Audio Player
Starting at:
John Norton: The 300-Year-Old Physics Mistake No One Noticed
June 27, 2025
•
1:53:13
•
undefined
Audio:
Download MP3
ℹ️ Timestamps visible: Timestamps may be inaccurate if the MP3 has dynamically injected ads. Hide timestamps.
Transcript
Enhanced with Timestamps
278 sentences
17,739 words
Method: api-polled
Transcription time: 112m 38s
The Economist covers math, physics, philosophy, and AI in a manner that shows how different countries perceive developments and how they impact markets. They recently published a piece on China's new neutrino detector. They cover extending life via mitochondrial transplants, creating an entirely new field of medicine. But it's also not just science, they analyze culture, they analyze finance, economics, business, international affairs across every region.
I'm particularly liking their new insider feature was just launched this month. It gives you it gives me a front row access to the economist internal editorial debates where senior editors argue through the news with world leaders and policy makers and twice weekly long format shows basically an extremely high quality podcast whether it's scientific innovation or shifting global politics the economist provides comprehensive coverage beyond headlines.
Tito's Handmade Vodka is America's favorite vodka for a reason. From the first legal distillery in Texas, Tito's is six times distilled till it's just right and naturally gluten-free, making it a high-quality spirit that mixes with just about anything.
That had produced so much fuss with somehow shocking. This literature has been teetering on the edge of nonsense for a hundred years.
Professor John Norton of the University of Pittsburgh has spent decades systematically dismantling sacred assumptions of physics. Norton's dome, for instance, demonstrates fundamental indeterminism in Newtonian physics itself. Now, you may be thinking of quantum uncertainty, but I'm talking about classical physics, which is breaking down in terms of unique predictivity. Beyond determinism, Norton critiques notions of causation itself,
Physicists routinely invoke causal language, but what if causation isn't fundamental? Even further, Norton's critique extends to thermodynamics. Landauer's principle, for instance, has guided decades of research into computing limits, and some even use it as the physical basis of Wheeler's it-from-bit. Norton demonstrates this principle misunderstands thermodynamics and entropy.
Both of which we talk about in extensive detail. We then cap it off with Einstein's contributions to old quantum theory and Einstein's disagreements with the new quantum theory.
a special thank you to The Economist for sponsoring this video. I thought that The Economist was just something CEOs read to stay up to date on world trends, and that's true. However, that's not only true. What I've found more than useful is their coverage of math, of physics, of philosophy, of AI, especially how something is perceived by countries and how it impacts markets. Among weekly global affairs magazines, The Economist is praised for its non-partisan reporting and being fact-driven.
This is something that's extremely important to me. It's something that I appreciate. I personally love their coverage of other topics that aren't just news based as well. For instance, the Economist had an interview with some of the people behind DeepSeek the week DeepSeek launched. No one else had that. The Economist has a fantastic article on the recent DESI dark energy data and it surpasses, in my opinion, scientific Americans coverage.
The economist's commitment to rigorous journalism means that you get a clear picture of the world's most significant developments. It covers culture, finance and economics, business, international affairs, Britain of course, Europe, the Middle East, Africa, China, Asia, the Americas, and yes, the USA. Whether it's the latest in scientific innovation or the shifting landscape of global politics,
The Economist provides comprehensive coverage that goes beyond the headlines. If you're passionate about expanding your knowledge and gaining a deeper understanding of the forces that shape our world, I highly recommend subscribing to The Economist.
It's an investment into your intellectual growth, one that you won't regret. I don't regret it. As a listener of Toe, you get a special 20% off discount. Now you can enjoy The Economist and all it has to offer for less. Head over to their website www.economist.com slash toe to get started. Make sure to use that link. That's www.com slash toe to get that discount.
Thanks for tuning in. And now back to the exploration of the mysteries of the universe with John Norton. All right, Professor John Norton, you're a legend in the physics scene and the philosophy of physics scene. So it's an honor to be with you here. Oh, thank you very much. It's very kind of you. You're known for Norton's dome for indeterminism and systematizing material induction, your views on thought experiments, the history of Einstein,
and disproving Landauer's Principle. We'll attempt to get to all of these today. Now, before we get to these, let's pick one. Norton's Dome. Why don't you tell me, how did you arrive at that construction? What were you trying to show? Were you trying to be contentious? Were you trying to disprove a colleague? Did something just not make sense? Like, walk me through leading to Norton's Dome.
It was actually completely trivial and that it produced so much fast with somehow shocking.
So here's the background. In the late 1980s, my colleague John Ehrman wrote a book, A Primer on Determinism, in which he pointed out that indeterminism was actually rampant throughout physics. And one of the places where it's quite rampant is in Newtonian physics, when you have systems with infinitely many degrees of freedom. So if you have infinitely many masses bouncing around in various ways, their behavior is going to be generically indeterministic.
So John and I were teaching a graduate seminar on causation and determinism. And, you know, I think that afternoon or the next day I was committed to giving a section on determinism and I was going to present the idea that Newtonian physics is generically indeterministic when you have infinitely many degrees of freedom. Well, what about the case of finitely many degrees of freedom? I was going to say, well, when you only have finitely many degrees of freedom,
Then you just always get to him and isn't everything fine and i thought i'll be saying that in front of a bunch of smart graduate students you know what's gonna happen next.
So i said i better have a look to see if there are counter examples so so you know elicits condition guarantees. Unique solutions for differential equations i looked up standard counter examples to elicits condition i took one of those standard counter examples and said how do you realize it physically and the answer was quite simple you have this. Don't shake very particular shape you put a mass point at the top that can move frictionlessly.
And the conditions violate lifshitz condition, and so the particle can spontaneously set itself into motion. And the mathematics is very simple. It's two or three lines, and there it is. So I used that in teaching. The students didn't seem terribly impressed. I was writing a paper on causation at the time, and I wanted to point out that the idea that Newtonian physics has always been deterministic.
was actually a mistake because the theory itself is not intrinsically deterministic so i included the dome in section three and almost immediately i started getting emails from people correcting correcting my mistake and i realized oh um there's something more going on here that's the story so what's the something more that's going on
What's going on is that the idea that Newtonian physics is deterministic is so deeply entrenched in the psyche of many physicists that it somehow seems to some sort of an epistate if I if I would be saying anything otherwise that I must have made a mistake and they have an obligation to discover what the mistake is and so
And that was the character. They weren't hostile, the response that I was getting. They were all very friendly, but friendly of the form of Dear Professor Norton. I saw your analysis of this dome. I just want to point out you're making a terrible mistake here. And then something follows, which never works.
Let's make this clear for people. So there are different types of continuity. Usually we'll say that a function is continuous, but there are various types like absolute continuity, uniform, and then there's lift shits.
which then is used in ODE classes to show that there are unique solutions. Now, if you remove this Lifshitz continuity condition, then you get non-unique solutions, so multiple solutions. And I'm not sure I believe Lifshitz is necessary, but not sufficient for non-uniqueness. You can. I think it's sufficient, but not necessary. But if you find very simple systems that violate the condition of Lifshitz continuity, then
I mean, the mathematics of the dome is just a very simple example. If you have the first derivative of a function varies with the square root of the function, that already violates the Lipschitz condition at the origin when the function has zero value. I mean, it's as simple as that, and that's the example instantiated in the dome.
I went to the second derivative so i could use newtons f equals ma but i think it already happens with the first derivative just d dx equals square root of x and solve that when x is equal to zero you already have non-unique solutions i think going from memory that that works.
Okay, so then what are people supposed to imagine as a consequence of this? Are you saying that Newtonian physics thus needs to assume Lipschitz in order to prove this uniqueness? And thus, if you're trying to say Newtonian physics is deterministic, you're already inserting that determinism. You're not concluding that deterministic. That's exactly right.
whether a particular new term in system is deterministic or not is something to be discovered not not stipulated and i'll mention again the important case if you have infinitely many systems interacting then you get indeterminism generically why does this matter well it's going to matter in the infinite case when you look at something like the thermodynamic limit.
So this is a case that i calculated we like to think of a very simple newtonian model for crystal consists of a whole bunch of mass points that connected together by springs and the thermally agitated and said that what about the idea is that.
As the number of mass points gets larger, as this lattice gets larger and larger, its behavior becomes closer and closer to a system that is going to behave thermodynamically in the ways that we expect. You're going to get Boltzmann's, the Boltzmann distribution is going to come out and so on, but you need to look at the very large lattice. So it's standard to say if you take the infinite limit,
That's when you get from dynamics back what do you have to be very careful about how you take that infinite limit if taking the infinite limit just means i will consider crystal letters of arbitrarily large size. I always find out that i was really large in size then the sequence of letters that you're considering will eventually stable out stabilize out to have nice dynamic properties. If you mean i'm going to consider an infinite letters.
And then investigate his properties. You'll discover that the, uh, that the lattice, uh, dynamics have become indeterministic. Uh, I've not kept this secret. It's in a paper I wrote published on, um, 19 11, uh, 2011, 2012 called approximation and idealization. That's the, one of the main points of the paper. It just says, it just says be careful taking infinite limits. You can really get into trouble.
So there are other types of continuity as well. So the underlying space is continuous. So the function itself is continuous and the function operates on a domain and that domain is space time. Now, I know we're dealing in Newtonian physics, so maybe not space time, but it doesn't matter. We say some manifold. Now, is it your contention that the manifold itself is also going to ultimately be discontinuous? Do you have a intuition there that is going to be discretized or do you think that you can zoom in all the way and it looks like Rn?
I'm well the example of the don't the don't surface is an ordinary euclidean surface. And it does have a cover to singularity at the at the apex but cover to singularity is at a at a point and nothing extraordinary in idealize newtonian systems think about the sharp edge of a tabletop.
Right now the horizontal and the vertical and they meet and we don't have any trouble shooting a particle across the horizontal surface. It then comes to the curvature singularity at the edge and then shoots off in a parabolic arc. It's the standard sort of idealization that we talk about. The singularity at the sharp edge of the tabletop is one order worse than the singularity in the
At the apex of the dome at the apex of the dome it's singularity in the curvature. The apex the singularity the sharp edge of a tabletop is a singularity in the first in the tangents. Yeah the tangents move jump discontinuously when you go over the edge so many ordinary Newtonian systems are deterministic.
All right and we're entirely used to that they always work out that way. Is it so surprising that if we go to extreme cases that we don't normally look at an ordinary life that we that we end up with something a little different. The case of the dome is not something we could ever realize in real life because it requires multiple violations of quantum mechanics.
You got to put the point that the mass point has to be located at rest exactly at the apex you need to have a surface that is exactly the right properties. The more interesting cases when you have been from the many masses that's the sort of idealization that people will take more seriously why doesn't the infinitely many masses also contradict quantum mechanics.
Um, it's Newtonian theory contradicts quantum mechanics and its foundations. So yes, it does as does every Newtonian analysis. So I'm not sure. I'm not sure what's worrying you here. This for me has been the perpetual puzzle. Um, I think the dome is just a rather ordinary piece of Newtonian physics. There's nothing very special about it. Uh, it just happens to have this, this odd property, but then
Yeah, some people I talk to just say, yeah, yeah, what's the big deal? Other people were saying there's something deeply troubling about this and I just don't know what that is. So it turns out that some Newtonian systems in these cases, rather exotic ones that could never be realized, you know,
What are the implications for quantum mechanics and relativity? I think that was behind one of your remarks. Not very much, because they're different theories. Relativity theory and quantum mechanics are very different theories. They turn out to be indeterministic in their own ways. In the case of quantum mechanics, the standard interpretation is indeterministic.
That's just the beginning of a long discussion if you're a bohemian you won't think that but that's another story and in order to realize determinism in relativity you need a koshi surface. You need all the nice conditions if you don't have a koshi surface then you can't even state the conditions of determinism which are the present fixes the future but you don't have a present so you can't have any you can't have any fixing i think if there's a moral.
The only moral is the following, be careful about what you assume about the world. Don't go into physics assuming and decedently that you have a wisdom that transcends what the empirical science will tell you. If you want to see what goes wrong, if you do that differently, think about what happened when quantum mechanics appeared in the mid-1920s and it became very apparent then that the theory was going to be indeterministic.
Up until then, everyone had simply assumed that for a system to be causally well behaved, it had to be deterministic.
Then quantum mechanics comes along and it's indeterministic and there was this tremendous outpouring of anxiety. Causality is lost was the plea. We would now say determinism. They then said causality. But in retrospect, it was simply an artifact of 19th century thinking. In the 19th century, they had identified causation with determinism. So for the world to be well ordered causally,
So let's talk about this graduate seminar then on causation. Did anything else controversial come out and what is causation? Well, as you know, I've written fairly extensively about this. I have a particular critique of causation. It is a critique of causal metaphysics
It is not a critique of causation per se. To be very clear here, I am quite comfortable with the idea that things interact with each other and connect with each other in all sorts of fascinating and interesting ways. Voltages drive electric currents and
And gradients of free energy produce them dynamic effects and so on and so on and so on all all the all the way through here. You can go to any science and you find all sorts of claims of how this causes that. My critique is the following calls on metaphysics seeks to do something that is antecedent to these empirical investigations.
A causal metaphysician says we cannot talk about causality until empirically until we have sat down and done some conceptual work and figured out what causation is. And once we have done that, then we understand what causation is and then scientists can come along and do the cleanup operation of figuring out how this causal principle that they come up with is going to be instantiated in the particular sciences.
So the general run of a causal metaphysician is saying, I know what causation is. It's this, right? So I understand your job is just to show me how that works in the world. And that is just a completely failed enterprise. The difficulty is that metaphysicians have not been able to come up with any principle of causation that has any practical content. And that also succeeds in the world.
We have thousands of years of failure at that particular enterprise so i'm rejecting the calls on the positions project completely and then okay so the question that becomes what is the place of causal talking in science why is it so pervasive. So why does scientist care about causation if there's no metaphysics underlying it. It's simply a matter of labeling what happens is we notice that there are all sorts of processes.
that we find comfortable to describe causally. So take Einstein's famous A&B coefficient analysis of stimulated emission. The idea is that if you have an excited atom in a radiation field where the frequency of radiation is at the right frequency that will stimulate an emission, it will stimulate the excited atom to drop back to a lower state. I would like to say
That causes it to do so i have no objection as long as you realize you're just declaring how you intend to use a word. And so my general claim is that when we have causal talk anywhere in science is actually avail definition it is simply someone who is saying oh i find it very convenient i find it pragmatically useful to describe this process using the word causation.
What they are not doing what they might realize is but what they're not doing is saying oh i have discovered the instantiation of some deep metaphysical truth lies and the seed prior to any science i haven't discovered that at all.
What are the advantages in using causal language in various places? It can almost immediately be psychologically helpful. It's very helpful when I think of Einstein's A&B coefficient paper to say, oh, so the external radiation field is stimulating an emission, it is causing an emission, and that's how lasers work.
That's the way we think about lasers. It's certainly very, very helpful. Otherwise, you just have a bunch of equations which gives you probabilities of various transitions. Or in the case of Jim Woodward's interventionist account of causation, he says that a causal process arises when we have two variables that are related by some connection, often probabilistic, but not necessarily if you read his account fairly carefully.
And if an intervention on one of them is associated with the change in the other right then we have a causal a causal relationship i just regard that is the definition. It's an immensely useful definition because if you tell me that this causes that i know that if i if i interfere on this then i will produce an effect on that. Right so so if you tell me that certain medical interventions will improve the health of the population.
Then I've learned something enormously useful. So if we abandon that causation is somehow fundamental or refers to something that has an essence, then is there anything that is in fundamental physics that's lost? So for instance, is there any theorem in quantum mechanics like Bell's theorem that then loses its power because Bell's theorem implicitly has a notion of causality in it? I don't know.
I don't think so, no. I looked into this, I didn't inventory of all the places where the term causation appears in physics and I found that almost invariably the term causation
Denoted one of two things either it was talking directly about the fact that we're in a minkowski space time or at least something or at least the space time that have a light cone structure right and so we talk about the causal structure of space time we're actually talking about the light cone structure of space time or the other the other one was that Propagations of physical processes are confined to lie on or within the light cone and that seemed to exhaust almost all of the
All of the causal talk that i could find i can't swear that i picked up every single case but that pretty much covered everything i notice what you what you're looking for here you're looking for a sense of loss would you never had it in the first place.
The the effort of causal message metaphysicians is to do a priori physics if they're providing you some kind of empirical fact about the world they are trying to do it prior to experience and if we learn one thing about thousands of years of side of investigation is that really doesn't work.
The world is far more creative than our imaginations. We always get into trouble when we try and guess ahead of time how things have to be. And if it's a causal metaphysics or a striking example of that, this is not to say that we have lost some sense of how things connect together. Spacetime has a light cone structure, call it causal structure. That's fine with me. Ordinary proper propagations, right? I can find to it. That's fine with me.
Where's the loss? So there are other counterfactual accounts of causation. Do you reject those? No, they're just definitions. Ford Blue Cruise hands-free highway driving takes the work out of being behind the wheel, allowing you to relax and reconnect while also staying in control.
Enjoy the drive in BlueCruise enabled vehicles like the F-150, Explorer and Mustang Mach-E. Available feature on equipped vehicles. Terms apply. Does not replace safe driving. See Ford.com slash BlueCruise for more details. Nothing wrong with that. This caused that because if I hadn't done this, that wouldn't have happened. Wouldn't have happened. Fine. You just told me
How you plan to use a word
Hi, everyone. Hope you're enjoying today's episode. If you're hungry for deeper dives into physics, AI, consciousness, philosophy, along with my personal reflections, you'll find it all on my sub stack. Subscribers get first access to new episodes, new posts as well, behind the scenes insights, and the chance to be a part of a thriving community of like minded pilgrimers. By joining, you'll directly be supporting my work and helping keep these conversations at the cutting edge. So click the link on screen here.
Okay, so let's get to thought experiments. So what is the standard view on thought experiments and then where do you stand on that view?
Don't know that there's a standard view, but I can tell you there's a long-standing debate. This goes back to the 1980s when the literature on thought experiments exploded. There were essentially two extremes in our understanding of thought experiments. One extreme is a completely deflationary view. That just says that thought experiments are ordinary argumentation. They don't do anything that ordinary argumentation cannot do. They just do it in a rather pretty and picturesque way.
The other extreme is it says no there's something more going on there's some magical power that capacity to do experiments. Is realized and the question is to articulate what that magical power is and the clearest articulation came from my colleague jim brown at toronto he said we can understand some experiments.
To be platonic in character. Uh, a really good thought experiment of just the right type literally opens the window, right? Um, onto, onto, onto Plato's heaven where we can actually see the, um, actually see the laws of nature. Uh, he, uh, he supports that with the, the, the experience that we have with a good thought experiment. There's this wonderful aha moment when suddenly you see it.
All right, and that's the moment of platonic perception. He's wrong, of course. I've spoken to James James Robert Brown. Yeah, yeah. Yeah, yeah. I've spoken to him. So one of the great thought experiments is that how is it that we could tell a priori that something should fall at the same rate of different masses? We can't.
Do you mean to tell me that a priori Aristotle's account of the motion of bodies was false a priori? No, that you could have a world in which things, in which you have a force needed to keep things moving. I'm not articulating my view. I'm articulating James's view from when I interviewed him. If I'm recalling correctly, it went something like this.
If heavy objects fall faster, then dropping, say, a heavy bag of marbles, okay, so comprises 300 marbles, next to a single marble means this single marble will fall slower. But then you look, the bag is just filled with many marbles. So those marbles each individually should be falling at a rate similar to if not equivalent to this marble. And then you have a contradiction. So thus, they all must fall at the same rate. That seems powerful. So tell me what your views are on that. It's very simple.
Why were you convinced by what you just said? Why were you convinced that the marble, the single marble and the bag of marbles have to fall at the same rate? There was an argument there. Yeah, that's thought experiment. It's an argument. That's all I'm saying. You just ran an argument. What's... Yeah, but I thought thought experiments are arguments, no? Or am I saying a view that's controversial by saying that?
You're agreeing completely with me. What you didn't have is any extra piece that Jim would want, where Plato's world of form somehow ended into things. You just look, every time someone, I mean, that exchange we had now is what happens all the time. Someone has a thought experiment, they run through the thought experiment, I'm listening to them go through the thought experiment I'm hearing,
Okay this just an argument it's a very simple straightforward argument if you know I can you know I can I can refute Galileo's you realize that this is not Jim's example this is one of the great classics in history of science it goes back to Galileo blah blah blah right okay but it's you know Galileo had a I think a musket ball and a cannon ball or something and then connected them with the thread
You just ran an argument and that's all thought experiments are. They're picturesque. I mean, they're compelling because you get this lovely mental picture and so it's easy for you to run through. But if it's simply purely a picture, I don't think it has any compelling force. There has to be an argument there. For example, can I prove the possibility of a perpetual motion machine by imagining one?
I visualize it it's a big brass gadget that's got bells and there's steam coming out and so on and oh look the wheel just keeps spinning and producing endless amounts of power. Just imagining it doesn't doesn't do anything. You there has to be that argument there or you don't have a cogent thought experiment and i say that's all that's all that's ever going on jim and i have been at this debate for forty years now it's it's.
little striking committee say that you know because what you're saying sounds sound and ordinary so i don't understand what jim would be objecting to because even with this articulation my articulation of this argument this is an argument i'm saying like if there's this then you have this then you have that their contradiction therefore the premises can't be true so it isn't just picture something
Now you have it you're in the same position as i am this is my view what we talk about the dome early run i don't understand why people are troubled by it i articulate the. It's the argument you thought experiments articulated i'm thinking well that's kind of obvious i wrote this paper i think in nineteen eighty six.
