fly. It's actually a very large mass. Not to say the plank length is large. Of course, it's very small.

But there's nothing fundamental about it. So people take that very seriously. Elon Musk recently said that, you know, that basically the existence of the plank scale sets an absolute limit on the number of digits of pie, which I found ridiculous. But, you know, he's an amateur physicist. I hope to have him on the podcast at some point. But getting back to my conjecture, if physicists were honest, let me just say, if I was honest, because I'm not going to impugn the reputations of my colleagues and friends, but I was honest, I would say to Jim Simons or the National Science Foundation, I'd say, look, we actually have no idea what would have

happen if inflation has an energy scale that's that's even detectable. But we know for sure that there must be a fluctuation of B mode fluctuations at a scale corresponding to 10 to the minus six, a tensor or a ratio of 10 to the minus six from what are called secondary perturbations. You can't explain this much better than I can't. But Robert, that's also, that is interesting to an experimentalist. We love lower limits. So there's a low. lower limit on the mass of the neutrinos. That provides a very tantalizing target that we can then optimize experiments such as the Simon's Observatory and the CMB Stage 4 project. We can optimize those to detect that lower limit as a worst case scenario. But for inflation or the lack

thereof, the lower limit comes from these secondary perturbations. Now, if we don't see those secondary perturbations, I claim that would be interesting also, because that would mean there's something wrong with general relativity in a very, yeah. So I think, but we know that to detect such perturbations is way beyond the reach of maybe a thousand Simon's observatories. In other words, a trillion dollar mission would not be sufficient to detect a threshold of 10 to the minus six and more than, you know, zero sigma essentially. So I claim my, I'll just say me because I don't impugn any of your friends or my friends, that we're not being honest because we're pitching this experiment as a definitive way

to ratify, justify, detect, or falsify inflation when it really can't do that. And ultimately, we should be saying, let's measure 10 to the minus six, except we want to do it in our lifetimes. And I think that's a sign of me being greedy. Who's to say that, you know, if Penzius and Wilson wanted to measure e-mode polarization with their first instrument in 1965, that would have been impossible too.

So there's no guarantee that nature will cooperate on a time scale of your technology. So I guess this is all a way of saying that experimentalists should not be praised too much because a lot of times we want to get the job done for our careers and for our, you know, for our own intellectual curiosity while we're alive, but it may not be possible. And so that's sort of my rant about experimentalist and not putting them on too much of a pedestal.

Yes, I agree with this wrong advertisement of the goal of sudden experiments. So I completely agree with everything that you said. But I think they make very good physics cases exactly for the kind of of experiments that you're working on. One of them is if you manage to find a B-moded, a cosmonautical primordial B-mode background, you should go after the tilt. Yes. Because this tilt relation, which I gave you, is something that string theory first predicted.

And so if you find such a tilt, that that would be great news. but there are also much more modest things that you can do. And maybe I can now turn to some of the other work that I don't only work on early universe cosmology. Yes. I have several pet topics, but one pet topic are cosmic strings. Yes. You actually tasked me with a project to do that when I was considering in a crisis state,

which I think all graduate students must go through at one point or another, where we totally question what we're doing, Robert. it. Now, I'll get your advice to, to young people at the very end of the podcast. But I had a crisis of confidence. I wasn't sure I really wanted to be an experimentalist. Mark Kamiankowski recently called me a closet theorist anyway. But I did a project with you and you assigned me cosmic strings. And it was about the deficit angle that they would induce and what type of polarization. And I never came even close to solving it. And I apologize, you know, Mayaculpah. later on we moved to

Wisconsin. But tell me, tell me about these cosmic strings. Why are they so mercurially, why are you so interested in it? This is 30 years I've known you. Why do they still fixate you? So delightfully so. Right. So there's nice physics,

but there's also good motivation. And that motivation comes from particle physics. So we know that the standard model of particle physics is incomplete because we've measured neutrino masses and lays dark matter in. Dark matter doesn't fit into the standard model.

