Sean Carroll's Mindscape: Science, Society, Philosophy, Culture, Arts, and Ideas - AMA | June 2024

Episode Date: June 3, 2024

Welcome to the June 2024 Ask Me Anything episode of Mindscape! These monthly excursions are funded by Patreon supporters (who are also the ones asking the questions). We take questions asked by Patreons, whittle them down to a more manageable number -- based primarily on whether I have anything interesting to say about them, not whether the questions themselves are good -- and sometimes group them together if they are about a similar topic. Enjoy! Support Mindscape on Patreon. Blog post with show notes, questions, and transcript: https://www.preposterousuniverse.com/podcast/2024/06/03/ama-jun-2024/

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Hello everyone. Welcome to the June 2024. Ask Me Anything Edition of the Mindscape podcast. I'm your host, Sean Carroll. Been a busy month here, of course, because I had a book out. That's always a busy month when a new book appears. The biggest ideas in the universe, Volume 2, Quanta and Fields, was published this month. So there was a little bit of touring around, very little bit, you know, got on the train. I didn't even get on an airplane to do this tour. So Boston, New York, Pennsylvania, Maryland kind of thing. And gave talk. about Quanta and Fields. And it was a little bit of an experiment, both giving the talks and the book itself. And I've been 90% pleasantly surprised, I would say, at the reception of the book. Because you all know by now, most of you know, the idea behind this three-volume trilogy of books is talking about the big ideas in modern physics, the established ideas, not the speculative ones, the ones that will still be true, 500 years from now, for a broad audience, but showing you the equations, teaching you what it means to understand the math, what the symbols

mean, really understand the quantitative way in which professional physicists think about things without being a textbook, without expecting you to grow up to be a physicist someday. That's an experiment. That's not a niche that is heavily populated in the popular book world. And for giving talks about it, you know, Volume 1 was classical physics and up to relativity. And I could pick out one equation, which was the culmination of that book, namely Einstein's equation for general relativity. And it's a complicated thing. It involves tensors and indices, Greek letters, but you could build up to it. And in one single, one-hour talk, you could teach people what that equation really meant. No way of doing that for volume two. Volume two, quantum and fields, teaches you quantum mechanics,

but just in a very quick, here's three chapters on quantum mechanics, and then really goes in to quantum field theory in the standard model. There's a lot going on from Feynman diagrams and Lagrangians to gauge symmetries, effective field theories, symmetry breaking, fermions and bosons. There's just an overwhelming amount of material in the same number of pages in volume two as in volume one. So there's no sort of single idea that it leads up to. There's many different ideas.

I took the poll on Patreon. You know, many of you know, Mindscape listeners, we have a Patreon that you can support. support, patreon.com slash Sean M. Carroll. And those are the people who ask the questions for the Ask Me Anythings that we're doing like right now. And sometimes I also ask the Patreon supporters for other advice, for example, what to talk about in a popular talk or a podcast about the book. And the idea that came through over and over again was symmetries, gauge theories, symmetry breaking, that kind of thing. So for the talk, I tried to, get into that. You can't do it at the level of equations in a one-hour talk. In the book,

it's done at the level of equations, but I tried to get across in some pictures and hand-waving, literally, as well as figuratively, the idea of what a gauge theory is and symmetry-breaking. The Higgs mechanism, confinement, all those things. And I was a little worried it wouldn't work, but people seem to really like it. You know, it's abstract, right? But the people who had the gumption to actually come to the talk, seem to be happy with it. You know, you can kind of tell. No one after the talk is going to say, ah, that sucked. But they will say, oh, yes, good that you gave a talk. But after this one, they were really enthusiastic. So it's similar to the solo episode I did recently. But there in the solo episode, I had the time to get in a little bit more to where particles come from,

from fields, and doing gauge symmetries wasn't quite as central. So hopefully on YouTube at some point before too long. There'll be a version of the talk if you want to see that. The pictures are nice, I got to say. And likewise for the book, the good news is it made the New York Times bestseller list slightly higher than volume one did. So that was very good news. Keeps my streak intact since the big picture of being on that list, which the publishers really like that. And of course, and look, this was 100% predictable. I 100% expected this, but opinions differ. about the book from professional reviewers as well as the people who leave comments on Amazon.com or wherever Goodreads, various book reviewing sites. This is why I try very, very hard to be

honest with people about what's in the book. There's a lot of equations in the book, and I do try to explain them. I try very, very hard to put a lot of effort into that. Some people are just not happy with that. And one thing that happens is, if you write more than one book, people expect all of your books to be pretty much the same, including being at the same level, right, the same challenge to read for the same audiences. Let's put it that way. I just can't do that. I can't live that way.

I like to write different kinds of books. This kind of book is for people who are interested in that deeper knowledge that want more than the hand-wavy stories. So before recording this intro to this AMA, I went to Amazon to look at the most recent reviews. of quanta and fields. And what I saw was exactly kind of what I anticipated. And still, sort of, it makes me a little sad that it's not overwhelmingly positive. But the very first, most recent review says, The Biggest Ideas in the Universe by Sean Carroll is a colossal letdown for anyone

seeking an accessible exploration of the profound concepts it promises to unveil. Market it as a gateway to comprehending the deepest mysteries of the cosmos, the book is instead a dense, impenetrable thicket of esoteric jargon and mathematical formalism, utterly impervious to the uninitiated one star out of five. You know, you're going to get some of those reviews, I definitely do. But then the very next review, or really the previous one, because it's some sort of reverse chronological order, says, I've read an uncertain number of quantum mechanics, pop science books, and I grew tired of the handwavy explanations of underlying concepts. And every now and then, one of these books would, in hushedones, hint at the

fact that there's an even more mysterious and complicated theory describing almost all of physics, quantum field theory. Dot, dot, dot. Major credit to Carol for finally writing a book that takes you beyond the pop science and into the equations, because the most amazing insight about our world is that you can really derive it from a few entirely mathematical principles, and quantum field theory suggests that nature just played with the simplest possible configuration of those principles to shape our universe. You cannot possibly understand that unless you look at these equations. So if you want some unbelievably quasi-religious insights into how our universe works, you really should read this book, five stars out of five. Again, this is more or less what I had

anticipated slash hoped for. For the right audience, I'm glad to see that the book is doing what I hoped to do. The audience is not everybody, and I try to be honest about that. I can see, when I write eventually the physics of democracy, there's going to be no equations in that book. It's going to be like a lot of fun stories and anecdotes and historical examples. I predict right now I'm going to get complaints that there's not enough equations and it's not high enough level of physics because people want the same thing over and over again. Anyway, I hope those of you who have read the book or listen to the podcast or whatever got a lot out of it. I'm having a lot of fun. I'm deep into writing Volume 3 and it's just tremendous fun.

Volume 3, Complexity and Emergence, is the dessert course of this three-course meal in the trilogy. And the topics are amazing. I'm still debating whether to sneak in a chapter on causation. I think I might. But it depends on the length. You know, we have an agreement with me and the publisher about how long these books are going to be. I have to reel myself in sometimes. But many thanks, as always, for those of you who listen to Mindscape and support it.

I get a lot of very useful feedback from all of you, and that's why I love doing these Ask Me Anything episodes so much. So let's go. Brendan Kay says, Suppose you had countless humans in a massive network of interlinked space stations, manually performing digital operations, perhaps with punch cards or some other primitive computational technology, that in total simulate vastly more slowly all the sensory inputs and computations of a human nervous system. would this interplanetary machine feel like a human, or do you think there is something inherent to the size, speed,

and or medium of the neuron that allows for our conscious intelligence? Clearly, this is a very similar question to the Chinese room experiment suggested by Frank Jackson years ago, where he said, if we had a room, I'm not going to get the details exactly right, but if we had a vast room with a card catalog inside, where the cards matched up in certain ways so that you could have input in English, and then it was input in English,

and then thinking in Chinese or the other way around. Yeah, I think that there's a person inside who could get input in Chinese and then go through the card catalog and do various things, various operations, then put out an answer in Chinese that would appear to the outside world like it was conversing. They didn't have large language models at the time, but it's the same basic idea. and Jackson's point was supposed to be

Wait, was it Frank Jackson? No, it was John Searle. Frank, oh boy, I'm not on my game today already. It's very early in the AMA. This is John Searle's experiment, of course. Frank Jackson was Mary the Color Scientist, confusing my arguments for non-physicalism about consciousness. Anyway, Searle's point was supposed to be,

surely you don't think, that this big room with cards in it is conscious, even though it would pass the Turing test or whatever. And here we're doing something a little bit similar, with space stations that are interlinked with each other. And the difference is in Brendan's question, it's not just words coming in and out. You're actually simulating all of the neurons, exactly.

So I don't think that there's anything inherent in the size speed or medium of actual physical neurons that allows for conscious intelligence. But there are real world limits to analogies like this also. one is, of course, we are more than our neurons, right? There are inputs and outputs from those neurons. The neurons in a human being are embedded in a body. There are just cells in the brain other than neurons, right?

And some of those inputs that we get are endogenous, as we say, from inside our body, some of from the outside world and whatever. It might make a huge difference to not have your brain embedded, your brain, embedded in your body. So maybe you want your system of space stations to include not just neurons, but everything going on in your body and it's immediate outside. And having done that, there is an issue of time scales, right? The time it takes signals to go back and forth from neurons or other cells in your body is relatively short. When it comes to space stations, there's the speed of light, which slows things down. And so the rate of the rate of

of thinking of some kind of chain of space stations like this would be much slower. The being would not have time to have a lot of thoughts in the amount of time it takes human beings to have thoughts. But with all those caveats in mind, sure, that would be 100% conscious. This is what is known as the idea of substrate independence of consciousness. It doesn't matter what the individual pieces are made out of. What matters is the information flow and computation and the results of computation action that goes on as a result of those things. And I get the intuition here because we think of this system of either the Chinese room in Searle's case or the space stations in Brendan's case. We can think of it as living inside, as us living inside it, right?

You know, we're here on Earth looking all those space stations, bouncing signals around. It doesn't look to us like a living conscious being. But if you zoom out, so you look at it from afar, so that this set of space stations looks like billions and billions of neurons bouncing back and forth, and you slow down your view of it so that it is effectively thinking just as fast as a human being, it would be just like a human being. It would be just as conscious as that. So I think that rather than actually being an argument against the physicalism of consciousness, these kinds of arguments are arguments against taking your intuition too seriously when you push that intuition into circumstances that are far, far, far beyond actual experience that we have in our everyday lives. Because our experience is trained on certain subsets of possible things happening,

and therefore when you imagine things outside that subset, it's easy to go astray if it's your intuition that you're relying on. Matthew Hines asks a priority question. Remember that priority questions are for patrons, people who support on Patreon, can not only ask AMA questions, but unfortunately we don't get a chance to answer all the AMA questions because there's too many of them.

So the priority question idea is that once in your life, you get to ask a question and I will do my best. best to answer it. So Matthew's question is, I'm working on a science fiction story, and I'm wondering if you could help me with something. For reasons that are vital to the story, I need a method of space travel that circumvents the light barrier, which is not a warp drive. So in other words, he needs something that is not a warp drive, but nevertheless lets you go faster than light. My conception is a burst of energy that tears a hole in the spacetime fabric, giving access to a kind of hyperspace through which vessels can pass. A trip to Mars from Earth is done in a subjective

instant, while trips to nearby star systems take a few minutes to a few hours, with the further reaches of our galaxy taking no more than a few days. Can you think of anything that would give scientific gloss to this idea? I realize it's a horrible affront to the laws of physics, but please trust me when I say that it's vital to the story and absolutely cannot be warp drive. I mean, I can tell you the obvious answer, which is you need a temporary wormhole. Wormholes are what you need when you don't want to use a warp drive and you want to get across vast distances in a short period of time. You need some shortcut through space time. And having a wormhole, you know, a little tube that connects two different regions of space time with a much shorter distance than it would

take if you didn't go through that tube, it's very natural for wormholes to be temporary. They want to be temporary. In the real world, as far as we know, even if you could make a wormhole, you couldn't actually travel through it because it would just collapse quicker than you could possibly travel through. There's always, that is, there's always the limit of the speed of light to travel when you're in the wormhole, and the wormhole tends to collapse faster than the time it takes light to go from one end of the wormhole to the other. So wormholes are generically non-traversible. Now, that's not a theorem. You can always play with things and try your best to build reversible wormholes, and that's what Kip Thorne and his friends talked about many years ago. But it's not at all hard to imagine

that if you allow yourself the gimmick of making a wormhole that you can travel through, then it would effectively close very quickly. So it wouldn't be like a permanent subway tunnel. It's just a temporary shortcut. One thing to keep in mind is when you say things like trips to nearby star systems take a few minutes to a few hours, you still have got to remember the theory of relativity. What does it mean to take a few minutes to a few hours for something that is effectively faster than the speed of light? You have to take relativity in account in whose reference frame is it taking a few minutes to a few hours? That's potentially an answerable question.

Maybe it's in the reference frame defined by the people who first did the explosion or whatever. I'm just saying that you have to take that into consideration. Anonymous says, as an expert in the field, what would you suggest is my responsibility to raise a voice that my field is getting excessive funding relative to a realistic expectation of societal benefit? I'm working in quantum computing adjacent fields for about 10 years, and I think you could classify me as a specialist. Based on my understanding and extrapolation of the rate of progress, I feel confident that there's no reason to expect it to provide practical benefits in the foreseeable future. It is pretty clear that the investments in the field are based on false

premises, plus you have to oversell to get the money attitude. The investments are also at the level of spending by governments for major humanitarian causes. So sadly, I feel obliged to advocate for reducing the funding. As you can imagine, that's very unpopular. What would you say I can, or I should do. I would say, you know, this is an individual thing. I think you have to answer for yourself what your standards are, but I think roughly there's not a moral argument that says you have to advocate for less funding for a field you think is interesting. I mean, if you think it's intellectually interesting, apart from the possible benefit to humanity, then you can make a good faith argument that it's worth funding. What I do for a living, I do not do because of potential improvements in

human standards of living or anything like that, I do it because we want to know the answer, and people are willing to pay some money to know the answer. We paid $10 billion for the Large Hadron Collider with essentially zero promise that it was going to lead to any technological benefit. We just want to know the answer. You can say the same thing for space telescopes and things like that. On the other hand, you shouldn't lie. You shouldn't say that there will be improvements in technology or whatever if you think that that's not true. I think that in the fields that I'm in anyway, I feel perfectly happy saying true things about the value of my field and advocating for funding for it. There's nothing wrong with that. I think that, so the issue here

is not whether or not your field will lead to improvements. That's hard to say, right? I mean, maybe you're right that it won't or is unlikely to, but it is hard to say. But it is easy to say that you shouldn't lie, that you should do your best to tell the truth about what the prospects are and nevertheless make whatever arguments you should or you can think of for funding for the field. I'm going to group three questions together. This was a common topic this week and for very good reasons. A goon in the gooniverse says, when a physics student starts out, they learn about particles. In grad school, they find out particles are actually excitations in fields,

and fields are fundamental things. Feynman gave us a way to understand field interactions using particle-like pictures, but it's all field theory. Similarly, when a student opens a textbook on string theory, it will begin by minimizing the action of a string's world sheet. But what are the underlying objects in string theory? Are strings like more complicated vibrations in a field, or is it something else?

Chris Mason says, I've listened to Minescape for a number of years and watched all the biggest ideas in the universe video series. Looking back, I am delighted with how much I have understood, including a popular level understanding of quantum field theory. However, listening to your latest podcast on string theory, I realized it is not clicked for me where string theory fits in with quantum field theory. If string theory turns out to be correct, does that mean QFT is wrong? Or would it be better to think of QFT as a limit of string theory in a particular regime?

And finally, Connor says, most succinctly, which I am in favor of, everyone who can write their questions succinctly, please try to do that. Quantum field theory says particles are really vibrations in quantum fields. string theory says particles are really strings. What are strings from the perspective of quantum field theory? These are a perfectly reasonable set of questions, ones that I had myself back in the day, especially when I was a grad student first hearing about these ideas. You learn when you take quantum field theory that particles, as we've said here, are excitations in quantum fields. A quantum field, when you take a field, which doesn't look at all particle-like at the class, classical level, and you apply the rules of quantum mechanics to it. So just like a harmonic

oscillator or an electron in an atom, suddenly you have energy levels that are discrete, and it turns out that those energy levels behave and act like sets of particles. So a quantum field can simultaneously describe zero particles, one particle, two particle states, and so on, all the way up to as many particles as you might want. So in a very real sense, that's a unification of the idea of particles and the idea of fields. It doesn't mean you can't talk about particles. Particles are perfectly good ways of talking about. That's what Feynman diagrams do.

But it suggests that at a philosophical level, the fields are the more fundamental things. And then string theory comes along, and string theory tries to generalize the idea of particles, which are point-like things, zero-dimensional, right, to the idea of strings, which are little one-dimensional, either line segments or circles.

And you can talk about those strings interacting and vibrating in different ways, et cetera. So it is very natural to ask what is the string theory version of field theory? What is the more fundamental thing, the excitations of which look like vibrating strings? And people have tried. People talked about doing this.

There is something called, guess what, string field theory. But, and you can look it up. There was actually just a review article by Ashok and Barton's Feedbox just the other day that appeared. So it's an ongoing research area. What is string field theory? It is slowed down for a couple of reasons. One is we're not really sure what string theory is.

We're pretty sure what quantum field theory is and what particles are. But you can see papers by people like Joe Polchensky called What is String Theory? And we're not exactly sure what the answer is. And you might say, well, how do we not know what string theory is with all these people working on string theory? The answer is we know certain aspects of string theory. We know certain versions of it and certain limits, as we talked about with Khamunvafa, et cetera, without necessarily knowing the complete once and for all story of it. That's not actually so difficult to wrap your brain around.

So it's not clear whether it is useful in the context of string theory to do the same thing you did with quantum field theory. that is to say to come up with a string field, a string version of field theory, the excitations of which are strings. Now, string theory reproduces conventional quantum field theory in the limit where the length scales you're looking at are much larger than the sizes of the string. And usually the strings are the plank scale across. So as long as you are looking at lower energies than that, longer wavelengths than that, things will look like quantum field. theory, that string theory reproduces the successes of quantum field theory. But whether string field theory is the best way of thinking about string theory still seems, as far as I can tell, to be an open question. One more important thing to say here is there's different ways of thinking about

quantum field theory. There's one way which says start with a classical field, quantize it, see that particles pop out. That is the way that I like to think about. about it myself. That's the way I talk about it in the podcast we did recently, the solo podcast, or in the book, Quantum and Fields. Start with the field, quantize that particles come out. But there is another way of thinking about quantum field theory, which starts with the particles. Start with a quantum mechanical theory of different kinds of states, different factors of Hilbert space, one of which describes zero particle states, the vacuum, one of which describes zero particle states, the vacuum, one of which another part of Hilbert Space describes one particle states, another part

describes two particle states, and so forth, the whole collection of all of them, and invent the rules that obey, you know, features like locality and Lorentzenvaryance and things like that for interactions of the particles within this theory that allows for different numbers of particles to be created or destroyed. And what you discover by doing that is that you have reinvented quantum field theory. So in other words, at least in certain limits, let's put it that way, at least in certain circumstances, the map between fields and particles goes both ways. You can either start with a classical field quantizing and get particles out, or you can start with an arbitrary and possibly changing number of particles and superpositions of number

particles and discover that it's really quantum field theory. So when people do string field theory, it's more like that latter way of doing it. It's not, again, I'm not an expert on this, so maybe things have changed, but in my very limited experience, they don't start with something that is the string theory version of field theory, quantize it, and find strings popping out. They start with Hilbert space that can describe different numbers of strings and allowing those strings to interact and change the number of strings and so forth, and put it all together to make something called a string field theory. Whether or not that that has been very successful so far, you would have to read the papers out there, but it can be done. Mark Slight says, could you talk a bit about

this problem of energy not being conserved when a wave function collapses? How problematic is it? Is it treated differently in different quantum mechanical theories? Is it a serious problem? Yeah, it's not a problem at all. It's zero problem, really. It's just a fact. The two, for those of you who don't know, well, in quantum mechanics, there are two different ways that wave functions evolve, according to the conventional Copenhagen textbook version that we tell our students about. One way is the Schrodinger equation. That's how wave functions evolve when we are not measuring the quantum mechanical system. And when that's true, as long as the law of physics, the Schrodinger equation, at the technical level, the Hamiltonian, as long as those

are independent of time, then energy is perfectly conserved. And that's exactly like classical physics, as long as the laws of physics are independent of time, Nerther's theorem tells us there's a conserved quantity. That's energy, okay? But in quantum mechanics, we have this other way for quantum states to evolve, and that is what happens when you do a measurement. The way function collapses, you're in a different state after the measurement. You're in the eigenstate. You're in the eigenstate of whatever observable it is that you are measuring. And typically, you have two options here. One is you can say, well, there's no such thing as energy. I don't know what energy is, so it's meaningless to say that energy is not conserved during that process. Some people take that

attitude, okay. But there's another thing you can do, which is a more straightforward thing, which is to say, look, when you weren't measuring it, there is a conserved quantity that is an energy. It is what we call the expectation value of the Hamiltonian, the expected value of the energy under observations. And so if you have a state where you can observe different things and maybe you can observe the energy directly, right, and you would get an outcome, but you're in a state where you could get different outcomes for the energy, just like if you're in a superposition of different spins or positions, you could get different outcomes for that. You can take the average. You

can take the weighted average of the value of energy you might observe times the probability of observing that. And that quantity, the expectation value of the energy, is perfectly 100% conserved under the Schrodinger equation. That's exactly the quantum mechanical version of Nerther's theorem. It is not conserved when wave functions collapse. And this is one of those facts that is sort of both trivially true and very surprising to people, even professional physicists, when you tell them about it, because they will say, well, that's because the energy went into the environment or you're measuring apparatus or whatever. And no, that is not right. They are wrong.