I thought, well, this is a bit of a doubt of a paper, you know, I'm just saying something that's so completely obvious. But then you discover there are all these people who want to take issue with you and you're trying to figure out why it's completely straightforward. Well, Jim's a friend of yours and you've spoken to him, like you've said for decades. Oh, yeah, yeah, yeah, we get along. So why don't you tell me what he would say other than you have to connect to a platonic world? I imagine that's not his sole point.
Well, he runs lots of examples. I think it's, I, I'd have to refresh my memory on his writing. I'm a little nervous about trying to channel him, but I think the thing, Jim, if you're watching, I apologize for getting it wrong. Uh, I think the thing for him is this moment of understanding that somehow seems to surpass just
You know just ordinary argumentation. So he's got a he likes doing philosophy of mathematics he's got an example where you can some numbers one two three four five and you got a little stack of blocks and you can look at the stack of blocks and suddenly you see all.
It's going to be five plus six divided by two. You can just see the way that works. You just suddenly see it instantly without apparently having to think about it. Those are the sorts of examples he likes. I just think they're arguments still because I say to him, well, I didn't see it. How does it work? And then he explains it to me and then he gives me an argument.
Okay, yeah, this moment of understanding sounds similar to Penrose when he's articulating the the Lucas argument or his version of the Lucas argument with girdle implying that the mind isn't computational. I don't know that well enough. I know all of it. I don't know the details. Okay, so how about let's get to something that you know, inside and out Landauer's principle. Why don't you outline what Landauer's principle is and then what your precise statement is either that Landauer's principle is false or it needs to be modified.
The argument or the project that Landau had was a very practical one. One of the things that we noticed in computing devices is that they always produce heat.
And that he of course is work that's been degraded. And so it is a cost for computation. It's been a long standing problem. Uh, we always need to cool down our computing processes. I don't know if you remember the Cray computers going back many years, but they would, they would sit in if I recall correctly, and that's free on free on in order to, you know, so, so the generation of heat in a computing device is a big deal. The question he was addressing is how far can we go?
before we have reached a limit beyond which we cannot go any further. In other words, how far can we reduce the amount of heat that's being generated in computing systems? The calculation can be done in terms of entropy. How much entropy is a computing device creating? If you think of the entropy as sitting in an isothermal heat bath, then the entropy creation is going to correspond
How to the heat passed the environment by the temperature of the heat bath give you give you first pass and how much the entropy is now his argument and as embellish and develop by Charles Bennett is that the logic of the process being implemented determines the minimum amount of heat generation. And if the process is logically reversible something like a bit flip.
All right then in principle you can execute that with minimal heat generation with minimal entropy creation if however it is a logically irreversible operation the classic case being erasure right then then necessarily there's going to be a certain amount of heat generation that's going to correspond to the Shannon information that you calculate for the two states so if you've got
What's wrong with that is just a very basic fact of the thermodynamics of systems at the molecular scale. You cannot do anything
Add molecular scales without creating entropy so something as simple as a bit flip. You can't flip a bit without having some driving force to push the bit from one state to another so very simple case is you you might have a charge and you want to move from one location to the other.
You're only going to be able to move from one location to the other if you have some kind of electric driving force that will push it. And what is that driving force working against? Remember, we're at molecular scales, and at molecular scales, that individual charge has its own thermal energy. It's bouncing around, right? And so you have to confine it. And in the process of confining it, you compress it over to one particular path, right? You're going to be doing work on it. That work is going to be lost as heat.
This is an extremely general result. This simply is Boltzmann's SSK log W. The best you can ever do at any process at molecular scales is to have a probability of success of completion. And Boltzmann's W tells you the probability of success of completion and the S associated with it tells you how much entropy you're going to have to create.
So if you don't, if you don't confine the charge very much, right, then it has its own thermal energy can jump out. Right. And so you have a probability that the charge is going to go back to the original state. So you can have a, but because you didn't confine it very much, you haven't created much entropy, but if you can find it a lot, right. So you really force that charge deeply into some kind of potential well.
Alright, then you have a good probability of success, but there'll be a lot of heat generated, a lot of entropy created. So the bottom line is the following. The amount of heat that will be generated in molecular scale processes is not determined by the logic. It's simply determined by the number of steps that you want to complete and the probability of completion that you determine for each step.
Again this seems so elementary. I've been arguing this for a dozen years now. I just don't understand why the Landau principle talk continues. If you're interested in the question of what's the minimum heat generation that you can have in any kind of molecular scale process, computational or not,
It doesn't matter. Ask how many steps are there in the process and what's the probability of completion that I want for each step and SSK log W will tell you the answer. It's done. So ordinarily in the calculation of Landau's principle, they use a principle of indifference to put 50, 50% odds for the zero and the one. And you're saying that the probabilities need to be physically dynamical. Yeah, I don't. Yeah, my recollection in Landau's original paper was he talked about
computing systems and the frequency in which they might be in different states. But go ahead. So let me try and summarize. If you try and form a lower bound based on logic, well, you shouldn't you should look at the precise implementation or the procedure. If you do this, you'd find that the minimum should be higher than K log two. Yes.
Absolutely hiding k log two if you just want a single process i've done the calculations i can't never wanted what the what the numbers are exact numbers are now but together.
A really modest probability of completion, I don't know, 90% or something, I can't remember the exact numbers, you will certainly create more entropy than the K log 2, it's 0.69K that is the one bit erasure case. If I remember correctly, if you want, I think 95% probability of success,
Are you create three k of entropy something like that but that's only one step remember in a computer device. Many many many steps right isn't this one step you got all the steps chain together and every single one of them is going to be dissipated. This is just a completely basic fact of of you know of molecular scale physics.
It doesn't take massive complicated fancy derivations the whole thing's done in two lines you just you just write down. I'm ssk log w or if you know you can find different expressions of it if you going to get formalism ssk log w will be expressed in terms of free energies you know and they're all essentially the same result.
This is interesting. So I'm currently writing an article. Maybe it's published already. I'll place it on screen if it's already out. And it's about this word in principle, in principle arguments. So my contention is that when most people just use that word, they use it loosely and you need to scrutinize what kind of in principle are they invoking. So are they referring to epistemological modalities or normal logical or metaphysical or logical possibility or something else entirely?
And even with these categories, there are frequent ambiguities and doubtfulness within. So what you're suggesting aligns with this. People invoke in my interpretation of what you've said, Landauer's principle. They're also employing, well, let's just idealize this scenario. Let's say it's an it's an in principle argument. But then even in such cases, you have to be careful and consider, OK, what are the practical implementations?
I'll say more than that. It's an inconsistent application of the idea in principle. I think you know a bit of the literature here. It goes back to Szilard's 1929 paper in which he introduced the Szilard engine. This was a version of the Maxwell demon. The idea was that you had a one molecule gas that would bounce around inside a chamber.
You would insert a partition, trapping the gas on one side and then you would isothermally expand it.
Thereby taking heat from the environment and converting it into into work now the key thing to understand about that is that the phenomenon that's allowed was looking at is a phone is a is a thermal fluctuation this was the literature in which he was writing thermal fluctuations going back to sell out and i'm starting and brownian motion and and so on and you know the fundamental question that was being asked is
If you look at some fluctuations to what extent can they reverse the second law of thermodynamics so if you look at brownian motion for example think about the brownian motion in a fluid when the brownian particle goes up and down. When it's going up heat from the environment is being converted into some microscopic notion of work because it's being elevated in the gravitational field so punk rate remark that
In this solar system we see through our microscope a Maxwell demon in action. So the question then became, is it possible to accumulate all of these microscopic violations of the second law of thermodynamics in order to produce a macroscopic violation of the second law of thermodynamics? And that was a serious project that was undertaken in the first decade of the 20th century.
Smolikowski came up with the answer and the answer is yes you get fluctuations that you might try and exploit, but every time you try and exploit those fluctuations you use other processes that have their own thermal fluctuations that will reverse everything. So this is the example of the Smolikowski trapdoor. So let's now go back to the Szilard engine.
The single molecule bouncing backwards and forwards is a case of a dramatic density fluctuation in a gas. It's the most extreme case. When you have larger numbers of molecules, the fluctuations are very small. As you decrease the number, then the fluctuations become large in relation to the total energy of the gas. And so Salad's question was, can we
I somehow exploit those fluctuations and add them up to get a violation of the second law and the trouble is when people analyze that they don't account for all the fluctuations that are in the apparatus that they're using. So think about the way the apparatus works you start out with the gas the one molecule gas bouncing around you put in a partition the mere fact of putting in a partition.
Is itself a thermodynamic process. If that partition is very light, it's going to have its energy of a half KT. You have to suppress that energy to get the damn thing to stick. That's going to be creating entropy. If you make it very massive so that the amount of KT is not half KT is not going to produce much motion, then you need frictionally to damp it. That's going to produce so it stops moving, it doesn't bounce out.
The short answer is, the analysis of the Szilard engine from Szilard's time up to the present simply ignores the totality of fluctuation phenomena that have to be suppressed in order to get the process to go through. So it is, to go back to your original point, it is a selective and incorrect use of in principle idealization. You're idealizing away half of the
I'm half of the fluctuations, but not the other half. And then you're claiming, then you're claiming a result. If you're going to, if you're going to, um, try and exploit fluctuations, you have to treat them consistently and look at the fluctuations throughout the system. If you just pick one particular subset of the fluctuations, you're going to get nonsense results in that. And so, uh, I mean, you, you probably sense frustration in my voice. This literature has been teetering on the, on the edge of nonsense for a hundred years.
This kind of selective treatment of fluctuations is just disaster is the course you get completely bogus results. The trouble is that every time a formula p log p appears. There's a tendency and natural reaction this is all we have a p log p. That must be thermodynamic entropy no it must not be. The conditions for a p log p to be associated with heat. In the way the clouds is requires that that p come about in a very particular way.
The mere fact that I don't know whether I have a coin I put in my pocket I don't know whether it's heads up or tails up that isn't that isn't the right way for there to be a thermodynamic entropy of a log two associated with the coin but that's the fallacy that's being committed over and over and over again so there it is there was even a nature article that says that they experimentally validated landau's principle
Yeah, they're doing exactly what they shouldn't be doing. What they showed is that you, I don't remember the details now, but what they showed is that you have a little tiny particle, a colloid or something that's free to move around like a Brownian particle. And if you, um, if you compress it right by moving a barrier and you do it slowly so you can get a reversible effect here, then you, uh, then you pass heat of, of K log two to the environment. Well, of course.
This has been this has been standard in thermodynamics for over a hundred and I don't know how many years. This is just the basic gases of the basic thermodynamics of ideal gases. Um, I did a lot of work on Einstein. It's abundantly clear in Einstein's work on Brownian motion that he understands is perfectly well. It is quite fundamental if that experiment had failed.
Then we would have to rethink the thermodynamics of ideal gases. So what's wrong with the experiment? Well, they've just looked at how much heat gets generated when you compress a one molecule gas in effect. It's actually a particle, but it's close enough to being a one molecule gas in its degrees of freedom. If you want to say that we've now instantiated Landau's principle,
And that's the and that's the lower limit. Um, well, that experiment doesn't show it. What about all the entropy that was created in all the other bits of apparatus that were being used? Right. It's a fluctuation phenomenon that you're looking at. What about all the fluctuations that were, that was suppressed in order that you could move your partition inwards? All right. That's all got to be part of the calculation or you simply don't have a result. And of course they didn't calculate any of that. So it's, it just, you know, um,
I mean i certainly accept the result you know yes a two to one isothermal compression of a of a single molecule and an ideal gas will pass um occasionally log two with heat to the environment the same thing will happen if you're in a fluid right you have a single brownian particle
What's up brownian particle is going to behave like a what like a one molecule gas this was the brilliance by the way by stein's analysis of brownian motion he realized that you could treat brownian particles in the same ways you treat molecules was it was a very beautiful analysis. Yeah i do want to get to einstein's views on old quantum theory versus new quantum theory will get to that shortly so. It sounds like what you're saying is nature is the article that i've shown maybe it will be on screen again right now is.
Not validating Landauer's principle. This is something that was predicted before Einstein died and Landauer came with the principle in the 1960s or so. It's wasn't that. It is an easy consequence of the standard thermodynamics of ideal gases. I mean, it's undergraduate physics stuff. Okay, it's lovely that we've done the very particular experiment and seen the result.
But boy it had to be right if they got if if they had any other result coming out right and it wasn't the result of some kind of procedural error it would have been traumatic for for statistical physics.
Because that is so fundamental that if you just have a single component, like a molecule, a one molecule gas, and you compress it two to one, you're going to, isothermal, you're going to pass a KT log two of heat, reversibly, by the way. What if someone says, okay, so what? So what if Landau's principle isn't the minimum bound? I mean, I can say Kurt's principle and set the minimum bound to zero, and then I'm still correct if you show that something's higher because, hey, my minimum hasn't been violated.
Remember the idea is that we can understand the minimum amount of heat generation in a computing device by looking at the logic of the processes being implemented. So if we want to minimize heat generation, then what we need to do is look carefully at the logical processes and minimize any irreversible irreversibility in the logic.
That is just mistaken and will mislead you that's the wrong answer the right answer is what matters is how many steps. You are expecting to complete whether it's a computing system or any other system whatever and the degree of probability of completion. And you need to understand that if you're serious about reducing the amount of pay the paying attention to the logic being implemented in the computational device is really not gonna help you. It's how many steps.
It matters, the implementation matters massively.
This episode is brought to you by State Farm. Listening to this podcast? Smart move. Being financially savvy? Smart move. Another smart move? Having State Farm help you create a competitive price when you choose to bundle home and auto. Bundling. Just another way to save with a personal price plan. Like a good neighbor, State Farm is there. Prices are based on rating plans that vary by state. Coverage options are selected by the customer. Availability, amount of discounts and savings, and eligibility vary by state.
Think Verizon, the best 5G network, is expensive? Think again. Bring in your AT&T or T-Mobile bill to a Verizon store today and we'll give you a better deal. Now what to do with your unwanted bills? Ever seen an origami version of the Miami Bull?
Jokes aside, Verizon has the most ways to save on phones and plans where you can get a single line with everything you need. So bring in your bill to your local Miami Verizon store today and we'll give you a better deal. So is something now allowed that we previously thought was disallowed?
because of this analysis your analysis or is something now disallowed that was previously thought to be allowed like what is the consequence the practical consequence of this the practical consequences is what i just said if you want to minimize the amount of heat generation in your computing systems pay attention to how many steps you've got and the probability of completion that's what you should be looking at and you also believe that this distracts researchers from simpler more general solutions to
Maxwell's demon like Louisville's theorem. Oh, yeah. Oh, yeah. No Yes, this is one of the one of the one of the papers that I wrote I do my research you did. Thank you You know the you know the idea that That notions of information and computation are going to help us understand why Maxwell demon must fail, right? That has so distracted everyone we spend all our time arguing about it
What's up for a long time john and i first wrote papers on this i wrote them by myself i kept saying no no no these ideas aren't helping us. It doesn't work we don't learn why max will demon must fail we don't know that it must fail from these considerations and we spend a lot of time thinking about that we just usually distracted by that then one one day i was sitting on the bus coming into the office i thought myself you know.
Maybe maybe i should ask the question is an actual demon possible forget about all this information stuff and within five minutes i mean in the course of a short bus ride and realize oh god the level theorem just prohibits it.
If you're assuming that the demon is to be implemented within classical physics, you can see with essentially no calculation at all that the Liouville theorem is going to block it. So I published that somewhere in the paper. And then after a while, I thought, you know, this is not a
This is not a really decisive argument because nothing at the scale that we're concerned about is actually classical, it's all quantum mechanical. And so I asked, is there an analog of the Liouville theorem?
I'm gonna mechanics yes there's analog and quantum mechanics and and the end you can run an exactly analogous argument and so i've got another paper in which i show i've got a two-column two columns you got the classical and that was on one side quantum and also on the other and they just match up match up perfectly so so yeah i'm we know that a maxwell daemon is impossible in so far as those versions of the level of theorem apply.
That explains why with all the nanoscale physics that we've been doing, no one's produced a Maxwell demon. Before we move on to Einstein's views, people are terribly interested in entropy.
And you mentioned a couple different definitions of entropy like Boltzmann and Shannon. So there are a variety of entropies. Can they be arranged such that one is a subset of the other, like Boltzmann is a special case of Shannon? Or are there entropy notions that are incompatible? And why are they all called entropy if they're incompatible? So if they are indeed some that are incompatible. So why don't you outline what is entropy supposed to be quantifying and then the different definitions and their relations? The basic idea of thermodynamic entropy is articulated
Well by clausius in his early papers i think was it eighteen sixty five or something i don't need it original papers date the idea is that that will tell you which processes will move forward spontaneously which phone dynamic processes will move forward spontaneously.
Now the notions of entropy that appear in thermodynamics adhere well to that. So Boltzmann's notion of entropy, SSK log W, is going to tell you which processes move forward. This was the rule that I told you before. If you want a process to advance, you want to have an end state that has a higher probability than the starting state.
S is k log w then tells you that the entropy of the end state is going to be greater than the entropy of the initial state and then that notion of entropy when you start to move into equilibrium systems is going to match nicely with the.
uh, with the notion that Clausius, uh, developed, uh, in the Gibbs formalism, it's more complicated. Uh, in the Gibbs formalism, you can connect, uh, the Gibbs entropy, the P log P with, um, um, uh, with, uh, thermodynamic entropy by, um, by giving an analysis that both Gibbs gives and Einstein also gives in one of his early papers where you look at a thermodynamically reversible process and you idealize it and you can match up all the quantities. Then there's Shannon entropy.
The sort of entropy that appears in information theory is a parameter for a probability distribution. And that's what it is. It's a measure of how smoothed out, of how uniform the distribution is. The highest entropy arises when you have a uniform probability distribution. And as the probability distribution becomes more peaked, then you're going to have lower and lower entropy.
It's just a different thing. I mean, there are connections. I mean, you know, take probabilities. There are many ways that probabilities appear in usage in the world. I don't know that I want to nestle one inside the other, but I'm kind of comfortable that Boltzmann's notion of entropy and the Gibbs notion of entropy and
uh and the clouds this notion all fit together very nicely now there are complications because when you move into quantum mechanics there's a phenomenon entropy literature saying well this doesn't exactly match up and i'll i'll i'll defer on that because uh because we're now getting into very delicate territory
I don't know how to interpret the density operators that appear in quantum statistical physics.
When you give the matrix form and you have a nice diagonal with p's that add up to one, are they probabilities or what are they? And if you can't answer that question and you don't really know what p log p is, which is going to be the entropy. So anyway, not my area. I've deferred to other people who write on this because I think we have
Great. Well, we can turn this into your area by talking about Einstein. So Einstein has some criticisms of new quantum mechanics and its statistical interpretations. And then I believe you mentioned that Einstein's fundamental contributions to old quantum theory have been forgotten because of these new criticisms.
So firstly, let's talk about the criticisms to get them out of the way, please. And then let's talk about his contributions to the old theory. Well, I think his his objections are very widely known. He simply did not believe in the indeterminism of quantum mechanics. He argued that there was some he was arguing for some sort of a hidden variable theory. The sort of hidden variable theory that he was arguing for
I don't think there's anything like the salt that we're thinking of you might think now for the bond theory is a kind of hidden variable theory of course i'm starting was encouraging to bone but that it's pretty clear that wasn't his theory. Einstein's hug was that his unified field theory would would somehow return this hidden variable theory.
I think you know the basic layout of the Hidden Variable, Einstein's Unified Field Theory. The program was pretty straightforward. He'd found that you could represent gravity in the same structure as the inertial properties of space and time and in the metric field. I'm not using geometric language here because he didn't. If you're curious on that, I just wrote a long paper on this explaining
Just a bit of a digression because please you know when you first when you first get a a Class nowadays in general activity and you learn about the structural metric and you learn about the structural radius Right one of the first things you're told is oh, but don't make the mistake of thinking that that's a singularity I know the formula blows up, but it's just a pure artifact of the coordinates Don't make that mistake and it's sort of you know, you're wanted to silly novice mistake, but why?
Why is it talked about so much. Well, who made the mistake answer prior to about 1950, everybody. Right. Um, Einstein was very clear that he regarded, uh, that he regarded the Schwarzschild radius as singular and he convinced everybody else of that as well. Now, when I say everybody else, I don't mean, you know, I don't, I don't mean trivial figures. I mean the world's greatest mathematician of the time, Hilbert.
I mean the world's greatest geometry of the time, Felix Klein, they all agreed with him. And Herman Weill, they all agreed. What on earth was going on? You know, I do a lot of work in history. I'm fascinated by history of physics. And I can only just tell you very briefly what the answer is. There are multiple ways of treating general relativity mathematically.
The geometrical approach that we now use is i believe the right approach and the correct way to do things and one that gives us the best and most productive results i don't want to in any way detract from that. Einstein dislike the geometric approach completely right he preferred kind of algebraic analytic approach which was all dependent on very particular expressions and their behaviors in the transformation properties and in the context of that approach.
It makes sense that he would come to the conclusions that he did now he wasn't coming those conclusions in ignorance of the possibility of another analysis. It was some of the nature who had already discovered that you could transform away the structural singularity.
I am and also a few of the client appointed out the so called mass horizon in the space time was could be could be transformed transformed away he knew all of that it's still knowing that he said i don't like this geometrical approach i don't take it seriously. We have to approach it and let me get a sense of how someone could possibly think that.