Now with Accelerate experiments, you can't really probe things beyond the standard model, like energy scales, beyond the standard model, very high. But with cosmology, you have the chance. Yes. So now I would divide particle physics models which go beyond the standard model. I would divide them into four categories. And let's make the analogy with different kinds of metals. So if you take a metal in the fluid state and you call it,

then certain metals will lead to defects, like crystal defects. Some metals will have no defects. Other metals will have point-like defects. another class of metals will have line defects, and a fourth class will have planar defects. And similar in terms of particle physics models, some particle physics models predict defects which are plainer. Those are already rolled out by cosmology. then others predict defects which are linear and those are very interesting signatures in cosmology

and they are constrainable and therefore they're very fun to work on and also interesting because if you could find a signal of a cosmic string in the sky you would have then shown that the way beyond the standard model of particle physics is in this one class of the four. So bottom line is that there's good motivation to look at, to look for the signatures of cosmic strings in the sky. Now, cosmic strings produce signatures in the microwave sky.

They produce lines in the sky, across which the temperature jumps, and they produce rectangles in the sky where there is extra polarization with a uniform direction and a linearly increase in magnitude. And that includes B mode polarization. So you could go after this and you could ask the question, if you have a map of polarization with a particular accuracy, how severely can you

constrain particle physics models which have cosmic strings. There's one free product in those models, and this is the tension of the strings. And the tension is already constrained because we haven't seen in temperature maps of the microwave background. We haven't seen these jumps. So there are things like that that you can. There's good motivation for looking at the microwave sky in polarization, independent of inflation. Mm-hmm. So, and there are, of course, many, many others. And I did not mean in any way to impugn the kind of deep passion that all of my colleagues find. As I said, the neutrino mass is amenable to cosmic microwave background polarization measurements. Let me ask you, parenthetically, Robert, if we measure with the Simon's observatory or maybe with the dark energy surveys or bearing an acoustic survey, some combination of cosmological experiments.

They measure, for the very first time in human history, the mass of an elementary particle, such as the neutrino. Will your fellow particle physics theorist? Will they believe us? Ambition comes in all shapes and sizes. At First Citizens Bank, we roll with your goals, because we're built for what you're building. Fit for your ambition for Citizens Bank.

Can I pass on that? Because it is a very good question. And you ask me to comment on what other people will say. And I simply don't, I don't have a good feeling. I don't know. But I'm... I'm... I'm...

...interversial comments about other things, but about this, I would like to pass. Okay, good. Very good. That's totally within your right. So when, to be, to be fair, to my audience members who are the brightest in the known universe, they will say things like, well, what else gives us credence in string theory? I agree. I often joke, and it's hard to do this in front of you, but I often say, you know, like quantum computers are very good at figuring out what quantum computers can do, as Feynman said. You know, they'd be very good at, you know, calculating a Lagrangian. But I don't know about you, Robert, but, you know, when I'm trying

aboard an airplane, I don't need my iPhone to diagnose a Hamiltonian. So that's not practical, so practical. Similarly, I feel like string theory in the mathematics associated with it is very, very advanced. It's very, very much, you know, in the spirit of being useful to string theory itself. And I wonder, you know, to my audience members who are wanting me to ask you, well,

what does string theory predict? What is the resolution of, you know, the swamp land? How do you reconcile this theory that past guest, Eric Weinstein, as a very good friend of Stefan Alexander and mine, has said that it's really devastated the careers of numerous young people because it kind of was a cartel for a long time in his mind. But he's not here to defend himself or even advocate for what he believes. but there's sort of a program that came from Natty Cyberg and Ed Witten and others that established a paradigm for the field over the last 30 or 40 years.

And it hasn't really borne fruit. And in fact, past guests, Jim Gates, who's been on the podcast many times, similarly, supersymmetry. These are things that no longer, they were very promising because of the beauty, elegance, simplicity, but do they have to connect to empirical? verification. What do you say to that? Right. So here I'll make a great defense for string theory. So first of all, I'm convinced that gravity has to be treated quantum mechanically. And you can do dead Duncan experiments. You can imagine little experiments where you can imagine little experiments where

you can show that you get the wrong result if you try to treat gravity classically and you keep a matter description of a quantum description of matter. So maybe I don't want to, I don't have a slide illustrating that. But so now. Can I just ask you, is that true also in black holes? Because I've had this debate with Sir Roger and I've said, said, there's no, you know, there's no letter from God that says that we, you know, have this unification. First of all, we don't even have, if I'm wrong, correct me, but we don't even have

a grand unified theory that's self-consistent. And I always joke, we're putting the gut in front of the toe or the toe in front of the gut. And we're now seeking a theory of everything, which would include quantum gravity and subsummit, but we don't even know how to unify the other forces. So it's like, you know, get the, get the dust like particle out of your eye. So anyway, how do you react to that? I mean, why do you say with confidence? So I would argue that we need to quantize gravity. So now let's, let me make another argument for that. Let's take a point particle. A point particle will have it has a particular mass. And it it creates a gravitational force, field.