So Jackie Lodman and I wrote a paper very explicitly pointing this out. And, you know, as usual, as predictable, the response to the paper was half of the people said, this is so obvious, why are you even bothering? And the other half said, this is completely wrong, why are you even bothering? So that's why it was a worthwhile paper to write, I think. But it's not a problem. Why would it be a problem? It would be a problem if it didn't fit the data.

That's what's a problem. You might not like it. You might think it is inelegant, or maybe you want to hope that the ultimate laws of physics don't have this feature. That's okay, because we don't know what the ultimate laws of physics are. As we point out in our paper,

whether or not energy really is conserved, will depend on your favorite attitude toward the foundations of quantum mechanics. In many worlds, it is conserved in the wave function of the universe because the wave function of the universe always obeys the Schrodinger equation. It is not conserved from the point of view of any one observer because one observer does not see the whole wave function.

They only see the branch that they're in. And so experimentally, you could absolutely see the average energy change. It's hard to know that it's changed because it's hard to know what it was before and after, but in principle, you could see that happen. In other theories, like objective collapse theories, the energy just changes, just not conserved during wave function collapse. Up and until you do an experiment that either confirms or falsifies this prediction, there's nothing problematic about it.

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almost always there are good reasons why those scenes were deleted. They're not as good as what's in there. And, you know, sometimes this happens when you're writing a book. Um, not only do you write more than you need, but some of it you realize, yeah, you didn't really need to write that. It's not very good. So the parts that I wrote about symmetries and whatever are, you know, dug into details about discrete groups like the triangle group and the square group and whatever, and a little bit of details about what kinds of matrices represent different smooth group transformations like SU2 and SU3 and so forth. All of it is sort of kind of small, it's kind of specific, and not that deep, really.

So I don't think the world really needs that. There's better places to go if you want to look about into group theory for its own sake rather than as we use it in physics. Tyler Smucker says, in one of the biggest ideas in the universe videos, you were wearing a shirt that said, licensed quantum mechanic. Where did you get that shirt? I want to buy one. You can't buy it.

Sorry, those shirts are given out to people who either have taken and passed or taught physics 125C at Caltech. At Caltech, there is a year-long course for juniors on quantum mechanics, physics 125, A, B, and C, because we're on the quarter system at Caltech. And Mark Wise, who taught 125C for a long time, invented a tradition where at the end of the day, at the end of the quarter, he would hand out free t-shirts to everyone who passed the course. And so I taught the course one year. I followed up the tradition, and I got my own t-shirt. that year, licensed quantum mechanic. So I can't give it to you unless you went to Caltech and passed the course.

However, I will point out, as long as you promise not to tell anybody, it's not that difficult to get a black t-shirt made with whatever words on it you want. So go for it. Nicola Ivanov says, is each point of the vacuum state a virtual superposition of all the quantum fields of quantum field theory and random quantum fluctuations can potentially make this point to be part of a quantum state of any field? In other words, is each point of the Hilbert space pregnant with all the particle, gauge, and scalar fields of the theory? I'm not sure I understand this question. Sorry about that. But let's approach it slowly. Let's think classically first,

okay? Classically, at every point in space, in a field theory, in a classical field theory, there will be different kinds of fields. Maybe the electric field, the magnetic field, and the gravitational field and the Higgs field or whatever. Those are all perfectly good classical behaving fields. It's easier to imagine classical behavior for bosonic fields than fermionic fields, but you could do it for fermions also. But the point is that they're all separately there at every point. So at the classical level, the space of states involves what the fields are doing, what each field is doing at every specific point. Now, once you're in quantum field theory, you create a Hilbert space out of superpositions of all those possibilities.

So I think maybe this is what you're getting at. The Hilbert space is the set of all possible superpositions, of all possible values of all the fields at every point. There's a lot going on in quantum field theory. But yes, the fields are there at every point in possible superpositions of everything you could possibly measure about them. Eric Chen says, Love the new episode with Khamra.

Could you give an intuitive explanation for what compactification is? What exactly does it mean that extra dimensions are compactified onto a six-dimensional Taurus or a Kalabiao manifold? Possibly, probably nonsensical third part of the question. Could we have classical theories in, say, 11 dimensions, but with the extra dimensions suitably compactified so as to yield our standard classical macroscopic physics? So yes, let's go with the third part first. Classically, absolutely. You could imagine classical

compactified theories. Indeed, the whole idea of compactifying, which was really first pursued by Kaluza and Kline, was an immediate spin-off of general relativity before we had a complete theory of quantum mechanics, much less quantum field theory. Kaluza-in-Kline noticed that once you had general relativity, so once you said that space time itself has curvature and a metric and is dynamical. You can imagine that a dimension of space time is compact. You know, compact doesn't mean small. It means in strictly mathematical language, it means topologically it's compact, which means it's not infinitely big, but it could still be finite but big, right? So a compact dimension could be topologically a circle, but it could be a very,

very big circle. Indeed, it's possible that all three of our observed dimensions are compact in some sense. However, usually, informally, when we say compactified as physicists, we also mean small, invisibly small to us. So Kaluza and Klein realized that if you had a circle as an extra dimension, there's instantly a symmetry in your theory because you can put whatever coordinates you like on that circle. So this is a gauge theory. This is a gauge invariance because at every different point in space, you could separately rotate your circle. And indeed, that is a U1 gauge in variance. If you put coordinates so that the circle is coordinateized by complex numbers, like E to the I theta,

where theta goes from zero to two pi, and theta tells you where you are on the circle, I can separately rotate theta at every point in space that is a U1 gauge invariance, almost exactly the same as electromagnetism. This was the reason for the original excitement about Kaluza Klein theory back in those days. Maybe it is a way to unify gravity in electromagnetism. Einstein was extremely excited by this possibility. It doesn't get you exactly conventional electromagnetism

because you have another thing that you can do with that circle, which is it can get bigger and smaller. So to the outside world, to people who are much larger than the size of the circle, that is a field. The size of the circle shows up as a field, as a scalar field in our ordinary macroscopic world, sometimes called the dilaton or the Kaluza-Klein scalar or what have you, and we don't have any evidence for such a field in the real world. And furthermore, you would like it so that you not only compactified the extra dimension or multiple dimensions, but you stabilized them.

as well. And this is something you can talk about classically. So the size of the extra dimension does, and the shape for that matter, doesn't want to shrink down to zero or expand to infinity. When Khrmunvava was talking about the difficulty of getting a positive cosmological constant in string theory, one of the things that is driving that intuition is that when you compactify extra dimensions, there's always a way to make the vacuum energy zero by many. making the extra dimensions bigger. And so if the vacuum energy is positive, and there's another way that you can arrange the extra dimensions of the vacuum energy is zero, that's going to have lower energy. Zero is a lower number than any positive number. So you can't perfectly stabilize

the extra dimensions, but maybe you can temporarily stabilize them. That would be the hope. So anyway, that question is the easy part of your question to answer. So I'm not quite sure what you mean by an intuitive explanation for what compactification is. Let me give the following stab. Remember that we're doing field theory. So remember that we, because as I said before, string theory reduces to field theory in the limit where you're much bigger than the strings. Let's imagine we're doing that limit, okay? So we're doing field theory on space time multiplied by a small compact spatial manifold, like a circle or some six, dimensional globial manifold or whatever. So you have fields that can take on every value at every point

in our observable space and in this little compact space. Okay, so the fields take on values everywhere. But the compact spaces are very, very small. So if the fields are exactly constant over the extra dimensions, that's fine. That doesn't cost any energy, right? It costs energy when the fields change from place to place, but when they're constant, it doesn't cost any energy. And if the extra dimensions are very, very small, then if those fields change at all from place to place within the extra dimensions, it costs a lot of energy. So therefore, in our low energy, late universe, where we live right now, it's almost like the extra dimensions aren't there. They give rise to extra fields, like that diletton field, or maybe like the electromagnetic field or other gauge fields

etc. But they don't, you're not, you can't see them. You can't see them directly because because they're small, it takes too much energy to see them. In quantum field theory, short distances are coupled to high energies. And so that's why people will sometimes say you need to build a particle accelerator that smashes particles together at the plank energy in order to reveal the extra dimensions or other signatures of string theory. So, of course, you're going to get different signatures depending on what the extra-dimensional shape is, but that's why we pay string theorists to figure that one out. Emmett Francis says,

I just had the chance to teach my first lecture in an engineering mathematics course, and it was challenging. Do you have any go-to tips for keeping students engaged during lecture while effectively and efficiently teaching the material? I mean, I don't have a short list or anything like that. You know, I think it depends a lot on what you're teaching, what the goals are of the course. I do vividly remember one anecdote that was in the introduction to a book, a textbook that I used as an undergraduate for a course on mathematical physics. So I don't know, you say engineering mathematics. I'm not exactly sure what that involves, but very often in an undergraduate physics curriculum, there will be a course called mathematical methods for physicists. And you'll learn about Fourier transforms and complex analysis and other things, you know, vector calculus, things that appear over and over again in different physics courses, better just to teach them in a single unified math

course, so the thinking goes, than to sprinkle all of those nuggets of wisdom among many different actual physics courses. Whereas something like differential geometry only appears in your general relativity course, and therefore you learn it there. Okay. But anyway, this intro to the textbook said when the author in his voice was writing, when I first started teaching, when I first started teaching, I forget what the book was, sorry, so I can't give the person credit. When I first started teaching mathematical physics, the students kept asking me for applications of the different ideas. And so I went to one of my senior colleagues and said, what do you do when your students ask you for applications of the concepts you're teaching in mathematical

physics? And the senior colleague said, I give them to them. The idea being that if you're teaching an engineering math course or mathematical methods for physics or for by biology or whatever, presumably every mathematical thing you're teaching is being taught for some reason because you use it for some engineering purpose down the line. So let them know that, right? Don't insist that we're going to study math for its own sake. Studying math for its own sake is great, and there's a way to do that, namely take a math course, and they can prove theorems and have epsons and deltas and what have you. But for a kind of applied math course, it's super important to keep people aware of why you're learning this. You know, I tell the slightly

amusing story in quantum fields that when I took that very mathematical physics course I'm talking about, when we were first taught Fourier transforms, I thought, wow, this is just totally useless and kind of tedious, but I guess I got to learn it just to pass the class, even if I never use it again. Of course, it's the most useful thing in the world once you start doing field theory and quantum mechanics. So tell people why. you're doing it. I think that's the single most important thing for the question you ask, which is how to keep people engaged. Of course, how to be a good teacher, how to get the lessons and the ideas across, that involves a lot of work, a lot of different strategies

for that, probably more than I have time to go into right now. Razie Ahmed said, Komran Vafa made a comment that the dimensionality of space at the very beginning is ambiguous, i.e. it's not clear whether to think of space as a zero-dimensional object or just a very small three-dimensional object. Did I understand that correctly? If it is that space was a zero-dimensional object at the beginning, did space ever go through a one or a two-dimensional existence? Well, we don't know. I think the right way to interpret what Komeran was saying was when you get either the compact dimensions or all the dimensions that we live in right now, small enough, small enough that quantum gravity becomes important. You know,

know, just as we say over and over again in quantum mechanics, there's not really any such thing as the position of the electron. There's a wave function that can tell you the probability of seeing different outcomes if you measure the position of the electron, but there's not a pre-existing thing called the actual position of the electron. Likewise, for dynamical space in quantum gravity, there's no such thing as the size of the extra dimensions or maybe even its dimensionality. That's sort of a limiting concept in the big classical limit. We don't know what was going on near the Big Bang as far as the dimensions of space time are concerned. Kermun Vafa actually wrote a well-known paper with Robert Brandenberger many years ago

where they studied a scenario where all – so if you're a string theorist, you believe there are 10 dimensions of space time, therefore nine dimensions of space, they imagined a scenario where all nine dimensions were compact and small, and they pointed out that if you had strings wrapped around these dimensions, You can easily come up with a scenario where you make use of the fact that the thing that is special about three dimensions of space is that strings intersect in them. If you have strings moving in three-dimensional space, they will generically run into each other, right? If you have points, two dots in three-dimensional space moving around, they will generally never hit each other. You can infinitely finally tune them so they do, but generically they.

won't. Whereas strings in three dimensions will generically hit each other. In four or more, even strings will not generically ever intersect each other. So Kumrun and Robert invented this theory where three dimensions of space started growing because basically the strings that were holding them together unwound because they kept intersecting in three-dimensional space. So that's the Brandenberger Vafa cosmology scenario. I think, it's cheating a little bit. I think it doesn't really work for arrow of time type purposes, but it's certainly a very fascinating idea. I often had the opposite idea. So, like, motivated by the arrow of time, I've always thought that these initial conditions that cosmologists

tend to imagine are super duper finely tuned and unfair. So why would all the dimensions of space be small at large times? So I've often imagined, well, what if all the dimensions were large, could you compactify some of the dimensions? Could you go from all large dimensions to smaller dimensions? And I wrote a paper with Matthew Johnson and Lisa Randall where we suggested exactly a way to do that. Our method doesn't quite play well with string theory because it's based on positive cosmological constants, but it is an intriguing possibility. So the point of this, the lesson here is that we have no idea whether how many dimensions were big or small at very, very early times. This is something where we have no data, so we're free to speculate.

Vicon Vorparian says, why is Petrus wine one of the most expensive Bordeaux wines, about $2,600 for a regular-sized bottle? Did you get to taste it when in France, and is it worth it? So, no, I have never got a chance to taste Chateau Petrus. I have gotten chances to taste various expensive Bordeaux wines. Probably the most expensive I've ever tasted was a bottle of 1982 Chateau Margot. You know, for these expensive wines, the vintage, the year that they're from, makes a big difference to the quality and the price also. 82 was apparently, I'm not quite enough of an expert to really verify this from experience,

but it is said to be a classic amazing vintage for Bordeaux. And so Chateau Margot is one of the first growth, that is to say, highest quality by the old classification scheme, Bordeaux wines. And I didn't buy the bottle. I think that I think Chateau Margot, 82, probably be around $1,000 right now. So we didn't buy it. It was served at a dinner that I happen to be lucky enough to participate in. Yeah, it's better than what you get if you pay $100 for a bottle of wine or $20 for a bottle of wine. There's a lot of variation here. It's not a strict relationship between cost and quality, especially because different people will experience the wines differently. And this is just science. You know, different people have different taste receptors and different experiences, different sensitivities. So if you personally, not necessarily you, Vicom, but if one personally has their favorite wine in the world that is $20, then they should absolutely go for that. There's no objective.

sense in which the more expensive ones are better. But there is an objective sense in which the more expensive ones are different. They last longer. They're more complex. They have more structure. They have more subtlety. You know, an 82 in a cheap bottle of wine is not going to be very drinkable right now. It's well past its prime. But these classic great bottles of wine can last 50 years and still be pretty awesome. Is it worth it? that depends on your income level. Was it worth it when I was a graduate student to drink a $2,600 bottle of wine? No, because I didn't have enough money to do that.

Is it worth it now? Also, no, probably not. I think that, you know, if I splurge or whatever, I could imagine at this point of my life spending a few hundred dollars for a bottle of wine, if it's, you know, a special anniversary or something like that, but a couple thousand dollars is still beyond my reach. But if someone just gifted me $10 million and said, you're not allowed to give this way to charity, you have to spend it on yourself. Would I buy a few bottles of Chateau Petrus and see what the fuss was about?

Sure, I'd be very happy to do that. I mean, there are bottles of wine that are $40,000 or something like that. There are silly bottles of wine also. When I was in France, we took a little class about Bordeaux wines, and the guy mentioned, I think it might be Chateau Petris. No, maybe it was Cheval Blanc. I forget, the most expensive bottle of wine ever sold. But it's not because it was the best bottle of wine ever sold.

It was because a few bottles were brought up to the International Space Station and then brought down again. It's just like, you know, these bottles from Thomas Jefferson's time or whatever, many of which were fake, but you're buying it for the gimmick. You're buying it for collector value, not because it's the world's best wine. But there are $40,000 bottles where the claim is that that's worth it, that that is worth the improvement in quality if you can afford that price. I have no experience at that verified level, so I can't tell you whether that's just whistling in the dark or, you know, something to talk about.

But anyway, yes, if I had infinite amounts of money, I'd be very interested in trying it. I completely disbelieve people who say there's no difference between a $1,000 bottle and a $20,000 bottle of wine. I think those people are just sour grapes. So there clearly are differences. Again, you don't have to like those differences, but they're there. Timothy Altman says, I believe you would agree we have little control over adoption of technology on a global scale.

AI, designer babies, and fossil fuels are all examples. Yet so far, we've been smart enough or lucky enough to mitigate downsides. Are you optimistic about the future of the human race, or do you think we are just rolling the dice over and over again until they come up snake eyes? That's quite a journey through your question there, Timothy. You know, the one thing to keep in mind is that the past is not necessarily a good guide to the future, because as technologies develop, the leverage that these technologies have is much greater.

200 years ago, the most powerful technologies we have just didn't have the capacity to wreak damage on the world in the same way that modern technologies or future technologies do. So we can't just make an argument that says, you know, we figured it out before it'll be okay again. I think it's legitimate to consider the challenges that we have now to be of a different order than the ones we had before. Secondly, the fact that we've survived so far, there's a bit of a selection effect there, isn't there? You know, you survive up until you die. And so it's very hard to extrapolate from your past successes, because if you hadn't

succeeded, you wouldn't be here to talk about them. In terms of mitigating downsides, you know, I don't know. We've mitigated some of the downsides. We're also causing disastrous changes to our climate, so we haven't done it perfectly well. Many, many people died from pollution and such things like that in the Industrial Revolution. Many people died when we dropped atomic weapons on Japan. There's lots of bad sides that we did not successfully mitigate. So I think it's a mistake to think that we know now whether we should be optimistic about the future of the human race or not. There's plenty to be optimistic about. There's plenty to be pessimistic about. We have to take an active role in trying to increase the chances for the optimistic scenarios and decreasing that

for the pessimistic ones. Richard Cashden says, I don't know if this question even makes sense. Consider time as the fourth dimension. I want to make a four-dimensional cube, i.e. the same size in all dimensions. I build a cube very quickly, wait some amount of time, and then destroy the cube quickly. This will create a 4D shape. But how long should the time be in order to equal the length of the cube? I'm guessing the amount of time it takes for light to travel that distance. Yes, that's exactly right. Or at least that's the closest you have to a meaningful comparison. You know, space and time are different. They're both part of space time, but we measure them using clocks versus rods. Of course, there's a conversion factor between them, and that

conversion factor is exactly the speed of light. So roughly speaking, what you want to do to do what you're asking is measure distances in light years and time in years, or distances in light seconds and time in seconds, which means basically that for any human scale distance measure for the cube that you're building, the time scale is going to be incredibly, incredibly tiny so that all the lengths of the 4D cube are equal or at least commensurable in some sense. Christian Hoffman says, in your recent book Quanta in Fields, you mentioned that the wave functions of particles spread out as time passes and that larger objects spread out slower. Why is that the case and how fast do everyday objects actually spread out? Well, how fast actual everyday objects spread out

depends on details, right? The details depend on the details, unsurprisingly enough. I think that if you want to sort of look past the details to get a moral of this story. Why is there some relationship between the mass of things and how quickly their wave functions spread? The answer is basically because the natural variables to discuss quantum mechanical systems are position and momentum. So in classical mechanics, we would say, I could completely determine the state of a system by giving you the position in velocity of every component, or equally well, I could give you position in momentum, because momentum and velocity are related.

Momentum is mass times velocity, right? But it turns out in quantum mechanics, and even in classical mechanics, if you look at it carefully enough, once you start talking about phase space in classical mechanics or conjugate observables in quantum mechanics, as appear in the Heisenberg Uncertainty principle, the natural thing to do is to use momentum, not position. So the uncertainty principle is not the uncertainty in position times the uncertainty

in velocity is greater than H-bar, the natural quantum unit. It's the uncertainty in position times the uncertainty in momentum is greater than H-bar. So if you have a certain momentum of something and you kind of fix that, then for different values of the mass, that corresponds to different velocities. And in particular, when the mass goes up, when you get something heavier and heavier, you need a smaller and smaller velocity to get that same momentum. So if you have an uncertainty in the velocity, a little uncertainty in the momentum, a little spread in the momentum part of the wave function, as you might say, for heavier objects, the actual speed, the velocity at which

the spread happens will be much slower than the speed with which the spread will happen for a low-mass particle, just because momentum is mass-times velocity. I think that's the essence of what you're asking about here. Dragon-sided D says, what are your thoughts in the current situation with Gaza, Hamas, and Israel? Yeah, well, that's a complicated one. I think it's tragic. That's the simple-minded thought about it. I think that there is a lot of blame and badness to go on all sides. I also think that not all sides are created equal, but they're all bad. They're all doing bad things in that sense. I think that neither side Palestine or Israel has leadership, which fairly reflects the views of the people on either side. And I think it's a shame that the

general people get blamed for some of the things that the leaderships do on either side. I also think that Israel is a much more powerful entity than Palestine is, and that creates a huge imbalance. Israel can do a lot more damage. The number of deaths caused by Israel in the conflict between the Palestinians and the Israelis is much larger than the number of deaths caused by the Palestinians. That's not to excuse the terrible terrorist attacks that Palestinian terrorists have pulled off. It's all bad. So it's just all bad. I think it's terrible.