Look at the way that Einstein's 1917 cosmology was introduced. He wanted to have a spherical geometry for space. So where does he get the spherical geometry from space where he wants to get the line element for a spherical geometry? But he says imagine a four dimensional Euclidean space with three dimensional sphere embedded inside and look at the geometry that is induced on the three dimensional sphere and bang there you get the nice line element.
But now do you take this this geometrical picture of a four-dimensional space inducing right in inducing a geometry on the three-dimensional space do you take that seriously do you really think there's a four-dimensional space there no all of this geometrical thinking is just confusing you all that matters in the end is line element in the space right so he called in correspondence with reichenbach he called in germany he called it a donkey bridge
Right bridge of asses in other words it's a it's a kind of easy way for people to the novices to learn things but don't take it seriously i think then it would call those intuition pumps yeah maybe so ass bridges were intuition pumps yes you you yeah i suppose he didn't use that expression i guess that would fit i you know i had to speak for him
Okay so so those those is objections and the the the epr thought experiment is i think it's transparently trying to argue that there's more to the system than the standard quantum mechanics allows in other words in the title what is it is quantum mechanical description complete something i can't remember and there's a criterion of reality you know if you can predict with certainty properties of some system
I'm without interfering with it then the system has those properties. This is the api argument everyone everyone knows it so what was contributions to quantum mechanics i'm really quite massive i think the major one was the light quantum of nineteen five completely extraordinary idea when you look at stein's amos marabas is your miracles in nineteen five.
Everything that he's doing there, accepting that is a completion of 19th century physics. So we can just go down the list. His argument for the reality of atoms brownian motion is completing the Maxwell Boltzmann tradition as statistical physics that had been well developed in the 19th century, but was making a great deal of resistance because there were no new phenomena.
The needed items if you understand special relativity you realize that the basic content is implicit and that's for laurence electrodynamics laurence had discovered in effect the orange group.
Mathematically articulated by Poincare. And once you have the Lawrence group and you understand how to think about it, you realize there's ineffective kinematics there in space and time. Einstein is excavating that and saying, oh, look, there's a kinematics of space and time built into, you know, this is the big discovery of the 19th century electrodynamics that space and time is actually a special logistic equals MC squared. It's already there in special cases in electrodynamics.
Amongst all of this, the huge discovery of the 19th century was the wave theory of light. You know that they are electromagnetic waves, the Maxwell-Lawrence theory. Then in 1905, Einstein says, no, wait a minute. In some thermodynamic sense, heat radiation has a particular character. One of the things that has fascinated me
for a long time is how Einstein made his discoveries. He didn't have anything that everyone else around him didn't also have. He basically had a pen and a paper and journals to read. He did very little experimentation, wasn't terribly good at it. Yeah, so what was different about how he came up with his discoveries? Well, in this particular case, the key thing about
The results of 1905 is that you could see significance in empirical results and other people couldn't see. So let me, um, let me give you the example with the, uh, with the light quantum. If you try and understand what he did with the light quantum as a correction to electromagnetic theory, it's unintelligible. How could this possibly be? We have Young's two-slit experiment. We have all of the massive successes of, um,
What you're doing is your. You're not putting the discovery in the right context the discovery live tonight's work in thermodynamics.
In the years leading up to 1905 Einstein was already working in thermodynamics. He was trying to understand the microscopic or the, I want to say molecular, I guess, molecular scale properties of matter. And what he recognized was that the molecular scale properties of matter get imprinted on their thermodynamic properties.
So the classic example the simplest example is this if you have a system whose pressure and temperature and volume conform with the ideal gas law. Then you know that it's molecular constitution consists of localized points of matter bouncing into each other but but independently moving otherwise.
I mean, that's where PV equals any NIT comes from. You model the gas as a whole bunch of molecules that move independently one another, but they bounce off the walls and they bounce into each other. The key thing is that PV equals NIT at the thermodynamic scale is a signature of that constitution. This, by the way, is why osmotic pressure obeys the ideal gas law. When you first learn this in a statistical thermodynamics class,
Why the hell should a dilute salt solution exert a pressure that's the same as the ideal gas? Well, because it's dilute, the salt, the salt molecules of the salt ions are moving around like independent, um, like independent molecules. Okay. So what does Einstein do? He's looking at the latest results on the thermodynamics of heat radiation. And what he recognizes in that thermodynamics is that same signature of a particular constitution.
In particular he realizes that if you take the plunk distribution which being empirically established by the experiments of blumer and pring's hymen in nineteen hundred and you wrote the entropy as a function of the volume. You got the entropy of high frequency radiation.
Are you actually looking in the rain regime so i don't come into this but never mind if you look at the in the rain regime you got the entropy of radiation there is with the logarithm of volume. And that is the same right that's the same as the ideal gas so i'm so look.
Here we have the fingerprint of the thermodynamic fingerprint of the molecular constitution and just as you can calculate the size of molecules once you once you know how big Boltzmann constant is and you've got the ideal gas law so you can calculate the size of the energy particles that are giving you s's k log w and of course what comes out of that is that the size of the little localized energy bundles
What is given it depends on the frequency and it's what we now call plants constant times frequency that's the big argument. Alright and he gives a very simple derivation of what we now call boltzmann's principle is his camera w is actually in stein's principle of the calls of boltzmann's principle in this paper and he gives a very simple derivation of it and they says this is now instantiated.
When you add in the various conditions that apply, you get SSK, as entry goes with the logarithm of volume. It's, I think, one of the most beautiful, most extraordinary of Einstein's contributions. I mean, there are many more. I'll just mention others that are important. Now, the next thing that comes up is the following. He's established that there's a particulate character, right? But he's only established that by looking at the Vien regime,
in the in the black body spectrum what happens if you look at the total regime going all the way down to the to the to the lower frequency and right.
Well if you give a similar analysis of the thermal properties in particular you look at the fluctuations of radiation pressure and energy you discover that the expression that you derive for the fluctuations in heat radiation is the sum of two terms one term has a particular character and the other has a wave character and they are arithmetically added together
This is the origin of wave-particle duality. This is where it first appears that radiation has this dual wave and particle character. And so it keeps going like this. And I just mentioned, of course, the A and B coefficients paper on the basis of lasers. This was 19, what, 16 and 17. And then, of course, those Einstein statistics in the early 1920s.
So the idea of the light quantum was greatly resisted. Bohr did not like it one bit and Einstein, it was regarded as a heterodoxy for 20 years until the Compton effect. It was the Compton effect that finally drove home the idea to physicists that Einstein's light quantum was in fact a good description of what was happening with heat radiation or radiation in general, electromagnetic radiation.
So professor, why don't we end this on what insights from your research into the beauty of how Einstein thought differently than his peers? Because as you mentioned, Einstein had access to the same data as his peers. What insights exist that you've gleaned that can be applied to young researchers today, such that a young researcher can watch this and say, OK, I should do more of that. It's the season for all your holiday favorites, like a very Jonas Christmas movie and Home Alone on Disney Plus.
Then Hulu has National Lampoon's Christmas Vacation. We're all in for a very big Christmas treat. All of these and more streaming this holiday season. And right now, save big with our special Black Friday offer. Bundle Disney Plus and Hulu for just $4.99 a month for one year. Savings compared to current regular monthly price. Ends 12-1. Offer for ad-supported Disney Plus Hulu bundle only. Then $12.99 a month or then current regular monthly price. 18 Plus terms apply.
Close your eyes, exhale, feel your body relax, and let go of whatever you're carrying today. Well, I'm letting go of the worry that I wouldn't get my new contacts in time for this class. I got them delivered free from 1-800-CONTACTS. Oh my gosh, they're so fast. And breathe. Oh, sorry. I almost couldn't breathe when I saw the discount they gave me on my first order. Oh, sorry. Namaste. Visit 1-800-CONTACTS.COM today to save on your first order. 1-800-CONTACTS.
I think a lot of it is good fortune. So let me say a couple of things. One thing that I don't think works is the following. There's this idea that you have to be young and in your twenties to make a great discovery, that there's something about youth. What's happened is we have a correlation, but not a causal connection. The process that seems to be at work is the following. When a new science opens up,
When you sign up opens up that's where the new discoveries are going to be made the established figures are working on the old sciences that they have put together.
Alright and so they keep working on those the new figures come along and they're asking where something new happening oh it's over there so they're gonna work in the new science and that's where the new discoveries and that's why they made more commonly by younger by younger people so don't you know so don't feel bad that you're young and you haven't made nice discovery yet it's got nothing to do with you with your age but also don't feel bad that you're old.
Yes, exactly. In fact, this is one of the things that I follow in my own research. This is just a side thing, but I mentioned before I get to the other point I wanted to make. Someone pointed out to me quite early in my career that when you enter a new field, most of the important novel ideas you have will come to you pretty early, and then you won't get much more. And I think that's right. So how do you exploit that?
Answer you keep jumping around right right so if you've been if you done your homework and you've looked at you've looked at the sort of papers that i published i'm all over the place you know we've just looked at a few of the things that i've done in in in philosophy of physics i'm you know i've i've written a whole bunch on inductive inference i'm writing a book on empiricism at the moment um you know um it's all it's all over the place because every time i go into a new field i'll have a new thought
Right. And if it's genuinely new, I'll publish it. So don't be afraid to jump around. This is one of the traps for young physicists. This is why you should be a philosopher of physics and not a physicist, because if you're a philosopher, if you're a physicist, you're trapped by the need to keep grant money going, which means you have to develop an expertise of sufficient caliber to enable you to keep the grant money going, which means and to keep your lab going and to keep your graduate students going.
So you can't escape. Philosophers of physics are supported by teaching. We can switch on a dime. I can change my mind tomorrow about what I'm working on, work on something else. As long as I keep teaching my classes, I'm supported. Now, let's get back to Einstein. What did we learn from Einstein? Einstein had a remarkable ability to look at results and see the significance in the results.
the empirical results that nobody else could see i've already i've already mentioned that with the light quantum right he could see the signature of of of distributed atoms there in special relativity he could see that the lawrence group was actually a kinematics of space and time right all of this is empirically in in the theory it has this property lawrence poincare they fully understood the mathematics they just didn't they just they just didn't see it
This was Einstein's, and he used this over and over again, this was Einstein's magical power that he could read in experimental results. Things started to change with general relativity. It had the same origin there. He recognized that the fact that all bodies, the Galileo result, that all bodies fall with the same acceleration had to be implemented exactly and perfectly. All right.
When people like Poincare and Minkowski were revising theories of gravity as they tried to do, they discovered that that law was broken in second order quantities. You would get a V on C squared dependency on the sideways velocity. So things that were moving with velocity sideways would not fall at the same rate as something that was falling vertically straight down.
This stein stein tells us just bothered him massive he just didn't see that that would be the right the vector possibly be right you can. Think of other cases and understand why that would be so might that mean that a kinetic gas would fall slow when it's harder because there's a lot of sideways motion. Maybe maybe not turns out not to be that simple so what does stein do we need to construct a theory.
In which that result is preserved it's so important and how did you construct that theory well with the principle of equivalence so if you have two bodies one at rest and one moving initially to the side and then you view that from an accelerating frame of reference then the resting body will fall and so will the body that has sideways motion but they will remain at exactly the same altitudes right so i'm stunned says that's the way a gravitational field has to be
Alright so let's ask what sorts of theories of gravity come out of that and since he's working in a minkowski space time you very rapidly gets rapidly.
For five years he gets to the idea of a semi rimani and space time to move from the casket space time to a semi rimani and space time so okay so that's the thing you need to have. There has to be a match this is now the jar of mold has to be a match between the problems that are right for the picking and your particular talent and expertise.
How does that work out with Einstein? Well, Einstein then moved on to his unified field theory, and he stopped using that facility. He started saying, I'm going to find the simplest possible rules that we can have for physics. And from the mid-20s onwards, when he was doggedly pursuing his unified field theory,
He just never produced anything that we know that we know actually works. He was he was no longer well matched to the problem. You ask who was well matched to the problem. Well, when quantum mechanics came along, it was it was just crazy. You had to be able you had to be someone who could tolerate bizarre contradictions and and and manage with them. And who could do that? Who could do that better than anybody else? Answer Niels Bohr.
I'm just gonna see electrons completely completely crazy.
And so he had this ability to just say, I know it's crazy, but you know, what's the quote? Is it crazy enough? I don't think it bore. I think maybe that was Pally or someone. And that was terrific because he could actually produce this theory, the Bohr-Zommerfeld theory of the atom, that led directly up to what happened in the
In the nineteen in the nineteen twenties of course just as with with einstein.
Then balls facility to tolerate silliness and contradiction became a massive liability because you then produce this this incoherent idea of complementarity which for which i don't think there's any precise sense right and he somehow managed to convince a whole generation of physicists to take this silly idea seriously it took a long time for people to to to get past the the the incoherence of balls ideas.
I can see you flinch there because there's a sub community in philosophy physics and hang on to the idea that ball had some kind of deep and profound inside now we buy for kate i'm clearly in the school that things not. I have no doubt that ball had strong powerful intuitions that he could communicate to other people that are at the core incoherent anyway so so so so the moral is if you're starting out.
Just do the work on what interests you. Look for places where you can see further than other people can see. That's your secret skill. When I talk to philosophers of science and we're trying to figure out where they should work, I often ask them this question. I say, can you remember when you've been in a discussion group and everyone gets tangled up over something and you're sitting there thinking, I don't get it.
It's perfectly clear and perfectly obvious what's going on. I can see straight through this. Ah, there's your magical power. The difficulty is that because you could see it so clearly, you think it's trivial and you think it's easy. Right. And so you tend not to value it. Rather you look at someone who can do something that you absolutely can't do and you're in amazement and you want to be them. Big mistake. They're good at it. You aren't.
Right. Do the things that you're good at. Do the things where you see your way through clearly faster than other people do. And that's where you'll make the breakthroughs. Anyway, look, that's the advice I give people. And it's as good as they paid me for it. So free advice is only as good as what you paid. I love that. OK. So most of the time we'll look at gymnasts and we'll just be wowed and we'll think, OK, I should do that because that's difficult. But then there are other tasks. That's exactly right.
It's taking me a long time, so I've worked hard on exactly where I have a skill. I'm not very good at the mathematics. I can do mathematics competently, but I don't have the sort of beautiful insight that a good mathematician can have. But my background is chemical engineering. I can tolerate the kind of vagueness that engineers thrive in.
I can survive when the situation is unclear. Do you thrive? Do you not just survive when the situation is unclear? Do you actually prefer that and do better in it than in situations where it's clearer? Oh yes, absolutely. And so I'll give you an example of that. I wrote a paper recently on the nature of thermodynamically reversible processes. I think that's roundly misunderstood all the way through here.
And it's not a question of mathematics the mathematicians of carthi dory going back to going back to the good in the group are they gave a beautiful math in the time version that they missed the essential point of what's really going on with him and the reversible process is i can see that.
One of the things that chemical engineers have to be good at is thermodynamics, because processes and chemical plants are all thermodynamic processes. So I was taught thermodynamics from scratch four times in my engineering degree, and it was only on the third time that suddenly I got it. I can still remember there was this moment when I realized, oh hell, it's all about thermodynamic reversible processes. That's the key concept. If you don't get that, you know, and so I just mentioned to you, maybe, maybe
Maybe this will be helpful to you. A standard mistaken view amongst physicists is that a thermodynamic reversible process is just a really slow process. No, here's a really slow process. Get a balloon and inflate it and then put a tiny little pinhole in it. That balloon is going to deflate as slowly as you like just by making the hole as small as possible, but that's
That is an irreversible expansion of the gas that is entropy increase. Now a thermodynamic reversal process has to be one where you have a near perfect balance of driving forces. The forces that are pushing the process forward have to be balanced almost perfectly exactly by the processes that are pushing it back.
Now that runs automatically into trouble because if you then notice i had to use weasel terms almost exactly almost perfectly well there's a reason for that if you um if the if the forces balance exactly nothing happens right when you have a perfect equilibrium of all driving forces no change happens right so you have to have some sort of an imbalance okay if you have an imbalance right then you have an entropy creating process so how are we to think of these things
What are the ways of doing it and that's what the papers about it includes a historical survey of everything i could find people but that comes out of out of a kind of engineering thinking i'd like to make my peace with these these these ideas.
This is interesting. You learn thermodynamics three times from scratch in order to truly four times. OK, great, because I was going to say something that relies on the number four. OK, I wonder if this is a general rule, because it's common to hear that one has to learn quantum field theory four times from scratch before one groks it. And I just applied that to QFT. I didn't apply that to computer science or to stat mech. But I'm wondering if
Maybe it's the case and you seem to validate the thermodynamic case. Yeah, no, I think that's right. Maybe it's the case in general. Now, what does it mean to learn something from scratch again? Because you could just take one course, thermodynamics one, and then you take thermodynamics to the next year and then they reteach you the fundamentals. Or you could take thermodynamics one, take a year off, retake the same course. Tell us what exactly does it mean from scratch? I'll give you my experience.
Give my experience with thermodynamics chemical engineers have an odd place in engineering because we don't just do one sort of engineering we have to have control of all of the different branches of engineering right so in a chemical plant i have to understand the chemical processes i have to have some understanding.
of the mechanical engineering of the structures of the pressure vessels that are being used. I have to have some understanding of the electrical system that's being used. And also chemical engineers are often involved in finance. So we had courses in discounted cash flow. We had courses in operations research. You're torturing yourself. This is so messy. Yeah.
Yeah so so we had to we had to be a jack of all trades and i enjoyed that immensely so we went to different departments. Alright so we we learned some dynamics in the physics because you need to know physics you go to the physics department you learn some dynamics there then you go to an engineering school.
I have to know the engineering and they teach you thermodynamics as well then you go to the chemistry department chemical engineers we need to know chemistry they teach you thermodynamics there and then you come back to chemical engineering right and then there's got their own version okay if you think across all of those different groups. They all have different ways of representing things so for example.
how the way a physicist will will talk about will talk about some dynamics is going to involve clouds entropy and so on when you go to the chemistry department the interesting thermodynamics is the thermodynamics of chemical reactions.
What is it that drives a chemical reaction for it is going to be an increase of entropy but how do you represent the entropy so it is applicable to the chemical process or if you're in an engineering school the thing that really matters is the efficiency of engines. So what's the best efficiency you can get out of an auto cycle in a gasoline engine.
All right now all of it's all from dynamics that they're being applied in so many different so many different ways all the way all the way across the board and it's getting all those different perspectives now the thing about thermodynamics is that there's an intrinsic beauty to it but a massive incompleteness because what thermodynamics actually talks about is never the complete theory.
You need to have, in addition to the basic thermodynamic concepts, a theory of the matter that's being involved. You need to understand the mechanics of fluid flow. You need to, you know, you need to understand if you're doing thermodynamics for quantum systems, you need to understand the peculiar quantum mechanics of those particular systems. So one of the questions that I got interested in for a while is what's the maximum efficiency of a solar cell, right?
What are the heat engines they're taking in heat radiation and producing electricity but that's a that's very much a quantum mechanical process that's doing it or something like what do you call these these cells that.
What what what what's going on and so and so many different ways in now i know any little quantum field theory that my impression is that it has a very similar sort of character.
There are basic ideas. You need to know the Hamiltonians or the Lagrangians. But then you might be looking, for example, at Feynman diagrams and scattering processes and so on. Or you might be looking at quark confinement, or you might go algebraic. You might have a course from one of the mathematicians who will get you to read Street and Whiteman. But what you're doing is you're approaching
The one phenomenon in the world with many different theoretical devices.
And it's only when you get a grasp on how all of these are bearing down that you see the commonality. I think quantum field theory is an especially difficult case. It is justly reputed to be a very difficult theory to learn. I think that's right because, well, I mean, part of it is you start to try and compute Feynman diagrams and very quickly you realize you've got a lifetime of integrals ahead of you. And so do you really want to get into that? And then you've only learned scattering theory, right?
And then there's all the stuff about re normalization and what do i make sense of that and the realization oh by the way when i when i started studying re normalization group it looked more like engineering to me than anything i've seen in fundamental physics before um it really it really got my engineer juices going i thought boy that's it that's how we do things in chemical engineering sorry yes well i was going to say i very much like this idea of approaching something from multiple points of view in order to understand it so
One analogy is that you could take a look at a cone, and if the light is shown from above, it just looks like a circle. If it's from the side, it just looks like a triangle. If it's from an obtuse angle, then it looks like an ice cream cone, like there's a little bit of a bulge there. And it takes you a while to understand the three dimensional structure there. Yeah, yeah, yeah. And all you have access to are the projections. And so to move around. And that also jives with your previous answer of, well, it's something I thought of as well, that maybe it's not mere youth that enables creativity.
It's instead the entry into a field that fosters that innovation. So Schrodinger was 40 or 50 when he began contributing to biology. Maybe it's just he had that foray into the unfamiliar that enabled the contributions. Yeah, I know. I noticed this with in philosophy as well. People look at some major work of philosophy and they say, well, that's, you know, but that answer to the problem is easy, right? I don't really understand what the fuss is.
Well the first is not the answer it's the question. The creativity in philosophy is framing things so that an analysis is possible and if you do that you create a new field and because you're the first person there you get the you can you know jump on what is likely the correct answer almost immediately and so you kind of win the day I mean this is this is what I feel happened with the stuff I did with thought experiments I mean
I just got very insistent on arguing that there's an epistemic problem here. How is it possible for thought experiments to give us novel knowledge of the world? And I made that the framing. I call that epistemic problem of thought experiments or the empirical problem. I can't remember which one of those two. And once you ask it very pointedly and then you're very rigorous in giving an answer, it's easy. Yeah, okay. It's the obvious answer.