Now, you make the mass higher and higher, and eventually the extent of the particle becomes smaller than the Schwarzschild radius. And instead of having a particle, you have a black hole. So if you treat matter quantum mechanically, you have to treat gravity quantum mechanically. So that's the starting point. So now, I would love if there were different candidates to do this,

but I view string theory as the most promising way to quantize matter and gravity in a unified way. Now, I said early on that we don't know how to do it in full generality. We don't have what I earlier called a non-perturbitantirative string theory. But I think that there are two aspects of a theory that is needed if you want to describe the Earth Universe and also physics are very high energy scales. And this is, we need both both quantum gravity and we need unification and a quantization of gravity.

So again, I'm not a string theorist. So I look around what is there in the market and string theory is promising. One of the reasons why string theory is promising is that there are no singularities associated with those singularities of the same type that they are for point particles. If you scatter point particles and do a calculation,

which is the next to simplest one, then you find that the probability that point particles scatter is infinity. And then you have to do something called renormalization. That's right. To get rid of this infinity. So now I was very fortunate to have taken quantum field, theory from a very good lecturer, Cindy Coleman, but I was so fortunate that there was a famous mathematician, the differential genre, Raul Bott, who was taking the class. Not just occasionally,

he would come to every class, he would sit in the front row, every time, take careful notes, and he would ask all the questions that we students were too embarrassed to ask. So this made the class really well, really good. And there was one point where Raulbot became a little bit not so polite. And this is when Sidney Coleman introduced the concept of realisation. And then he laughed out, is this what you physicists do? And he continued to note. But it was absolutely clear to me that there was no way in what Rolbott accepted.

this renormalization. Now, this renormalization happens not to matter if you do experiments at CERN, it works fine. Right. Which gravity is involved, you simply cannot throw away these infinites. That's the cosmological constant problem. And is this, I should point out, that Raoul is credited as being the thesis advisor for Eric Weinstein. although Eric says he did not have, he was not his, well, in prints and practice, he was not his advisor, but I'll let Eric respond at some other point to that. But so, yes, it is true. I mean, Feynman accepted re-normalization, but he did, in the electromagnetic context, but he did not accept it in a string theoretic concept.

Of course, by the time he died, the cosmological constant problem really wasn't known in 1988 when he, unfortunately, passed away. way. But you did mention, you know, this unification. And I guess, you know, just again, to push back with respect. So I did have on Shelley Glashow three years ago, two or three years ago. And we talked about, you know, his SU5. And I always say that, you know, we're kind of, we're kind of led along the path that financial advisors, financial advisors tell us we should not Oops, sorry, my computer assistant is now pinging me, but that's okay. Financial advisors will tell you that past performance is no guarantee of future results. And I think sometimes there is so much success in the realm of unification and symmetry and so forth,

that it became almost an expectation that the successor theory to provide quantum gravity would be in those same vein. as, as, you know, Shelley tried to do after the success of the lecture week theory with Weinberg and, and, why am I blanking on their third colleagues, and ad de salam? So they were very successful, but not as successful looking at, looking at, you know, a concept like SU5. And I know this is not, you know, again, it's not something you specialize in, but, do you think we really need more of that kind of, you know, the more research along this, this realm will provide and bear fruit? Or is it really going to take one of the young people that's, as you say, maybe listening to this in high school or in college, you know,

or freshman in college, some new ideas that we have become, you know, kind of overbeholden to what got us here, but it's not going to keep going along the path that we need to travel? Yes. So for me, string theory is a promising approach if we want to understand the very old universe, and if we want to develop a theory which is also true at the highest energies, smallest length scales. Now, do we have the tools right now to make detailed predictions, especially for particle physics, and there the answer is no. we need new insights. And I think we might need a completely new approach through string theory, but I think this new approach will not go back to point particles.