I would like a ceasefire right away. Ultimately, I would absolutely like the Palestinian people to have a nation of their own. and they could govern it on their own. And I think that if Israel were smart, rather than trying to starve people and bomb infrastructure and destroy hospitals and universities, they would flood Palestine with money. They would support the well-being of Palestinians to lead comfortable, happy lives in their nation, and then it would be much less likely and less tempting to have terrorist attacks against Israel. but no one seems to be listening to me when it comes to those particular geopolitical issues.

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Tim Giannitzos says, David Deutsch argued during your conversation that he was not a Bayesian, but he is an Everettian. Is this a contradiction? It seems that an Everettian must speak a probability in terms of ratings or credences like a Bayesian would, as opposed to the limiting behavior of many identical experiments like a frequentist would. Well, I probably shouldn't have answer this question honestly, because I do have a policy that I don't want to try to interpret what other people are saying if I don't understand what they're saying very well. I have not understood why David Deutsch doesn't like Bayesianism, even though we talked about it on the podcast. I still came out of it not quite understanding that. I mean, I know that part

of it is a philosophy of science question. Of course, by the way, Bayes has a theorem, right? There's Bayes' theorem, which relates the probability, certain conditional probability, to other conditional probabilities and can be used to update your credences when new information comes in. Nobody disagrees with the theorem, not David Deutsch or anybody else. That's not what it means to be not Bayesian. There is something that goes beyond the theorem, which is to say Bayesian epistemology, to say that the way we should think about hypothetical scenarios is to assign them all credences and then update them when new evidence comes in. And David thinks that that that doesn't work. He thinks it doesn't actually do what you wanted to do. He has a paper

that he has coming out, or maybe it came out already. We did talk about it during the podcast that basically argues following a theorem of Carl Popper that the kinds of things you learn about when you update in using Bayes' theorem are only more or less redundant with whatever evidence you collected. They're not actually telling you anything about independent parts of the theoretical structure you're considering. Again, I don't quite see why that theorem gets him where he wants to go, but he's a Popperian when it comes to the philosophy of science. Popper, remember, emphasized conjectures and refutations. That was the name of one of his books and the idea of falsifiability, the idea that the way that science goes forward is you put every possible conjecture out there

that you can think of, and then you falsify. You refute as many of them as you can, and what is left-standing, is supposed to be closer and closer to the truth. Notice that the word credence never appeared there. So there's a slight change in emphasis. But that's about theories, not about which world you live in. Okay? So, I mean, maybe David would be perfectly happy

to be a Bayesian about what branch of the wave function you end up in. Again, it's not what he actually does. he actually, you know, when he first very famously offered up a derivation of the born rule in many worlds, he did not use Bayesian language. He did not use credences or anything like that. He just used expectation values and decision theory and stuff like that. So it's possible he would argue that even in that choice, not what theory do you choose, but what branch of the wave function are you on, there's no good reason to be basing about things. Again, I probably shouldn't say. You should probably ask him, Kilngod says, why is a photon its own antiparticle, as you say in quantum quantum in fields?

You know, it's not exactly, I hope, I forget exactly what I said. It's a little bit sloppy to say that a photon is its own antiparticle. The more honest thing to say is that not all particles have antiparticles. The idea of an antiparticle, you know, let's put it this way. There's a whole bunch of fields that exist and various features of quantum field theory and the mathematics underlying what fields you're. dealing with, indicate that you need to have certain properties and certain symmetries within those fields.

And when your fields carry a conserved quantity like spin or electric charge or things like that, quantities that can take on opposite values, spin up, spin down, charge plus one, charge minus one, then you will have something like an antiparticle. Actually, spin is probably a bad example, isn't it? Photons have spin, and they have equal and opposite spins in two different helicities, as we say. There's a positive helicity, which has been clockwise along the line of motion, and there's negative helicity, which has been counterclockwise along the lines of motion. That's not really an antiparticle, but that's that same kind of symmetry between them.

What photons don't have is electric charge. So they don't need to have the same kind of antiparticles. that electrons have, where you have a positively charged positron as the antiparticle of the negatively charged electron. All of this, the point is, about all of this, is that words like particles and antiparticles are useful for human beings. What matters is what interactions there are between different kinds of fields and their associated particles. So there's an interaction where an electron and a positron annihilate into photons or other particles. So that kind of annihilation process can be thought of as particle, anti-particle destroying each other, right,

and the energy going into some other kind of field behavior. For photons, two photons can come in and do the opposite. They can convert into an electron and a positron. Okay. So the two photons both disappeared. There you go. That in some sense, that's kind of like the photon being its own antiparticle, even though those two photons that came in are the same kind of particle. their vibrations in the same field, the underlying electromagnetic field. So it's a case where the language of particles and antiparticles doesn't quite fit comfortably onto the reality of photons, or for that matter, gravitons and other particles like that.

Genson says humanity managed multiple times in its history to cause widespread chronic lead poisonings, with all their consequences including imbecility and madness. The last time it was due to tetralethylase, led. Many people tried to prevent it this time, like Yandel Henderson in 1925. Okay, I should have edited this part out. Sorry. How can we trust our political system or science with anything? Honesty, justice, or fairness, given that they were unable to handle even such obvious stuff? Or was it actually handled well because the poisoning was stopped after all? Well, I think when you say,

how can we trust our political system or science? There's a kind of a question being begged there. Should we trust our political system or science? I don't think that the idea of trusting our political system or trusting science is a good idea. It's more complicated. It's not a bad idea either. It's not that you should distrust our political system or science. It's just that that is a far too simplistic way of approaching an attitude towards our political system or science. Our political system, as well as our scientific system, these are vast collections of many people doing all sorts of kinds of things. Systems that will sometimes do very good things, sometimes do very bad things. The idea of like simply having an on-off switch for trust for our political system or for science is, I think, way too simplistic. We need to think about the situation. We need to understand that there will be conditions, circumstances under which our political systems will systematically fail us. And we need to fight that. We need to be whistleblowers and support other whistleblowers when they exist. we might need to protest, you might need to try to change the system in various ways.

Likewise for science. Science is in some narrow conception, just trying to learn true things about the universe. But of course, in a broader conception, it's part of a process of technology and engineering and the real world, capitalism, etc., where it can be put to good use or bad use. It can be manipulated in various ways. True, scientific findings can be hidden. False ones can be promulgated. etc. So you have to be careful about it. You have to be wise to the fact that experts know more than non-experts do. Experts are not always right. Both of those things are true at the same time. Scientists are generally trying to find the truth. Sometimes they're malicious people who have other agendas. Both things can be true at the same time. You just have to keep your wits about you.

That's all I can say. Edward Crump says, please give your elevator pitch to better understand emergence. I honestly don't see what's so hard about understanding emergence. If I have a box of gas with many different atoms in it, I could describe it telling you the state of every single atom. Or it turns out, and this is a highly non-trivial fact, that I could take little regions of space inside the box of gas and consider the average behavior of the atoms. I can throw away an enormous amount of information. I can forget about the specifics of the many, many, many atoms in some little cubic millimeter of space, and instead just tell you the total density, total energy, average momentum, things like that. And it turns out, miracle of miracles, that even though you've thrown away almost all of the information

and kept only a tiny little bit of the remnant information, that is still enough to make very, very accurate predictions about the future. That is what Dandenick called a real pattern lurking in the coarse-grained dynamics of the system, and that to me is what emergence is all about. DMI says, can you explain how the Re-Schleider theorem can be true? So the Re-Schleider theorem is this remarkable theorem in quantum field theory, and it's about the vacuum state. It's about empty space. It's one of those things that convinces you that even the vacuum,

even empty space in quantum field theory is interesting, even before you start talking about particles and Feynman diagrams and whatever. And roughly the theorem says that if I have some region of space in the vacuum of quantum field theory, there are things I can do to it, essentially observations I can make, such that after the observation is made, depending on the observation outcome, the rest of the state, things, you know, many miles or light years away, can be literally anything. or arbitrarily close to literally anything. This is sometimes called the Taj Mahal theorem,

because one way of making it vivid is to say that there's a measurement I can do here in a laboratory here on my basement, that after doing it and getting a certain measurement outcome, there's now a Taj Mahal, a copy of the Taj Mahal on the moon, or on the moon in a different galaxy, for that matter. This seems very strange to people because it's the vacuum state, it's empty space.

It's the emptiest that space could be, but that's all because of quantum mechanics and quantum field theory being subtle in various ways. So to understand where the theorem comes from, at least at the hand wavy level, there's sort of two steps. One is to think about entanglement. Okay, so if you've heard the conventional story of EPR or Bell or whatever, where you have two particles with spins, spin up and spin down, and you have Alice and Bob. and Alice has her spin, and it could be in a superposition of spin up and spin down. So that means that she doesn't know what she's going to get when she measures spin up and spin down. She's going to measure it along some particular axis, right? She's going to set up a magnetic field in the Z direction and then measure the spin along that axis

and the particles in a state where it's a 50-50 chance of getting either one. But it can be the case that Alice's particle is entangled with Bob's particle, and the entangled state has the property that Bob, who could be a million miles away or an Alpha Centauri or whatever, also doesn't know what answer he would get if he measures his spin in the Z axis also, but they're entangled in such a way that we know the spins are opposite. So whatever Alice gets, we know that Bob is going to get the opposite one. That's just the usual EPR story. Now there is another layer there, still talking about the first part of the Rieslider theorem.

There's another implication of this, which is Alice didn't need to measure her particle along the Z axis. She could have measured it along the X axis or the Y axis or any combination, any diagonal axis, okay? She will always get, by the rules of quantum mechanics, one of two possible outcomes, either spin up or spin down with respect to the axis along which she's measuring it, okay? and it is something you can show, using the mathematics of quantum mechanics, that when she gets a measurement, like spin up along the x-axis, maybe that's not a good one to pick. When she gets a measurement of spin-up along some axis, you know, you can always, with set of measure zero, you can make a measurement so you get a hundred percent chance of getting a certain outcome and zero percent chance of getting the other one. So forget about that very, very unlikely possibility. For a generic choice of spin axis, whatever answer she gets, we know that Bob has now a spin,

which is aligned exactly the opposite. Okay? So it's not just that Alice can measure spin in the Z direction, and when she gets her measurement outcome, now we know Bob has the opposite spin. It's even when Alice measures along some other axis. It's still true that Bob's spin is now pointed in the opposite. direction along that same kind of axis. So in a very real sense, there is a possible measurement outcome Alice could get by doing all sorts of different measurements. She only gets to do one,

but it's possible she would get an outcome with the implication that Bob's spin is now in almost any situation we could want, almost any state, depending on Alice's measurement outcome. Crucially, Alice can't choose what measurement outcome she gets. So the theorem is not Alice can force Bob Spin to be in any state. It's that there exist measurement outcomes that Alice could see that would imply that Bob Spin is in any state now. Okay. So that's one feature of entanglement. The other aspect of the Breed Slider theorem is thinking about quantum fields.

And, you know, when we think about the vacuum state of quantum fields, we often think about a wave stretching through all of space or many, many waves with different wavelengths, stretching through all of space. And we think of, you know, we build up the space of all possible quantum states as superpositions of all those things. And we ask, what is the lowest energy state? And so there's an answer. There's a unique answer.

What is the lowest energy state globally to the quantum field theory? You can't see, because this is audio only, but I'm waving my hands to indicate that we're stretching throughout all of space. Alternatively, we could look at one region of space and another region of space separately. And that's just another way. It's basically another choice of coordinates in the space of fields. So we can talk about what the modes of the field are doing in region A for Alice, and separately what they're doing in region B for Bob.

And that's not all of space. There's all sorts of other regions of space where neither Alice or Bob live, but let's just look at those two regions. in each region, given that overall we are in the vacuum state of the quantum field theory, there is a superposition of many different states of different energies in each region because it is because of entanglement, not just entanglement, but because of interactions between the quantum fields. Like, let's think of it this way.

I know there's an overly long explanation. Sorry about that. But think about a situation where I once again have two spins. like Alice and Bob did. So I'm not thinking about quantum field. I think it spins again. But now there's a magnetic field. So the magnetic field is in the Z direction.

So it's in the sense that the energy of the spin is a little bit less when the spin is pointing in the Z direction than opposite to the Z direction. Okay, so there's two different energies for spin up and spin down. So left to themselves, both spins would like to be in the lowest energy configuration, spin up. But imagine that I bring the spins together and there's an interaction between them,

which says that it's more energy when the spins are the same and less energy when the spins are opposite, right? Now there's two forces pushing them in opposite directions. One force says by themselves, they want to be spin up along the magnetic field, but because of the interaction between them, they want to be opposite. They can't both be spin up and opposite. So the actual ground state of that system will be a superposition of spin up and spin down for each of them and also spin up and spin up and spin down.

All of those possibilities will be superimposed in exactly the right way to make the ground state of the system. Okay. The same thing is true in quantum field theory. If I divide space into different regions, I can't just separately put each region in its lowest energy state and think that that's going to be the lowest energy state overall. There are interactions between the fields next to each other

that will relate what they're doing. doing. And so if I know that overall, the quantum field theory is in its lowest energy state, that is a superposition of local things in each region, which are not in their individual lowest energy states. Okay. So all of the things that the field can do in any region actually contribute to the overall vacuum state. And I know it's a long answer. Sorry about that. And all of the regions are entangled. what the fields are doing in every region of space is entangled because of features of quantum field theory. That is what, just like with the spins, that is going to turn out due to the dynamics of quantum field theory to be the lowest energy state. So basically, the little fields that you're thinking about as localized to the region in front of Alice have a state that is entangled in all of their different possibilities.

Like everything the fields could be doing in front of Alice are controlled. to this entangled state with everything the fields that could be doing in front of Bob. And therefore, when Alice makes a measurement in her region, there is a chance, an arbitrarily small chance, generally very, very small chance, but still a chance that her measurement outcome will imply that Bob's state is literally anything, almost anything. There's different little mathematical footnotes there, but essentially anything, including a picture of the Taj Mahal. Again, she can't force it to happen, but there is so much entanglement in the vacuum state of quantum field theory that those things are always going to be possible even if they are very, very unlikely. Jim Murphy says, as I've been listening to on participating in the AMA episodes over the years, the number of questions has increased dramatically. Obviously, this is good for you, but I can't help but feel a little bit selfishly frustrated by the sheer number of questions that have been answered many times over. I would gladly pay more money for content discussing deeper technical points.

Would you ever consider something like this? You know, I'm certainly open for patrons to ask for or suggest ways to organize the AMAs differently. I think I don't want to do – I think there's a consensus that having one AMA per month and the other episodes per month be conversations with different smart people is a good balance overall. But right now, the way that the AMAs work is I just try to pick the questions I can give the most interesting answers to in my own personal opinions. If there's some other way that there's a consensus that AMAs could work, then I'm happy to do that. But, you know, I would guess not. And I think that I know that different people who are very kindly supporting the podcast have different sets of questions and different levels of questions and different goals and asking questions.

thinking of the AMAs or the Minescape podcast in general as a physics tutoring system is probably just going to lead to frustrations. That's not what we're here to do. I mean, the AMAs are about off-the-cuff answers from me to various kinds of questions. They're not systematic. They're not overly pedagogical. They're not very deep. And I suspect that's not what they're going to be. If there's some topic that everyone's on Patreon is really, really interesting,

hearing, then maybe just suggest a solo episode. And that is something I would absolutely think about doing. Also, I should mention that, yeah, this month in particular, we had a lot of questions asked in the AMAs where I have answered them before. And so I'm trying not to answer them here. And I feel bad, because they're perfectly good questions, but I've answered them before. So I'll remind people we have a deep archive. And it's completely searchable on, certainly on preposterousuniverse.com and also on Patreon, you can look for the possibility that you have a question that's already been answered. And even if not, you can listen to AMAs from months past. Maybe that would be fun to do. Okay, Chris Murray says, in quantum fields, each plane wave mode of a field configuration is described by a height variable and a wave vector, but phase is not mentioned.

Does the phase somehow not matter, or is it contained in the height variable as a complex value, or what's going on? Very briefly, yeah, in the book, I frequently glossed over complex numbers. In particular, the way that Fourier transforms work, that is to say, the way that you switch from discussing a function by giving its value at every point to giving the different contribution of waves of every wavelength, inevitably involves complex numbers. Fourier transforms are generally complex valued, even if you start with a field that is completely real. So that happens all the time in quantum field theory. There really are complex numbers there. We just didn't talk about it in the book because it was sort of not centrally important for the physics that is what we cared about at the end of the day. Peter Becker says, I've been wondering whether there is some good philosophical reason why the smallest things in the universe, say extremely high energy photons,

could have as much energy as the largest things in the universe like stars, black holes, etc. Is there any good reason why the shorter the wavelength of the photon gets the more energy it has? Well, there is a good reason for that. I'm trying to figure out a way to say it that is not just repeating it. You know, in wave mechanics generally, okay? So forget about quantum mechanics specifically. Think about electromagnetism, wherever that matter, waves on the ocean. If you have waves of a fixed amplitude, so the fixed height of the wave going up and down,

as the wave length gets smaller, the wave has to change. change more rapidly, right, to go up and down in a shorter distance. That takes more energy. That is a higher energy configuration, and that's just as true in quantum field theory as it is everywhere else. So the general rule is that higher energy things have shorter wavelengths. That's just always true. The reason why it seems counterintuitive is because in the classical world, we don't care about the wavelengths of things. When I think about a dumbbell or the earth, and I think about how much mass they have, those systems have a center of mass coordinate that has a wavelength in quantum mechanics, but that wavelength is absurdly tiny because the systems are very massive, as we talked

about before. When you have very, very massive systems, both position and momentum, sorry, both position and velocity can be very highly localized because mass is very large. So what we think of as the size of a dumbbell or the earth or whatever is it's physical extent in space classically, not its quantum mechanical wave function. So for classical things, heavier generally corresponds to bigger, because there's more mass there. There's more stuff that can contribute. It's only when you get to sufficiently small things that you have only one particle that there is a different kind of effect that kicks in, and you can't make things smaller than their Compton wavelength. Otherwise, you start making more particles. So it's just there are

different reasons why the energy is going up in the classical regime and the one particle quantum regime. Marcin Chady says, as a physicist and wine aficionado, do you consider it a sacrilege to bring red wine to room temperature, when a previously open bottle has been stored in the fridge overnight, say, by heating it up in a microwave? I am not religious, so it's not sacrilege, but I certainly would never do it. you run a danger if you microwave wine of changing its delicate composition and chemistry, even though you're trying not to.

I don't actually know. Maybe it's perfectly okay. Maybe if you do it just a little tiny bit, it doesn't matter that much. But I will mention two things. Number one, I'm completely happy with chilled red wine. That's fine. In fact, I think that it's a little bit of a myth to think that you need to serve red wine. wine at room temperature. It depends on the wine. Different red wines respond differently to different

temperatures, but a little bit lower than room temperature is entirely appropriate. And the wine sort of behaves better in storage if it's a little colder. You know, yes, it is true that in the ancient days, they would not have refrigerators when they stored their red wine, but they would have dank basements in the chateau, which got pretty chilly. And that's the temperature which you would serve your wine. So serving wine at, you know, 60 degrees or 65 degrees Fahrenheit is actually good. And, you know, we keep our red wine in a special wine fridge. We have a little tiny wine fridge in the kitchen. And, you know, we keep the wine at, you know, 55 or 60 degrees so that when you bring it out and let it sit there for a little while, over the course of opening it up

and drinking it, it goes from 60 degrees to 70 degrees or whatever. And that, you know, goes through the range of the best possible temperatures. So that's what I would advocate doing. Oh, and the other thing is, I don't think you have to store the wine in the refrigerator. It's much better. Again, I think this is true. I'm not a super expert. But much more important to remove the oxygen from the bottle.

If you have a half, if you have a half full wine bottle, so you open the wine bottle, you do not, and you should not feel obligated to finish all the wine. You drink as much as you want. But then it will go back. if it's exposed to air for a very long time. So you can buy a very cheap device called a vacuum vint, which will basically vacuum pump the air out of the wine bottle and then put a little rubber stopper in it, okay?

That actually works, at least for a day or two, of keeping the wine. It wouldn't work for weeks, et cetera. But if you do that, you don't have to refrigerate the wine. Alan Lubel says, I listened again to your Max Tagmark interview and really enjoyed it. I'd like to ask when Max says, if I make a measurement of a particle that is in two places at once, and if in advance I've decided that if it's here I'm going to go for a drink and if it's in the other place I'm going to watch Netflix,

is he saying that in order for branching to occur, you have to be making a decision or choosing a certain action and not just sitting around doing nothing? No, he is certainly not saying that. And notice, he did not say that. He said, if I made a measurement and in advance I decided to react in certain ways when that measurement is made. what he's doing is not branching the wave function of the universe by his decision. He's branching it by making a measurement of a particle. That's when the branching happens. What he's doing is making the two branches macroscopically different

by deciding ahead of time to behave in two different ways depending on the measurement outcome. So very often, you know, if you have a single radioactive particle that decays or a single spin that is measured or whatever, in principle you branch the wave function of the universe into two universes, but who cares? They're indistinguishable for all macroscopic purposes. You don't notice most of these branching events.