But you got there first and people say what's the big deal with the big deal is I knew the right question to ask. It's the same thing with causation. Right. I knew the right question to ask, of course, cause causal metaphysicians aren't happy with me, but yeah, that's a problem. Is there any epistemic gain that can come from thought experiments that cannot come from formal deductions? Yes. Um, um, you've, you've narrowed things down by saying formal deductions.
uh, by argument, I have a much looser and more general idea. I mean, informal argumentation. Um, and that certainly includes, uh, inductive inference. And you'll find in some of the most famous thought experiments, a lot of inductive inference going on. Um, you know, Einstein's magnet conductor thought experiment. I'll just say in the abstract, what, what, what the point is some of the key steps in thought experiments are inductive inferences. Uh, you produce an effect in a particular case.
And then you say, and this is general, right? It's an inductive entrance where you generalize from the one case, but because the particular case is so compelling, people are willing to go along with the inductive inference, which might be good or it might be bad. All right. Oh, we, so we, we saw it in the, uh, in Einstein's, um, uh, principle of equivalence.
We have all bodies will fall the same in the uniform accelerating frame of reference that's a gravitational field in the nine senses and everything else will go the same as well that's that's one hell of an inductive inference at that point we've only got the effect for falling bodies we haven't got the effect for light propagation. Right but it's gonna work for light so it's gonna work for everything he says that you know that you you happily generalize you gonna say that all gravities like that.
It isn't just uniform acceleration. It's gravitational fields that are that are in homogeneous. There's lots of inductive inference going on here. Yes. Now your work on material induction, if I recall correctly, is against this. It's more like saying there are local ways that we can do induction, but you can't globally apply them. It's not as if there's a one size fits all induction. Yeah. Yeah. Correct. Yeah. So this comes out of the fact that I'm a science lover.
I love science, I love history of science, and I want to be able to say that our best science is somehow privileged over other endeavors, and it is privileged for empirical reasons. It's because it is well supported by the evidence, and the character of that support is inductive. I did not find accounts of inductive inference in the philosophy of science literature that were able to sustain that result.
What we find just a fragmentation of many different accounts and you kind of go doctor shopping you find some particular example and you want to say well why is this a good use of evidence will you shop around until you found the account of inductive entrance it fits then you slap it on now we need a single account that is to be applied everywhere. I'm what after took me a while to say this but after a lot of probing what i realized is that there are no universal rules of inductive inference.
I don't play everywhere that's the uniformity that you're talking about rather what you have a inductive systems that apply locally and they are specifically warranted by facts why don't you give an example okay i'm the simplest example one that i use in chapter one of the book.
Is marie curie prepares a tenth of a gram of radium chloride it's the only sample of radium chloride any laboratory in the world in nineteen three she looks at its crystallographic properties and declares radium chloride has such and such a crystallographic properties what i think we're now saying i think monoclinic was the way we tell you but she says it's the same as barium chloride.
If you think about that in terms of other accounts of inductive inference, what would it be? Well, it could be an enumerative induction. This A is B, therefore all A's are B.
Boy, that's a bad form to use because almost every occasion when this A is B, all A's are not B, right? So this sample of radium chloride was prepared by Marie Curie. It's not going to be true. You know, if I see the sample of radium chloride is in Paris, they won't all be. The sample of radium chloride is a tenth of a gram. They won't all be a tenth of a gram. Or all swans are black or all swans are white.
The idea that you can authorize that inference by looking at a general rule just doesn't work. But she wasn't doing that, right? So why is she so secure in making the inference that it was so secure it was even unremarkable? Well, the answer is factual investigation of the nature of crystals all the way through the 19th century.
All right, people had looked at, you know, what sorts of forms do crystals have? Uh, this was a work in, in atomic theory. This was work in mathematics. This is one of the places where the discrete, uh, the theory of discrete, uh, uh, finite groups, uh, got underway. And it turns out that if you build up lattices, right. Um, uh, they fall into one of six or seven families, depending on, uh, depending on how you count them. So if you find.
A crystalline substance that falls into one of those families, then you know that many more of those samples will fall in that one particular family. And so you can make the generalization. Now it is inductive. It's a little bit risky because there are some substances that are dimorphic or polymorphic, which means that they have forms that exist in multiple different families. Uh, the familiar case of polymorphism isn't exactly doesn't exactly map onto here, but it's the case of carbon.
It can be a diamond or it can be graphite but there are many other cases of minerals that have that have this so so what was justifying your entrance. Was with facts about crystalline substances hard one through the course of the nineteen century very difficult facts to learn because to characterize these families to go tremendous amount of work.
Alright, and it got regularized as a thing called Ouille's principle after one of the early starters. So the fact is, the Ouille's principle. And so the argument of the material theory of induction is, it's all like that. Whenever someone's doing an inductive inference, if it's cogent, and you want to ask why is this an appropriate inference,
The answer is going to come back to effect. Now this is going to apply specifically also to people using probabilistic inferences inductively. Um, if you're going to use probabilities, right? Um, the way I argue it out is the following. There is no default that every time you're uncertain about something, you can rep, you can responsibly represent the uncertainty by probability. You can't do that.
You have a positive obligation to demonstrate that a probabilistic representation is appropriate to the case in hand. So for example, in population genetics, you know, you know, you know, typically what you will do is you say this particular instance has been
It has been randomly sampled from the population so if we're going to do DNA typing and you want to say oh yes it's very very probable that you know that this perpetrator has a blood sample that matches the blood found at the
I'm perfectly happy with those probabilities, but it is essential that the probabilities are anchored by some fact, and the fact is that we can treat the case as if the person was randomly sampled. If that isn't the case, if you can't treat that suspect as being randomly sampled from the population, then all bets are off.
Alright who knows that they might have been planted in some way but they might have been planted you know you can figure out all sorts of ways it could come could come on stock this know what what happens when you when you don't do this seriously when you run into all sorts of.
Silly arguments that don't work if you send the simulation argument yes the one that says that we are very probably a simulation yeah yeah tell me about that. That's a spectacular example where we using probabilities without any factual yeah so what works is the following we end up with a position where we convince ourselves somehow that there are very many possibilities for the way our experience of the world come about.
Right. And the idea, and we somehow convince ourselves, I think these arguments already are pretty shaky, but I'm looking at a particular fallacy. We convince ourselves that there are vastly many ways that our experiences could come about if we were computer simulations and relatively fewer cases in which they could come about if the world is truly as it seems.
Let's just take that as a starting point i think it's already do this that we got there. Now we ask now we ask the question that what's the next step with the next step is to say we have no idea which is ours. I would say you stop at that point you have no idea which is ours but wait a minute but i'm going to say no i'm going to represent my uncertainty by probability.
Right and when i represent my uncertainty by probability i find that the vast. Mass of the probability ends up on the on the computer simulation case and any very small amount ends up what's the fantasy. What the fantasy is you have no factual grounding for that probability you have just loaded fall from the sky and the result is simply an artifact of a misapplied inductive logic.
It's as simple as that it's an egregious fallacy but you need something like a material theory to tell you if instead you say i'm going to use the principle of indifference and i can use probabilities well you're going to be in big trouble because the principle of indifference contradicts probabilities in cases of genuine and extreme ignorance and this is a case of genuine and extreme ignorance.
Also, another simple case is like with a die and you just color two of them blue and then the rest of them red. And you could say, OK, well, is it going to be red or is it going to be blue? Well, we're indifferent. And so it's 50-50, but that's not exactly. Yeah, this goes back to Cain's. You'll find Cain's in his I think it's called treatise on probability early 1920s. He has all the classic examples there. Professor. Thank you for spending so long with me. It's been a blast.
Well, thank you. I've enjoyed talking to you. You've got a really wonderful podcast. There's something subtle. You know the questions to ask. I've received several messages, emails and comments from professors saying that they recommend theories of everything to their students. And that's fantastic. If you're a professor or lecturer and there's a particular standout episode that your students can benefit from, please do share. And as always, feel free to contact me.
Hey Kurt, you've spoken to so many people in the fields of theoretical physics, philosophy, and consciousness. What are your thoughts?
Also, thank you to our partner, The Economist.
Firstly, thank you for watching, thank you for listening. If you haven't subscribed or clicked that like button, now is the time to do so. Why? Because each subscribe, each like helps YouTube push this content to more people like yourself, plus it helps out Kurt directly, aka me. I also found out last year that external links count plenty toward the algorithm,
Which means that whenever you share on Twitter, say on Facebook or even on Reddit, et cetera, it shows YouTube, hey, people are talking about this content outside of YouTube.
which in turn greatly aids the distribution on YouTube. Thirdly, you should know this podcast is on iTunes, it's on Spotify, it's on all of the audio platforms. All you have to do is type in theories of everything and you'll find it. Personally, I gained from re-watching lectures and podcasts. I also read in the comments that hey, toll listeners also gain from replaying. So how about instead you re-listen on those platforms like iTunes, Spotify, Google
You also get early access to ad free episodes, whether it's audio or video.
Thank you so much.
▶ View Full JSON Data (Word-Level Timestamps)
{
"source": "transcribe.metaboat.io",
"workspace_id": "AXs1igz",
"job_seq": 2117,
"audio_duration_seconds": 6757.69,
"completed_at": "2025-11-30T21:21:32Z",
"segments": [
{
"end_time": 26.186,
"index": 0,
"start_time": 0.009,
"text": " The Economist covers math, physics, philosophy, and AI in a manner that shows how different countries perceive developments and how they impact markets. They recently published a piece on China's new neutrino detector. They cover extending life via mitochondrial transplants, creating an entirely new field of medicine. But it's also not just science, they analyze culture, they analyze finance, economics, business, international affairs across every region."
},
{
"end_time": 53.217,
"index": 1,
"start_time": 26.186,
"text": " I'm particularly liking their new insider feature was just launched this month. It gives you it gives me a front row access to the economist internal editorial debates where senior editors argue through the news with world leaders and policy makers and twice weekly long format shows basically an extremely high quality podcast whether it's scientific innovation or shifting global politics the economist provides comprehensive coverage beyond headlines."
},
{
"end_time": 79.616,
"index": 2,
"start_time": 53.558,
"text": " Tito's Handmade Vodka is America's favorite vodka for a reason. From the first legal distillery in Texas, Tito's is six times distilled till it's just right and naturally gluten-free, making it a high-quality spirit that mixes with just about anything."
},
{
"end_time": 103.78,
"index": 3,
"start_time": 79.77,
"text": " That had produced so much fuss with somehow shocking. This literature has been teetering on the edge of nonsense for a hundred years."
},
{
"end_time": 131.323,
"index": 4,
"start_time": 105.93,
"text": " Professor John Norton of the University of Pittsburgh has spent decades systematically dismantling sacred assumptions of physics. Norton's dome, for instance, demonstrates fundamental indeterminism in Newtonian physics itself. Now, you may be thinking of quantum uncertainty, but I'm talking about classical physics, which is breaking down in terms of unique predictivity. Beyond determinism, Norton critiques notions of causation itself,"
},
{
"end_time": 153.456,
"index": 5,
"start_time": 131.323,
"text": " Physicists routinely invoke causal language, but what if causation isn't fundamental? Even further, Norton's critique extends to thermodynamics. Landauer's principle, for instance, has guided decades of research into computing limits, and some even use it as the physical basis of Wheeler's it-from-bit. Norton demonstrates this principle misunderstands thermodynamics and entropy."
},
{
"end_time": 163.302,
"index": 6,
"start_time": 153.456,
"text": " Both of which we talk about in extensive detail. We then cap it off with Einstein's contributions to old quantum theory and Einstein's disagreements with the new quantum theory."
},
{
"end_time": 192.875,
"index": 7,
"start_time": 163.695,
"text": " a special thank you to The Economist for sponsoring this video. I thought that The Economist was just something CEOs read to stay up to date on world trends, and that's true. However, that's not only true. What I've found more than useful is their coverage of math, of physics, of philosophy, of AI, especially how something is perceived by countries and how it impacts markets. Among weekly global affairs magazines, The Economist is praised for its non-partisan reporting and being fact-driven."
},
{
"end_time": 216.903,
"index": 8,
"start_time": 192.875,
"text": " This is something that's extremely important to me. It's something that I appreciate. I personally love their coverage of other topics that aren't just news based as well. For instance, the Economist had an interview with some of the people behind DeepSeek the week DeepSeek launched. No one else had that. The Economist has a fantastic article on the recent DESI dark energy data and it surpasses, in my opinion, scientific Americans coverage."
},
{
"end_time": 241.476,
"index": 9,
"start_time": 216.903,
"text": " The economist's commitment to rigorous journalism means that you get a clear picture of the world's most significant developments. It covers culture, finance and economics, business, international affairs, Britain of course, Europe, the Middle East, Africa, China, Asia, the Americas, and yes, the USA. Whether it's the latest in scientific innovation or the shifting landscape of global politics,"
},
{
"end_time": 255.742,
"index": 10,
"start_time": 241.476,
"text": " The Economist provides comprehensive coverage that goes beyond the headlines. If you're passionate about expanding your knowledge and gaining a deeper understanding of the forces that shape our world, I highly recommend subscribing to The Economist."
},
{
"end_time": 281.152,
"index": 11,
"start_time": 256.084,
"text": " It's an investment into your intellectual growth, one that you won't regret. I don't regret it. As a listener of Toe, you get a special 20% off discount. Now you can enjoy The Economist and all it has to offer for less. Head over to their website www.economist.com slash toe to get started. Make sure to use that link. That's www.com slash toe to get that discount."
},
{
"end_time": 310.111,
"index": 12,
"start_time": 281.152,
"text": " Thanks for tuning in. And now back to the exploration of the mysteries of the universe with John Norton. All right, Professor John Norton, you're a legend in the physics scene and the philosophy of physics scene. So it's an honor to be with you here. Oh, thank you very much. It's very kind of you. You're known for Norton's dome for indeterminism and systematizing material induction, your views on thought experiments, the history of Einstein,"
},
{
"end_time": 335.282,
"index": 13,
"start_time": 310.794,
"text": " and disproving Landauer's Principle. We'll attempt to get to all of these today. Now, before we get to these, let's pick one. Norton's Dome. Why don't you tell me, how did you arrive at that construction? What were you trying to show? Were you trying to be contentious? Were you trying to disprove a colleague? Did something just not make sense? Like, walk me through leading to Norton's Dome."
},
{
"end_time": 343.695,
"index": 14,
"start_time": 337.875,
"text": " It was actually completely trivial and that it produced so much fast with somehow shocking."
},
{
"end_time": 371.8,
"index": 15,
"start_time": 344.206,
"text": " So here's the background. In the late 1980s, my colleague John Ehrman wrote a book, A Primer on Determinism, in which he pointed out that indeterminism was actually rampant throughout physics. And one of the places where it's quite rampant is in Newtonian physics, when you have systems with infinitely many degrees of freedom. So if you have infinitely many masses bouncing around in various ways, their behavior is going to be generically indeterministic."
},
{
"end_time": 400.725,
"index": 16,
"start_time": 372.398,
"text": " So John and I were teaching a graduate seminar on causation and determinism. And, you know, I think that afternoon or the next day I was committed to giving a section on determinism and I was going to present the idea that Newtonian physics is generically indeterministic when you have infinitely many degrees of freedom. Well, what about the case of finitely many degrees of freedom? I was going to say, well, when you only have finitely many degrees of freedom,"
},
{
"end_time": 411.169,
"index": 17,
"start_time": 401.425,
"text": " Then you just always get to him and isn't everything fine and i thought i'll be saying that in front of a bunch of smart graduate students you know what's gonna happen next."
},
{
"end_time": 439.974,
"index": 18,
"start_time": 411.425,
"text": " So i said i better have a look to see if there are counter examples so so you know elicits condition guarantees. Unique solutions for differential equations i looked up standard counter examples to elicits condition i took one of those standard counter examples and said how do you realize it physically and the answer was quite simple you have this. Don't shake very particular shape you put a mass point at the top that can move frictionlessly."
},
{
"end_time": 466.8,
"index": 19,
"start_time": 440.452,
"text": " And the conditions violate lifshitz condition, and so the particle can spontaneously set itself into motion. And the mathematics is very simple. It's two or three lines, and there it is. So I used that in teaching. The students didn't seem terribly impressed. I was writing a paper on causation at the time, and I wanted to point out that the idea that Newtonian physics has always been deterministic."
},
{
"end_time": 488.746,
"index": 20,
"start_time": 467.312,
"text": " was actually a mistake because the theory itself is not intrinsically deterministic so i included the dome in section three and almost immediately i started getting emails from people correcting correcting my mistake and i realized oh um there's something more going on here that's the story so what's the something more that's going on"
},
{
"end_time": 516.852,
"index": 21,
"start_time": 489.821,
"text": " What's going on is that the idea that Newtonian physics is deterministic is so deeply entrenched in the psyche of many physicists that it somehow seems to some sort of an epistate if I if I would be saying anything otherwise that I must have made a mistake and they have an obligation to discover what the mistake is and so"
},
{
"end_time": 537.585,
"index": 22,
"start_time": 517.244,
"text": " And that was the character. They weren't hostile, the response that I was getting. They were all very friendly, but friendly of the form of Dear Professor Norton. I saw your analysis of this dome. I just want to point out you're making a terrible mistake here. And then something follows, which never works."
},
{
"end_time": 548.78,
"index": 23,
"start_time": 538.473,
"text": " Let's make this clear for people. So there are different types of continuity. Usually we'll say that a function is continuous, but there are various types like absolute continuity, uniform, and then there's lift shits."
},
{
"end_time": 578.814,
"index": 24,
"start_time": 549.428,
"text": " which then is used in ODE classes to show that there are unique solutions. Now, if you remove this Lifshitz continuity condition, then you get non-unique solutions, so multiple solutions. And I'm not sure I believe Lifshitz is necessary, but not sufficient for non-uniqueness. You can. I think it's sufficient, but not necessary. But if you find very simple systems that violate the condition of Lifshitz continuity, then"
},
{
"end_time": 602.005,
"index": 25,
"start_time": 579.343,
"text": " I mean, the mathematics of the dome is just a very simple example. If you have the first derivative of a function varies with the square root of the function, that already violates the Lipschitz condition at the origin when the function has zero value. I mean, it's as simple as that, and that's the example instantiated in the dome."
},
{
"end_time": 620.828,
"index": 26,
"start_time": 602.381,
"text": " I went to the second derivative so i could use newtons f equals ma but i think it already happens with the first derivative just d dx equals square root of x and solve that when x is equal to zero you already have non-unique solutions i think going from memory that that works."
},
{
"end_time": 641.049,
"index": 27,
"start_time": 621.647,
"text": " Okay, so then what are people supposed to imagine as a consequence of this? Are you saying that Newtonian physics thus needs to assume Lipschitz in order to prove this uniqueness? And thus, if you're trying to say Newtonian physics is deterministic, you're already inserting that determinism. You're not concluding that deterministic. That's exactly right."
},
{
"end_time": 667.807,
"index": 28,
"start_time": 641.374,
"text": " whether a particular new term in system is deterministic or not is something to be discovered not not stipulated and i'll mention again the important case if you have infinitely many systems interacting then you get indeterminism generically why does this matter well it's going to matter in the infinite case when you look at something like the thermodynamic limit."
},
{
"end_time": 683.814,
"index": 29,
"start_time": 668.387,
"text": " So this is a case that i calculated we like to think of a very simple newtonian model for crystal consists of a whole bunch of mass points that connected together by springs and the thermally agitated and said that what about the idea is that."
},
{
"end_time": 710.555,
"index": 30,
"start_time": 684.377,
"text": " As the number of mass points gets larger, as this lattice gets larger and larger, its behavior becomes closer and closer to a system that is going to behave thermodynamically in the ways that we expect. You're going to get Boltzmann's, the Boltzmann distribution is going to come out and so on, but you need to look at the very large lattice. So it's standard to say if you take the infinite limit,"
},
{
"end_time": 740.077,
"index": 31,
"start_time": 711.032,
"text": " That's when you get from dynamics back what do you have to be very careful about how you take that infinite limit if taking the infinite limit just means i will consider crystal letters of arbitrarily large size. I always find out that i was really large in size then the sequence of letters that you're considering will eventually stable out stabilize out to have nice dynamic properties. If you mean i'm going to consider an infinite letters."
},
{
"end_time": 767.841,
"index": 32,
"start_time": 740.418,
"text": " And then investigate his properties. You'll discover that the, uh, that the lattice, uh, dynamics have become indeterministic. Uh, I've not kept this secret. It's in a paper I wrote published on, um, 19 11, uh, 2011, 2012 called approximation and idealization. That's the, one of the main points of the paper. It just says, it just says be careful taking infinite limits. You can really get into trouble."
},
{
"end_time": 796.954,
"index": 33,
"start_time": 769.36,
"text": " So there are other types of continuity as well. So the underlying space is continuous. So the function itself is continuous and the function operates on a domain and that domain is space time. Now, I know we're dealing in Newtonian physics, so maybe not space time, but it doesn't matter. We say some manifold. Now, is it your contention that the manifold itself is also going to ultimately be discontinuous? Do you have a intuition there that is going to be discretized or do you think that you can zoom in all the way and it looks like Rn?"