It will have something that looks like strings in it. Is this related to the matrix theory, Yeah, this is related. Can you go ahead to slides, to slide 53, please, or 52, please, and then share that. Yeah, continue to share that. So in matrix theory, cosmology, again, I'm just a simple, humble experimentalist that you remember, you know, breaking things on the roof of Barrison Holly. But the notion of emergence comes up a lot. What does it mean that time emerges in matrix theory, Cosmo?

What does emergence even mean? To me, it's construction. So maybe I should go back a little bit. I know that Neil Troach, when he was on your show, he showed a technical slide. So I will now show a technical slide as well. You get one per episode, Robert. One per episode.

That's right. And so he showed this slide, his slide, and he sort of argued that this was very elegant. There were a lot of symbols here. So now, what I'm showing you here, this quantity called L, this is the model. This is all that's contained in the model. And these X-E-I, these matrices. And here there is something. that contains a time duration.

So here in this model, there is an initial time. We take this quantum mechanical model in a finite temperature state, so we then have to construct a new time. Okay, so out of these matrices, we have to build something that acts like time. That's what emergent means to me. So it's a mathematical, it's a kinematical. emergent. It's not to be taken, like, in other words, Hawking in his work would talk and Hartle would talk about imaginary time. And then the imaginary time would sort of cleave off from

being complex into being real. That's right. He has this a trick, but he called it a trick in the book if you read it. Is this a trick or is it real? I think it's a trick. Okay. So if he called it a trick in the book, I agree with that statement. Good. Very. Good. So, okay, so everything comes out of these matrices. Now, if you look at the details of these matrices, there's something hidden and there's hidden in this D sub t that's hidden the fact that there's another matrix. So there's actually 10 matrices, 10 of space time.

And I am associated with this matrix here. Let me digress a little bit, technically. These are emission matrices, so we can diagnose one of them. We diagnose this, the diagonal elements of time. So see, this matrix gives us time, and these XI matrices give us space in a way that we make precise. Interesting. So your countryman, your country of origin is, of course, Switzerland. And this gentleman here attended an institution there called ETH.

It's Albert Einstein, for those that are only listening. There are many, many listeners out there into the impossible landscape. And he was influenced by Lorenz and others, who, Lawrence, I believe, said that, you know, time and space are illusory, and they're doomed, you know, in a certain sense. And again, it's one of these kind of, you know, slogans that I never really understood. And what does that mean that space time is doomed? Does it mean that, like, in the future, we'll think, I can't even think about it because we've always thought about, I mean, maybe in the past, we thought, well, this magnet is different than an electric, you know,

field, but now, I mean, I don't think the average person thinks, oh, when I see a magnet, that's just a manifestation of U1 gauge symmetry. And it's actually the same thing as an electric. No, they think of it as a magnetic field deflects a compass and put something on my refrigerator that my kid drew. And an electric field is, you know, responsible for charging my Tesla. But what does it mean that here to four space time are doomed and so forth? What was Lorenz talking about?

And why did Einstein, your country, what did he make of it? Okay. So if you take flat space with no matter, then there's still space and time coordinates. Yes. But they don't mean anything physically because there's nothing to measure anything. There's battery to measure anything. Right. There's empty.

It's empty. Right. Now let's take cosmology, let's take a universe which is the same everywhere, which is homogeneous in isotropic, but it is filled with the microwave background. So now you can measure the temperature of the microwave background, and we can use that as a clock. Yes. So Lawrence was not considering, he was considering empty space time.

So I think that as coordinates, the coordinates, X and T, which physicists often use, they have no well-defined physical meaning. But as soon as you have matter in the system, then you can define physically well-defined block variables. These are relational time. So similarly, in this matrix model, these are matrices. These are matrices. There's the part of the matrix which is homogeneous.

there's a part which is fluctuating. So there is matter plus emergent space and time. So the time coordinate can actually measure something. So this is emergent time with a physical meaning. Ah. Very good. Well, you've done it again because you're one of the best educators that I've ever met, Robert. And I often try to ape and mimics.

you, but I do a poor, poor job. But one thing I'm curious about, when you teach cosmology now, this is an ethical dilemma that I struggle with. Do I teach them about positive curvature universes, negative curvature universes, when I know from my colleague, my late great mentor, Andrew Lang, and of course my current friends, Lyman Page and others who are very much mentors to me, that the universe is flat and the spatial curvature is flat and it's flat as far back as we can really constrain it. But it's so mathematically entertaining to talk about a positive space time. And I remember you teaching it to me.