So what Max is just doing is a Schrodinger's cat-like thought experiment where he's saying, I'm going to figure it out, I'm going to set up a system where the two branches truly are different macroscopically. Griffin Kistler says, with your accomplishments and position, do you encounter imposter syndrome? If so, do you have any strategies you could share that would be helpful in mitigating it or navigating it with the assumption that your advice is directed at a Sean Carroll of Unusorough

of another discipline. You know, I think we all have our psychologies, you know, with positive aspects and negative aspects. Imposter syndrome has generally not been mine. You know, I've certainly been intimidated by talking to people who I, in other words, I think I've had imposter syndrome when I deserved to have it when I really was an imposter. Let's put it that way. But less, not so much when I didn't deserve to have it. I think that's true, roughly speaking. Again, there's all, you all, one always makes mistakes. Sometimes one errs on the side of being too arrogant, sometimes of being not arrogant enough. I just think, you know, you have to recognize the difference between your inner

psychological state and the objective external reality. It's very, very possible to be able to say, I objectively know that this is not true and nevertheless I feel like it is, right? And I act psychologically like it is. I think that's what you have to work to overcome, to both to objectively understand where people can be very annoying when they act like experts but aren't. That's a known annoying thing. It's not quite as annoying, but also a failure mode to not recognize when you are an expert or accomplished even though you are. It's hard to correctly calibrate that, but try to do it. Try your best to do it. That's all I can say. I don't think that's very helpful advice, but I think ultimately that's what we got to try to do.

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that as a practical issue, that is certainly true. I can imagine a single molecule or a single particle that we put into its ground state to a very high confidence anyway. I mean, maybe not to perfect confidence. Maybe that's what people mean by not reaching absolute zero, but we can get, you know, arbitrarily close. It's very, very, very difficult to do that for a whole bunch of reasons. We don't have control over, you know, the way in which systems cool down. Like if systems are cooling down by emitting photons, you could in principle emit them, you know, if there's a smooth continuum of states as you approach zero energy, then you can get there in a series of steps that would take you infinitely long to get to absolute zero. And moreover, the world is a noisy place. You and I are

emitting a whole bunch of radiation in infrared wavelengths. So if you just yourself in front of you in your eyeballs have a system you're trying to get to absolute zero, the fact that you yourself are heating it up becomes a real problem. So I think there's all sorts of practical issues that are more relevant than the theoretical impossibility that is sometimes implied. But the other one that is very important is that you shouldn't talk about absolute zero for a single molecule. You shouldn't talk about temperature for a single molecule. really only begins to make sense when you have many, many molecules and you reach some kind of thermodynamic limit. And in that case, it becomes, you know, all of those issues we discussed

as making it hard to make a single molecule in its ground state become even more difficult because you have many molecules with relative random motions and it becomes all that harder to get rid of all the energy in that system. So, you know, I think that we can contemplate systems in absolute zero temperature, but we're never going to actually make them. Zach McKinney says, in your recent solo episode on the coming transition in how humanity lives, you spoke about the possibility of a coming phase transition in human society with reference to Jeffrey West's recent lecture showing evidence of an approaching technological singularity. What physically observable quantities do you believe will be the most fundamental to recognizing

or characterizing such a phase transition? In particular, are you thinking of this phase transition primarily in terms of economic metrics, such as rates of technological innovation adoption, or do you think there are also important social metrics that may be used for identifying characterized radical changes in the dynamics about humans behave? Both. I think that, you know, one, and it could be wrong, of course, but under the analogy with physical systems, you generally have multiple measurable quantities that undergo phase transitions at the same time. Really, a phase transition is sort of a change of the collective behavior that you get from all these individual constituents interacting with each other. The difference between solid and liquid water,

okay? There's a lot of differences. One, of course, is the viscosity, I guess you want to put it that, the solidity of it, but also things like the equation of state, the speed of sound, all these things, the density, they all change at the same exact point. And I suspect that under for good reasons, I suspect that the analogy works for human societies as well, and if there is going to be some phase transition, it'll probably be at more or less the same moment for more or less different kinds of metrics, both economic and social. Jeffrey Clark says, it seems the very foundation of modern cosmology is the Hubble Law of Expansion. With a good telescope, we find galaxies containing heavier elements, several generations of stars, with red shifts which place them

observed less than 300 million years after the Big Bang. If we pretend we are ignorant over the expansion-caused redshift, might we solve some of these quandaries, i.e. the sage, dispersive medium, etc. Did Hubble send us down a rabbit hole we are afraid to crawl out of? No, Hubble did not send us down a rabbit hole we were afraid to crawl out of. What is important to understand here is that, you know, Hubble discovers the relationship between apparent velocity and distance of galaxies,

back in the 1920s, and then you say, okay, the universe is expanding. But since then, in the almost 100 years since then, there's been enormous and completely independent lines of evidence that support the same idea, not to mention the fact that general relativity predicts the same idea, but we have nucleosynthesis, we have large-scale structure formation, we have the microwave background, we have various concordances between ages of stars and galaxies and the universe and the whole bit. There's no way of getting out of the overall Big Bang model. So that is absolutely solid. I don't think that there's evidence that there's been several generations of stars in very early galaxies, but it's true that we have better telescopes and we discovered galaxies that are

very early in the history of the universe. That's a challenge for galaxy formation. It is possibly a challenge for star formation. Two things we don't know a lot about. It is absolutely not in any way a challenge for the overall Big Bang model or the Hubble expansion. Kyle Capasares says, you mentioned you were open to giving dating slash relationship advice in a previous episode, so here's a softball. In your opinion, what is the biggest red flag and biggest green flag when choosing a romantic partner?

You know, I think that these kinds of questions are just too vague. I think that there's no useful answer to a question like that because people are different. and I know I end up saying this all the time, but people are different. Different kinds of relationships will work. Different kinds of romantic partners will work depending on your particular needs or incompatibilities.

So I think it's a mistake to think that there is some list of red flags and green flags that is universally applicable to all sorts of different kinds of people. In fact, you know, the real difficulty in dating sites and things like that, which in general I'm in favor of, I think there's lots of different ways to meet people, no reason why not to use technology to do it. But the idea that you have some kind of checklist, that here is what you want in a partner, and here's what you don't want in a partner, and you're going to find partners by matching and comparing checklists, is just completely contrary to all evidence. As well as if you think about the problem, there's no reason to think that should work.

You have to talk to people, you have to meet them, you have to interact with them, and you have to get a feeling for how you respond to them before knowing whether it was. works. So rather than thinking in terms of red flags and green flags, I do think that you can trick yourself, you can fool yourself. I mean, I know I have. I'm sure many other people have. I'm sure that there are things that other people do, that your potential romantic partners do, that should lead you to realize that they are not good romantic partners for you, that you convince yourself aren't actually that bad. So I think you should look for the red flags in yourself, but not really red flag so much as blind spots. It's an interesting question because, of course,

there are things about people that might get in the way of a successful relationship, but are changeable, are fixable, and there are other things that are just intrinsic to who they are and what they're not going to fix. And that's a difficult thing to decide about. I think that maybe, again, along the lines of think about yourself more than fixing or finding flaw in the other person, if you find that you are embarrassed about certain things that another person does or you're making excuses or when you

tell your friends about your partner and you find that mostly you're complaining, then that kind of thing is a red flag for the relationship. You know, you should mostly be happy. in a successful relationship. If you find that you're constantly making excuses, if you find that they're not trying to make you happy, if you're trying, if you are in love with the idea of who they might be,

if they were a little bit different than who they actually are, those are all relationship flags that you should pay attention to, not so much flags about that individual person. All right, I'm going to group two questions together, one from Joseph Dundee. Regarding your recent episode, excellent podcast with Kermun Bafa. What do you think is the likelihood of finding a deviation in Newton's inverse square law at the micron range?

I read the such result either confirming or disproving a deviation should be obtainable experimentally within the next three years or so. And Michael Wall says, regarding your discussion with Kumran Bafa, are you able to comment on the idea of a dark dimension with length of order 10 microns? From what I gather, only the modes of the graviton live in this dimension, but where does that leave standard model particles? How is it possible to do any experiments if standard model particles don't move in that dimension? Yeah, the whole idea, which started back in the late 90s from a bunch of different people talking about it. I think that who were the authors on the paper, Demopolis, Davali, Arkani Ahmed, I'm going to leave people out. But the idea came from the realization that in string theory, there are higher dimensional brains, B-R-A-N-E-S, as well as one-dimensional strings, one-spatial dimensional strings. So imagine that all of space was not compactified, right? Imagine that there were nine dimensions of space that were just infinitely big, but embedded in that space, there was a three-dimensional brain, okay, a three-brain. So it turns out that various fields can be confined to only propagate on the brain. So if you have fields like quarks and electromagnetism and other forces that we know and love from

the standard model, but that are stuck on a brain that is three-dimensional, then the world would appear effectively three-dimensional to you, even if it were embedded in higher dimensions. The one exception to that is gravity. Gravity is a feature of the curvature of space-time, and therefore you cannot confine it to a brain. There are slight exceptions to that. Randall Sundrum warped extra-dimension models are slightly different than that, but basically the idea is that you could have extra dimensions where only gravity propagates. So as long as you're not asking questions about gravity, everything looks like it's three-dimensional. Now, that's interesting because gravity is harder to experimentally probe than other forces because it's so weak.

You know, we say we're probing gravity at scales of millimeters or microns or whatever. That sounds pretty good, but we're probing electromagnetism and the strong and weak nuclear forces at much, much, much smaller length scales than that, precisely because they're stronger and easier to probe down there. So it is plausible that one or more extra dimensions are bigger than a micron. Well, bigger than particle physics distances, okay? Certainly much bigger than the plank scale. How plausible is it? What is the likelihood? I don't know. I honestly don't know. The original motivation back in the late 90s was that if you had two extra dimensions, then you could understand why gravity seems so weak in our macroscopic world because it sort of is diluted by the large extra dimensions.

They would be, you could actually have the plank scale, the real plank scale, which we normally think of as much, much higher than particle physics energies. You could actually have it quite close to the electroweak scale that was being probed by the large Chadron Collider, if you have two, specifically two, extra dimensions. Why two? Well, because there's a relationship between how big the extra dimensions are and how weak gravity gets. And there was an interesting coincidence that two dimensions could affect the force of gravity, so that the plank scale is at the electro-week scale, and the two extra dimensions are large enough to be experimentally testable. But they did the experimental test. But they did the experimental test.

and they didn't find any evidence of two large extra dimensions. So if you have one large extra dimensions like Vafa was talking about, that would not have this unification, as far as I understand it, between the Plank scale and the Electro-Weak scale. It would be a different kind of thing, which is necessary because we turned on the LHC and we didn't find gravitons or anything like that. But in the 1990s, that was a thing to think about, finding gravitons at the Large Hadron Collider.

It didn't work. It didn't happen. Not yet anyway. But that was something to think about. So I think it's something to think about. You know, I wouldn't put it individually plausible. I think there's lots of other possibilities out there. I shouldn't say plausible.

Likely, I don't think it's individually likely. It's completely plausible, okay? So I think we've got to be open-minded because we're a little stuck right now about where to go beyond the Electro Week scale. So this idea seems as good as I need to meet. Voltaire O says, if you were to have a tattoo, what would it be? assuming you don't already have one. I don't already have one. I kind of don't have any plans to have one. Getting a tattoo seems to be like a bargain you make with your future self, that you'll still find it amusing to have one when you're 20 years older than you are now.

I'm not quite sure I have the confidence to do that, but also I don't have any special desires to get a tattoo. I've joked that for people of my generation who played dungeons and dragons when it first became popular, circa the late 70s, early 80s, I do have. a sentimental fondness for those old illustrations from the Dungeons and Dragons books. There's all these crazy pictures of monsters and things like that. It's slightly amateurishly done, but often with something of a sense of humor. So there's this wonderful drawing of a lurker above. That was one of the monsters in the Monster Manual. It would disguise itself as a ceiling. It was kind of a flat pancakey thing, the lurker above. And it would disguise itself as the ceiling of room you're in, and then it would fall on you. And there's just great drawing.

in one of the books of Lurgor above falling on a poor warrior with their look of surprise and their sword drawn, that's a tattoo I could imagine myself getting. It's not going to happen, don't worry, but that was the joke that I was happy to go along with. Samuel Benjamin says, I've been a long-time listener to and patron of Mindscape and Love the AMAs. The podcast you did with Joe Rogan, however, still stuck in my mind as some of the most effective communication on quantum mechanics, many worlds, and other typical mindscape topics by you or anyone else. I think it was being asked questions by a layperson that made it so clear and engaging. Plus, Joe, for all his myriad faults, is not afraid of asking stupid questions.

My question is, have you ever considered doing something like this set up on Mindscape or on someone else's podcast where you answer a layperson's question on a given topic? Well, I did something like that when something deeply hidden came out. Rather than doing a solo podcast where I talk about many worlds, I did an inverse podcast with Robert Reed where he asked me questions. He was a little bit obviously more expert than Joe Rogan was. You know, I don't know what the answer is to the specific question, but let me, you know, mention a certain reality of the situation. The audience, for Minescape, is going to be full of people with different levels of knowledge, right? Some are going to have heard a lot about quantum mechanics already.

They don't want to hear the same thing over and over again. But many will be absolutely new to it, and they will not have heard anything at all. So it is difficult to keep everyone happy at once. And I try in the AMAs, for example, to mix things up. So some people get frustrated because there are somewhat technical questions, like about the Riesch-Lydra theorem. Other people get frustrated because there are basic questions, like, you know, how many times per second is the world branch or something like that?

And I have to try to guess from the question what level of answer would be appropriate. Sometimes I guess right. Sometimes I guess wrong. there's no perfect solution to this, right? You know, someone else asked just earlier in the AMA, could you have more technical, deeper things going on in the solo episodes or the AMAs? There's no one right way to do it.

So I try to do different things at different levels for different audiences in different circumstances, and I do a lot of things, but I can't do them all. So let me know through various methods, if you think that in some way I could be doing it better, I'm always happy to take suggestions. Now I'm going to group two questions. Actually, the last question, these next two are kind of grouped together,

but they're separate, so I'm grouping just these two, having just answer the last one. Shambles says, I recently listened to a debate between the archaeologist Flint Dibble and journalist-sledo-suchist Graham Hancock on a popular podcast. It's Joe Rogan's podcast. You don't have to hide that. We're allowed to say it out of that.

here. Unsurprisingly, the Hancock fans hailed this as a great victory for him and his wacky ideas, despite the total lack of evidence to support them. Be it this or other debates between experts and conspiracy theorists or science deniers, do you think these public exchanges are useful, or do they just give oxygen and legitimacy to nonsense? And then Cole Justo says, recently a clip of Terrence Howard on Joe Rogan went viral on Twitter. In the clip, he claims that the periodic table is wrong and that a better version was revealed to him in a dream when in his mother's womb. This is obviously crazy, but many people online seem to want to hear him out and defend him against legitimate scientists who made their

best efforts to debunk it. In general, the anti-establishment sentiment, anti-establishment sentiment, the scientists are hiding some deep truth about the universe and are untrustworthy just bummed me out. Do you have any ideas for ways to rebuild the trust between our institutions of knowledge and the common citizen? So, you know, both questions have to do with how one deals with bad science in public fora, such as Joe Rogan's podcast or anywhere else. And, you know, I think that once again, not to be wishy-washy about it, but it's going to depend on the listener, what kind of strategy works the best. You have to ignore the fact that some people are just going to believe nonsense no matter what you do to them, right? You can't be frustrated by that. It might be

frustrating, might be annoying, but that doesn't mean there aren't other people who you could reach by some effective methods. You have to think about and strategize focused on the people who might be persuadable, not the people who are already lost to reason and common sense. So I'm not going to try to convince Terrence Howard. I might try to convince someone who is mildly curious about Terrence Howard, and likewise Graham Hancock and his fans. Once you're a deep fan of Graham Hancock that I'm not going to try to convince you I've moved on. But if you've never heard about it before and maybe you think that it's potentially interesting, then I think it's very, very useful that someone like Flint Dibble will take the time to say, no, here is why

real serious archaeologists don't talk this way, okay? But you can also overdo it. If you spend all of your time debunking nonsense, then you don't have any time to get out the good stuff. So as part of thinking that there are different strategies and different ways to communicate good science and build trust and things like that, my own personal preference is to talk about the good stuff, to lead by example, if you want to put it that way. I don't want to spend my time debunking nonsense. I've done it in the past. I'm happy to do it when the occasion calls for it, but I don't want to spend most of my time doing it. I think that in our urge to debunk nonsense, we very often don't have time to talk about all the cool stuff that's going on. So Mindscape in particular

is devoted to talking about the cool stuff that is going on. And I know that Mindscape is never going to be the biggest podcast out there. You know, it has a very good-sized audience by my expectations when I started it. But it's never going to be, you know, number one on the charts or top 10 on the charts or anything like that. It's for the audience that wants nothing but the good stuff that is not attracted to the conspiracy theories, the wild alternative, pseudoscientific nonsense, things like that. And those people deserve to hear even more good stuff. That's what I'm all about and that's what I'm going to spend most of my time doing. James Allen says, when reading your books on Kindle, where can we see, we can see

where other people have made highlights. As the author, do you ever go through and see what other people are highlighting to see what parts are resonating particularly with readers? Not so much, to be honest. I have seen it, because I do download Kindle versions

of my own books, just so I can have them on my iPad, which is where I read Kindle, and it's very good as a resource sometimes, and then you notice when there are underlining and things like that. But what I've noticed is, it's not, you know,

there's no relationship between the things that I think are most interesting and insightful and the things that get underlined by readers. Because if I'm writing a book on something, I've thought about it a lot and read about it a lot and more knowledgeable about what has been discussed over the years. And what people underline is often like the most obvious stuff for the things that has been established for the longest. And so less interesting to me. So you got to say it. You got to say the things, you know, no one is born being an expert in anything. So it's a first time that you learn any fact that's crucially important. I try to do a good

job at explaining the well-known facts to people, but it's sort of not the part that is most interesting to me, of course, writing the book. So I'm happy when people underline things, but it doesn't affect my writing or reading very strongly. Matthew Wright says, what are some of the cutest things that Ariel and Caliban have done recently? Ariel and Calabin do a lot of cute things all the time. You know, we were just on a trip to France for 10 days. So we had a cat sitter come in every day and visit Ariel and Caliban. And they're both, especially Caliban, well, they have different personalities. Caliban is very social. He wants to be with people. You know, when people come over, he visits them and says hi. When we're here, he wants to be close to us at all

times. So he is just a lovemonger. He, you know, wants attention. And when we're gone for a long time, he gets annoyed by the fact that we're gone. He doesn't like it. Ariel is much more of a delicate flower, and she doesn't, you know, if there's people over, she's hiding. People don't see Ariel. Our cat sitter is now a regular cat sitter, so she's made friends with the cat sitter, so she'll come out for her. But most other people, she's not going to try to socialize with, but she's also needy. You know, she wants, you know, she sleeps in the bed with us at night. She needs that time. She has special places around the house where she will go to to get petted and things like that. And after you come back from a long trip, she wants extra pets and extra

reassurance that we're here. We love her. We're not going to abandon her. So it's not specific cute things that they've done recently so much as just they've been wanting reassurance that our absence for 10 days is not the sign of anything to come. And so we've been giving them that. Jonathan Good says, does eternal inflation have an anthropic preference for young universes since they are most recently undergoing inflation. If so, could it be used as an argument against Boltzmann brains? Well, this is gesturing toward an important, unclear problem in eternal inflation, which is called the cosmological measure problem. If you have, so not to, I don't want to spend too much time explaining eternal inflation, but basically in many models of

inflationary cosmology, which makes the universe expand at a super fast rate at early times, in some region of space, inflation ends, and the universe gets hot, and it looks afterward like the Big Bang, looks like the kind of universe we live in. But in other parts of the universe, inflation keeps going and it keeps going forever. So in an infinite amount of time, you make an infinite amount of universe and an infinite number of different things go on. And now, of course, you want to make predictions in that kind of universe, and it's hard to do because an infinite number of things go on. And if you want to say, well, what is the ratio of A happening to B happening, A and B are both going to happen infinitely many times? So you're dividing infinity by infinity, and that's hard to do. That's the cosmic measure problem. I don't think it's been solved. I don't think we have any decent way of answering these questions. And I think that people kind of under-emphasize this problem. I mean, there are people who are over-emphasizing it also. People like Paul Steinhower. who is a very thoughtful guy, one of the pioneers of inflationary cosmology, I think he's gone too far to the other side. He will say now that because of these infinities in eternal

inflation, inflation makes no predictions whatsoever and is completely non-scientific. I think that's going too far. I think we have to think carefully about how to make predictions under these circumstances, and guess what? I think it's the perfect kind of thing for philosophers and physicists to get together and work to try to solve. They haven't done that, so I don't know what the correct predictions are. There are plenty of attempts that make silly predictions, and some of them do have what is called the Youngness Paradox, but I do not think that that actually has any relationship to reality.

Neither way, no approach that I know about help solve the argument with Boltzman brains, because as soon as inflation does end in any one part of the universe, you don't know when you are in the universe, much less where you are in the universe. If you're just asking where could I possibly find myself, any part of the universe, if there is a possibility of Boltzman brains existing, eventually the Boltzman brains dominate. There's going to be much more Boltzman brains than not. It's very hard to wiggle out of that by making predictions carefully in some inflationary scenario. Matthew Cushman says, listening to your recent solo episode on AI and your interview with Gavin Schmidt, it seems to me that you would be concerned with both the environmental and animal welfare impacts of food.