},
{
"end_time": 823.183,
"index": 34,
"start_time": 800.418,
"text": " I'm well the example of the don't the don't surface is an ordinary euclidean surface. And it does have a cover to singularity at the at the apex but cover to singularity is at a at a point and nothing extraordinary in idealize newtonian systems think about the sharp edge of a tabletop."
},
{
"end_time": 850.009,
"index": 35,
"start_time": 823.729,
"text": " Right now the horizontal and the vertical and they meet and we don't have any trouble shooting a particle across the horizontal surface. It then comes to the curvature singularity at the edge and then shoots off in a parabolic arc. It's the standard sort of idealization that we talk about. The singularity at the sharp edge of the tabletop is one order worse than the singularity in the"
},
{
"end_time": 876.032,
"index": 36,
"start_time": 850.503,
"text": " At the apex of the dome at the apex of the dome it's singularity in the curvature. The apex the singularity the sharp edge of a tabletop is a singularity in the first in the tangents. Yeah the tangents move jump discontinuously when you go over the edge so many ordinary Newtonian systems are deterministic."
},
{
"end_time": 899.002,
"index": 37,
"start_time": 876.357,
"text": " All right and we're entirely used to that they always work out that way. Is it so surprising that if we go to extreme cases that we don't normally look at an ordinary life that we that we end up with something a little different. The case of the dome is not something we could ever realize in real life because it requires multiple violations of quantum mechanics."
},
{
"end_time": 923.609,
"index": 38,
"start_time": 899.309,
"text": " You got to put the point that the mass point has to be located at rest exactly at the apex you need to have a surface that is exactly the right properties. The more interesting cases when you have been from the many masses that's the sort of idealization that people will take more seriously why doesn't the infinitely many masses also contradict quantum mechanics."
},
{
"end_time": 954.053,
"index": 39,
"start_time": 925.418,
"text": " Um, it's Newtonian theory contradicts quantum mechanics and its foundations. So yes, it does as does every Newtonian analysis. So I'm not sure. I'm not sure what's worrying you here. This for me has been the perpetual puzzle. Um, I think the dome is just a rather ordinary piece of Newtonian physics. There's nothing very special about it. Uh, it just happens to have this, this odd property, but then"
},
{
"end_time": 974.735,
"index": 40,
"start_time": 954.753,
"text": " Yeah, some people I talk to just say, yeah, yeah, what's the big deal? Other people were saying there's something deeply troubling about this and I just don't know what that is. So it turns out that some Newtonian systems in these cases, rather exotic ones that could never be realized, you know,"
},
{
"end_time": 1000.043,
"index": 41,
"start_time": 975.538,
"text": " What are the implications for quantum mechanics and relativity? I think that was behind one of your remarks. Not very much, because they're different theories. Relativity theory and quantum mechanics are very different theories. They turn out to be indeterministic in their own ways. In the case of quantum mechanics, the standard interpretation is indeterministic."
},
{
"end_time": 1026.032,
"index": 42,
"start_time": 1000.452,
"text": " That's just the beginning of a long discussion if you're a bohemian you won't think that but that's another story and in order to realize determinism in relativity you need a koshi surface. You need all the nice conditions if you don't have a koshi surface then you can't even state the conditions of determinism which are the present fixes the future but you don't have a present so you can't have any you can't have any fixing i think if there's a moral."
},
{
"end_time": 1055.026,
"index": 43,
"start_time": 1026.578,
"text": " The only moral is the following, be careful about what you assume about the world. Don't go into physics assuming and decedently that you have a wisdom that transcends what the empirical science will tell you. If you want to see what goes wrong, if you do that differently, think about what happened when quantum mechanics appeared in the mid-1920s and it became very apparent then that the theory was going to be indeterministic."
},
{
"end_time": 1062.858,
"index": 44,
"start_time": 1055.486,
"text": " Up until then, everyone had simply assumed that for a system to be causally well behaved, it had to be deterministic."
},
{
"end_time": 1091.288,
"index": 45,
"start_time": 1063.387,
"text": " Then quantum mechanics comes along and it's indeterministic and there was this tremendous outpouring of anxiety. Causality is lost was the plea. We would now say determinism. They then said causality. But in retrospect, it was simply an artifact of 19th century thinking. In the 19th century, they had identified causation with determinism. So for the world to be well ordered causally,"
},
{
"end_time": 1121.647,
"index": 46,
"start_time": 1091.783,
"text": " So let's talk about this graduate seminar then on causation. Did anything else controversial come out and what is causation? Well, as you know, I've written fairly extensively about this. I have a particular critique of causation. It is a critique of causal metaphysics"
},
{
"end_time": 1141.203,
"index": 47,
"start_time": 1122.108,
"text": " It is not a critique of causation per se. To be very clear here, I am quite comfortable with the idea that things interact with each other and connect with each other in all sorts of fascinating and interesting ways. Voltages drive electric currents and"
},
{
"end_time": 1163.865,
"index": 48,
"start_time": 1141.527,
"text": " And gradients of free energy produce them dynamic effects and so on and so on and so on all all the all the way through here. You can go to any science and you find all sorts of claims of how this causes that. My critique is the following calls on metaphysics seeks to do something that is antecedent to these empirical investigations."
},
{
"end_time": 1192.09,
"index": 49,
"start_time": 1164.326,
"text": " A causal metaphysician says we cannot talk about causality until empirically until we have sat down and done some conceptual work and figured out what causation is. And once we have done that, then we understand what causation is and then scientists can come along and do the cleanup operation of figuring out how this causal principle that they come up with is going to be instantiated in the particular sciences."
},
{
"end_time": 1218.097,
"index": 50,
"start_time": 1192.363,
"text": " So the general run of a causal metaphysician is saying, I know what causation is. It's this, right? So I understand your job is just to show me how that works in the world. And that is just a completely failed enterprise. The difficulty is that metaphysicians have not been able to come up with any principle of causation that has any practical content. And that also succeeds in the world."
},
{
"end_time": 1247.022,
"index": 51,
"start_time": 1218.097,
"text": " We have thousands of years of failure at that particular enterprise so i'm rejecting the calls on the positions project completely and then okay so the question that becomes what is the place of causal talking in science why is it so pervasive. So why does scientist care about causation if there's no metaphysics underlying it. It's simply a matter of labeling what happens is we notice that there are all sorts of processes."
},
{
"end_time": 1274.428,
"index": 52,
"start_time": 1247.346,
"text": " that we find comfortable to describe causally. So take Einstein's famous A&B coefficient analysis of stimulated emission. The idea is that if you have an excited atom in a radiation field where the frequency of radiation is at the right frequency that will stimulate an emission, it will stimulate the excited atom to drop back to a lower state. I would like to say"
},
{
"end_time": 1301.476,
"index": 53,
"start_time": 1274.889,
"text": " That causes it to do so i have no objection as long as you realize you're just declaring how you intend to use a word. And so my general claim is that when we have causal talk anywhere in science is actually avail definition it is simply someone who is saying oh i find it very convenient i find it pragmatically useful to describe this process using the word causation."
},
{
"end_time": 1317.449,
"index": 54,
"start_time": 1301.476,
"text": " What they are not doing what they might realize is but what they're not doing is saying oh i have discovered the instantiation of some deep metaphysical truth lies and the seed prior to any science i haven't discovered that at all."
},
{
"end_time": 1341.442,
"index": 55,
"start_time": 1317.892,
"text": " What are the advantages in using causal language in various places? It can almost immediately be psychologically helpful. It's very helpful when I think of Einstein's A&B coefficient paper to say, oh, so the external radiation field is stimulating an emission, it is causing an emission, and that's how lasers work."
},
{
"end_time": 1369.411,
"index": 56,
"start_time": 1341.698,
"text": " That's the way we think about lasers. It's certainly very, very helpful. Otherwise, you just have a bunch of equations which gives you probabilities of various transitions. Or in the case of Jim Woodward's interventionist account of causation, he says that a causal process arises when we have two variables that are related by some connection, often probabilistic, but not necessarily if you read his account fairly carefully."
},
{
"end_time": 1399.172,
"index": 57,
"start_time": 1369.411,
"text": " And if an intervention on one of them is associated with the change in the other right then we have a causal a causal relationship i just regard that is the definition. It's an immensely useful definition because if you tell me that this causes that i know that if i if i interfere on this then i will produce an effect on that. Right so so if you tell me that certain medical interventions will improve the health of the population."
},
{
"end_time": 1425.265,
"index": 58,
"start_time": 1399.582,
"text": " Then I've learned something enormously useful. So if we abandon that causation is somehow fundamental or refers to something that has an essence, then is there anything that is in fundamental physics that's lost? So for instance, is there any theorem in quantum mechanics like Bell's theorem that then loses its power because Bell's theorem implicitly has a notion of causality in it? I don't know."
},
{
"end_time": 1441.63,
"index": 59,
"start_time": 1425.845,
"text": " I don't think so, no. I looked into this, I didn't inventory of all the places where the term causation appears in physics and I found that almost invariably the term causation"
},
{
"end_time": 1471.749,
"index": 60,
"start_time": 1442.039,
"text": " Denoted one of two things either it was talking directly about the fact that we're in a minkowski space time or at least something or at least the space time that have a light cone structure right and so we talk about the causal structure of space time we're actually talking about the light cone structure of space time or the other the other one was that Propagations of physical processes are confined to lie on or within the light cone and that seemed to exhaust almost all of the"
},
{
"end_time": 1486.015,
"index": 61,
"start_time": 1472.278,
"text": " All of the causal talk that i could find i can't swear that i picked up every single case but that pretty much covered everything i notice what you what you're looking for here you're looking for a sense of loss would you never had it in the first place."
},
{
"end_time": 1504.753,
"index": 62,
"start_time": 1486.357,
"text": " The the effort of causal message metaphysicians is to do a priori physics if they're providing you some kind of empirical fact about the world they are trying to do it prior to experience and if we learn one thing about thousands of years of side of investigation is that really doesn't work."
},
{
"end_time": 1532.619,
"index": 63,
"start_time": 1504.753,
"text": " The world is far more creative than our imaginations. We always get into trouble when we try and guess ahead of time how things have to be. And if it's a causal metaphysics or a striking example of that, this is not to say that we have lost some sense of how things connect together. Spacetime has a light cone structure, call it causal structure. That's fine with me. Ordinary proper propagations, right? I can find to it. That's fine with me."
},
{
"end_time": 1558.677,
"index": 64,
"start_time": 1533.933,
"text": " Where's the loss? So there are other counterfactual accounts of causation. Do you reject those? No, they're just definitions. Ford Blue Cruise hands-free highway driving takes the work out of being behind the wheel, allowing you to relax and reconnect while also staying in control."
},
{
"end_time": 1588.78,
"index": 65,
"start_time": 1559.821,
"text": " Enjoy the drive in BlueCruise enabled vehicles like the F-150, Explorer and Mustang Mach-E. Available feature on equipped vehicles. Terms apply. Does not replace safe driving. See Ford.com slash BlueCruise for more details. Nothing wrong with that. This caused that because if I hadn't done this, that wouldn't have happened. Wouldn't have happened. Fine. You just told me"
},
{
"end_time": 1590.93,
"index": 66,
"start_time": 1589.189,
"text": " How you plan to use a word"
},
{
"end_time": 1621.135,
"index": 67,
"start_time": 1591.63,
"text": " Hi, everyone. Hope you're enjoying today's episode. If you're hungry for deeper dives into physics, AI, consciousness, philosophy, along with my personal reflections, you'll find it all on my sub stack. Subscribers get first access to new episodes, new posts as well, behind the scenes insights, and the chance to be a part of a thriving community of like minded pilgrimers. By joining, you'll directly be supporting my work and helping keep these conversations at the cutting edge. So click the link on screen here."
},
{
"end_time": 1644.889,
"index": 68,
"start_time": 1621.135,
"text": " Okay, so let's get to thought experiments. So what is the standard view on thought experiments and then where do you stand on that view?"
},
{
"end_time": 1675.486,
"index": 69,
"start_time": 1645.964,
"text": " Don't know that there's a standard view, but I can tell you there's a long-standing debate. This goes back to the 1980s when the literature on thought experiments exploded. There were essentially two extremes in our understanding of thought experiments. One extreme is a completely deflationary view. That just says that thought experiments are ordinary argumentation. They don't do anything that ordinary argumentation cannot do. They just do it in a rather pretty and picturesque way."
},
{
"end_time": 1702.875,
"index": 70,
"start_time": 1676.084,
"text": " The other extreme is it says no there's something more going on there's some magical power that capacity to do experiments. Is realized and the question is to articulate what that magical power is and the clearest articulation came from my colleague jim brown at toronto he said we can understand some experiments."
},
{
"end_time": 1731.032,
"index": 71,
"start_time": 1703.2,
"text": " To be platonic in character. Uh, a really good thought experiment of just the right type literally opens the window, right? Um, onto, onto, onto Plato's heaven where we can actually see the, um, actually see the laws of nature. Uh, he, uh, he supports that with the, the, the experience that we have with a good thought experiment. There's this wonderful aha moment when suddenly you see it."
},
{
"end_time": 1751.408,
"index": 72,
"start_time": 1731.391,
"text": " All right, and that's the moment of platonic perception. He's wrong, of course. I've spoken to James James Robert Brown. Yeah, yeah. Yeah, yeah. I've spoken to him. So one of the great thought experiments is that how is it that we could tell a priori that something should fall at the same rate of different masses? We can't."
},
{
"end_time": 1781.357,
"index": 73,
"start_time": 1753.148,
"text": " Do you mean to tell me that a priori Aristotle's account of the motion of bodies was false a priori? No, that you could have a world in which things, in which you have a force needed to keep things moving. I'm not articulating my view. I'm articulating James's view from when I interviewed him. If I'm recalling correctly, it went something like this."
},
{
"end_time": 1809.974,
"index": 74,
"start_time": 1781.578,
"text": " If heavy objects fall faster, then dropping, say, a heavy bag of marbles, okay, so comprises 300 marbles, next to a single marble means this single marble will fall slower. But then you look, the bag is just filled with many marbles. So those marbles each individually should be falling at a rate similar to if not equivalent to this marble. And then you have a contradiction. So thus, they all must fall at the same rate. That seems powerful. So tell me what your views are on that. It's very simple."
},
{
"end_time": 1836.596,
"index": 75,
"start_time": 1810.776,
"text": " Why were you convinced by what you just said? Why were you convinced that the marble, the single marble and the bag of marbles have to fall at the same rate? There was an argument there. Yeah, that's thought experiment. It's an argument. That's all I'm saying. You just ran an argument. What's... Yeah, but I thought thought experiments are arguments, no? Or am I saying a view that's controversial by saying that?"
},
{
"end_time": 1861.869,
"index": 76,
"start_time": 1836.664,
"text": " You're agreeing completely with me. What you didn't have is any extra piece that Jim would want, where Plato's world of form somehow ended into things. You just look, every time someone, I mean, that exchange we had now is what happens all the time. Someone has a thought experiment, they run through the thought experiment, I'm listening to them go through the thought experiment I'm hearing,"
},
{
"end_time": 1888.148,
"index": 77,
"start_time": 1862.193,
"text": " Okay this just an argument it's a very simple straightforward argument if you know I can you know I can I can refute Galileo's you realize that this is not Jim's example this is one of the great classics in history of science it goes back to Galileo blah blah blah right okay but it's you know Galileo had a I think a musket ball and a cannon ball or something and then connected them with the thread"
},
{
"end_time": 1918.046,
"index": 78,
"start_time": 1890.026,
"text": " You just ran an argument and that's all thought experiments are. They're picturesque. I mean, they're compelling because you get this lovely mental picture and so it's easy for you to run through. But if it's simply purely a picture, I don't think it has any compelling force. There has to be an argument there. For example, can I prove the possibility of a perpetual motion machine by imagining one?"
},
{
"end_time": 1944.48,
"index": 79,
"start_time": 1918.473,
"text": " I visualize it it's a big brass gadget that's got bells and there's steam coming out and so on and oh look the wheel just keeps spinning and producing endless amounts of power. Just imagining it doesn't doesn't do anything. You there has to be that argument there or you don't have a cogent thought experiment and i say that's all that's all that's ever going on jim and i have been at this debate for forty years now it's it's."
},
{
"end_time": 1966.766,
"index": 80,
"start_time": 1944.957,
"text": " little striking committee say that you know because what you're saying sounds sound and ordinary so i don't understand what jim would be objecting to because even with this articulation my articulation of this argument this is an argument i'm saying like if there's this then you have this then you have that their contradiction therefore the premises can't be true so it isn't just picture something"
},
{
"end_time": 1985.964,
"index": 81,
"start_time": 1967.278,
"text": " Now you have it you're in the same position as i am this is my view what we talk about the dome early run i don't understand why people are troubled by it i articulate the. It's the argument you thought experiments articulated i'm thinking well that's kind of obvious i wrote this paper i think in nineteen eighty six."
},
{
"end_time": 2014.292,
"index": 82,
"start_time": 1986.34,
"text": " I thought, well, this is a bit of a doubt of a paper, you know, I'm just saying something that's so completely obvious. But then you discover there are all these people who want to take issue with you and you're trying to figure out why it's completely straightforward. Well, Jim's a friend of yours and you've spoken to him, like you've said for decades. Oh, yeah, yeah, yeah, we get along. So why don't you tell me what he would say other than you have to connect to a platonic world? I imagine that's not his sole point."
},
{
"end_time": 2044.343,
"index": 83,
"start_time": 2015.811,
"text": " Well, he runs lots of examples. I think it's, I, I'd have to refresh my memory on his writing. I'm a little nervous about trying to channel him, but I think the thing, Jim, if you're watching, I apologize for getting it wrong. Uh, I think the thing for him is this moment of understanding that somehow seems to surpass just"
},
{
"end_time": 2064.667,
"index": 84,
"start_time": 2045.043,
"text": " You know just ordinary argumentation. So he's got a he likes doing philosophy of mathematics he's got an example where you can some numbers one two three four five and you got a little stack of blocks and you can look at the stack of blocks and suddenly you see all."
},
{
"end_time": 2089.667,
"index": 85,
"start_time": 2065.111,
"text": " It's going to be five plus six divided by two. You can just see the way that works. You just suddenly see it instantly without apparently having to think about it. Those are the sorts of examples he likes. I just think they're arguments still because I say to him, well, I didn't see it. How does it work? And then he explains it to me and then he gives me an argument."
},
{
"end_time": 2120.623,
"index": 86,
"start_time": 2091.169,
"text": " Okay, yeah, this moment of understanding sounds similar to Penrose when he's articulating the the Lucas argument or his version of the Lucas argument with girdle implying that the mind isn't computational. I don't know that well enough. I know all of it. I don't know the details. Okay, so how about let's get to something that you know, inside and out Landauer's principle. Why don't you outline what Landauer's principle is and then what your precise statement is either that Landauer's principle is false or it needs to be modified."
},
{
"end_time": 2132.807,
"index": 87,
"start_time": 2121.391,
"text": " The argument or the project that Landau had was a very practical one. One of the things that we noticed in computing devices is that they always produce heat."
},
{
"end_time": 2163.183,
"index": 88,
"start_time": 2133.234,
"text": " And that he of course is work that's been degraded. And so it is a cost for computation. It's been a long standing problem. Uh, we always need to cool down our computing processes. I don't know if you remember the Cray computers going back many years, but they would, they would sit in if I recall correctly, and that's free on free on in order to, you know, so, so the generation of heat in a computing device is a big deal. The question he was addressing is how far can we go?"
},
{
"end_time": 2191.067,
"index": 89,
"start_time": 2163.712,
"text": " before we have reached a limit beyond which we cannot go any further. In other words, how far can we reduce the amount of heat that's being generated in computing systems? The calculation can be done in terms of entropy. How much entropy is a computing device creating? If you think of the entropy as sitting in an isothermal heat bath, then the entropy creation is going to correspond"
},
{
"end_time": 2219.923,
"index": 90,
"start_time": 2191.732,
"text": " How to the heat passed the environment by the temperature of the heat bath give you give you first pass and how much the entropy is now his argument and as embellish and develop by Charles Bennett is that the logic of the process being implemented determines the minimum amount of heat generation. And if the process is logically reversible something like a bit flip."
},
{
"end_time": 2249.701,
"index": 91,
"start_time": 2220.213,
"text": " All right then in principle you can execute that with minimal heat generation with minimal entropy creation if however it is a logically irreversible operation the classic case being erasure right then then necessarily there's going to be a certain amount of heat generation that's going to correspond to the Shannon information that you calculate for the two states so if you've got"
},
{
"end_time": 2278.899,
"index": 92,
"start_time": 2250.026,
"text": " What's wrong with that is just a very basic fact of the thermodynamics of systems at the molecular scale. You cannot do anything"
},
{
"end_time": 2300.896,
"index": 93,
"start_time": 2279.292,
"text": " Add molecular scales without creating entropy so something as simple as a bit flip. You can't flip a bit without having some driving force to push the bit from one state to another so very simple case is you you might have a charge and you want to move from one location to the other."
},
{
"end_time": 2330.179,
"index": 94,
"start_time": 2301.203,
"text": " You're only going to be able to move from one location to the other if you have some kind of electric driving force that will push it. And what is that driving force working against? Remember, we're at molecular scales, and at molecular scales, that individual charge has its own thermal energy. It's bouncing around, right? And so you have to confine it. And in the process of confining it, you compress it over to one particular path, right? You're going to be doing work on it. That work is going to be lost as heat."