The only cosmology class I ever took was by you. I audited it as a graduate student. I don't even think I finished it, but the point being it had such an impact upon me. I remember you teaching us about it. But that was in 1996, three years before Boomerang, Maxima, and the Tocco experiment. So, Robert, as a professional, you know, dishing back and forth, do you teach your students about positive curvature universes or do you just skip it altogether? No, I do. Okay. Because observationally, we don't know that the universe is absolutely spatially flat.

We just know that the spatial curvature is very, very small. As I do, the microwave experiments have given the bounds. That's right. We don't know whether on scales much larger than the visible universe, whether space continues to be flat. So yes, do teach. Okay, good. I do include spatial coverage. Okay.

In my discussion. So that part of my course has not changed. Okay, very good. Was there more that you wanted to say about that, what is at hoof limit? What does that refer to? I'm hoping to have Gerard on the podcast at some point. I've communicated through Lenny Suskin once

before, but tell me, what does that mean the hoof limit? At hoofblum. So you see that in this model, in this capital L, there are two free parameters. There's this G, which is like a coupling constant,

like the coupling constant, which you have in electromagnetic, And then there's a capital N, which is the size of the matrix. And so the TIF limit simply means that you take this limit when N goes to infinity, adjusting this coupling such that the G-square times N remains fixed. I see. Okay, very good. Was there more that you wanted to say about these slides before we come to the conclusions of both the episode and the presentation? No, I think you should decide where you want the discussion to head.

Well, I guess I would like to talk about a step back before we get any more deep into the weeds of cosmology, which I could talk about all day. And that's to talk about kind of the things that you're passionate about as a scientist and as an educator. Again, I think of you as an educator, both of my best friend, Stefan, and me personally and many, many other students. And also bringing through Brown University, many people who would go on to be my mentor like Alexander Polnarev, who is a student of Yaakov Zeldovich. And so it connected me to these greats of history. And I want to express my gratitude to you, but also to express that I utilize advice that you give. We have a lot of young people, mostly men, but I'm gratified to say there's a lot of young women. I'm hoping, you know, your daughter will listen.

My daughters will listen at some point to this podcast. They're very brilliant. But I have a lot of young people that listen. And some are academicians like us. I want to ask you, you once told me a very, very sage piece of advice. You said, before you move institutions, you said, Brian, you're going to move institutions many times. And you were right. You were 100% right.

I went from Brown to Wisconsin, Wisconsin to Stanford, Stanford to Caltech. Ultimately, I went east to west, and then I went north to south. And now I'm in San Diego. I told my wife, next stop is the Tijuana Institute of Technology and so forth. And I've been to Antarctica multiple times. So you're right. I'm going to move many times. And you said at each place you go, write a paper and keep it in your drawer.

This is back when we used to use drawers. Do you remember telling me this, Robert? And you said, have that paper. Because when you get to a new institution, you're going to want to have their masthead. You're going to want to have their, because they're now your boss, Brian, you said to me, and they're going to want something for their return on investment. And I thought, you know, maybe that's true. But all that matters is me.

It's just my career. So, no, it's not true. It actually, the profession of being a professor, at least, hasn't changed. And it's very important to give attribution and to attribute to the place that you're at. I want to ask you, Robert, how is being a professor evolved since you started 30 years ago? And how would you do it again? Would you enter into this field again as a professor? Right.

So I think as a young person who's a debating whether to start graduate school, then I would ask them, do they, I would ask you, do you want to go for a career as a teacher or a career in business? a 95 job where you have to dress up in suit and tie, not just this jacket that I have, suit and tie. Or do you want a job where you can think about things, you can teach, you have a varying amount of teaching obligations, but you have quite a bit of independence and free time and security.

Maybe you don't have the highest salary. Right. This is a basic choice. And then you see that I don't give the student the possibility say, I want to be a research professor at Caltech. That's completely unrealistic. Right. So if you say, I want to go to the teaching track, then yes, you should study.

First of all, you should study what you're interested in. But within the general area that you're interested in, you should study, you should pick a promising area. And for me, a promising area is an area in which there are deep questions and data. And there can be the balance between deep questions and data that can vary. And when I mean data, it's not data that's already there, but it's data that's going to come in. Now, when I started in cosmology, I got into cosmology by pure accident, there was essentially no data, and there were deep questions. And in the intervening time, there's been lots of data, but the deep questions have remained. So, now what about the data?