What are your thoughts on ethical eating, e.g. veganism, vegetarianism, pescatarianism, meatless Mondays, or whatever. I think that, number one, the environmental and animal welfare impacts are both perfectly legitimate things to talk about, but two very, very separate issues. I wouldn't want to get them mixed up with each of, other. But more importantly, in other contexts, I've said this, and in this context, I think I said this too, I think that it's a mistake to address these issues as concerns of personal virtue, that, you know, you are making the world a better place by not eating the hamburgers or whatever. I mean, maybe it's true, but it's such a tiny, tiny impact on the world that I want to roll my eyes and say, you're not really helping the world that much. The way to help the world is to change the

system. Okay? If you think that, and it's true as we talked with Hennar Ritchie, for example, meat, beef especially, exerts a disproportionately bad impact on the environment, and therefore it would be better if we ate less beef, even if you have, forgetting about the ethical questions, even if you thought that it was fine to eat beef, but the environmental, packs are bad, then eating less would be a good idea. I personally don't eat that much, but I eat some a little bit. But to make the world a better place, what you should do is make beef more expensive, make it less attractive to eat beef systematically for everyone in the world. That's how to make the world a better place. For example, you could make alternatives. I'm a huge fan of meat alternatives

in various ways. I think that's the right way to make to actually have a better impact on the world. David Wright says, your guest, Kermenvafa, surprised me by dismissing supersymmetry as no longer an acceptable research area. Can you identify the research that has led to his conclusion? I'm aware the LHC has not found the LSP yet,

but has the entire theory been ruled out. So I'm not sure exactly what you're referring to, but certainly Kermovva of all people does not dismiss supersymmetry as an acceptable research area. string theory relies on supersymmetry. You need supersymmetry. But what he was referring to, I think, I'm not, again, I'm not exactly sure what quote you have in mind here, but what he's referring to is the fact that at low energies, very low energies, well below the large Hadron Clyde or the energies of the ordinary world where we see electrons and protons and things like that, there is no supersymmetry. There's no supersymmetry manifest. There is not a particle with equal mass and charge to the electron, but in different space. There would have to be such a particle if there was unbroken supersymmetry at low energies. I think that's all he was saying.

We know that supersymmetry is not manifest in the low energy world. It could be broken, and then it would only be manifest at higher energies. We were very, very hopeful that that would be the large Hadron Collider. We would see supersymmetry by now, but that turned out not to be the case, at least not yet. But string theorists definitely need to be optimistic that it's broken at some energy scale, that it exists at very high energies. So Vopha in particular has been an enormous amount of work on supersymmetry. So he does not dismiss it as an acceptable research area.

SAAS, SOZ, asks a priority question. I'm wondering how one can argue for the passage of time. I can see how it is possible to argue for an asymmetry of time. Assuming this asymmetry, we can arrive at a B-series convention of time to use McTaggart's terminology. So event A before B, but no spatially extended nashmated. Yet what eludes me is how one then ascribes a dynamic notion of passing or flowing to this order of events. You alluded to the possible misconception of thinking of time is flowing in Chapter 1 from eternity to hear. However, could we think of passage of time in a sort of B series way?

I do not like the A series B series distinction. I think that that is sort of not a useful way of thinking about time. But I am an eternalist, a block universe kind of guy. I think that the best way of thinking about reality is as, or at least classical universe reality, is a four-dimensional space time where all moments of time are just as real as each other, just as we ordinarily think of different points of space as just as real as each other, even if we're not there. And if in that case, there is no physical process called the passage of time.

All elements of time exist. So the question you want to ask really is, why do human beings find it useful to speak a language of time passing. And I think that eventually comes down to entropy increasing and the arrow of time, and in particular, how that increase of entropy affects our human scale perception of the world evolving through time. Roughly speaking, what's going on is that human beings in their minds have images of what they are doing right now, of what they were doing a moment in the past, and what they will be doing a moment in the future. And they are constantly updating because the moments are different, right? Each moment, you have a different idea of what

you're doing now, what you're doing in the past, what you're doing in the future, and there's an imbalance between how you think about that past and how you think about that future, and that constant updating is what gives rise to a feeling that time is passing. It's not a feeling that bears closer examination, right? Because time is passing with respect to what? With respect to time? That's not kind of a meaningful thing to do. But I don't think the passage of time is a fundamental thing. I think it's a way that we talk, and it's perfectly respectable to ask why we find it useful to talk that way. Josh Charles says, I'm wondering if I misunderstood something about the Boltzmann Brain hypothesis.

If a Boltzmann brain did emerge from randomness, wouldn't there be a preference to sticking around, rather than randomly fluctuating back out of existence, because of the interactions that happen once the configuration is in place? It feels like there's a preference for higher order complexity because once it appears, it's by definition, more resilient against random fluctuations. Well, no, no, that's not true. There is no preference for higher order complexity in thermal equilibrium. You know, all of our intuitions about how the world works are trained on a world where there's a very strong arrow of time because there's a very low entropy past from which we are still evolving.

So our guesses as to how things work don't extend very well to the Boltzman brain scenario where you start from thermal equilibrium, from maximum entropy, and you randomly fluctuate into a lower entropy state. That's not something that ever happens in our experience, but eventually it would happen if you waited long enough, and that's where the Boltzmann Brain scenario starts. But then if you ask, what is the most likely future of such a configuration, it's exactly the time reverse of the most likely past,

because there is no arrow of time in this situation. So whatever situation you get into, the prediction for the future is you're going to get out of it in exactly the time reversed way. There's no preference for a complex system to stay complex. The preference is to go back to thermal equilibrium. Rue Phillips says, tell us about your best France experiences. I just booked a trip for my family to go to Chamonie in the Alps and Avignon in the south. We're trying to get more out into country and nation. and we've done in Paris and Normandy more than once.

My favorite red wine is Pinot Noir, and I hear that red burgundy from France is like that. Do you have experience with Burgundy, or do you prefer other French wines? Yeah, I hate to sound like a broken record, I guess, but look, people are different. We're going to have different experiences in France. Jennifer and I are not get out into the country people. We're happy to do that, happy to get out in the country, but that's not our primary drive when we go elsewhere to visit around. We're more city people and sometimes individual excursions like this. I don't, sorry, I need to slow down here because when I put up the call for questions on Patreon,

I mentioned that I was going to France for about 10 days. I had just come back and we had a lot of wine and a lot of asparagus. Asparagus must have been in season. It was on every menu that we went to while we were in France. So the questions reflect this. And I don't know if the people who are listening, who had not read that Patreon post, know what we're talking about here. We're talking about my recent trip to France. Anyway, so we went to Bordeaux, which was a lifelong dream, or at least a dream that Jennifer and I had had for many years, because those are our favorite kinds of wines.

Bordeaux and Burgundy are probably the two biggest wine-producing regions in France, but there are many others, Cote d'Aone and the Loire Valley and so forth, not to mention champagne. Very, very roughly speaking, burgundy wines are lighter, and yes, they are mostly Pino-Nois. Whereas Bordeaux wines, well, there's the right bank and the left bank. The left bank is mostly going to be Cabernet, and the right bank is going to be mostly Merlot, but they all mix together. In Bordeaux, there's a list of six varietals of grapes that you're allowed to use. I don't even think Pino-Nois is one of them, so you're not even allowed to use Pinoir in Bordeaux.

But we like Bordeaux's the best. The thing we learned is that, and this might not be true, but the impression we got from our few days in Bordeaux is that at the less expensive level, at the wines you might pay $20 or $30 a bottle for, and they're going to be generally, they're not going to last as long. They're going to be drinkable within a few years. You're not going to want to wait 20 years to drink them. In that category, we liked the Wright Bank wines. better, santa milione and regions like that. But the more expensive wines, we like the left bank wines better. Chateau Margot is one of our favorites, actually, as I already mentioned. So Chatego Margot is the one we got to visit, and we visited Chateau Presac in the right bank. And, you know, maybe our experience is absolutely not very comprehensive here. So our impressions might be wrong, but we like the ways that the left bank, the Medoc region wines, age better than we did. We got more out of them than the pricier right bank wines.

In terms of experiences, yeah, we like to visit around a little bit, walk as much as we can, because walking is a great thing in France in a way that the United States is just not adapted to that. It's always fun to go to museums, but May is sort of the height of tourist season, and they're all very crowded, so we didn't do much of that. So a lot of it, you know, a lot of our time was spent, other than visiting the vineyards, we took one class about Bordeaux wines, which was super interesting, and then we sat around and ate and drank, not like into excess, but to excess in time, not an amount of food or drink, but we would just, you know, have a good meal and sit in the cafe

and watch people walk by and have a great time. and we didn't do any work. We brought our laptops because we are inseparable from our laptops, but we almost didn't open them up while we were there, which was a great thing to do. But France, like many other countries, is a whole country. There's many other things to do. I have friends who visit France regularly just to ride bikes across the countryside.

I mean, obviously there's a lot of history there, a lot of great landscape and places you can go to the country and escape. I wouldn't be the person to ask about that, but if you love it, then it's a great place to do those kinds of things. Brian Mendoza says, if it was discovered that the United States had been concealing contact, possession, or knowledge of non-human technology, would you find that upsetting or justified? Well, let's be very clear. I think that the chances that's true are essentially zero. So I'm not worried about this question, really. But let's put it this way. If the United

States does discover such things, do I think they should keep them secret or let people know? they should let people know. I think that I suspect that governments overall err on the side of keeping secrets more than they should, and certainly for something as super duper important to the nature of being a human being, as that I think that they should let people know right away. Kevin James says, I was listening to your solo podcast number seven, 270, and at the point where you were talking about AGI and cyborgs, it seemed to be that you were so close, putting these two together to have a new worry of a super intelligent cyborg? What if this ends up being our path to super AGI? Would you increase your credence to this outcome occurring in the next 20 years? I suppose it's not purely artificial. I don't think I'm worried about cyborgs.

You know, cyborgs, I take it, and maybe different people have different attitudes towards it, but I think that to me a cyborg is one that still has the human mind, the human brain, but is adding cybernetic parts to its body. in some way. That might be very, very important and very useful. I'm slightly of the opinion that improvements in biology are going to lead to bigger differences in how human bodies are repaired and modified in the future than in other kinds of technology. But who knows? I'm certainly very, very open to different possibilities there. I just don't see that as a major phase transition. unless what you mean is somehow melding silicon-based thinking to more biological-based thinking.

I don't know whether that counts as your scenario. That's something that I'm very, very open to by I know nothing about, so I have not even enough information to worry about it right now. I'm going to group two questions together. One is from Jonathan Cart. Where do you stand on the positive integers summing to minus 112th? My understanding is that there are useful implications of this result in string theory. Is this mathematical hocus pocus, or is it hinting at something interesting about the nature of infinity? And Scott Liewicki says, an infinite number of mathematicians walk into the 29th Street Tavern.

Each beer costs a dollar. The first one pays for one beer. The second one pays for two beers. The third one pays for three beers and so on. In the end, the bar owner lost eight and a third cents, one one-twelfth of a dollar. Some particle physicists are tabled nearby, drinking wine, of course, see this, toast mathematicians and decide to apply this to obscure particle physics. I am sitting at a corner table very, very confused watching this and decide to switch to hard liquor. Please, please explain

what just happened. So I don't know what brought on two different questions about this exact same topic, maybe the fact that we had a string theory episode recently, but there's a well-known mathematical curiosity that is sometimes explained as if you take the positive integers, one, two, three, four, and you add them together, one plus two, plus three, plus four, etc. What answer do you get? You might say, well, the answer is infinity, but you're told that the answer is actually minus a 12th. What in the world can that possibly mean? How in the world can you add up integers and get an answer that is not an integer? How in the world can you add up an infinite number of positive numbers and get a number of increasing positive numbers and get a number that is not

infinite? How can you add a number of positive numbers and get a negative number? Like all of this makes no sense at all. So the answer is that, of course, when you're told the sum of the positive integer is minus 112. You have to define what you mean by that. And that people are intentionally hiding from you what they mean by that because it's kind sounds boring when you actually explain it. But the provocative claim gets more people talking about it. So of course, the sum of the positive integers stated just like that is meaningless.

It's not a number, right? There's no actual limit that you approach as you add up all those numbers together. when you can add, you can add an infinite number of numbers together if the sum of them approaches a limit. Like you can add one half plus a quarter plus an eighth, one over two to the end. There's an infinite number of them, but they approach the limit of the sum being one, and that's perfectly well defined in a unique way. That's not the case for one plus two plus three plus four, et cetera. So what you do is, in the back of your mind or explicitly, you say, look, rather than adding up the positive integers, I'm going to write down a sum. of numbers as a function of some other numbers.

So I'm going to add up, I forget what it is. You're going to, I'm going to get it wrong. You know, if you add up n to the power A, for n goes from zero to infinity, okay, but as a function of the number A, right? I'm not going to tell you what A is, but just as a general function, we'll leave A undetermined, add up n to the power A. And that would be something you could do, for example, if A is minus a hat, then you get the sum we just said, a half plus a quarter plus et cetera.

But then you can look at it for different values of A. And so you play a trick like this where you have something which for certain values of the parameter, A, is perfectly well defined. And then you extend it and you take a limit and you say that, okay, I'm going to approach a limit where this sum looks like 1 plus 2 plus 3 plus 4 plus 5 plus 6. et cetera, and I find that the limit of this function as it approaches that value is equal to minus 112th. So basically what you've done is you've regularized the problem. You've expanded the question, what is 1 plus 2 plus 3 plus 4, to a different question? What is the sum of, what is the

function defined by the sum of these numbers? And then you take a limit in a certain way to get the answer, it's minus 112th. And then you proclaim that that is actually the answer. to the question that you started with. Is it? Well, you know, it is with all the additional caveats that that's what you really meant by that. It turns out that this particular question in the string theory is very well defined. You're calculating the vacuum energy and string theory. On the string world sheet itself, this kind of mathematical expression shows up. So I don't think it's anything very deep. It's kind of both at the same time a trick and something that is true in the particular case where you

about it in string theory. It's certainly not anything to worry about too much. No one is pulling the wool over your eyes, nor is there something deep about the nature of infinity that is hard to understand. Neither one of those is the case. Nevada City Bob says, as I understand it, during hawking radiation, one particle with positive energy escapes from the black hole, while another nearly identical particle with negative energy remains inside. Does negative energy exists anywhere other than black holes? Well, again, this is an example, much like the previous one where people are telling you somewhat sensational things because it sounds more impressive than the reality. What do you mean by energy in this case? The thing about being inside a black hole,

remember, is that you can't be stationary inside a black hole from the perspective of someone who's outside the black hole because you're separated by an inventorizing. From the perspective of the people inside the black hole, you'd have to be moving faster than the speed of light to be outside the black hole. So what is actually going on is that you can define a quantity which has the interpretation of the energy of a particle as it would be measured by an observer outside the black hole, indeed infinitely far away from the black hole, if they could do that. A slightly weird quantity to find, but mathematically you can do it, right? What would the, what is the energy of the particle as seen by an observer at infinity. Okay. And that actually is a meaningful thing. Because

if you think about it in relativity, relativity, the word relativity means that things like velocities are only defined relative to something else. And the energy of a particle certainly depends on it, depends on its velocity. Right? The kinetic energy depends on its velocity. So when you're inside a black hole versus outside, that's a tricky thing to define. There is a way to do it, but what it leads to is that there can be particles, which from the perspective of someone at infinitely far away from the black hole, the energy of a particle of a certain kind of particle inside the black hole, can be negative. Now, they're infinitely far away, right? It doesn't matter. You can't make a negative energy particle right in front of you. If you were falling into the black hole

and you asked about the energy of the two particles making up the hawking radiation, one going in and one going out, they would both have positive energy. But that doesn't matter to the point of view of someone who is infinitely far away. They're the ones, the infinitely far observer, who are going to measure how the black hole as a whole is changing in its energy. And the answer is it's going down in its energy because it's emitting radiation to the outside. So it sort of has to be, it has to be absorbing particles of negative energy from the perspective of the outside of observer. Chris Gunter says, would you use a source of, Star Trek teleporter, one that disassembles you on one side and reassembles you on the other.

Let's assume it's as reliable as in the show, but what if you effectively die when going in and a different consciousness pops out on the other side? I don't think that's true that you do die when you go in. I know people have said this, but this is another classic example of where our intuition doesn't work, because our intuition is not trained on teleporter machines. We don't have any such things, transporter machines, they would actually be called in Star Trek. So because we're actually trained in situations where there is physical continuity over time in most of the stuff that makes up our bodies, individual atoms come and go inside our bodies, right? But it takes a while. Overall, the bones and the organs in our bodies are more or less persistent over time. So we associate

that with something real, something fundamental. There is you. You are a person. You are a person. You have a body, there you are, et cetera, et cetera. If you're more strict about it, if you're more careful, then the you that exists at one moment of time is not the same you that exists a minute later, even in the regular old world. Forget about transporter machines, et cetera, okay? You're in a slightly different configuration of stuff, you're in a slightly different position in space, and so forth. But there are natural, obvious reasons why it makes sense to associate that as one single, person evolving over time rather than talking separately about you at 1 p.m., you at 101, you at 102, etc. The physical continuity there is goes hand in hand with some informational continuity. So not only are they

the same molecules in your body, but they're in that more or less similar pattern, right? The pattern is slightly changed over time, but it persists. And what happens in the transporter machine is that the pattern reappears, but with different atoms, somewhere else. That is not something that we ever deal with in the real world. But to me, what matters is the pattern, not the actual atoms that you're made out of. So to me, you're just still alive. I have no trouble whatsoever stepping into a transporter machine, if it is perfectly reliable, because I think I would call the me that came out the other side exactly the same me.

is the one that went in in precisely the same sense that the me at 1 o'clock is the same as me at 2 o'clock. Mark Kumeri says, I was under the impression that cosmic inflation was generally well accepted among cosmologists and theoretical physicists. Recently, it seems that several prominent physicists have expressed their doubts with inflation. Listening to one of your podcasts, it seems like you are not entirely convinced as well, as I believe you think a better theory might come along, even if inflation might be the best one today. Can you elaborate on your concerns with inflation and perhaps discuss the viability of the inflationary multiverse? This is a very long conversation.

I would encourage you to read my book from Eternity to Here, where I talk exactly about this. I think that inflation is a great theory, and it may or may not be right. At the most basic level, the energy scales and the physical processes that we talk about during inflation are very, very, very far away from anything we've directly probed, experimental. So in that sense, it is entirely speculative, which is fine. Speculation is fine, but we shouldn't get too attached to our speculations. The other big worry is, of course, that I think that we don't have a good theory of how and why inflation started.

People cheat about that all the time. They think that if it's simple, it can't be too difficult for it to start, but it's very, very low entropy, the condition you need to make inflation go. and as Roger Penrose has been emphasizing for many, many years, you need to explain why a physical situation is so low entropy, because low entropy means there's a very, very, very tiny fraction of all the possible microstates you could have been in that you actually are in. Someone like David Albert, philosopher of science, will just say,

well, that's a law of nature. There's a law of nature that you started in this kind of low entropy state. I think most physicists would want an explanation of that, and we don't have one. And then finally, the multiverse, of course, as we just discussed in an earlier question, has these, raises these problems with predictability and being able to understand why certain things are more likely than others, as Paul Steinhardt and others would argue. So I think that there's plenty of reasons to worry that inflation is not the final answer, despite the fact that it's a very good theory. And I think that in that situation, you have to keep an open mind. I think that's fine to do. But you're right, a lot of working cosmologists just take it for granted that inflation,

is right, I think that they're a little bit premature in doing that. Humberto Nani says, so, how did Ariel manage to get the Quanta and Fields book? For those of you who have bought Quanta and Fields, the dedication is to Ariel. Book one was dedicated to Jennifer. We have a three-person household here. And, sorry, well, me, plus three others, Jennifer, Ariel, and Caliban. So Caliban will get the next one. He will get complexity and emergence, which will be volume three. Given that Jennifer got the first one, which I think makes sense, the question was between Ariel and Caliban, who should get the quantum mechanics book and who should get the

complexity and emergence book, Caliban's just more of a chaos agent than Ariel is, whereas Ariel is a little delicate and unpredictable, so I thought that Ariel fit better with quantum mechanics. Caliban fit better with complexity. But honestly, they could have gone either way. Now, of course, we have a stray cat puck who hangs around outside. Maybe. Maybe. I should write a fourth volume just to give him something to dedicate to. Alex says, we all remember pictures of particle tracks and bubble chambers. They allow us to determine momentum and location at the same time. It looks like a contradiction to the Heisenberg uncertainty principle.

What am I missing? You're missing numbers. So look, I've seen pictures of cars moving through time, right? That doesn't violate the uncertainty principle, just because the uncertainty is small. And I think the same thing is going on with the tracks in the bubble chamber. If you actually run through the numbers and look at the precision with which you are measuring the location of those particles, it is not infinite. In fact, it's a little crude, right? And if you try to improve the precision with which you are measuring the locations of those particles,

you would find that their momenta become disturbed by those measurements in 100% compatibility with the uncertainty principle. So people would have noticed if that was actually a contradiction. Don't worry. David Maxwell says it seems to me there's a tension between a kill switch to prevent AI getting out of control and the right to life of a conscious AI when the latter is potentially a key argument for the former. But how will we tell if an AI develops consciousness given its subjectivity? Yeah, I think it's a good question. I literally have no good things to offer here. I kind of think that we've done a crappy job, both within science and philosophy, of taking seriously.

this question of when will AI really count as conscious? It's nowhere close, in my opinion, right now, as I've said in other places, we have developed these large language models that are incredibly good at mimicking consciousness without actually getting it, but that's a different thing. We should take that difference seriously. There's a great threat on Twitter where I forget who did it. I would like to give them credit, but they talk about a professor who did the following thing. took a pencil, and he attached two googly eyes to the pencil, and then he held it up to his class, and he said, hi, I am Tim, the helpful pencil. I will help you think and write and express yourself in useful ways. I'm really glad that we're going to have a relationship where we both work together

better. And then the professor suddenly snaps the pencil in two. And the whole class goes, they're shocked. How could you kill Tim like that, the helpful pencil? Of course, it's just a pencil, right? but the professor then says, this is why there's a lot of hype about AI. And that's exactly right. AI, again, as I've said many times, is going to be hugely transformative in many ways. That doesn't mean that it's actually a conscious agent. What it means is that they figured out a way to make it act like a conscious agent. And we human beings, again, because of all of the training that we have had in dealing with the world before computers came along,

is that things that act conscious are conscious. Now we have something different, things that act conscious without being conscious, and we don't know how to deal with it. We assign, once again, Dan Dennett explained to us years ago. We assign agency, we assign intentionality to things that seem to exhibit it. But we have to think a little bit more carefully about whether that assignment is correct or worthwhile in a practical sense in regimes where we have not yet been experienced to previously in human history. Michael Gibbs says, I've recently seen several articles claiming evidence has been found that dark energy is weakening over time and how this is rocking the foundations of physics. To me, this falls into category of extraordinary claims require extraordinary evidence. I'm curious if you think the data is strong enough to take this seriously, and if so, what are the major implications?