},
{
"end_time": 2356.374,
"index": 95,
"start_time": 2330.52,
"text": " This is an extremely general result. This simply is Boltzmann's SSK log W. The best you can ever do at any process at molecular scales is to have a probability of success of completion. And Boltzmann's W tells you the probability of success of completion and the S associated with it tells you how much entropy you're going to have to create."
},
{
"end_time": 2381.561,
"index": 96,
"start_time": 2356.664,
"text": " So if you don't, if you don't confine the charge very much, right, then it has its own thermal energy can jump out. Right. And so you have a probability that the charge is going to go back to the original state. So you can have a, but because you didn't confine it very much, you haven't created much entropy, but if you can find it a lot, right. So you really force that charge deeply into some kind of potential well."
},
{
"end_time": 2408.592,
"index": 97,
"start_time": 2381.886,
"text": " Alright, then you have a good probability of success, but there'll be a lot of heat generated, a lot of entropy created. So the bottom line is the following. The amount of heat that will be generated in molecular scale processes is not determined by the logic. It's simply determined by the number of steps that you want to complete and the probability of completion that you determine for each step."
},
{
"end_time": 2433.302,
"index": 98,
"start_time": 2409.121,
"text": " Again this seems so elementary. I've been arguing this for a dozen years now. I just don't understand why the Landau principle talk continues. If you're interested in the question of what's the minimum heat generation that you can have in any kind of molecular scale process, computational or not,"
},
{
"end_time": 2462.927,
"index": 99,
"start_time": 2433.797,
"text": " It doesn't matter. Ask how many steps are there in the process and what's the probability of completion that I want for each step and SSK log W will tell you the answer. It's done. So ordinarily in the calculation of Landau's principle, they use a principle of indifference to put 50, 50% odds for the zero and the one. And you're saying that the probabilities need to be physically dynamical. Yeah, I don't. Yeah, my recollection in Landau's original paper was he talked about"
},
{
"end_time": 2484.07,
"index": 100,
"start_time": 2463.37,
"text": " computing systems and the frequency in which they might be in different states. But go ahead. So let me try and summarize. If you try and form a lower bound based on logic, well, you shouldn't you should look at the precise implementation or the procedure. If you do this, you'd find that the minimum should be higher than K log two. Yes."
},
{
"end_time": 2495.196,
"index": 101,
"start_time": 2485.572,
"text": " Absolutely hiding k log two if you just want a single process i've done the calculations i can't never wanted what the what the numbers are exact numbers are now but together."
},
{
"end_time": 2522.961,
"index": 102,
"start_time": 2495.776,
"text": " A really modest probability of completion, I don't know, 90% or something, I can't remember the exact numbers, you will certainly create more entropy than the K log 2, it's 0.69K that is the one bit erasure case. If I remember correctly, if you want, I think 95% probability of success,"
},
{
"end_time": 2544.07,
"index": 103,
"start_time": 2522.961,
"text": " Are you create three k of entropy something like that but that's only one step remember in a computer device. Many many many steps right isn't this one step you got all the steps chain together and every single one of them is going to be dissipated. This is just a completely basic fact of of you know of molecular scale physics."
},
{
"end_time": 2566.459,
"index": 104,
"start_time": 2544.701,
"text": " It doesn't take massive complicated fancy derivations the whole thing's done in two lines you just you just write down. I'm ssk log w or if you know you can find different expressions of it if you going to get formalism ssk log w will be expressed in terms of free energies you know and they're all essentially the same result."
},
{
"end_time": 2596.118,
"index": 105,
"start_time": 2568.251,
"text": " This is interesting. So I'm currently writing an article. Maybe it's published already. I'll place it on screen if it's already out. And it's about this word in principle, in principle arguments. So my contention is that when most people just use that word, they use it loosely and you need to scrutinize what kind of in principle are they invoking. So are they referring to epistemological modalities or normal logical or metaphysical or logical possibility or something else entirely?"
},
{
"end_time": 2620.35,
"index": 106,
"start_time": 2596.442,
"text": " And even with these categories, there are frequent ambiguities and doubtfulness within. So what you're suggesting aligns with this. People invoke in my interpretation of what you've said, Landauer's principle. They're also employing, well, let's just idealize this scenario. Let's say it's an it's an in principle argument. But then even in such cases, you have to be careful and consider, OK, what are the practical implementations?"
},
{
"end_time": 2644.701,
"index": 107,
"start_time": 2621.425,
"text": " I'll say more than that. It's an inconsistent application of the idea in principle. I think you know a bit of the literature here. It goes back to Szilard's 1929 paper in which he introduced the Szilard engine. This was a version of the Maxwell demon. The idea was that you had a one molecule gas that would bounce around inside a chamber."
},
{
"end_time": 2651.834,
"index": 108,
"start_time": 2645.179,
"text": " You would insert a partition, trapping the gas on one side and then you would isothermally expand it."
},
{
"end_time": 2678.933,
"index": 109,
"start_time": 2652.227,
"text": " Thereby taking heat from the environment and converting it into into work now the key thing to understand about that is that the phenomenon that's allowed was looking at is a phone is a is a thermal fluctuation this was the literature in which he was writing thermal fluctuations going back to sell out and i'm starting and brownian motion and and so on and you know the fundamental question that was being asked is"
},
{
"end_time": 2707.807,
"index": 110,
"start_time": 2678.933,
"text": " If you look at some fluctuations to what extent can they reverse the second law of thermodynamics so if you look at brownian motion for example think about the brownian motion in a fluid when the brownian particle goes up and down. When it's going up heat from the environment is being converted into some microscopic notion of work because it's being elevated in the gravitational field so punk rate remark that"
},
{
"end_time": 2737.09,
"index": 111,
"start_time": 2708.439,
"text": " In this solar system we see through our microscope a Maxwell demon in action. So the question then became, is it possible to accumulate all of these microscopic violations of the second law of thermodynamics in order to produce a macroscopic violation of the second law of thermodynamics? And that was a serious project that was undertaken in the first decade of the 20th century."
},
{
"end_time": 2759.65,
"index": 112,
"start_time": 2737.363,
"text": " Smolikowski came up with the answer and the answer is yes you get fluctuations that you might try and exploit, but every time you try and exploit those fluctuations you use other processes that have their own thermal fluctuations that will reverse everything. So this is the example of the Smolikowski trapdoor. So let's now go back to the Szilard engine."
},
{
"end_time": 2784.923,
"index": 113,
"start_time": 2760.145,
"text": " The single molecule bouncing backwards and forwards is a case of a dramatic density fluctuation in a gas. It's the most extreme case. When you have larger numbers of molecules, the fluctuations are very small. As you decrease the number, then the fluctuations become large in relation to the total energy of the gas. And so Salad's question was, can we"
},
{
"end_time": 2811.374,
"index": 114,
"start_time": 2785.35,
"text": " I somehow exploit those fluctuations and add them up to get a violation of the second law and the trouble is when people analyze that they don't account for all the fluctuations that are in the apparatus that they're using. So think about the way the apparatus works you start out with the gas the one molecule gas bouncing around you put in a partition the mere fact of putting in a partition."
},
{
"end_time": 2841.613,
"index": 115,
"start_time": 2811.92,
"text": " Is itself a thermodynamic process. If that partition is very light, it's going to have its energy of a half KT. You have to suppress that energy to get the damn thing to stick. That's going to be creating entropy. If you make it very massive so that the amount of KT is not half KT is not going to produce much motion, then you need frictionally to damp it. That's going to produce so it stops moving, it doesn't bounce out."
},
{
"end_time": 2867.398,
"index": 116,
"start_time": 2841.971,
"text": " The short answer is, the analysis of the Szilard engine from Szilard's time up to the present simply ignores the totality of fluctuation phenomena that have to be suppressed in order to get the process to go through. So it is, to go back to your original point, it is a selective and incorrect use of in principle idealization. You're idealizing away half of the"
},
{
"end_time": 2897.056,
"index": 117,
"start_time": 2867.739,
"text": " I'm half of the fluctuations, but not the other half. And then you're claiming, then you're claiming a result. If you're going to, if you're going to, um, try and exploit fluctuations, you have to treat them consistently and look at the fluctuations throughout the system. If you just pick one particular subset of the fluctuations, you're going to get nonsense results in that. And so, uh, I mean, you, you probably sense frustration in my voice. This literature has been teetering on the, on the edge of nonsense for a hundred years."
},
{
"end_time": 2927.108,
"index": 118,
"start_time": 2897.381,
"text": " This kind of selective treatment of fluctuations is just disaster is the course you get completely bogus results. The trouble is that every time a formula p log p appears. There's a tendency and natural reaction this is all we have a p log p. That must be thermodynamic entropy no it must not be. The conditions for a p log p to be associated with heat. In the way the clouds is requires that that p come about in a very particular way."
},
{
"end_time": 2956.254,
"index": 119,
"start_time": 2927.858,
"text": " The mere fact that I don't know whether I have a coin I put in my pocket I don't know whether it's heads up or tails up that isn't that isn't the right way for there to be a thermodynamic entropy of a log two associated with the coin but that's the fallacy that's being committed over and over and over again so there it is there was even a nature article that says that they experimentally validated landau's principle"
},
{
"end_time": 2984.548,
"index": 120,
"start_time": 2956.783,
"text": " Yeah, they're doing exactly what they shouldn't be doing. What they showed is that you, I don't remember the details now, but what they showed is that you have a little tiny particle, a colloid or something that's free to move around like a Brownian particle. And if you, um, if you compress it right by moving a barrier and you do it slowly so you can get a reversible effect here, then you, uh, then you pass heat of, of K log two to the environment. Well, of course."
},
{
"end_time": 3007.875,
"index": 121,
"start_time": 2985.162,
"text": " This has been this has been standard in thermodynamics for over a hundred and I don't know how many years. This is just the basic gases of the basic thermodynamics of ideal gases. Um, I did a lot of work on Einstein. It's abundantly clear in Einstein's work on Brownian motion that he understands is perfectly well. It is quite fundamental if that experiment had failed."
},
{
"end_time": 3031.698,
"index": 122,
"start_time": 3008.422,
"text": " Then we would have to rethink the thermodynamics of ideal gases. So what's wrong with the experiment? Well, they've just looked at how much heat gets generated when you compress a one molecule gas in effect. It's actually a particle, but it's close enough to being a one molecule gas in its degrees of freedom. If you want to say that we've now instantiated Landau's principle,"
},
{
"end_time": 3061.869,
"index": 123,
"start_time": 3032.022,
"text": " And that's the and that's the lower limit. Um, well, that experiment doesn't show it. What about all the entropy that was created in all the other bits of apparatus that were being used? Right. It's a fluctuation phenomenon that you're looking at. What about all the fluctuations that were, that was suppressed in order that you could move your partition inwards? All right. That's all got to be part of the calculation or you simply don't have a result. And of course they didn't calculate any of that. So it's, it just, you know, um,"
},
{
"end_time": 3082.432,
"index": 124,
"start_time": 3062.875,
"text": " I mean i certainly accept the result you know yes a two to one isothermal compression of a of a single molecule and an ideal gas will pass um occasionally log two with heat to the environment the same thing will happen if you're in a fluid right you have a single brownian particle"
},
{
"end_time": 3112.278,
"index": 125,
"start_time": 3082.432,
"text": " What's up brownian particle is going to behave like a what like a one molecule gas this was the brilliance by the way by stein's analysis of brownian motion he realized that you could treat brownian particles in the same ways you treat molecules was it was a very beautiful analysis. Yeah i do want to get to einstein's views on old quantum theory versus new quantum theory will get to that shortly so. It sounds like what you're saying is nature is the article that i've shown maybe it will be on screen again right now is."
},
{
"end_time": 3140.145,
"index": 126,
"start_time": 3112.654,
"text": " Not validating Landauer's principle. This is something that was predicted before Einstein died and Landauer came with the principle in the 1960s or so. It's wasn't that. It is an easy consequence of the standard thermodynamics of ideal gases. I mean, it's undergraduate physics stuff. Okay, it's lovely that we've done the very particular experiment and seen the result."
},
{
"end_time": 3156.186,
"index": 127,
"start_time": 3140.674,
"text": " But boy it had to be right if they got if if they had any other result coming out right and it wasn't the result of some kind of procedural error it would have been traumatic for for statistical physics."
},
{
"end_time": 3186.084,
"index": 128,
"start_time": 3156.527,
"text": " Because that is so fundamental that if you just have a single component, like a molecule, a one molecule gas, and you compress it two to one, you're going to, isothermal, you're going to pass a KT log two of heat, reversibly, by the way. What if someone says, okay, so what? So what if Landau's principle isn't the minimum bound? I mean, I can say Kurt's principle and set the minimum bound to zero, and then I'm still correct if you show that something's higher because, hey, my minimum hasn't been violated."
},
{
"end_time": 3211.749,
"index": 129,
"start_time": 3186.664,
"text": " Remember the idea is that we can understand the minimum amount of heat generation in a computing device by looking at the logic of the processes being implemented. So if we want to minimize heat generation, then what we need to do is look carefully at the logical processes and minimize any irreversible irreversibility in the logic."
},
{
"end_time": 3240.503,
"index": 130,
"start_time": 3212.295,
"text": " That is just mistaken and will mislead you that's the wrong answer the right answer is what matters is how many steps. You are expecting to complete whether it's a computing system or any other system whatever and the degree of probability of completion. And you need to understand that if you're serious about reducing the amount of pay the paying attention to the logic being implemented in the computational device is really not gonna help you. It's how many steps."
},
{
"end_time": 3243.507,
"index": 131,
"start_time": 3240.845,
"text": " It matters, the implementation matters massively."
},
{
"end_time": 3273.848,
"index": 132,
"start_time": 3245.111,
"text": " This episode is brought to you by State Farm. Listening to this podcast? Smart move. Being financially savvy? Smart move. Another smart move? Having State Farm help you create a competitive price when you choose to bundle home and auto. Bundling. Just another way to save with a personal price plan. Like a good neighbor, State Farm is there. Prices are based on rating plans that vary by state. Coverage options are selected by the customer. Availability, amount of discounts and savings, and eligibility vary by state."
},
{
"end_time": 3286.476,
"index": 133,
"start_time": 3274.565,
"text": " Think Verizon, the best 5G network, is expensive? Think again. Bring in your AT&T or T-Mobile bill to a Verizon store today and we'll give you a better deal. Now what to do with your unwanted bills? Ever seen an origami version of the Miami Bull?"
},
{
"end_time": 3309.48,
"index": 134,
"start_time": 3286.937,
"text": " Jokes aside, Verizon has the most ways to save on phones and plans where you can get a single line with everything you need. So bring in your bill to your local Miami Verizon store today and we'll give you a better deal. So is something now allowed that we previously thought was disallowed?"
},
{
"end_time": 3338.234,
"index": 135,
"start_time": 3309.872,
"text": " because of this analysis your analysis or is something now disallowed that was previously thought to be allowed like what is the consequence the practical consequence of this the practical consequences is what i just said if you want to minimize the amount of heat generation in your computing systems pay attention to how many steps you've got and the probability of completion that's what you should be looking at and you also believe that this distracts researchers from simpler more general solutions to"
},
{
"end_time": 3365.23,
"index": 136,
"start_time": 3338.49,
"text": " Maxwell's demon like Louisville's theorem. Oh, yeah. Oh, yeah. No Yes, this is one of the one of the one of the papers that I wrote I do my research you did. Thank you You know the you know the idea that That notions of information and computation are going to help us understand why Maxwell demon must fail, right? That has so distracted everyone we spend all our time arguing about it"
},
{
"end_time": 3389.957,
"index": 137,
"start_time": 3365.589,
"text": " What's up for a long time john and i first wrote papers on this i wrote them by myself i kept saying no no no these ideas aren't helping us. It doesn't work we don't learn why max will demon must fail we don't know that it must fail from these considerations and we spend a lot of time thinking about that we just usually distracted by that then one one day i was sitting on the bus coming into the office i thought myself you know."
},
{
"end_time": 3404.821,
"index": 138,
"start_time": 3390.418,
"text": " Maybe maybe i should ask the question is an actual demon possible forget about all this information stuff and within five minutes i mean in the course of a short bus ride and realize oh god the level theorem just prohibits it."
},
{
"end_time": 3423.729,
"index": 139,
"start_time": 3405.35,
"text": " If you're assuming that the demon is to be implemented within classical physics, you can see with essentially no calculation at all that the Liouville theorem is going to block it. So I published that somewhere in the paper. And then after a while, I thought, you know, this is not a"
},
{
"end_time": 3440.64,
"index": 140,
"start_time": 3424.394,
"text": " This is not a really decisive argument because nothing at the scale that we're concerned about is actually classical, it's all quantum mechanical. And so I asked, is there an analog of the Liouville theorem?"
},
{
"end_time": 3470.009,
"index": 141,
"start_time": 3440.64,
"text": " I'm gonna mechanics yes there's analog and quantum mechanics and and the end you can run an exactly analogous argument and so i've got another paper in which i show i've got a two-column two columns you got the classical and that was on one side quantum and also on the other and they just match up match up perfectly so so yeah i'm we know that a maxwell daemon is impossible in so far as those versions of the level of theorem apply."
},
{
"end_time": 3486.254,
"index": 142,
"start_time": 3470.742,
"text": " That explains why with all the nanoscale physics that we've been doing, no one's produced a Maxwell demon. Before we move on to Einstein's views, people are terribly interested in entropy."
},
{
"end_time": 3516.596,
"index": 143,
"start_time": 3486.954,
"text": " And you mentioned a couple different definitions of entropy like Boltzmann and Shannon. So there are a variety of entropies. Can they be arranged such that one is a subset of the other, like Boltzmann is a special case of Shannon? Or are there entropy notions that are incompatible? And why are they all called entropy if they're incompatible? So if they are indeed some that are incompatible. So why don't you outline what is entropy supposed to be quantifying and then the different definitions and their relations? The basic idea of thermodynamic entropy is articulated"
},
{
"end_time": 3534.889,
"index": 144,
"start_time": 3516.817,
"text": " Well by clausius in his early papers i think was it eighteen sixty five or something i don't need it original papers date the idea is that that will tell you which processes will move forward spontaneously which phone dynamic processes will move forward spontaneously."
},
{
"end_time": 3562.125,
"index": 145,
"start_time": 3535.452,
"text": " Now the notions of entropy that appear in thermodynamics adhere well to that. So Boltzmann's notion of entropy, SSK log W, is going to tell you which processes move forward. This was the rule that I told you before. If you want a process to advance, you want to have an end state that has a higher probability than the starting state."
},
{
"end_time": 3577.022,
"index": 146,
"start_time": 3562.125,
"text": " S is k log w then tells you that the entropy of the end state is going to be greater than the entropy of the initial state and then that notion of entropy when you start to move into equilibrium systems is going to match nicely with the."
},
{
"end_time": 3605.486,
"index": 147,
"start_time": 3577.381,
"text": " uh, with the notion that Clausius, uh, developed, uh, in the Gibbs formalism, it's more complicated. Uh, in the Gibbs formalism, you can connect, uh, the Gibbs entropy, the P log P with, um, um, uh, with, uh, thermodynamic entropy by, um, by giving an analysis that both Gibbs gives and Einstein also gives in one of his early papers where you look at a thermodynamically reversible process and you idealize it and you can match up all the quantities. Then there's Shannon entropy."
},
{
"end_time": 3633.712,
"index": 148,
"start_time": 3606.271,
"text": " The sort of entropy that appears in information theory is a parameter for a probability distribution. And that's what it is. It's a measure of how smoothed out, of how uniform the distribution is. The highest entropy arises when you have a uniform probability distribution. And as the probability distribution becomes more peaked, then you're going to have lower and lower entropy."
},
{
"end_time": 3660.606,
"index": 149,
"start_time": 3634.974,
"text": " It's just a different thing. I mean, there are connections. I mean, you know, take probabilities. There are many ways that probabilities appear in usage in the world. I don't know that I want to nestle one inside the other, but I'm kind of comfortable that Boltzmann's notion of entropy and the Gibbs notion of entropy and"
},
{
"end_time": 3679.394,
"index": 150,
"start_time": 3660.606,
"text": " uh and the clouds this notion all fit together very nicely now there are complications because when you move into quantum mechanics there's a phenomenon entropy literature saying well this doesn't exactly match up and i'll i'll i'll defer on that because uh because we're now getting into very delicate territory"
},
{
"end_time": 3692.381,
"index": 151,
"start_time": 3679.394,
"text": " I don't know how to interpret the density operators that appear in quantum statistical physics."
},
{
"end_time": 3717.193,
"index": 152,
"start_time": 3692.961,
"text": " When you give the matrix form and you have a nice diagonal with p's that add up to one, are they probabilities or what are they? And if you can't answer that question and you don't really know what p log p is, which is going to be the entropy. So anyway, not my area. I've deferred to other people who write on this because I think we have"
},
{
"end_time": 3743.166,
"index": 153,
"start_time": 3717.568,
"text": " Great. Well, we can turn this into your area by talking about Einstein. So Einstein has some criticisms of new quantum mechanics and its statistical interpretations. And then I believe you mentioned that Einstein's fundamental contributions to old quantum theory have been forgotten because of these new criticisms."