I see new observation windows popping up, for example, 21-7 meter cosmology. So right now, if a graduate student wants to work with me on cosmology, then I would say it is still promising, because there are still the deep questions and there's still data. But I think this is a question that has to be revisited every decade. And it does change. It does almost... It changes. Because there are areas which have become, their fields of physics which have become stale. The basic questions have been addressed, and there are also only details that have to be worked out.

One thing that's always typified you, to me, is your intellectual parapetetism that you are not an experimentalist, but you are convergent with the potential. of any given experiment. You are, as I say, to my students, I kind of reverse what you would say to me. And I say my experimental students, you don't have to do theory, but you have to know theory. In other words, you don't have to come up

with an original theory or model, like a theoretical graduate student might have to, or maybe not, who knows what they do over there nowadays. But you should be conversant. What is the minimum that a theorist should know about experiment, a young person? Peak pollination season and my business is scaling fast. To keep the nectar flowing, I need a phone plan with top priority data speeds. That's why I chose GoogleFi wireless.

My connections stay strong even when the hive is buzzing. Plus, unlimited plans started $35 a month. Now, that's a deal that doesn't stay. Explore GoogleFi wireless plans today. Plus taxes and government fees. GoogleFi Wireless is not subject to data traffic deprioritization during times of high network usage. You know, this is a question that I should ask you. You should ask me the other question, Amy, what is, what amount of theory should a young experimentalist know?

Right. I guess I feel that I am going to be advising experimental students and you're going to be advising theoretical students. So what I try, so back to your question, with my students, I try to have them follow what's happening in experimental cosmology. So we have a joint genre club between experimental and theoretical cosmology. So I don't know if I'm doing enough and if I'm doing the right thing, but this is what I'm what I'm trying to do.

And you know that I tried to do it up around. You did, yeah. And I'm trying to do it at McGill as well. In fact, we have a very strong group here at McGill on the experimental cosmology side. Very many of them are my colleagues on Simon's Observatory, Simon's Array, and other projects. So in that same vein, here at UC San Diego, I am the associate director of the Arthur C. Clark Center for Human imagination. And Sir Arthur C. Clark had many, many aphorisms and quips. And I like to run them by you and get your response to them in sort of a final session before we wrap up when it gets

too late, where it's getting very late and close to evening there. But I want to start with his first and maybe his best known aphorism, which is the following. Any sufficiently advanced technology is indistinguishable from magic. I want to invert that and ask you the following question, Robert. If you're how to communicate to an alien civilization and they're going to come and devour the earth unless Robert Brandenberger tells them, no, don't do it because we have created the following magic. What would that be? Would it be a technology? Would it be a theoretical called discovery? Would it be something you did? What aspect of humanity is sort of the most impressive to you as an insider, but talking to an outsider? Actually, you know, physics is not

the only thing. I think you asked some of your guests also about questions outside of physics. I would actually say that it is all of the art that we have produced. For example, classical music, which I really like. Yes. And all the literature. And I actually view science as in part art. But my pencil and paper scientific work, I think I'm, obliged to sell it a bit as art because our universities are publicly funded.

And we need to give back something. So for me, it's very, very important to give back. But so would I, so I would include Einstein's equations into my list of cultural. things that I would try to use to persuade the aliens not to destroy humanity. I'm sure in your capable voice and mind would be a slam dunk that they should keep us

alive, at least for the entertainment. Another saying, and by the way, I do agree with you 100% because my late great colleague here in San Diego, Hans Parr, who was a student of Leon Letterman's at Columbia, he used to say that relativity, GR, was the culmination of Western civilization. What are you talking about? You know, have you ever seen the Sistine Chapel or, you know, have you ever, you know, heard a Bach fugue?