I mean, the data are strong enough to make you be aware of the possibility. The data are not nearly strong enough to make you think it's true with some high level of confidence. What Michael's referring to is various claims, especially from an instrument called the dark energy spectroscopic instrument, D-E-S-I, DESI. Desi. There's too many things called DESE in physics, sadly, so you have to spell it out every time. But they have a new result that says without a lot of statistical significance that their data is most compatible with the dark energy slowly decaying over time. I'm not going to get too excited about it. These are very, very difficult observations to make. the dark energy could decay over time. That's absolutely possible. I think that having it be constant over time is much more robust and plausible. So I'm going to bet that. I'm going to put most of my

credence on that until the evidence becomes a lot stronger than it does than it is right now. Joel Rembach says, if we can't access any of the many worlds, what is the purpose of studying it when there are still many discoveries to be investigated in the reality we exist in? Look, I've said before, I don't care about the other worlds. I care about, I care about the laws of physics. The question is, we have problems with quantum mechanics as it is taught. It is not a sensible, rigorous, coherent theory. We make things up, like observations and wave function collapse that aren't rigorously defined. Many Worlds is a well-defined theory that replaces the ill-defined Copenhagen interpretation and lets us actually do science with it. The point of many worlds is not the other

worlds. It's that we've answered the question of what is a measurement, why do you get probabilities and things like that? And equally importantly, there's the fact that we don't know the fundamental laws of physics. We're not done with physics yet. We're trying to build better laws of physics. And I strongly think that taking quantum mechanics seriously and thinking about what is the correct foundational version of quantum mechanics will be useful to that program. So again, it's not about the worlds. People who really obsess about the other worlds are the ones who haven't really internalized many worlds. Many worlds is just, it's always obeying the Schrodinger equation. That's the essence of the theory. G. Agnes, oops, I'm sorry, I should have practiced

ahead of time. Aganesian says, listening to the podcast with Claudia Duram about how gravity could be an emergent force and your own explanations, how the macroscopic reality we observe is emerging from underlying elementary physics, I have a naive question. Is it possible that we may be missing a force similar to gravity that is emergent and acts in a much bigger scale than gravity, say at architectural scale of galaxies and even galaxy cluster levels, not trying to contradict Einstein? It's possible. Many things are possible. But of course, we've thought about that. You know, we've thought about both modifying gravity and adding new forces in. So far, the theories that we have, are certainly not better than general relativity plus dark matter.

They're usually worse in some way or another, but there's always going to be a limit where they become indistinguishable. So there's no evidence for any kind of thing like that, and there's no obvious benefit to doing it. So it's not a very popular way of thinking right now, but it is possible. And so we still keep contemplating these other theories because unless you write down what the theory is

and think about what it predicts, you don't know how to test it, right? So that's what we're trying to do as modern cosmologists right now. Mark Baranger says, I hope you enjoyed your trip to France. What other places in the world or off world do you like to visit, and why? I'm going to erase off world from that. That's a whole other category that I haven't really thought about, and we don't have the capacity to do. But in the world, you know, I've traveled a lot, but not a lot a lot.

Like I'm not a super-duper world traveler like some of my academic colleagues are. Never been to India. never been to North Africa. I would love to go to the Maghreb region, right, Tunisia, Morocco, Algeria, those kinds of places. I've been to Spain, but only very, very quickly, and not really very seriously. I've not been to Eastern Europe, really. I've never been east of Germany within Europe. So I have done a lot of Western Europe, South America,

different places in Asia. And it's always a temptation. Like we had so much fun when we went to Hong Kong and we had so much fun when we went to Japan and we were very, very briefly in Singapore and that was great. And Vietnam, all those places in Southeast Asia, would love to go back to them because we didn't spend enough time. But then again, I've never been to Marrakesh or to New Delhi. So like, do we go to someplace new? I don't know. I would love to do all these things. It's a big world out there. I don't think I'm ever going to run out of places I want to go. Tomer Hakoen says, are there examples of math notation you find particularly nice or elegant? What's the most commonly used notation in your opinion?

Sorry, what's the worst commonly used notation in your opinion? Oh, the worst notation. Actually, I'm sorry, I didn't really read this question carefully. I only read the first half of it. So the first half of it, I think my answer is index notation in differential geometry and relativity. In fact, I had this joke back from graduate school that the reason why notation was so much more beautiful in general relativity than in quantum mechanics or quantum field theory is because in quantum mechanics and quantum field theory, the theories have just been so useful and important ever since they were invented that people just put them to work right away and spent time modifying the theories and changing them. whereas the pace of change and progress in relativity is much slower so people had the time to come up with really good notation. Index notation is a way of dealing with the fact that there are these higher order tensors like the remon tensor and so forth.

There's versions of it in field theory, but they're not very beautiful and different people use different notations and things like that. I don't know. I think that mathematicians like different fonts, they like different kinds of notation, and it's, a little off-putting to the outsiders, and I'm not deep enough into it to be very well-versed in different kinds of mathematical notation. So I'm just going to stick to my own wheelhouse and say index notation in differential geometry. The worst notation, I don't really know. I don't have any, I'm not going to, I'm not, I haven't dwelt on that. So I'm sure if I went through all the notations I can think of, I would be able to come up with something, but nothing pops into my

head right now. Captain Brick says, I've thoroughly enjoyed your book something deeply hidden. One concept I've grappled with is the self-locating uncertainty in the thickness of the branch. I think I've conceptualized the thickness of the branch as the number of copies of each possible outcome. For instance, if an observed event has two possible outcomes, A and B with probabilities 0.3 and 0.7, the world splits into 100 branches 30 with outcome A and 70 with outcome B. And then the question goes on a little bit. Is this a valid way of thinking about the thickness of the branch or my way off? Well, I would say that it's halfway valid. Let's put it that way. In quantum mechanics, if you have two branches of the way you function of the universe, one with probability 0.3,

the other with probability 0.7, you have two branches of the way you function in the universe. You don't have 100, right? So the statement, the world splits into 100 branches, that's an empirical question. Does it or doesn't it? What you can do is say, if I split, the world into branches with the proviso that all branches needed to have equal amplitude. Let's ask that question. Could I split the world further? It's now two branches, one with probability 0.3, one with probability 0.7. I want to keep splitting it so they all have equal, well, you shouldn't, you shouldn't call them probabilities. If I'm being a careful philosopher here, what do you mean is weight. weight is given by the amplitude squared of the wave function.

And the question we're trying to ask is, is it okay to identify the weight with the probability? And well, if you want to ask, if I were to keep branching the universe until I had equal weights on all the branches, then it would be true that the relative number of remaining branches is given by the weight. So if you start with weight.3 and weight point seven and kept branching until you had equal numbers of branches, sorry, equal weights to all the branches, then the ratio of branches of type A to branches of type B would be 0.3 divided by 0.7. And that would be the probability also. So that would be perfectly sensible. But the reason why that's not an automatically obvious thing to do is that it just doesn't necessarily happen, that the universe does. as a matter of fact, branch into branches with equal weights. The skeptic would say that sort of is begging the question, right? Why should I care about branches with equal weights?

What is so special about those? Once you make the statement that branches with equal weights are special, in particular they deserve to be given equal probability, then you get the born rule. Then the probability just comes right out. That's the big step. The math is not the hard part. In fact, if you say when and only when I have branches with equal weight, they give equal probability.

That seems like a very natural thing to say. Then you get the born rule. Then you get the whole thing. You get the probability is the way function squared. That is the only extension. That's the only generalization of the statement that branches with equal weights get equal probabilities. But that's a contentious statement. Some people are going to buy that and some people are not.

I don't know what to say. Paul Hess says, growing up in the 70s, it seemed we were evolving out of an emphasis on the melting pot and toward an emphasis on individual cultural pride, which seems like a good and noble thing. Over the decades, that emphasis kept increasing to the point where melting pot-type perspectives were even looked down upon. Has the pendulum swung too far? Do you think this led to the increased divisiveness within our society? Do you agree with my observation that the emphasis shifted in the first place? Well, I don't know.

I mean, when you say things like there was an emphasis, Where? Who had that emphasis? I think that we live in a very big country. This is a very U.S. centric question, I think. Different people had different emphases, okay? I think something that I would get behind is the idea that in the 70s, maybe starting in the 60s, but certainly in the 70s and 80s, an increasing number of people realized that the melting pot way of thinking, even though it kind of sounded virtuous and good, you know, we're all in this together, etc, et cetera, et cetera, all of that kind of rhetoric where, you know, let's all get together, we're all virtuous and good, let's all be one unified country that tends to end up as a

practical matter favoring the people who are in the better position already, the dominant sectors of society, and squelching or ignoring the people who are in smaller, less powerful sectors of society. So there was a countervailing current, and so here I'm agreeing with you, that said, I wouldn't put it about cultural pride. I don't think that's a big deal, but you can respect differences between people while giving equal dignity to all different kinds of people. You can be different yet deserving equal dignity. I think that's the point. That's the best way of putting it. As the pendulum swung too far, you know, like, I'm not a big believer in individual cultural pride. I think that it's fine if it's completely frivolous. Like, look, I'm a

sports fan. I root for the Philadelphia 76ers for completely non-rational reasons. Not irrational reasons. It's not like bad to root for the Philadelphia of 76ers, but I only root for them because I grew up in the suburbs of Philadelphia, and they were really good when I was growing up, and I became a fan. I am not at all a fan of the Boston Celtics or the Los Angeles Lakers, but maybe if I grew up in those regions, I would be. I think that that's just harmless, right? That's fun. You know, you can root for your team. I mean, it's not super fun to be a Sixers. fan, I have to admit right now, but in principle, it could be harmless fun. But to take too much pride in what country you were born in or whatever, I think that to the extent that that helps motivate equality and fairness overall, it's good. To the extent that it puts other people down, it's bad. And so I think you have to balance it a little bit. Rad Antenov says, could you please clarify what Vafa was getting at with his argument about black hole mass versus charge in plank units? Yeah, this is something called the weak gravity conjecture.

And the idea is supposed to be a conjecture came from Nimar, Connie Hamed, and others originally, that gravity is the weakest of all the forces. So that sounds like a sensible conjecture. Gravity is pretty weak, right? It seems to be weaker than electromagnetism or the strong nuclear force or even the weak nuclear force for that matter. But here's the problem with gravity as the weakest force. if you calculate the force between two neutrons, neutrons have gravity because they have mass, but they don't have any electromagnetic force between them.

So in what sense, because they're neutral, so in what sense is gravity between two neutrons weaker than the electromagnetic force between two neutrons? So what you have to do is define very carefully what you mean by the claim that, the gravity is the weakest force. And of course, you look around at electromagnetism, and similar arguments will work for the nuclear forces, but it's more complicated, so forget about those. You notice that when particles have a non-zero electric charge, there's a minimum value, right?

One. Actually, a third for, because quarks can have plus or minus one-third electric charge. But anyway, there's a minimum value. And so you need to define what you mean by gravity being the weakest force as the gravitational force between charged particles always being weaker than the electromagnetic force between charged particles. So there's a way to turn that into a statement about black hole masses versus charges, but that's basically the important thing

that he was trying to get at. The idea that gravity is the weakest force. Eric Coker says, I'm loving the new book. It's like I have the text to go along with the class now. I'm still struggling with the whole modes to number of particles thing in QFT. A specific mode gives you energy levels, and the amplitude of the mode gives a number of particles of that energy, but what about location?

Specifically, on page 94, you show how to get a wave packet out of a combination of modes. What leads to the tying down of that combination of modes in QFT? The guitar string analogy makes sense for the wave function of a particle, but these modes of field seem like they should extend out forever, and so any combination of them would do the same. Right. So this is clearly a failure on my part, because I did try to explain this in the book, but apparently it didn't come across. And that makes perfect sense because it is very abstract. So when you have the wave function of a particle, you normally, more often than not, even though you don't have to, think about it as a function of position, right, psi of x. And then psi of x goes to zero at plus or minus infinity because the wave function is normalized, right? The integral of the square of the wave function

equals 1. So you can't have infinitely much wave function. You only have a finite amount of wave function, so it has to go to zero at infinity. When we go to quantum field theory, we start thinking about the wave function of a mode. And a mode means a certain profile of the field with a fixed wavelength stretching forever throughout all of space. The only thing that in this slight simplification, the only thing that matters about the mode is how is its amplitude. I hesitate to use the word amplitude because it doesn't mean the quantum amplitude, just means the height of the wave. And so I call it the height in the book.

So we have the wavelength, that's fixed, but the height of the wave is something that we can think about. So the wave function of the field is a wave function of the height of the wave. It does not have a dependence on where you are in space. Okay. So the tying down that is relevant is that the wave function of the height has to go to zero as the height goes to infinity. Does that make sense? You have sigh of the height of the mode. And you have that separately for each different kinds of modes. And so through the magic of Fourier transforms, you can sum up modes in such a way that you have a wave packet that has a relatively localized profile in space. So it's very abstract. It's a lot of steps. to get there. The math all works out, but I'm sympathetic if it doesn't make perfect sense the first time through. Ben P. Stein says in the string theory podcast and his recent review paper, Professor Vafa seems to say that almost all naively consistent effective field theories would be ruled out in a quantum theory of gravity. Is the effective quantum field theory explained in your new book an example of a

naively consistent one that is ruled out? We have no idea. I mean, we hope not. String theorists hope not. So the idea here of the swamp land is that, as Ben just said, most effective theories that you could write down are actually not consistent in a world with gravity. There is no ultraviolet completion of them. So they are in the swamp land. They are not in the landscape. But we don't have a very detailed view of which ones are ruled out and which ones are not. So if the standard model of particle physics plus gravity is in the swamp land and is ruled out is not consistent, that would mean that string theory can't be right because that's the theory that works well in our world.

But we don't know. That's something that we're trying to figure out. Jonathan Goodson says, a question about information loss. When the Schrodinger wave collapses and a specific outcome is observed, is the information that was contained in the wave lost? Or are the specifics of the wave not considered information? Yes, information is lost.

And I do apologize. There was another question, maybe more than one question, I didn't get around to this time, about different notions of information. So, yeah, there are different notions of information. In the context of the phrase information loss in quantum mechanics or quantum gravity, the information we're talking about is the information contained in the wave function. The information needed to completely specify the quantum wave function. And measurement that collapses the wave function destroys that information.

One way of saying this is, if I give you a wave function and say, I'm going to measure it, what is the probability of getting different measurement outcomes? I can tell you that, right? I can just square the wave function. I can tell you the probabilities. If I instead say, I got a measurement outcome, the spin was up, what was the wave function before I measured it? You have almost no idea, right?

It could have been many, many different wave functions that could have given you that measurement outcome. So information has been lost. There's no going backwards in the conventional. view of quantum mechanics. Brian says, I love teaching. I have a bunch of degrees, but I don't care, but I don't care about teaching. Should I and why do you like teaching especially for general audiences?

Oh, I'm sorry. I got very confused by Brian's questions there. His question started, I love learning, not I love teaching. So he says, I love learning. I have a bunch of degrees, but I don't care about teaching. Should I and why do you like teaching especially for general audiences? No, I don't think you should. Some people like it. Some people don't. Some people are willing to do it because it's what gets them a job. Some people do it well. Some people don't do it well. Some people are just devoted to doing research or doing learning or whatever. Look, some people don't even like research. They just like learning the things that other people have already figured out. You know, research is defined as figuring out something brand new. Some people would be happiest if they could get paid just to learn the physics that other people had discovered. Sadly, the world. does not work itself out so that we can get paid to do whatever it is we most like, right?

There's some optimization problem. We each have to go through balancing what we actually want to do versus what the world will let us get away with doing. So very, very often, if what you want to do is academic research, your job is also going to involve teaching. I like it for lots of reasons. I like it because not necessarily in order, but it improves my understanding, right? When I really think about things and try to explain them, I end up understanding those things better. It's a reason to learn new things. Sometimes I teach classes where I only know a bit about the subject, and so I can force myself to learn by teaching it. I get joy out of other people understanding things. That's why I have a podcast.

That's why I write books. That's why I teach and give talks and things like that. It improves people's lives. People like it. People appreciate it. I constantly get, constantly is an exaggeration, but I frequently get people saying, you know, yeah, I read your book years ago and that made me become a physicist, or that just gave me happiness at a time when it was very useful to do that. And so I personally get a lot of value out of it. If you don't, that is not a moral failure on your part. There's plenty of things that other people value and get value from that I don't. That's okay. Lots of different people out there in the world. Catherine Traub says, when you're eating a spear of asparagus, see, I told you, I mentioned asparagus in the call for questions.

When you're eating a spear of asparagus or drinking a glass of wine, are you thinking about physics? Sometimes I am. Sometimes I'm thinking about physics. Sometimes I'm not. One of the beautiful things about theoretical physics or philosophy for that matter is you can think about them at any time. So it is absolutely true that sometimes when I'm having dinner or walking down the street or whatever, I'm deeply thinking about problems in physics or. philosophy. Often not, if I'm having a conversation with somebody that is not about physics, I am not thinking about physics while I am doing that. Tim Converse says, with regard to the arrow of time in the past hypothesis, to what extent was the early universe lower entropy than the present simply because it was denser? Can we imagine alternative early universe configurations that would have been equally dense but much higher entropy? Yes, very, very easily. The early universe was

smooth. It was homogeneous. And because gravity was so strong, a less smooth configuration would generically have had higher entropy. A universe with a lot more black holes at that early time would have had a lot higher entropy. So it is very easy to have much higher entropy states than we had in the early universe. So it's not just about the density. It's much, much more about the smoothness. Dan Cohen says, I love the biggest ideas in the universe books, not done with the second one yet, but so far so good. But I really wish I could follow the math better. Are there any online courses you think are good foundations or not two textbooky books? For example, in the first book, once things got to tensors, it got hard for me to follow, and it even took me a couple

tries just to figure out that linear algebra was the math topic I was looking for. Short answer is no. I do not know specific good online courses, et cetera, but, you know, they're there. I know that. I know there are online courses and also look for lecture notes, like for whatever reason, and I've done this myself, but scientists and mathematicians love to take time out of their busy day and write up pedagogical lecture notes that you can find online about different topics that you're interested in. So very often you can find something like that. I don't know because, you know, I did the whole physics education, undergrad, grad school, postdoc thing. So that's how I learned it. And then. that was many years ago, so even the resources that were best back then are not the best ones now. So I don't know which ones are there, but I'm sure they're there, and I encourage you to look for it. Cooper says, is there an intuitive explanation for why the SU3 group being non-Abelian leads to gluons carrying the color charge? Or is it simply a fact that comes out of the math and doesn't lend itself to analogy or simplification? explanations that I've seen have jumped between these two facts without explaining the connection.

I suspect the answer is that I don't know of a really good intuitive explanation for that. I can say words that are true, but whether they add up to something that you qualify as a helpful explanation, I can't promise you that. I mean, when a group is non-abillion, that means that there's some symmetry transformation, like you're rotating a sphere or whatever, with the property that it matters when you do two different operations, which order you do them in. So if you think about a circle,

and I have rotations of the circle, so I could rotate it clockwise by 20 degrees and then counterclockwise by 5 degrees, right? So the overall change is a clockwise rotation by 15 degrees, 20 minus 5. It didn't matter whether I did the 20 degrees clockwise first, first and then the five degrees counterclockwise or the other order. They go and they add up the same way either way. So that is an abelian transformation. Whereas if I have a sphere, so like a two-dimensional sphere embedded in three dimensions, and I rotate it by 90 degrees around the x-axis and then by 90

degrees around the y-axis, I end up with the sphere in a different configuration than if I did the x-axis first and then the x-axis or the y-axis first or whatever it is. If I change the order of the operations. So that is a non-Abelian group. And very roughly, the gauge symmetries based on non-ab-ab... Well, this is true. Gage symmetries based on non-abili groups have gauge bosons, which interact with each other. You can say that they carry the color charge, that there's a truth behind that, but I think the relevant thing is they interact directly with each other, gluons, W-bosons, Z-bosons, and photons, which... which are based on an abelian gauge group, do not interact directly with each other.

They interact indirectly because they interact with charged fields like electrons and positrons. And then they interact through virtual particles, but there's no direct interaction photons to photons. So roughly, the difference is that the gauge bosons can be thought of as carrying with them knowledge about an infinitesimally tiny rotation. an infinitesimally tiny symmetry transformation. The technical terminology would be the Lee algebra of the Lee group. That's a completely useless bit of nomenclature for you, if you're not into it already, but just so you know, if you ever hear it, an infinitesimally tiny symmetry transformation is the algebra associated with the group.

And likewise, if the group is not a billion, the algebra is not a billion, et cetera, et cetera. That goes hand in hand. And so you can think of different kinds of gauge boson. as individually representing different infinitesimal symmetry transformations. And then the leap where you're not going to be happy with this, but the leap is if these different kind of symmetry transformations, if it matters what order you do them in, then at the level of the particles that arise under quantization of this,

that means the particles bump into each other. That means the particles can interact with each other. I could go into a little bit more specificity, if you were happy with thinking about the Lagrangian of the fields, the kind of Lagrangians on which you base the equations of motion for these guys involve basically boson 1 times boson 2 minus boson 2 minus boson 1. And the minus sign is important there because you're trying to maintain gauge invariance. And if the symmetry is abelian, then boson 1 times boson 2 minus boson 2 times boson 1 equals 0.