},
{
"end_time": 3770.572,
"index": 154,
"start_time": 3743.439,
"text": " So firstly, let's talk about the criticisms to get them out of the way, please. And then let's talk about his contributions to the old theory. Well, I think his his objections are very widely known. He simply did not believe in the indeterminism of quantum mechanics. He argued that there was some he was arguing for some sort of a hidden variable theory. The sort of hidden variable theory that he was arguing for"
},
{
"end_time": 3791.288,
"index": 155,
"start_time": 3771.032,
"text": " I don't think there's anything like the salt that we're thinking of you might think now for the bond theory is a kind of hidden variable theory of course i'm starting was encouraging to bone but that it's pretty clear that wasn't his theory. Einstein's hug was that his unified field theory would would somehow return this hidden variable theory."
},
{
"end_time": 3819.07,
"index": 156,
"start_time": 3791.664,
"text": " I think you know the basic layout of the Hidden Variable, Einstein's Unified Field Theory. The program was pretty straightforward. He'd found that you could represent gravity in the same structure as the inertial properties of space and time and in the metric field. I'm not using geometric language here because he didn't. If you're curious on that, I just wrote a long paper on this explaining"
},
{
"end_time": 3848.456,
"index": 157,
"start_time": 3819.07,
"text": " Just a bit of a digression because please you know when you first when you first get a a Class nowadays in general activity and you learn about the structural metric and you learn about the structural radius Right one of the first things you're told is oh, but don't make the mistake of thinking that that's a singularity I know the formula blows up, but it's just a pure artifact of the coordinates Don't make that mistake and it's sort of you know, you're wanted to silly novice mistake, but why?"
},
{
"end_time": 3876.715,
"index": 158,
"start_time": 3848.951,
"text": " Why is it talked about so much. Well, who made the mistake answer prior to about 1950, everybody. Right. Um, Einstein was very clear that he regarded, uh, that he regarded the Schwarzschild radius as singular and he convinced everybody else of that as well. Now, when I say everybody else, I don't mean, you know, I don't, I don't mean trivial figures. I mean the world's greatest mathematician of the time, Hilbert."
},
{
"end_time": 3900.538,
"index": 159,
"start_time": 3877.108,
"text": " I mean the world's greatest geometry of the time, Felix Klein, they all agreed with him. And Herman Weill, they all agreed. What on earth was going on? You know, I do a lot of work in history. I'm fascinated by history of physics. And I can only just tell you very briefly what the answer is. There are multiple ways of treating general relativity mathematically."
},
{
"end_time": 3926.698,
"index": 160,
"start_time": 3900.879,
"text": " The geometrical approach that we now use is i believe the right approach and the correct way to do things and one that gives us the best and most productive results i don't want to in any way detract from that. Einstein dislike the geometric approach completely right he preferred kind of algebraic analytic approach which was all dependent on very particular expressions and their behaviors in the transformation properties and in the context of that approach."
},
{
"end_time": 3945.128,
"index": 161,
"start_time": 3927.108,
"text": " It makes sense that he would come to the conclusions that he did now he wasn't coming those conclusions in ignorance of the possibility of another analysis. It was some of the nature who had already discovered that you could transform away the structural singularity."
},
{
"end_time": 3966.834,
"index": 162,
"start_time": 3945.452,
"text": " I am and also a few of the client appointed out the so called mass horizon in the space time was could be could be transformed transformed away he knew all of that it's still knowing that he said i don't like this geometrical approach i don't take it seriously. We have to approach it and let me get a sense of how someone could possibly think that."
},
{
"end_time": 3996.442,
"index": 163,
"start_time": 3967.227,
"text": " Look at the way that Einstein's 1917 cosmology was introduced. He wanted to have a spherical geometry for space. So where does he get the spherical geometry from space where he wants to get the line element for a spherical geometry? But he says imagine a four dimensional Euclidean space with three dimensional sphere embedded inside and look at the geometry that is induced on the three dimensional sphere and bang there you get the nice line element."
},
{
"end_time": 4024.104,
"index": 164,
"start_time": 3996.8,
"text": " But now do you take this this geometrical picture of a four-dimensional space inducing right in inducing a geometry on the three-dimensional space do you take that seriously do you really think there's a four-dimensional space there no all of this geometrical thinking is just confusing you all that matters in the end is line element in the space right so he called in correspondence with reichenbach he called in germany he called it a donkey bridge"
},
{
"end_time": 4046.476,
"index": 165,
"start_time": 4024.616,
"text": " Right bridge of asses in other words it's a it's a kind of easy way for people to the novices to learn things but don't take it seriously i think then it would call those intuition pumps yeah maybe so ass bridges were intuition pumps yes you you yeah i suppose he didn't use that expression i guess that would fit i you know i had to speak for him"
},
{
"end_time": 4073.797,
"index": 166,
"start_time": 4046.476,
"text": " Okay so so those those is objections and the the the epr thought experiment is i think it's transparently trying to argue that there's more to the system than the standard quantum mechanics allows in other words in the title what is it is quantum mechanical description complete something i can't remember and there's a criterion of reality you know if you can predict with certainty properties of some system"
},
{
"end_time": 4099.275,
"index": 167,
"start_time": 4074.104,
"text": " I'm without interfering with it then the system has those properties. This is the api argument everyone everyone knows it so what was contributions to quantum mechanics i'm really quite massive i think the major one was the light quantum of nineteen five completely extraordinary idea when you look at stein's amos marabas is your miracles in nineteen five."
},
{
"end_time": 4122.722,
"index": 168,
"start_time": 4099.804,
"text": " Everything that he's doing there, accepting that is a completion of 19th century physics. So we can just go down the list. His argument for the reality of atoms brownian motion is completing the Maxwell Boltzmann tradition as statistical physics that had been well developed in the 19th century, but was making a great deal of resistance because there were no new phenomena."
},
{
"end_time": 4136.647,
"index": 169,
"start_time": 4122.722,
"text": " The needed items if you understand special relativity you realize that the basic content is implicit and that's for laurence electrodynamics laurence had discovered in effect the orange group."
},
{
"end_time": 4164.241,
"index": 170,
"start_time": 4136.749,
"text": " Mathematically articulated by Poincare. And once you have the Lawrence group and you understand how to think about it, you realize there's ineffective kinematics there in space and time. Einstein is excavating that and saying, oh, look, there's a kinematics of space and time built into, you know, this is the big discovery of the 19th century electrodynamics that space and time is actually a special logistic equals MC squared. It's already there in special cases in electrodynamics."
},
{
"end_time": 4191.596,
"index": 171,
"start_time": 4164.872,
"text": " Amongst all of this, the huge discovery of the 19th century was the wave theory of light. You know that they are electromagnetic waves, the Maxwell-Lawrence theory. Then in 1905, Einstein says, no, wait a minute. In some thermodynamic sense, heat radiation has a particular character. One of the things that has fascinated me"
},
{
"end_time": 4214.718,
"index": 172,
"start_time": 4192.466,
"text": " for a long time is how Einstein made his discoveries. He didn't have anything that everyone else around him didn't also have. He basically had a pen and a paper and journals to read. He did very little experimentation, wasn't terribly good at it. Yeah, so what was different about how he came up with his discoveries? Well, in this particular case, the key thing about"
},
{
"end_time": 4243.968,
"index": 173,
"start_time": 4215.094,
"text": " The results of 1905 is that you could see significance in empirical results and other people couldn't see. So let me, um, let me give you the example with the, uh, with the light quantum. If you try and understand what he did with the light quantum as a correction to electromagnetic theory, it's unintelligible. How could this possibly be? We have Young's two-slit experiment. We have all of the massive successes of, um,"
},
{
"end_time": 4266.544,
"index": 174,
"start_time": 4244.36,
"text": " What you're doing is your. You're not putting the discovery in the right context the discovery live tonight's work in thermodynamics."
},
{
"end_time": 4289.701,
"index": 175,
"start_time": 4267.056,
"text": " In the years leading up to 1905 Einstein was already working in thermodynamics. He was trying to understand the microscopic or the, I want to say molecular, I guess, molecular scale properties of matter. And what he recognized was that the molecular scale properties of matter get imprinted on their thermodynamic properties."
},
{
"end_time": 4311.903,
"index": 176,
"start_time": 4290.196,
"text": " So the classic example the simplest example is this if you have a system whose pressure and temperature and volume conform with the ideal gas law. Then you know that it's molecular constitution consists of localized points of matter bouncing into each other but but independently moving otherwise."
},
{
"end_time": 4341.476,
"index": 177,
"start_time": 4312.415,
"text": " I mean, that's where PV equals any NIT comes from. You model the gas as a whole bunch of molecules that move independently one another, but they bounce off the walls and they bounce into each other. The key thing is that PV equals NIT at the thermodynamic scale is a signature of that constitution. This, by the way, is why osmotic pressure obeys the ideal gas law. When you first learn this in a statistical thermodynamics class,"
},
{
"end_time": 4371.186,
"index": 178,
"start_time": 4341.937,
"text": " Why the hell should a dilute salt solution exert a pressure that's the same as the ideal gas? Well, because it's dilute, the salt, the salt molecules of the salt ions are moving around like independent, um, like independent molecules. Okay. So what does Einstein do? He's looking at the latest results on the thermodynamics of heat radiation. And what he recognizes in that thermodynamics is that same signature of a particular constitution."
},
{
"end_time": 4393.097,
"index": 179,
"start_time": 4371.561,
"text": " In particular he realizes that if you take the plunk distribution which being empirically established by the experiments of blumer and pring's hymen in nineteen hundred and you wrote the entropy as a function of the volume. You got the entropy of high frequency radiation."
},
{
"end_time": 4411.715,
"index": 180,
"start_time": 4393.456,
"text": " Are you actually looking in the rain regime so i don't come into this but never mind if you look at the in the rain regime you got the entropy of radiation there is with the logarithm of volume. And that is the same right that's the same as the ideal gas so i'm so look."
},
{
"end_time": 4436.135,
"index": 181,
"start_time": 4412.637,
"text": " Here we have the fingerprint of the thermodynamic fingerprint of the molecular constitution and just as you can calculate the size of molecules once you once you know how big Boltzmann constant is and you've got the ideal gas law so you can calculate the size of the energy particles that are giving you s's k log w and of course what comes out of that is that the size of the little localized energy bundles"
},
{
"end_time": 4461.869,
"index": 182,
"start_time": 4436.135,
"text": " What is given it depends on the frequency and it's what we now call plants constant times frequency that's the big argument. Alright and he gives a very simple derivation of what we now call boltzmann's principle is his camera w is actually in stein's principle of the calls of boltzmann's principle in this paper and he gives a very simple derivation of it and they says this is now instantiated."
},
{
"end_time": 4488.592,
"index": 183,
"start_time": 4462.21,
"text": " When you add in the various conditions that apply, you get SSK, as entry goes with the logarithm of volume. It's, I think, one of the most beautiful, most extraordinary of Einstein's contributions. I mean, there are many more. I'll just mention others that are important. Now, the next thing that comes up is the following. He's established that there's a particulate character, right? But he's only established that by looking at the Vien regime,"
},
{
"end_time": 4498.37,
"index": 184,
"start_time": 4488.882,
"text": " in the in the black body spectrum what happens if you look at the total regime going all the way down to the to the to the lower frequency and right."
},
{
"end_time": 4523.712,
"index": 185,
"start_time": 4498.933,
"text": " Well if you give a similar analysis of the thermal properties in particular you look at the fluctuations of radiation pressure and energy you discover that the expression that you derive for the fluctuations in heat radiation is the sum of two terms one term has a particular character and the other has a wave character and they are arithmetically added together"
},
{
"end_time": 4546.391,
"index": 186,
"start_time": 4524.036,
"text": " This is the origin of wave-particle duality. This is where it first appears that radiation has this dual wave and particle character. And so it keeps going like this. And I just mentioned, of course, the A and B coefficients paper on the basis of lasers. This was 19, what, 16 and 17. And then, of course, those Einstein statistics in the early 1920s."
},
{
"end_time": 4575.299,
"index": 187,
"start_time": 4547.807,
"text": " So the idea of the light quantum was greatly resisted. Bohr did not like it one bit and Einstein, it was regarded as a heterodoxy for 20 years until the Compton effect. It was the Compton effect that finally drove home the idea to physicists that Einstein's light quantum was in fact a good description of what was happening with heat radiation or radiation in general, electromagnetic radiation."
},
{
"end_time": 4605.265,
"index": 188,
"start_time": 4576.988,
"text": " So professor, why don't we end this on what insights from your research into the beauty of how Einstein thought differently than his peers? Because as you mentioned, Einstein had access to the same data as his peers. What insights exist that you've gleaned that can be applied to young researchers today, such that a young researcher can watch this and say, OK, I should do more of that. It's the season for all your holiday favorites, like a very Jonas Christmas movie and Home Alone on Disney Plus."
},
{
"end_time": 4628.268,
"index": 189,
"start_time": 4606.869,
"text": " Then Hulu has National Lampoon's Christmas Vacation. We're all in for a very big Christmas treat. All of these and more streaming this holiday season. And right now, save big with our special Black Friday offer. Bundle Disney Plus and Hulu for just $4.99 a month for one year. Savings compared to current regular monthly price. Ends 12-1. Offer for ad-supported Disney Plus Hulu bundle only. Then $12.99 a month or then current regular monthly price. 18 Plus terms apply."
},
{
"end_time": 4658.234,
"index": 190,
"start_time": 4628.66,
"text": " Close your eyes, exhale, feel your body relax, and let go of whatever you're carrying today. Well, I'm letting go of the worry that I wouldn't get my new contacts in time for this class. I got them delivered free from 1-800-CONTACTS. Oh my gosh, they're so fast. And breathe. Oh, sorry. I almost couldn't breathe when I saw the discount they gave me on my first order. Oh, sorry. Namaste. Visit 1-800-CONTACTS.COM today to save on your first order. 1-800-CONTACTS."
},
{
"end_time": 4689.514,
"index": 191,
"start_time": 4660.35,
"text": " I think a lot of it is good fortune. So let me say a couple of things. One thing that I don't think works is the following. There's this idea that you have to be young and in your twenties to make a great discovery, that there's something about youth. What's happened is we have a correlation, but not a causal connection. The process that seems to be at work is the following. When a new science opens up,"
},
{
"end_time": 4700.998,
"index": 192,
"start_time": 4690.009,
"text": " When you sign up opens up that's where the new discoveries are going to be made the established figures are working on the old sciences that they have put together."
},
{
"end_time": 4725.811,
"index": 193,
"start_time": 4701.34,
"text": " Alright and so they keep working on those the new figures come along and they're asking where something new happening oh it's over there so they're gonna work in the new science and that's where the new discoveries and that's why they made more commonly by younger by younger people so don't you know so don't feel bad that you're young and you haven't made nice discovery yet it's got nothing to do with you with your age but also don't feel bad that you're old."
},
{
"end_time": 4756.169,
"index": 194,
"start_time": 4726.305,
"text": " Yes, exactly. In fact, this is one of the things that I follow in my own research. This is just a side thing, but I mentioned before I get to the other point I wanted to make. Someone pointed out to me quite early in my career that when you enter a new field, most of the important novel ideas you have will come to you pretty early, and then you won't get much more. And I think that's right. So how do you exploit that?"
},
{
"end_time": 4783.456,
"index": 195,
"start_time": 4756.527,
"text": " Answer you keep jumping around right right so if you've been if you done your homework and you've looked at you've looked at the sort of papers that i published i'm all over the place you know we've just looked at a few of the things that i've done in in in philosophy of physics i'm you know i've i've written a whole bunch on inductive inference i'm writing a book on empiricism at the moment um you know um it's all it's all over the place because every time i go into a new field i'll have a new thought"
},
{
"end_time": 4811.305,
"index": 196,
"start_time": 4784.104,
"text": " Right. And if it's genuinely new, I'll publish it. So don't be afraid to jump around. This is one of the traps for young physicists. This is why you should be a philosopher of physics and not a physicist, because if you're a philosopher, if you're a physicist, you're trapped by the need to keep grant money going, which means you have to develop an expertise of sufficient caliber to enable you to keep the grant money going, which means and to keep your lab going and to keep your graduate students going."
},
{
"end_time": 4841.015,
"index": 197,
"start_time": 4811.852,
"text": " So you can't escape. Philosophers of physics are supported by teaching. We can switch on a dime. I can change my mind tomorrow about what I'm working on, work on something else. As long as I keep teaching my classes, I'm supported. Now, let's get back to Einstein. What did we learn from Einstein? Einstein had a remarkable ability to look at results and see the significance in the results."
},
{
"end_time": 4870.009,
"index": 198,
"start_time": 4841.22,
"text": " the empirical results that nobody else could see i've already i've already mentioned that with the light quantum right he could see the signature of of of distributed atoms there in special relativity he could see that the lawrence group was actually a kinematics of space and time right all of this is empirically in in the theory it has this property lawrence poincare they fully understood the mathematics they just didn't they just they just didn't see it"
},
{
"end_time": 4896.92,
"index": 199,
"start_time": 4870.845,
"text": " This was Einstein's, and he used this over and over again, this was Einstein's magical power that he could read in experimental results. Things started to change with general relativity. It had the same origin there. He recognized that the fact that all bodies, the Galileo result, that all bodies fall with the same acceleration had to be implemented exactly and perfectly. All right."
},
{
"end_time": 4925.333,
"index": 200,
"start_time": 4897.108,
"text": " When people like Poincare and Minkowski were revising theories of gravity as they tried to do, they discovered that that law was broken in second order quantities. You would get a V on C squared dependency on the sideways velocity. So things that were moving with velocity sideways would not fall at the same rate as something that was falling vertically straight down."
},
{
"end_time": 4952.278,
"index": 201,
"start_time": 4925.435,
"text": " This stein stein tells us just bothered him massive he just didn't see that that would be the right the vector possibly be right you can. Think of other cases and understand why that would be so might that mean that a kinetic gas would fall slow when it's harder because there's a lot of sideways motion. Maybe maybe not turns out not to be that simple so what does stein do we need to construct a theory."
},
{
"end_time": 4981.63,
"index": 202,
"start_time": 4952.79,
"text": " In which that result is preserved it's so important and how did you construct that theory well with the principle of equivalence so if you have two bodies one at rest and one moving initially to the side and then you view that from an accelerating frame of reference then the resting body will fall and so will the body that has sideways motion but they will remain at exactly the same altitudes right so i'm stunned says that's the way a gravitational field has to be"
},
{
"end_time": 4991.886,
"index": 203,
"start_time": 4982.176,
"text": " Alright so let's ask what sorts of theories of gravity come out of that and since he's working in a minkowski space time you very rapidly gets rapidly."
},
{
"end_time": 5013.763,
"index": 204,
"start_time": 4992.483,
"text": " For five years he gets to the idea of a semi rimani and space time to move from the casket space time to a semi rimani and space time so okay so that's the thing you need to have. There has to be a match this is now the jar of mold has to be a match between the problems that are right for the picking and your particular talent and expertise."
},
{
"end_time": 5038.097,
"index": 205,
"start_time": 5014.292,
"text": " How does that work out with Einstein? Well, Einstein then moved on to his unified field theory, and he stopped using that facility. He started saying, I'm going to find the simplest possible rules that we can have for physics. And from the mid-20s onwards, when he was doggedly pursuing his unified field theory,"
},
{
"end_time": 5066.288,
"index": 206,
"start_time": 5038.626,
"text": " He just never produced anything that we know that we know actually works. He was he was no longer well matched to the problem. You ask who was well matched to the problem. Well, when quantum mechanics came along, it was it was just crazy. You had to be able you had to be someone who could tolerate bizarre contradictions and and and manage with them. And who could do that? Who could do that better than anybody else? Answer Niels Bohr."
},
{
"end_time": 5080.009,
"index": 207,
"start_time": 5066.664,
"text": " I'm just gonna see electrons completely completely crazy."
},
{
"end_time": 5105.367,
"index": 208,
"start_time": 5080.418,
"text": " And so he had this ability to just say, I know it's crazy, but you know, what's the quote? Is it crazy enough? I don't think it bore. I think maybe that was Pally or someone. And that was terrific because he could actually produce this theory, the Bohr-Zommerfeld theory of the atom, that led directly up to what happened in the"
},
{
"end_time": 5111.476,
"index": 209,
"start_time": 5105.367,
"text": " In the nineteen in the nineteen twenties of course just as with with einstein."
},
{
"end_time": 5141.647,
"index": 210,
"start_time": 5111.971,
"text": " Then balls facility to tolerate silliness and contradiction became a massive liability because you then produce this this incoherent idea of complementarity which for which i don't think there's any precise sense right and he somehow managed to convince a whole generation of physicists to take this silly idea seriously it took a long time for people to to to get past the the the incoherence of balls ideas."
},
{
"end_time": 5168.251,
"index": 211,
"start_time": 5141.647,
"text": " I can see you flinch there because there's a sub community in philosophy physics and hang on to the idea that ball had some kind of deep and profound inside now we buy for kate i'm clearly in the school that things not. I have no doubt that ball had strong powerful intuitions that he could communicate to other people that are at the core incoherent anyway so so so so the moral is if you're starting out."
},
{
"end_time": 5196.988,
"index": 212,
"start_time": 5169.616,
"text": " Just do the work on what interests you. Look for places where you can see further than other people can see. That's your secret skill. When I talk to philosophers of science and we're trying to figure out where they should work, I often ask them this question. I say, can you remember when you've been in a discussion group and everyone gets tangled up over something and you're sitting there thinking, I don't get it."
},
{
"end_time": 5225.572,
"index": 213,
"start_time": 5197.312,
"text": " It's perfectly clear and perfectly obvious what's going on. I can see straight through this. Ah, there's your magical power. The difficulty is that because you could see it so clearly, you think it's trivial and you think it's easy. Right. And so you tend not to value it. Rather you look at someone who can do something that you absolutely can't do and you're in amazement and you want to be them. Big mistake. They're good at it. You aren't."