He said, no, no, no. Because to make relativity, it required the work of thousands of people in different cultures and different nationalities and different locations throughout space and time, language, and deeply influential poetry, and so forth. So I agree with you. And I agree with my late colleague Hans. I miss him tremendously. But it is overlooked because we often think that the main purpose of science is to produce

technology. And I didn't hear any technology in your talk today. And I think that's perfectly acceptable because that's what makes. us uniquely human. You don't look at a baby and say, oh, what technology can it produce? Okay. So I very, very much appreciated what you said, and I do believe it will work to prevent our devouring by aliens. Okay. Next question is, it involves Arthur C. Clark's famous movie, the 2001, a space odyssey. And there are these monoliths. I don't know if you've ever seen it, but there are these monoliths, these kind of, we don't know what they are.

It could be a time capsule. It could be a warning. It could be something ominous. It could be something benign. We don't really know. But I like to think of it as sort of a last will and testament. And I want to ask you, in Judaism, we have a concept called the ethical will, a Zavaha. And the Zavah is what you want to bequeath in terms of wisdom.

maybe knowledge, but mostly wisdom and not monetary. So I want to ask you, if you were to write an ethical will for when you depart the mortal coil at age 120, please, no sooner, what would you put in an ethical will to give as wisdom to generations of not just your biological errors, but your ideological errors that I am lucky enough to consider myself a part of? Okay, I will answer that question from a point of view of a teacher, in particular, from the point of view of a student advisor. And the message will be that every person has their own strengths. And you should build on the strengths and at the same time try to induce the person to work on their weaknesses. Very good. This is something that can be applied in all areas, I think. And I think it's appropriate for you as a teacher, because, as I said, when you told me this thing, I remember it 30 years later.

So it's obviously very meaningful to me about, you know, kind of the obligations we have as employees to our employers and to the pursuit of science and a grand tradition. But I also have scaled that up, that I teach it to my students, you know, who are like your grand students or your grand advice. in some sense. And so it scales. And your lessons live on, and they already are influencing people ideologically. So I thank you for that, Robert. Okay.

We're almost done. Another comment on that. So maybe this is a message to the students who are listening. So this treating your fellow students, realizing that they all have their strengths. That's important also for students. While I was at Brown, I actually saw students discriminating against students,

other students, just because they had different color of the skin and because they had a different scientific background. I remember you were known for having students from this far away as Brazil and as close as New York and Trinidad and it's quite remarkable. But it never, it wasn't noteworthy to me. For some reason, I just thought that was natural of you. And I didn't think, oh, Robert's going out of his way to mentor an African American or a Brazilian or someone from the former Soviet bloc countries.

I just felt that's just Robert. But now I see it is. Unfortunately, I've seen very different things happening. Yeah. So I think you're right. So, but let me ask you one more or two more questions. If you'll pardon and have your patented forbearance and indulgence of me, Robert. And the first one is another quote by Sir Arthur.

Well, I'll give you a bonus quote. So one of his favorite quotes of mine, at least of his that I like, is he says that for every expert, there's an easy. equal and opposite expert. I won't ask you to comment on that, but I do use that on occasion when my department chair gets out of hand. But I will now pivot to two of his final comments. And the first one is this. When an elderly but distinguished scientist says something is possible, he is very much likely to be correct or she. But when he or she says something is impossible, they're very likely to be wrong.

First of all, do you agree with that? Second of all, what have you changed your mind on? What have you been wrong about Robert, if anything? Okay, so in the 80s, I worked on cosmic strings as a competitor to inflation, and the boomerang data proved that this was wrong. So now, on a smaller scale, I often do make mistakes in calculations, and then I have to realize that there was a mistake. And usually, hopefully you catch them when you repeat calculations many times,

but there are some cases when you don't catch them, and then you have to live up to it and write the neuratum. So there's one time when I wrote a paper with a friend of mine, and then we got a letter from a Stony Brook professor saying that, no, we were wrong. And, well, we argued for a while. We didn't just immediately believe it, but then eventually we agreed.

We had been wrong, and then we wrote to an erratum, and then that storybook professor woke back and said, I'm very happy that you wrote this erratum. Fortunately, I've never had to do that in my career. Oh, wow. What that what that

Sony book professor had actually done and then I realized why. Well, I have a special bit of affection for... Can I also tell you something that my de facto PhD advisor, Bill Press. Yes. what he told me,

the advice that he gave me, he said that if you want to do something really new, you have to risk being wrong. And you see, when I'm working on this matrix cosmology, which I'm presented a little bit of, I may be wrong.