There's nothing there. But if they're non-a-billion, then it doesn't equal zero, and so that shows up as an interaction between the particles. That is wildly unhelpful as an attempt at an intuitive explanation, but it's the best I can do. Sorry. Nate Heller says, what are your thoughts about organized labor in academic research, specifically at the graduate level? I asked because our graduate union is currently on strike to obtain a fair contract. I'm super in favor of it. You know, I think that I understand that academia thinks of itself as spousy.

and it's a calling. It's not a mere job. But guess what? Most graduate students aren't going to continue in that calling. They're not going to get a tenured faculty job someday. It is, in addition to being a calling, it is also a job. And I think that students who are graduate students deserve the protections that a union can provide, so I'm all in favor of it. Okay, I'm going to group two questions together. Murray Cantor says, I understand the solutions to the Schrodinger wave equations are quantized. even though time and space are continuous. That said, please explain why you seem to be insistent on space time and space time being continuous, since removing infinities entails ignoring values below the plank length. The continuum is probably a powerful approximation to a lattice space time. And then Lee Vermilion says, how confident are you that there is actually infinity in physics, whether that the universe is infinitely large or that there are infinitely many worlds?

I am not sure where this impression came from, that I have any confidence or any insistence that the world is infinite or smooth or continuous. Quantum mechanics is smooth, right? The way that we set up the mathematical formalism for quantum mechanics absolutely centrally involves smooth time evolution. There you go. But quantum mechanics might not be right. that's completely okay. So what I will say when I'm trying to explain quantum mechanics is that a continuum is invoked by the theory, and therefore we're going to need to deal with that. But maybe nature is different. Maybe quantum mechanics is an approximation. That's completely fine. I have no, in fact,

I literally wrote a paper pointing out that you can slightly quantify, sorry, slightly modify quantum mechanics to make it completely finite, to make it non-continuous. It's kind of a trivial observation once you start thinking about it, but it's a lot of people sort of start with something like a lattice and then put quantum mechanics on top of it, and they gloss over the fact that now you've made it continuous, because there's a parameter in the Schrodinger equation called T, which is time, and that's a smooth variable. So it's a little bit more work to make a version of quantum mechanics that is truly discrete, and it is a modification of quantum mechanics. It's not really the same thing. Also, parenthetically, the continuum is probably not a lattice space time, probably a powerful approximation of lattice space time in the sense that space time is probably not a lattice in any naive sense. We know that because of non-localities in quantum gravity. Lattices are overly simplistic. They're overly cheap, overly local. They break Lorentzen variants. They only allow for generally local interactions, not non-local ones. Once you have things like, black holes and holography and stuff like that, the idea of a simple lattice underlying space time is seen to be overly naive. We don't know what the right structure is because we don't

know what quantum gravity is, but we're going to need to think it would be, we would have thought of it already if it was just a lattice underlying space time. Roland Weber says, can you please tell us a bit more about the Santa Fe Institute? How many people are there permanently or fractal. Is it a place where everyone knows each other or is it too big for that? Are the folks there all scientists from different fields or also people of other professions? Yeah, I guess it's medium-sized. I don't actually know the numbers. The number of people who are there permanently is relatively small. So, you know, the number of people who are always there, not literally always, always employed by there, even if they might be visiting someplace else. How many of them

are there? The back of my mind, I feel like it's about a dozen, but maybe it's high as 20 and I'm just not counting everybody, I don't know. But like many other successful research institutes, it's mostly a big empty building, which they fill with visitors, either postdocs or graduate students or simply programs that are going on where people in some area of common interest come and spend time there and talk to each other. So when you visit, the great thing about visiting is you always meet different people. You know, it's a different collection of people who are there all the time. And one of the amazing features of SFI is that they have been very, very good at picking the right people to have a come visit. And by the right people, I mean ones who get it,

who get the spirit of the place, ones who are willing to talk outside their field and to think big and to ask slightly crazy questions, but in a rigorous, ultimately grounded way. That's a tough little dividing line to hit very carefully. And I think that SFI does it very well. So it's mostly scientists, but there are people, you know, there are some writers, some artists who pass through in various capacities just because of the nature of the people who are the majority of people there, they're also interested in those other areas. So the last workshop I was at where Dan Dennett was also there in an investigating reality workshop, you know, we had a talk from a modern composer, a classical music composer who played

one of his pieces on the piano, and it contributed to the discussion. They're all in favor of that kind of thing, as well as, I think, at least two different fiction writers gave talks at that workshop. So that's the kind of place that it is. Mikhail Maliki says, can you speculate about what kinds of physics and fundamental ontology of the world would be developed by intelligent species that never evolved eyesight? Well, I think it would be exactly the same as the kind that we developed. You know, we develop an ontology. the world that involves things like quantum fields and neutrinos and gravitons, even though we don't see those or experience them directly with our senses, not to mention Higgs bosons and top quarks

and so forth. The ontology of the world is highly constrained. You can discover it with all sorts of different possible sensory modalities, but I think there's an underlying factness, facticity, about what it is. The path to discovering it might be very, very different. but I think that you would ultimately discover the same thing. I could be wrong about that, but I think, you know, blind people, even here on Earth, I could imagine a bunch of scientists, all of whom were blind. I think they would discover physics just like we did. Dan O'Neill says, why are there so many exponents in the laws of physics, values squared, cubed, etc.

That's a good sounding question, but I think it might be too general to have a simple answer there. different examples of exponents come about for different reasons. You know, a very fundamental one is that space time is three-dimensional, right? So when you have things like Newton's inverse square law of gravity, that's squared in one over-distance squared, that comes about because the area of a sphere centered around a point goes as the square of the radius. That's a geometric reason why that exponent appears. Whereas if you look at the kinetic energy, one-half mv squared, that's because there's sort of a power series expansion where it's M, so just MC squared in the rest-mass energy, plus one-half M-V squared, plus then higher powers of V is the right ways that things appear.

So that has nothing to do with the dimensionality of space-time. That would be exactly the same, even if space had a different dimensionality. So I think the sad, deflationary answer to the question is for different reasons, depending on what law you're talking about. Paul Conti says, just out of curiosity, including family and friends, students, colleagues, et cetera, approximately how many messages posts and emails you receive every day and you usually manage to read them all. I do manage to read all my – well, that's not true. I was going to say I usually manage to read all my emails. I usually manage to read the ones that I don't already know I don't have to read.

Like when Amazon sends me an email saying your package has been shipped, I'm just going to archive that. I'm not going to read that one in any detail, okay? But the number, I get, I think, I don't know the exact number. Of course, it's going to vary by a lot. And also, I have a lot of filters, you know, certain, I have a whole bunch of crackpots who send me multiple emails every day for years now. and they get filed right away. I'm not going to, I just delete them. I'm not going to go through all those.

So if you just take the ones that I actually read, it's maybe 100 emails a day of that order of magnitude, which is just to say it's between 10 and 1,000. But, you know, 100 might be a reasonable approximation. And many of them I can just file away and ignore. It's still far too many. I can't actually answer them, even the ones that I really should or would like to with any care.

It's a broken system. I got to figure out how to do better at that. Martin Leitner says, regarding your recent appearance on the Closer to Truth channel, can you tell me how much thought and effort went into setting up the background? Was there professional advice involved, or did you do that yourself? No, well, I mean, there's no professional advice involved. I think, I'm not remembering this exactly right, but I'm pretty sure. So I did a video for Closer to Truth with Robert Kuhn, one of the various videos I did for when the new book came out.

and I did it in the same studio that I am sitting in right now, studio in quotation marks, just a room in my house where I record the podcasts. And otherwise, it is used as storage for books and music equipment and things like that. So, no, there's been zero professional thought into the background. It's the same background that people who are Patreon supporters have seen in any other video I ever put up on Patreon. So I send along my appreciation for the fact that you use.

might have thought there was any professional advice involved. Kauschuk Mitra says, since my early 20s, I chose not to have children for various reasons, the most compelling being the challenges of life. Though I didn't encounter any major issues, the daily struggles and hardships seem to outweigh the few moments of happiness. I question the ethics of bringing someone into the world without their consent. Over time, I realized that my perspective aligns with the anti-natalist viewpoint, as proposed by Schopenhauer and others. However, sometimes I feel a sense of emptiness due to my decision, as I believe we are biologically programmed to be parents. And without that, life can seem even more meaningless. My question to you is, what are your views on living a child-free life by choice, antinatalism, and the existential insignificance that can accompany being child-free?

Well, so I will give you my personal views. Do not try to extend them to other people without their consent, or even take us any implication that I think that other people should have the same views, because These are completely personal views, namely that I am child-free and perfectly happy about that, and I don't make a big deal out of it. I don't think that it is a moral, I don't think there's any moral need or necessity or even vague push towards either having children nor not having children. I don't think morality has anything to do with it. I tend to think that the existence of living creatures, including self-aware creatures like human beings, is overall a good thing.

But we have a lot of them, so I don't think there's any need on the part of any individuals to add even more to that number. There's plenty being added all the time. The population of the world is going up right now. I think that questions about existential insignificance

are not well addressed by either having children or not having children. It's a tough question. I'm not dismissing the question because, as I've done, said in other contexts, you have to take seriously the fact that even though I exist right now, and once I die, I will no longer exist, and therefore it might be tempting to think that what happens after I died shouldn't matter to me. Right now, I carry with me views, projections,

predictions, expectations about what might happen in the future, and my current state of mind is very naturally affected by those projections. into the future. So I think it's okay to either be proud of the fact that you're raising good children and they might live fulfilling lives themselves after you're gone or worry about the fact that you're not, or for that matter, be like I am, be perfectly happy with the choice that you made not to have children and to do other things instead. You know, you shouldn't be surprised to hear me say, there are other ways of getting value and meaning in your life, whether it's right here in the moment or with an eye to the far future after you're gone, that do not rely on

procreation. If they do, for many people, they will, and that's great. For others, they won't. That is also great. I think that there's many ways to live a meaningful life. Freddled gruntbugly, I'm tempted. I've sworn off guessing when names are pseudonyms and real, but grunt-bugly. Anyway, the question is, I've just finished your excellent book The Big Picture and have a question about compatibilism and causality. On face value, it seems eminently reasonable that there are different compatible ways of talking about the same underlying reality. However, there also seem to be prohibitions about mixing emerging descriptions with more fundamental ones. there are no tables and chairs in the core theory. Are there not, however, many, many examples of emergent objects, e.g. stars, having effects

on microscopic levels like the fusing of hydrogen nuclei. Well, two things. One is just for your own vocabulary help going forward. This is not a question about compatibilism. The word compatibilism is traditionally used specifically about free will, about whether or not the idea of free will is in. some sense compatible with deterministic underlying laws of physics. So this is more about emergence, actually.

You know, how do you talk about the relationship between levels of emergent description? There's this question of downward causation within the discussion about emergence. Can higher level phenomena have a causal impact on what is going on at the lower levels? I think that if your lower level is literally particles and fields, fundamental physics, then the answer is no. There cannot be separate causal influences of higher-level things on lower-level things. The example you offer, stars leading to the fusing of hydrogen nuclei, that is not, I think, the right way to think about fusion at the lower level. At the lower level, you can talk perfectly well about the fusion of hydrogen nuclei. You say if I have these set of hydrogen

nuclei and they're moving at these velocities, there will be a certain fraction of them that will fuse together. You never need to refer to the existence of a star. You can also talk at the higher level. You can say, here is a star, it has a certain mass, it has a certain composition, it is going to release a certain amount of energy, live for a certain time, et cetera, without ever mentioning hydrogen nuclei fusing. So this is a very clear example to me of two separate descriptions, which are perfectly good in their domains of applicability, which do not need to have any cross-talk between them. But to complicate things, just to open the door a little bit here, if you want to talk about the emergence of, let's say, society from a quote-unquote microscopic theory that was made

of people, right? So your microscopic theory is individual humans, and your macroscopic theory are collections of humans. Then the distinction, the sort of dividing line, because you're between purely macroscopic effects and microscopic ones might not be as clear. It might be possible that in that kind of case, because the microscopic theory is itself non-local and the individual constituents are themselves complex and have many, many internal states and things like that, then it might open the door for crosstalk between different levels. That's something I'm open to, but I don't actually have my opinions perfectly well pinned down by that, about that question quite yet.

Hugin says, what do you think are the most likely sorts of experimental observations, if any, that may change our credence about the current ideas of string theory? Well, I don't know if there are any likely sorts of experimental observations. There are observations we could do that would change our current ideas, our credence, about the ideas of string theory. For example, we could discover extra dimensions. You know, if Vafa is right, if there is an extra dimension, a single one that is about microns in size, then that would mean that we would have to, you know, you could have extra dimensions without string theory. But usually in sort of the collutes a clen way of having extra dimensions, they have to be really, really small.

Otherwise, you would notice them in particle physics experiments, et cetera. So if you discover a large extra dimension, that is very good evidence in favor of string. theory, because string theory allows to have these higher dimensional brains, B-R-A-N-E-S, where the fields of the standard model can live. Again, maybe you could have that without string theory, but string theory was certainly responsible for promoting the idea. So that's one way that it could happen. Had we discovered supersymmetry, that would increase our credence in string theory, but it

would not drive it toward one because you could still have supersymmetry without string theory. the fact that we have not yet discovered supersymmetry should lower your credence in string theory from whatever it was, but how much it should lower it depends on your likelihood function, so that's up in the air. Personally, I think the thing that we should do with string theory is develop the theory more rather than fret about observations

because we don't understand what the predictions are. We haven't connected string theory to the empirical world yet. That's a job for theorists to try to work harder on. Eric DeVigy says, I love how your biggest ideas books are so pro-math communication. Why do you think people tend to be so afraid of math? Is there something anti-math about our society or educational culture? I don't think it's that. You know, what do I know?

I mean, it could be, but I'm not familiar enough with other societies or cultures to be able to answer this with any data in mind. I think math is hard. You know, math is fun, but it's also hard. both of those things can be true. Mathematics is not how we were evolved. Our brains are not evolved to do math. We can do it. It's possible to do it. But it is not something that was useful 10,000 years ago in the same way that is useful now. None of the equations that are in my books were written down 10,000 years ago. And that's a relatively short time on an evolutionary time scale. I was very amused to discover when large language models became so popular that they were bad at arithmetic.

Because it's always been interesting that, you know, the human brain is infinitely more, not infinitely, but much, much more powerful as a computer than, you know, a simple pocket calculator or something like that. But pocket calculators are way better at multiplying big numbers than the human brain is. So somehow all of our computational capacity, has been optimized for something different than doing arithmetic. And in a computer, it's easy to optimize to do arithmetic relatively perfectly. But somehow large language models also didn't optimize for that. So they also kind of are computers that are bad at math.

Now, in that case, it's easy enough to train them to call a subroutine that does math perfectly well. But that's exactly the same as handing you a pocket calculator, right? It's just the extended cognition hypothesis. Anyway, my point is that it's a slightly unnatural way of thinking, math. And some people are going to adapt to it relatively quickly. Some people are not. And so I am sympathetic to that. That's completely fine.

What I would object to is a psychological attitude that makes it, that brings up some defensiveness about it. And I even have gotten this from a few interviews I've done on podcasts and radio and things like that about my new book because, you know, people are like, well, I like science, but this is hard. And, you know, they get defensive about it. They blame me. Like that review of the book that I read at the very beginning of the podcast, right? I think that's a bad attitude. That maybe we can blame society for that. If you don't like math, just say, okay, that's fine. There's things I don't like. That's also fine. But you don't need to provide an excuse for it or blame people who do like it. or sort of act like it's less important or nerdy or whatever. It's just, it's not your bag. That's okay. Get on with your life. Artem Vorostov says, I'm reading your book Quantin Fields.

I have a question about the wave function as a function of momentum, which is the Fourier transform of the wave function as a function of, which is the Fourier transform of the wave function as a function of the coordinate. The fact that a snapshot sigh of X and T at the particular time moment T0 contains full information of momentum looks counterintuitive to me. For example, a bell curve centered at zero is transformed to a bell curve centered at zero. However, to my understanding, the average momentum should depend on how the bell curve sigh of X and T evolves in time.

Well, yes, it should. But guess what? The Schrodinger equation, I'm guessing, Artem, that you're just a little bit about the math here from the way you ask the question. It's a very good way. So for those of you who are listening who are not, I listen to the math, apologize for that. But the Schrodinger equation is a first-order differential equation in time.

That's a fancy way of saying that the right-hand side of the Schroeder equation says D-Sy-D-T with a single time derivative. So what that means is that the wave function itself entirely defines, entirely determines how the wave function evolves in time. A wave function, in classical mechanics, in Newtonian mechanics, let's put that way, Newtonian mechanics, F equals MA, that is a second order equation in time, because acceleration is the second derivative of position with respect to time. And that means to solve that equation, you need to give me the position and its first derivative,

the velocity. You need to give me two pieces of data to solve a second order differential equation. But a first order differential equation, you just need to give me the wave, the wave itself tells me how the wave evolves with time. Now, that, so therefore, I could, I could sort of declare victory and say, all the information is in the wave function. I don't separately need to tell you how it evolves in time. Of course, there is something that I should separately tell you, which is there's a real part and an imaginary part. As we briefly discussed earlier in the AMA, wave functions are complex numbers. The phase of the wave function does really matter. And so that might be

obscured in here, and that's going to affect the relationship between the position space wave function and the momentum space wave function. But it is all there. If you work it out in detail, it does fit. Don't worry. We're not hiding anything from you. Pete Faulkner says, given your trip to France and your obvious love of good food, it seems only natural to ask, what is the greatest cuisine in the world, or at least your favorite? Okay, I'm going to get people upset, but my answer is American. Of course, it depends a lot on what kind of cuisine you're talking about in the sense of are we just imagining what people have at home on a typical weeknight? Are we imagining what kind of restaurant you might walk into randomly on the street? Are we imagining fine

dining at a place where you would plan to go to and spend a lot of money? Are we talking about the variety of cuisines available, et cetera? There's a lot of different ways you can think about what is the greatest cuisine in the world. You know, I give the United States of America some credit, as much as I give it a hard time, but it's pretty good of bringing together at, you know, cherry picking the best from different areas. When you get to oat cuisine, I know there's a lot of wonderful places in Europe and Asia and all over the world, but I'll put the United States up against any of those places, to be perfectly honest. My favorite restaurant in the world is Alinea in Chicago. and I've been to a lot of restaurants. I like going to restaurants. I do think that one of the great things about the U.S., it doesn't really count as the greatest cuisine in the world question, but many cities will have a whole bunch of really good different cuisines represented, right? Any big city will have all sorts of Asian food and European food as well as good old American food. I mean, low-level, fast food level American food.

food is terrible. It's much worse than you get in Europe. In Europe, you can get, maybe not in England, but in France or Italy, you can certainly get quite good food at quite cheap, affordable, everyday places. England, you really have to work, man. I mean, England, you can get amazingly good food. But if you don't pay attention, if you walk into a random restaurant that looks plausible in the UK, you might get in trouble in a way that you probably wouldn't in Italy or France, at least in my experience. And I would put the U.S. in the same boat as the U.K. in that particular regard. But at the upper levels, you know, the French restaurants are great, but there's a kind of a similarity there.

French cuisine is a thing that is more well-defined, just like Italian cuisine, Mexican cuisine, Japanese cuisine. These are all a little bit less flexible that American cuisine is. Like America helps itself to the best of all these different things. So, and when it comes to great cuisine, that's a benefit. That is a strong point there. So I'm going to be, yeah, I'll be a little patriotic there against type, but there you go. Jay says, to confirm any model of bedrock physics, we must perform experiments. But any experiment is built on bedrock, the very thing we're trying to understand.

Are we caught? Does this mean we're ultimately limited from ever-confirming physics bedrock? Yeah, I think that you're not supposed to think about. what we do in physics or in science more generally as looking for bedrock. I know it's a nice metaphor, but it's literally a metaphor that I try to debunk in the big picture. You're trying to find ideas that hang together, that have some coherence, some consistency between them, whether it's math, physics, data, experiment, et cetera. You need a story to tell that includes all these different elements and hangs together. But any one of them could be wrong, right? There's no one bedrock thing.

That was a dream going back to René Descartes, maybe even earlier, but he was the most explicit about it. And he was very careful and realized, no, you can't do it unless you invoke God or something like that. So if you're not going to do that, bedrock is not what you're looking for. Bob Ritchie says the old advice was to shut up and calculate. Do you spend much time actually doing the math and working the equations, or do computers now do most of the grunt work? I'm still and always have been very much a pencil and paper calculator kind of guy, not a computer calculator kind of guy. not a computer calculator kind of guy. You know, the kinds of work that one does affects a lot on what the tools are.

If you're doing a numerical simulation, if you're trying to understand galaxy formation, let's say, I've written one paper on galaxy formation, okay, on large-scale structure formation, and we did indeed just do pencil and paper calculations. It was on effective field theory in large-scale structure formation. But if you really want to get the details of what galaxies look like, etc., you're going to need to put it on a computer. So it depends on what you're doing. And in fact, as I'm becoming more interested in complex systems and things like that,

those are areas where doing simulations becomes more and more helpful. So I'm trying to get good at that. I'm not very good at it right now. I can do the very most basic things. But, you know, the time in between when I write a little Python script and, you know, the next time I do it is so long and I've forgotten everything about how to do it. It's not yet second nature to me. So I'm still in the process of getting good at that and getting natural at it, whereas just putting pencil to paper or pen to paper and doing the calculations that I'm very comfortable with.