They may be, since I'm not as strengthiest, I'm going out on the limb. But it's exciting. And so you have to risk being wrong. And if I'm proven wrong, then I could make sure. Sometimes as a, when I am wearing my podcasting hat, I will say in the name of one of my mentors and podcasting, James Altitcher, he says, I never publish something I'm not afraid to publish.

I think that's an interesting rule. It doesn't mean that you should do stuff that's knowingly wrong or risky and are unethical. But nevertheless, it's good to have that self-doubt. and but also simultaneously to have a little bit of swagger, to have confidence that you've been right in the past and look back not on your, you know, to-do list, but on your have-done list. So the last question, Robert, brings us back to the very beginning, and this is going to be soliciting advice to your former self or a young person. As I said, a lot of young men, young women, listen to this podcast.

I want to ask you in the name of Sir Arthur C. Clark, he said the following. He said, the only way to determine the limits of the possible is to go beyond them into the impossible. So I'd like to ask you, advice to your 20-year-old self, if I could have known you the same age that I started at Brown, what advice would you give that young Robert or anybody as a stand-in for you, to give you the courage to do as you've done? to go into the impossible, the name of this podcast? A big promising area to try to explore and explore it. And not be led by other motivations, perhaps? No.

But you see, I gave this young Robert only two options, one option, a business career, And the other option being a teacher, for example, at a community college or in Quebec, Sejep or in Switzerland, it would be gymnasium. I didn't give that person the option of wanting definitely a research professorship at a major university. Because you didn't think it was possible or it was so out of the realm of possibility, or it was just too grandiose at the time? Why did you not give that young Robert that opportunity? It's, see, it's something that you can, you can dream of, but you shouldn't consider that to be a probable possibility.

I didn't. Yeah, me neither. I didn't even believe it until maybe after I became a professor. And actually, I don't think, I mean, you touched on this briefly, but I'm worried about the future. Right now, we had a fact. search for a teaching faculty, we got 200 applications for one position. I joke that, you know, there are more people playing in the professional NBA, or let me turn it to the Canadiens up there in Montreal. There's way more people that are, you know, in the National Hockey League or in the

Canadian Hockey League than our cosmology professors. And yet, and yet there's perhaps five times as many people who want to be that, that are in the minor leagues, if you will. And I'm not saying that pejoratively. I'm saying there are postdocs. Are there too many of them? Are there too many graduate students? I think overall, there's not enough. I think I would love to have a million cosmology students and postdocs and professors if it could be sustained, because I think that could lead to our flourishing as a species. And physicists, in general, mathematicians, but right now, I think we might have too many. What do you think?

I think we have too many people who are dreaming only of a academic career at a major research university. And you don't have enough who would be eager to go into a teaching career at a lower level position. Well, I have to say, Robert, that you are in no small part to blame or to thank for setting me on a path as a paradigm. Again, I'd never thought, you know, Stefan and I, we were in Barrison Holly room, you know, 144 in the basement dungeon down there. We used to call it. And you'd come by every now and then. And you were inspiring to us. But we never thought we'd be professors, him at an Ivy League school, me at a top

research university as well. We never thought we'd be professors. But that didn't stop us from being fascinated by what you were teaching us inside and outside of the classroom. And so on behalf of me and my students and my future students to come, I want to thank you so much, not just for being on the podcast. And I hope this will only be a part one. and I hope part two will be in person at some point because I miss you and I would love to be, you know, to see you in person.

But I hope this is just the beginning of our rekindling our connection if you'll, if you'll again indulge me with your patented forbearance. Well, I'm very proud of what you've done. So it's always nice to see students succeed. and that's one of the pleasures of being a professor to succeed and having fun and doing you a thing. It is. It is a great source of satisfaction. Robert Brandenberger, professor, a long-time inspiration to many young generations of cosmologists and future and in the present. Robert, thank you so much for joining us. Enjoy your evening. And I do hope, as I say, we'll see it be important. person not too long from there. Thank you very much for the invitation.

Any sufficiently advanced technology is indistinguishable from magic. Thanks for listening. Keep in touch, inspired and informed by signing up for Professor Keating's Monday magic email at briankeating.com slash list. And if you have a dot edu domain, we'll send you an artifact older than the earth, forged in the fire of an exploding star in the form of an authentic meteorate fragment. Thanks to all our viewers and listeners for helping us reach 150,000 subscribers on YouTube and putting us into the top 1% of science podcasts.

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