Jason Hale says the last 15 minutes, the last podcast with Kermor and Vafa was crazy good. Did you read any papers, as you mentioned, or do you have any thoughts on the near future experiments referenced? I haven't read the paper yet. I link the paper in the show notes there, the Swamp Landish Unification paper, where he gives a brief overview of these ideas. And then I went on vacation. Then I went on a book tour. Then I went on vacation. Let's put it that way. So I've not yet had a chance to do that, but I'm looking forward to doing it. It does, you know, look, I think we have to both be interested in this and excited in it if you're that kind of person. And also hold back from being overly excited because people are

always saying, well, I figured it all out. You know, it all fits together, and I have the theory that makes everything make sense. You have to try to do that. You can't be discouraged, but you can't fall in love too much with any particular one scenario. Steve ECPW says, in your last AMA, you said something like there are many unanswered questions in theoretical physics. Let's say theoretically that all the questions were answered about gravity, dark matter, string theory, to name a few. What would it be the practical benefit to humankind, other than our knowing how the universe works, would there be any useful application of this knowledge? Roughly speaking, no, and there might be, you never know for sure, right? You never

know that once you have this new understanding, by definition, it's new, you don't have it yet, and so you might realize once you have it that there is some wonderful application of it. But there's no rule that says there has to be an application of it. And, you know, I've made this point before, but fundamental physics has decoupled from technological innovation quite a while ago. I mean, arguably, it's been since like the 1950s that discoveries in fundamental physics at the level of particle physics and gravity and things like that have had any direct relevance to technological progress at all. Mewons, pyons, things like that, find a little bit of application. But mostly, as I've many times, we understand the laws of physics that govern our everyday life regime, and the stuff

that happens outside that regime is either very hard to access or goes away, decays away very quickly, et cetera. So you can build a large collider and make Higgs bosons, but you're not going to make a Higgs boson, iPhone, because you can't carry around the large Hadron Collider on your wrist, and you need the large Hadron Collider to make the Higgs boson. So it's just of no help. There will be plenty of technological innovations, but they will come from. taking the ingredients that we have and putting them together in novel and interesting ways, and that there's an enormous amount of room to do that. So there's plenty of room for technological innovations, but not from, probably not from fundamental physics. Henry Jacobs says, I'm banging

my head on a QFT textbook, Schwartz, and I'm very lost as to what an observable is in this context. In the case of non-relativistic quantum mechanics of particles, I get it, because I could imagine concretely measuring the position momentum spin of a single particle. However, I can't imagine observing an entire field configuration since it's an infinite dimensional object. Yes, fair enough. When we do quantum field theory, you know, as you know, if you're going through a QFT textbook, in practice, what we do is we talk about the mathematics of quantum field theory, we use it to then say that you can write Hilbert space as Fox Space, which is a collection of many different kinds of particles, superpositions of different numbers of particles, and then we start talking

about particles. And that's entirely fine for the most part. You know, there are certain circumstances like inside a strongly interacting proton or neutron or something like that, where you have to do the field theory for its own sake, not just the particles, but mostly you can think about particles. So you don't need to worry about these questions about what are the field observables. And to simplify our lives, we make this wonderful simplification that you can imagine observing the value of the field at every point in space all at once. And then you can make a basis for your Hilbert space on the basis from the results of that, the actual field configuration basis. But of course, as a practical matter, you can't do that. You don't have an infinitely big detector to measure the field all throughout space all at once.

So what you can imagine doing is just measuring the value of the field at a single point. That's something you can do, phi of x. If phi is some scalar field or some other kind of field, you could imagine measuring it at some point, and then you get a value. The problem is, once you become familiar with how these things go, if you were going to get a reasonable answer for the question of what is the field configuration overall space, asking what it is at a single point is kind of not reasonable because you have sort of infinitely focused in and very, very, very roughly speaking, the uncertainty principle comes

in to bite you in the butt. You're asking about what is going on at zero distance, right? Zero extent in space because you're asking about what happens at a single point. That's going to mean that, you know, everything else blows up. And so you're typically going to get infinitely big answers. So what people can sometimes do, you really cared about this question, you could smear out your point in space. So you could invent some function, F of X, that is zero almost everywhere, but sort of is a bump, like a bell curve or whatever, centered around to the point you care about, X. And then instead of measuring phi of X, you can measure the integral of five of X times F of X. So you basically have a lens

or a filter, let's put it that way, that focuses you in on the value of phi at that one point, and zeroes out everything far away. It's not clear why you want to do that. I mean, sometimes you want to do that because you're trying to literally build the detector or whatever. But if that's true, then probably you can just get away with thinking of everything as particles rather than fields. So there's a interplay that goes back and forth,

and you won't find very detailed discussions of any of these issues in most quantum field theory textbooks because, like I said, they just leap right to particles and go, from there. Johnny O. says, what does your demon do? Maxwell's demon violates the second law by de-equilibrating a system without applying work. The Humian demon knows everything that ever happened and ever will, ignorant of physical laws. Laplace's demon calculates all that ever happen and ever will by knowing the physical laws in the current state of everything. What does Carol's demon do? This is a great question. I love this question. I almost didn't pick it because I

don't have any good ideas. I didn't have when you asked the question any notion of what my favorite demon would do. But thinking about a little bit and thinking about your examples, which are great, by the way, you know, I actually, there wasn't really a Humian demon, but I know what you mean. It makes sense in retrospect that we can talk about the Humian demon. I thought once of like writing a little article or something like that about, you know, 19th century demonology and physics, because clearly that was an idea. Laplace, by the way, never called it a demon. Maxwell called his idea a demon. Laplace said, imagine a vast intelligence. I think that Laplace was too much of an atheist to invoke demons here, but later commentators called it a demon. So having thought about

this question a little bit, here's what my demon would do. In contrast with Laplace's demon, Laplace's demon basically knows all the microscopic information about the world and calculates everything that would happen. And people debate, this literally happened at that Santa Fe Institute workshop I was just at on investigating reality, people debate, does Laplace's demon know about higher level emergent things? Does Laplace's demon know about temperature or entropy or human beings or intentions or free will or whatever, right? And I think that the simplest answer, there's, of course, Laplace's demon doesn't exist. It's fake. So you can make it up. You can answer however you want. But I think the simplest version of Laplace's demon doesn't know any of those higher-level things.

It doesn't need to. If you know exactly what all the particles in your box of gas are going to do, you don't need to talk about temperature or entropy or whatever. You just follow all the particles. So what Carol's demon does is it thinks about the dynamics of the system, and it tells you not only what the microscopic laws of physics are, but it tells you all of the emergent patterns at higher levels and how they fit together, how you can derive one level from another. So it does what Dandenet sort of imagined one could possibly do, figure out the ways to throw away information to coarse grain,

to forget some of the things that Laplace's demon knows, and nevertheless have some patterns that tell you what happens in the world. Carol's demon would be very, very helpful. I wish I could meet Carol's demon. And that would be a very illuminating conversation and a good question there. BG167 says, how does being a celebrity science affect your research and teaching? I imagine there must be some advantages, but also some disadvantages. I presume this means in the sense that, you know, I have podcasts and books and people know who I am and things like that.

And the answer is it affects it almost not at all. I'm not that much of a celebrity. I've actually, you know, when I've been teaching, sometime, you know, I literally would run into a student from my class in the hallway. or waiting for the room to open or whatever, and they said, yeah, you know, I heard you on someone else's podcast yesterday. I keep forgetting that you're famous outside. Like, you're just my professor. I think that's usually what it is. Like, I'm nowhere near a level of celebrity where most people in the world recognize me on the street or anything like that.

Or even, let's put it this way, most times that I'm out on the street, no one recognizes me. The vast, vast, vast, vast, vast majority. There are occasional counter examples, which are pretty hilarious, but I'm pretty safe. from true celebrity issues. So the students in my class often have never heard of me before. The fellow scientists, of course, they have heard of me because I'm a fellow scientist. They might have also known that I have books and things like that. But the thing is that, you know, how you think about a person depends on the aspects of their life that you are most familiar with. So if someone, you know, I have a lot of younger scientists.

physicists who, physicists, who know me because of my general relativity textbook, right? That was their first exposure to me. So they think of me as the textbook guy, the general relativity textbook writer. People my age think of me from my research, right? That's how they got to know me, medic conferences, things like that, etc. So when I'm talking to scientists, they, for the most part, did not get to know me first through podcasts or books or whatever. So in their minds, yes, I also write books and have podcasts, et cetera, but mostly I'm a scientist writing science papers, right? And whereas people who are fans of the podcast or fans of the books barely know about the physics papers that I write or the philosophy papers for that matter. So who you are depends on the lens that people see you through. Georgio says, given that we have trouble understanding how complex life can arise from simple physical and chemical processes, is it respectable to have a high credence in the theory that the earth,

might have received some sort of interstellar pollination from an alien civilization sending their seeds out. You know, you're allowed to have whatever credence you want in that. It's very speculative. I don't think that, I mean, it's respectable to have a high credence. I don't think you should. I don't have a high credence in that. Basically because given that we have trouble understanding how complex life can arise

from simple, simple physical and chemical processes, that's just as true on alien worlds as it is on our world, right? You haven't made anything easier by saying that that unknown process happened somewhere else. You've made it harder because you say, well, it happened somewhere else and then it had to travel across interstellar space, which sounds difficult. You know, again, it's very possible. Like maybe it only happens once in the universe and then this alien civilization spreads its seeds out. But that, I mean, that's a little weird. Why would the alien civilization do that? Why would they spread out little molecules or primitive organisms? in a way that they wouldn't even know what the results of that were.

Like, why not just send spaceships or something like that? I think far in a way, the most likely thing is that life began here on Earth. We'll have to find out whether or not that's true or not. Well, it's still a research problem there. Schleyer says, if you were given the power to intervene in human history and cause humans to never be able to access fossil fuels, would you do so? No, I would certainly not do so. fossil fuels have been enormously helpful in building technology and growth of productivity and wealth

and therefore other kinds of technological innovations like medicines and things that make our lives generally better. Now, we have clearly overused them. Yeah, that's true. If I had the power to intervene in human history, I would have started the transition to cleaner energy much earlier. Let's put it that way. but it would have been hard. You know, it took a while to get to the technological point where renewable energies are competitive with fossil fuels in the way that they are now. But again, if I could magically intervene in human history,

that is what I would cause to start happening much earlier. Johnny says, do you listen to music while you work or full silence? Curious what music you use to focus, if any. I usually just work in silence. I get distracted. So let's put it this way. I can't really do work if there's music going on that has lyrics. If the music has lyrics, then I will start thinking about the lyrics.

And your best, whether it's doing writing or doing physics or doing philosophy or whatever, it's for me personally, if I'm going to make progress, I need to be somewhat very carefully focused on that particular thing. And lyrics get in my way. They engage the part of my brain that should be doing work, and that's counterproductive. Sometimes I will listen to instrumental music. I have a playlist on iTunes of, you know, writing music, but most of the time I forget to turn it on. But sometimes I do. You know, it's a weird mix of, you know, some classical things, some instrumental jazz things, but not like too wild stuff and some, you know, world music kind of things. Again, but all super instrumental background that it is, it generates a good feeling in the background without distracting you from the, important work you're supposed to be doing. I know that other people are completely different.

Other people would like to blare really loud music with lyrics and that helps them work, but it depends very much on the kind of work you're going to try to do. Nanu says, I truly enjoyed listening to your episode with Dr. Vafa. It was interesting listening to him to defend the potential existence of extra curled up dimensions in the real world. As a theoretical physicist over the decades, how did your intuition shift and mold after big discoveries like the acceleration of the universe and others? In other words, how do you approach new ideas with minimal, preconceived notions based on

senses of your body? Does it take practice in time like a muscle? I think in the case of... I mean, it's an interesting question because the kinds of big discoveries that have happened over my scientific career have not been that difficult to incorporate

into our intuition. The acceleration of the universe was the biggest, but I had literally already written a review article on the possibility of that happening. So it wasn't like I had erratically change my pre-existing knowledge base. Something like the invention of quantum mechanics or the Big Bang or relativity, that would have been a much bigger shift of perspective. And I cannot honestly say how I would have reacted to that. As I often have said, in some very real sense, physicists still haven't taken quantum mechanics to heart. And I would like them to do that. So there's,

absolutely some barrier to completely shifting your intuition. Quantum mechanics is the clearest example because there's this difference between the machinery we use to actually do calculations and make predictions and then the observations that we actually see at the end of the day. I think people really struggle with distinguishing between those things and figuring out how they could fit together well. But other people disagree. Nicholas Dillon says, what is the most underrated or overrated thing about Paris? I don't know. You know, I think in practice, like I said earlier, I think, if you're there at a heavy part of tourist season, going to museums is a little bit overrated. There's a lot of waiting in lines. Like, we foolishly had the idea we were walking around

in the morning and we're like, okay, oh, the Louvre is right there. Let's just go to the Louvre and check it out. And it's been years. And the line was like three hours. And, you know, we're not standing in line people at this stage of our lives. So we did not do that. And even at the, I don't know, the lingerie, which is this tiny little museum, it was like an hour-long line. Why bother with that? You know, I like Paris because you can walk around, you can look at stores and shops, you can sit at the cafe, you can have a good meal, you can have a glass of wine, you can enjoy the river and everything, you can enjoy the neighborhoods. One of the underrated things about Paris is, I don't know whether this is just because it's a big enough city or whether it's European or whether there's a lot of history or whatever.

But you can get free entertainment very easily. Some of my favorite experiences in Europe have been going to concerts in cathedrals that are, you know, held by candlelight or whatever. Just put on for free. They're not the highest level of classical music, but they're very good. And the atmosphere is unbeatable, right? And you can just walk in on the spur of the moment and enjoy something like that. So I think that But as I've said before, and it's not very helpful to say, everyone's version of what to do in a city like Paris is going to be different.

So try different things. Like I've never gone to a jazz club in Paris. I think that would be fun, but I just have never had the chance to do that. So someday, I'll go back. Mark Slight says, I read that nowadays your applied physics guys have gotten interference patterns out of quite large molecules through the slits. This struck me as odd, but I guess that's just bad.

intuition. Is this unsurprising? What are the theoretical and practical limits or difficulties? Could I, in principle, interfere with myself? Yeah, you could, in principle, interfere with yourself. You have a wave function. You diffract a little bit when you walk through a doorway every time, but that little bit is a very, very, very little bit. To actually, you know, the obstacle to you interfering with yourself in a double slit experiment is not just that your wave function, because you are very, very massive. It's almost impossible to get your wave function to pass through two slits. Okay, that's one problem.

Your wave function is far, far, far too localized. Not to mention that your body is bigger than the slits. So you need to make the slits as big as doors. So you're not going to get a lot of interference. But in principle, it's there. There's another problem, though. It's not just that your wave function is very localized because you're massive. It's that you're made of a huge number of particles, right?

and all these particles are constantly vibrating and giving off radiation and interacting with the rest of the world. So basically you would decoher right away. It would be the version of the double slit experiment where you're observing all the time, which slits you go through because you're interacting with the rest of the world and becoming entangled with it. And then finally, even if you got rid of that effect,

the fact that you are evolving over time in sort of different sort of jiggly ways means that the U that hits a detector on the other side of the slits would not be the same. The one that goes through the left slit and the one that goes to the right slit would have maybe very, very likely evolved in slightly different ways. So when you have a single particle going through two slits, there's no internal degrees of freedom for a single particle or there's not that many of them. So it's crucially important that in order to get interference on the other side of the double

slit experiment, you have contributions to exactly the same final state of the particles. Contributions to the particle being in an exactly specified quantum state at this point on the detecting device, having gone through one slit or the other. But if you go through one slit or the other, chances are you will evolve in slightly different ways going through the left slit and going through the right slit. So you will not end up at the detector screen in exactly the same quantum state. therefore you will not interfere. So that's why your intuition is not very good at this, because it is very, very, very far away from being practically reasonable. Sandro Stuki says,

in quantum fields, you explain how a quantum field consisting of a single mode has discrete energy levels that look like those of a quantum harmonic oscillator. You also say that any field configuration can be obtained as a sum of possibly infinitely many modes. But it's not obvious to me that the solution of the Schrodinger equation or the resulting energy levels for the sum of two warm modes still looks like those for a single mode. There seem to be nonlinear terms in the energy density. How do we still get a harmonic oscillator? Or sorry, do we still get a harmonic oscillator? If not, does the nice picture of discrete energy levels corresponding to discrete numbers of particles break down once we have particles corresponding to different modes? This is actually a very,

very subtle question. If you look carefully at the discussion in quanta and fields, I'm talking about a free field theory very, very specifically, which means I have a very, very specific energy of the theory, which is just the kinetic energy for, let's call it phi, some scalar field, plus the gradient energy, whereas phi changes from place to place, plus a very specific kind of potential energy, namely phi squared, times some parameter. And that means that all that terms, all the terms of that energy density are quadratic in phi. They're order phi squared. That means that the equations of motion that you get by roughly speaking differentiating with respect to phi are linear in phi. That means there are no non-linearities.

You can solve the equation exactly. And that's when you get this nice behavior of particles. In the real world where you have interacting fields, so you have terms in the energy density or the Lagrangian that are cubic or quartet or even more or whatever, then as you point out or as you're gesturing toward, you will not have. this ability to cleanly solve the equations and get energy levels like a harmonic oscillator. You will have nonlinearities and they will be important. So usually you say, okay, but those interactions are weak. They're small and that's when we can do perturbation theory. Now you're halfway on your way to inventing Feynman diagrams. That's exactly what Feynman diagrams do. They answer the question.

How do you extend from a completely free field theory point of view where you're you can identify the particles precisely to an interacting field theory point of view where the particles are going to bump into each other and potentially change their identities. This turns out to be super subtle because the particles, the fields rather, are constantly interacting with each other. And so you have to invent an elaborate formal structure of scattering theory, where you start, you literally set up your initial conditions by imagining that you have turned off the interactions. You take, you know, so there's some coupling constant, like the fine

structure constant of electromagnetism. You set it equal to zero. And so you do have a free theory, and you can sensibly say, oh, there's a photon, there's an electron or whatever, and then you send them toward each other, and then you invent a mathematical technique by which you can gradually turn on the interaction before the particles get close to each other, and then they interact, and then they leave, and then you turn off the interaction again, and then you measure at the end of the day. It's slightly non-mathematically respectable this whole thing. There's a lot of work that goes into making it even plausible, and as a practical matter, it works, right? We get the right answers for doing this. But taking that all of those complications seriously is, in fact, very,

very important. We didn't have time to go into it in quantum field and fields, but a real quantum field theory book, pick up Peskin and Schroeder. It will actually go about this in great detail, the LSZ reduction formula, the interaction picture, words like that will appear in the discussion. Okay, we've gone a long time here. The final question comes from Dan Berliner. What is the secret to making a good pizza crust? Ah, very good question. I feel like the underlying theme of today's AMA is lots of different things are possible. Lots of different ways to be a good person are possible, lots of different scientific way, operating are possible. It's also possible lots of different ways to make a good pizza crust. And I enjoy all sorts of different pizzas. I know that, you know, it's popular to pick a certain kind of

pizza and dogmatically insist that it is the only right one, whether it's, you know, Brooklyn-style pizza or Italian-style pizza or Chicago-style pizza or whatever. I am not that guy. My love of pizza is ecumenical. I love all these kinds of pizzas. it's great to like go to Italy or go to some tiny little shop. When I visited recently the University of Pittsburgh and I gave talks there, etc., I was taken to a nice little pizza shop where, you know, the owners, the proprietors are clearly right from Italy and they make you, you know, that personal style, thin crust pizza with really fresh ingredients, which is amazing.

You know, I love that. It is what you get in Italy. But also I spent seven years living in Chicago eating deep dish pizza, which, as cartoonist Rubin Bowling once put it, is some kind of bread-based lasagna food. It's not really pizza at all. But I ate an embarrassingly large amount of deep dish pizza when I was in Chicago. And when I make pizza myself, I've actually not perfected like the thin crust Italian style. I had a friend back in L.A. who did, who like owned a pizza oven and he would have parties and we would make our individual pizzas. and that was kind of amazing, but I have not been able. I've not tried too hard, but that's actually one of the, one ambition that I have. I do have a way of making pretty killer pizza pizza, which is very, very simple. You can go to Whole Foods and they sell you like a little plastic baggy of pizza dough. So you don't even have to make the pizza dough yourself. And you might fear that this pizza dough is not very good, but in fact, it's quite good. And they will also sell you the sauce. You can do better than the Whole Food sauce. You can get Rouse.

R-A-O-A-O-A-O-A-Posophie S, Rouse, pizza sauce, some mozzarella cheese, pepperoni, onions, whatever you want to put on it. And all you have to do is get a good cast-iron skillet. Coat the cast-iron skillet with some olive oil and maybe some garlic and some breadcrumbs, if you have those, and then smush down the pizza dough into your cast-iron skillet, cover it with your cheese and your toppings, put the whole thing, skillet and pizza and everything in the oven at 400 and some degrees. until it's done. I don't know, it takes 15, 20 minutes to do it. So it's deep, it's not

Chicago-style deep-dish pizza, because that's like layers of things, right? This is pan pizza, but it is so good. This cast-iron skillet pizza with Whole Foods pizza dough is amazingly good and super simple. So that's my level of commitment to making good pizza at home. I would like to be better at making sort of flatbread Italian-style pizza, but I'm young. is not finished with me yet. I have not yet acquired all the skills I will acquire before I die. So life is a journey. I'm looking forward to living it. And I thank all of you out there in Patreon land and Minescape land more generally for listening along, supporting the podcast, and we had a fun AMA. See you next month. Bye-bye.