},
{
"end_time": 5255.282,
"index": 214,
"start_time": 5226.032,
"text": " Right. Do the things that you're good at. Do the things where you see your way through clearly faster than other people do. And that's where you'll make the breakthroughs. Anyway, look, that's the advice I give people. And it's as good as they paid me for it. So free advice is only as good as what you paid. I love that. OK. So most of the time we'll look at gymnasts and we'll just be wowed and we'll think, OK, I should do that because that's difficult. But then there are other tasks. That's exactly right."
},
{
"end_time": 5281.203,
"index": 215,
"start_time": 5255.725,
"text": " It's taking me a long time, so I've worked hard on exactly where I have a skill. I'm not very good at the mathematics. I can do mathematics competently, but I don't have the sort of beautiful insight that a good mathematician can have. But my background is chemical engineering. I can tolerate the kind of vagueness that engineers thrive in."
},
{
"end_time": 5305.964,
"index": 216,
"start_time": 5281.8,
"text": " I can survive when the situation is unclear. Do you thrive? Do you not just survive when the situation is unclear? Do you actually prefer that and do better in it than in situations where it's clearer? Oh yes, absolutely. And so I'll give you an example of that. I wrote a paper recently on the nature of thermodynamically reversible processes. I think that's roundly misunderstood all the way through here."
},
{
"end_time": 5324.428,
"index": 217,
"start_time": 5306.34,
"text": " And it's not a question of mathematics the mathematicians of carthi dory going back to going back to the good in the group are they gave a beautiful math in the time version that they missed the essential point of what's really going on with him and the reversible process is i can see that."
},
{
"end_time": 5353.251,
"index": 218,
"start_time": 5324.565,
"text": " One of the things that chemical engineers have to be good at is thermodynamics, because processes and chemical plants are all thermodynamic processes. So I was taught thermodynamics from scratch four times in my engineering degree, and it was only on the third time that suddenly I got it. I can still remember there was this moment when I realized, oh hell, it's all about thermodynamic reversible processes. That's the key concept. If you don't get that, you know, and so I just mentioned to you, maybe, maybe"
},
{
"end_time": 5376.544,
"index": 219,
"start_time": 5353.66,
"text": " Maybe this will be helpful to you. A standard mistaken view amongst physicists is that a thermodynamic reversible process is just a really slow process. No, here's a really slow process. Get a balloon and inflate it and then put a tiny little pinhole in it. That balloon is going to deflate as slowly as you like just by making the hole as small as possible, but that's"
},
{
"end_time": 5395.452,
"index": 220,
"start_time": 5376.749,
"text": " That is an irreversible expansion of the gas that is entropy increase. Now a thermodynamic reversal process has to be one where you have a near perfect balance of driving forces. The forces that are pushing the process forward have to be balanced almost perfectly exactly by the processes that are pushing it back."
},
{
"end_time": 5424.224,
"index": 221,
"start_time": 5395.452,
"text": " Now that runs automatically into trouble because if you then notice i had to use weasel terms almost exactly almost perfectly well there's a reason for that if you um if the if the forces balance exactly nothing happens right when you have a perfect equilibrium of all driving forces no change happens right so you have to have some sort of an imbalance okay if you have an imbalance right then you have an entropy creating process so how are we to think of these things"
},
{
"end_time": 5439.838,
"index": 222,
"start_time": 5424.872,
"text": " What are the ways of doing it and that's what the papers about it includes a historical survey of everything i could find people but that comes out of out of a kind of engineering thinking i'd like to make my peace with these these these ideas."
},
{
"end_time": 5465.486,
"index": 223,
"start_time": 5441.305,
"text": " This is interesting. You learn thermodynamics three times from scratch in order to truly four times. OK, great, because I was going to say something that relies on the number four. OK, I wonder if this is a general rule, because it's common to hear that one has to learn quantum field theory four times from scratch before one groks it. And I just applied that to QFT. I didn't apply that to computer science or to stat mech. But I'm wondering if"
},
{
"end_time": 5495.162,
"index": 224,
"start_time": 5466.237,
"text": " Maybe it's the case and you seem to validate the thermodynamic case. Yeah, no, I think that's right. Maybe it's the case in general. Now, what does it mean to learn something from scratch again? Because you could just take one course, thermodynamics one, and then you take thermodynamics to the next year and then they reteach you the fundamentals. Or you could take thermodynamics one, take a year off, retake the same course. Tell us what exactly does it mean from scratch? I'll give you my experience."
},
{
"end_time": 5516.254,
"index": 225,
"start_time": 5495.469,
"text": " Give my experience with thermodynamics chemical engineers have an odd place in engineering because we don't just do one sort of engineering we have to have control of all of the different branches of engineering right so in a chemical plant i have to understand the chemical processes i have to have some understanding."
},
{
"end_time": 5542.841,
"index": 226,
"start_time": 5516.578,
"text": " of the mechanical engineering of the structures of the pressure vessels that are being used. I have to have some understanding of the electrical system that's being used. And also chemical engineers are often involved in finance. So we had courses in discounted cash flow. We had courses in operations research. You're torturing yourself. This is so messy. Yeah."
},
{
"end_time": 5561.442,
"index": 227,
"start_time": 5543.456,
"text": " Yeah so so we had to we had to be a jack of all trades and i enjoyed that immensely so we went to different departments. Alright so we we learned some dynamics in the physics because you need to know physics you go to the physics department you learn some dynamics there then you go to an engineering school."
},
{
"end_time": 5583.029,
"index": 228,
"start_time": 5561.578,
"text": " I have to know the engineering and they teach you thermodynamics as well then you go to the chemistry department chemical engineers we need to know chemistry they teach you thermodynamics there and then you come back to chemical engineering right and then there's got their own version okay if you think across all of those different groups. They all have different ways of representing things so for example."
},
{
"end_time": 5601.203,
"index": 229,
"start_time": 5583.541,
"text": " how the way a physicist will will talk about will talk about some dynamics is going to involve clouds entropy and so on when you go to the chemistry department the interesting thermodynamics is the thermodynamics of chemical reactions."
},
{
"end_time": 5626.425,
"index": 230,
"start_time": 5601.203,
"text": " What is it that drives a chemical reaction for it is going to be an increase of entropy but how do you represent the entropy so it is applicable to the chemical process or if you're in an engineering school the thing that really matters is the efficiency of engines. So what's the best efficiency you can get out of an auto cycle in a gasoline engine."
},
{
"end_time": 5650.043,
"index": 231,
"start_time": 5626.817,
"text": " All right now all of it's all from dynamics that they're being applied in so many different so many different ways all the way all the way across the board and it's getting all those different perspectives now the thing about thermodynamics is that there's an intrinsic beauty to it but a massive incompleteness because what thermodynamics actually talks about is never the complete theory."
},
{
"end_time": 5676.834,
"index": 232,
"start_time": 5650.435,
"text": " You need to have, in addition to the basic thermodynamic concepts, a theory of the matter that's being involved. You need to understand the mechanics of fluid flow. You need to, you know, you need to understand if you're doing thermodynamics for quantum systems, you need to understand the peculiar quantum mechanics of those particular systems. So one of the questions that I got interested in for a while is what's the maximum efficiency of a solar cell, right?"
},
{
"end_time": 5689.292,
"index": 233,
"start_time": 5677.568,
"text": " What are the heat engines they're taking in heat radiation and producing electricity but that's a that's very much a quantum mechanical process that's doing it or something like what do you call these these cells that."
},
{
"end_time": 5715.094,
"index": 234,
"start_time": 5689.821,
"text": " What what what what's going on and so and so many different ways in now i know any little quantum field theory that my impression is that it has a very similar sort of character."
},
{
"end_time": 5745.981,
"index": 235,
"start_time": 5715.981,
"text": " There are basic ideas. You need to know the Hamiltonians or the Lagrangians. But then you might be looking, for example, at Feynman diagrams and scattering processes and so on. Or you might be looking at quark confinement, or you might go algebraic. You might have a course from one of the mathematicians who will get you to read Street and Whiteman. But what you're doing is you're approaching"
},
{
"end_time": 5751.681,
"index": 236,
"start_time": 5746.766,
"text": " The one phenomenon in the world with many different theoretical devices."
},
{
"end_time": 5782.09,
"index": 237,
"start_time": 5752.176,
"text": " And it's only when you get a grasp on how all of these are bearing down that you see the commonality. I think quantum field theory is an especially difficult case. It is justly reputed to be a very difficult theory to learn. I think that's right because, well, I mean, part of it is you start to try and compute Feynman diagrams and very quickly you realize you've got a lifetime of integrals ahead of you. And so do you really want to get into that? And then you've only learned scattering theory, right?"
},
{
"end_time": 5812.005,
"index": 238,
"start_time": 5783.268,
"text": " And then there's all the stuff about re normalization and what do i make sense of that and the realization oh by the way when i when i started studying re normalization group it looked more like engineering to me than anything i've seen in fundamental physics before um it really it really got my engineer juices going i thought boy that's it that's how we do things in chemical engineering sorry yes well i was going to say i very much like this idea of approaching something from multiple points of view in order to understand it so"
},
{
"end_time": 5841.613,
"index": 239,
"start_time": 5812.363,
"text": " One analogy is that you could take a look at a cone, and if the light is shown from above, it just looks like a circle. If it's from the side, it just looks like a triangle. If it's from an obtuse angle, then it looks like an ice cream cone, like there's a little bit of a bulge there. And it takes you a while to understand the three dimensional structure there. Yeah, yeah, yeah. And all you have access to are the projections. And so to move around. And that also jives with your previous answer of, well, it's something I thought of as well, that maybe it's not mere youth that enables creativity."
},
{
"end_time": 5871.032,
"index": 240,
"start_time": 5842.056,
"text": " It's instead the entry into a field that fosters that innovation. So Schrodinger was 40 or 50 when he began contributing to biology. Maybe it's just he had that foray into the unfamiliar that enabled the contributions. Yeah, I know. I noticed this with in philosophy as well. People look at some major work of philosophy and they say, well, that's, you know, but that answer to the problem is easy, right? I don't really understand what the fuss is."
},
{
"end_time": 5900.06,
"index": 241,
"start_time": 5871.288,
"text": " Well the first is not the answer it's the question. The creativity in philosophy is framing things so that an analysis is possible and if you do that you create a new field and because you're the first person there you get the you can you know jump on what is likely the correct answer almost immediately and so you kind of win the day I mean this is this is what I feel happened with the stuff I did with thought experiments I mean"
},
{
"end_time": 5924.838,
"index": 242,
"start_time": 5900.657,
"text": " I just got very insistent on arguing that there's an epistemic problem here. How is it possible for thought experiments to give us novel knowledge of the world? And I made that the framing. I call that epistemic problem of thought experiments or the empirical problem. I can't remember which one of those two. And once you ask it very pointedly and then you're very rigorous in giving an answer, it's easy. Yeah, okay. It's the obvious answer."
},
{
"end_time": 5952.022,
"index": 243,
"start_time": 5925.247,
"text": " But you got there first and people say what's the big deal with the big deal is I knew the right question to ask. It's the same thing with causation. Right. I knew the right question to ask, of course, cause causal metaphysicians aren't happy with me, but yeah, that's a problem. Is there any epistemic gain that can come from thought experiments that cannot come from formal deductions? Yes. Um, um, you've, you've narrowed things down by saying formal deductions."
},
{
"end_time": 5981.783,
"index": 244,
"start_time": 5952.5,
"text": " uh, by argument, I have a much looser and more general idea. I mean, informal argumentation. Um, and that certainly includes, uh, inductive inference. And you'll find in some of the most famous thought experiments, a lot of inductive inference going on. Um, you know, Einstein's magnet conductor thought experiment. I'll just say in the abstract, what, what, what the point is some of the key steps in thought experiments are inductive inferences. Uh, you produce an effect in a particular case."
},
{
"end_time": 6004.48,
"index": 245,
"start_time": 5982.227,
"text": " And then you say, and this is general, right? It's an inductive entrance where you generalize from the one case, but because the particular case is so compelling, people are willing to go along with the inductive inference, which might be good or it might be bad. All right. Oh, we, so we, we saw it in the, uh, in Einstein's, um, uh, principle of equivalence."
},
{
"end_time": 6033.166,
"index": 246,
"start_time": 6004.804,
"text": " We have all bodies will fall the same in the uniform accelerating frame of reference that's a gravitational field in the nine senses and everything else will go the same as well that's that's one hell of an inductive inference at that point we've only got the effect for falling bodies we haven't got the effect for light propagation. Right but it's gonna work for light so it's gonna work for everything he says that you know that you you happily generalize you gonna say that all gravities like that."
},
{
"end_time": 6061.596,
"index": 247,
"start_time": 6033.456,
"text": " It isn't just uniform acceleration. It's gravitational fields that are that are in homogeneous. There's lots of inductive inference going on here. Yes. Now your work on material induction, if I recall correctly, is against this. It's more like saying there are local ways that we can do induction, but you can't globally apply them. It's not as if there's a one size fits all induction. Yeah. Yeah. Correct. Yeah. So this comes out of the fact that I'm a science lover."
},
{
"end_time": 6086.937,
"index": 248,
"start_time": 6061.954,
"text": " I love science, I love history of science, and I want to be able to say that our best science is somehow privileged over other endeavors, and it is privileged for empirical reasons. It's because it is well supported by the evidence, and the character of that support is inductive. I did not find accounts of inductive inference in the philosophy of science literature that were able to sustain that result."
},
{
"end_time": 6114.036,
"index": 249,
"start_time": 6087.346,
"text": " What we find just a fragmentation of many different accounts and you kind of go doctor shopping you find some particular example and you want to say well why is this a good use of evidence will you shop around until you found the account of inductive entrance it fits then you slap it on now we need a single account that is to be applied everywhere. I'm what after took me a while to say this but after a lot of probing what i realized is that there are no universal rules of inductive inference."
},
{
"end_time": 6131.374,
"index": 250,
"start_time": 6114.258,
"text": " I don't play everywhere that's the uniformity that you're talking about rather what you have a inductive systems that apply locally and they are specifically warranted by facts why don't you give an example okay i'm the simplest example one that i use in chapter one of the book."
},
{
"end_time": 6157.346,
"index": 251,
"start_time": 6131.374,
"text": " Is marie curie prepares a tenth of a gram of radium chloride it's the only sample of radium chloride any laboratory in the world in nineteen three she looks at its crystallographic properties and declares radium chloride has such and such a crystallographic properties what i think we're now saying i think monoclinic was the way we tell you but she says it's the same as barium chloride."
},
{
"end_time": 6170.64,
"index": 252,
"start_time": 6157.944,
"text": " If you think about that in terms of other accounts of inductive inference, what would it be? Well, it could be an enumerative induction. This A is B, therefore all A's are B."
},
{
"end_time": 6194.531,
"index": 253,
"start_time": 6171.237,
"text": " Boy, that's a bad form to use because almost every occasion when this A is B, all A's are not B, right? So this sample of radium chloride was prepared by Marie Curie. It's not going to be true. You know, if I see the sample of radium chloride is in Paris, they won't all be. The sample of radium chloride is a tenth of a gram. They won't all be a tenth of a gram. Or all swans are black or all swans are white."
},
{
"end_time": 6221.886,
"index": 254,
"start_time": 6194.94,
"text": " The idea that you can authorize that inference by looking at a general rule just doesn't work. But she wasn't doing that, right? So why is she so secure in making the inference that it was so secure it was even unremarkable? Well, the answer is factual investigation of the nature of crystals all the way through the 19th century."
},
{
"end_time": 6250.009,
"index": 255,
"start_time": 6222.346,
"text": " All right, people had looked at, you know, what sorts of forms do crystals have? Uh, this was a work in, in atomic theory. This was work in mathematics. This is one of the places where the discrete, uh, the theory of discrete, uh, uh, finite groups, uh, got underway. And it turns out that if you build up lattices, right. Um, uh, they fall into one of six or seven families, depending on, uh, depending on how you count them. So if you find."
},
{
"end_time": 6279.872,
"index": 256,
"start_time": 6250.009,
"text": " A crystalline substance that falls into one of those families, then you know that many more of those samples will fall in that one particular family. And so you can make the generalization. Now it is inductive. It's a little bit risky because there are some substances that are dimorphic or polymorphic, which means that they have forms that exist in multiple different families. Uh, the familiar case of polymorphism isn't exactly doesn't exactly map onto here, but it's the case of carbon."
},
{
"end_time": 6302.056,
"index": 257,
"start_time": 6279.872,
"text": " It can be a diamond or it can be graphite but there are many other cases of minerals that have that have this so so what was justifying your entrance. Was with facts about crystalline substances hard one through the course of the nineteen century very difficult facts to learn because to characterize these families to go tremendous amount of work."
},
{
"end_time": 6326.63,
"index": 258,
"start_time": 6302.534,
"text": " Alright, and it got regularized as a thing called Ouille's principle after one of the early starters. So the fact is, the Ouille's principle. And so the argument of the material theory of induction is, it's all like that. Whenever someone's doing an inductive inference, if it's cogent, and you want to ask why is this an appropriate inference,"
},
{
"end_time": 6353.183,
"index": 259,
"start_time": 6327.005,
"text": " The answer is going to come back to effect. Now this is going to apply specifically also to people using probabilistic inferences inductively. Um, if you're going to use probabilities, right? Um, the way I argue it out is the following. There is no default that every time you're uncertain about something, you can rep, you can responsibly represent the uncertainty by probability. You can't do that."
},
{
"end_time": 6372.142,
"index": 260,
"start_time": 6353.592,
"text": " You have a positive obligation to demonstrate that a probabilistic representation is appropriate to the case in hand. So for example, in population genetics, you know, you know, you know, typically what you will do is you say this particular instance has been"
},
{
"end_time": 6389.428,
"index": 261,
"start_time": 6372.637,
"text": " It has been randomly sampled from the population so if we're going to do DNA typing and you want to say oh yes it's very very probable that you know that this perpetrator has a blood sample that matches the blood found at the"
},
{
"end_time": 6413.183,
"index": 262,
"start_time": 6389.94,
"text": " I'm perfectly happy with those probabilities, but it is essential that the probabilities are anchored by some fact, and the fact is that we can treat the case as if the person was randomly sampled. If that isn't the case, if you can't treat that suspect as being randomly sampled from the population, then all bets are off."
},
{
"end_time": 6428.37,
"index": 263,
"start_time": 6413.524,
"text": " Alright who knows that they might have been planted in some way but they might have been planted you know you can figure out all sorts of ways it could come could come on stock this know what what happens when you when you don't do this seriously when you run into all sorts of."
},
{
"end_time": 6453.882,
"index": 264,
"start_time": 6428.712,
"text": " Silly arguments that don't work if you send the simulation argument yes the one that says that we are very probably a simulation yeah yeah tell me about that. That's a spectacular example where we using probabilities without any factual yeah so what works is the following we end up with a position where we convince ourselves somehow that there are very many possibilities for the way our experience of the world come about."
},
{
"end_time": 6481.698,
"index": 265,
"start_time": 6454.326,
"text": " Right. And the idea, and we somehow convince ourselves, I think these arguments already are pretty shaky, but I'm looking at a particular fallacy. We convince ourselves that there are vastly many ways that our experiences could come about if we were computer simulations and relatively fewer cases in which they could come about if the world is truly as it seems."
},
{
"end_time": 6506.92,
"index": 266,
"start_time": 6483.029,
"text": " Let's just take that as a starting point i think it's already do this that we got there. Now we ask now we ask the question that what's the next step with the next step is to say we have no idea which is ours. I would say you stop at that point you have no idea which is ours but wait a minute but i'm going to say no i'm going to represent my uncertainty by probability."
},
{
"end_time": 6533.131,
"index": 267,
"start_time": 6507.432,
"text": " Right and when i represent my uncertainty by probability i find that the vast. Mass of the probability ends up on the on the computer simulation case and any very small amount ends up what's the fantasy. What the fantasy is you have no factual grounding for that probability you have just loaded fall from the sky and the result is simply an artifact of a misapplied inductive logic."
},
{
"end_time": 6561.442,
"index": 268,
"start_time": 6534.275,
"text": " It's as simple as that it's an egregious fallacy but you need something like a material theory to tell you if instead you say i'm going to use the principle of indifference and i can use probabilities well you're going to be in big trouble because the principle of indifference contradicts probabilities in cases of genuine and extreme ignorance and this is a case of genuine and extreme ignorance."
},
{
"end_time": 6591.698,
"index": 269,
"start_time": 6562.517,
"text": " Also, another simple case is like with a die and you just color two of them blue and then the rest of them red. And you could say, OK, well, is it going to be red or is it going to be blue? Well, we're indifferent. And so it's 50-50, but that's not exactly. Yeah, this goes back to Cain's. You'll find Cain's in his I think it's called treatise on probability early 1920s. He has all the classic examples there. Professor. Thank you for spending so long with me. It's been a blast."
},
{
"end_time": 6617.295,
"index": 270,
"start_time": 6592.005,
"text": " Well, thank you. I've enjoyed talking to you. You've got a really wonderful podcast. There's something subtle. You know the questions to ask. I've received several messages, emails and comments from professors saying that they recommend theories of everything to their students. And that's fantastic. If you're a professor or lecturer and there's a particular standout episode that your students can benefit from, please do share. And as always, feel free to contact me."
},
{
"end_time": 6644.957,
"index": 271,
"start_time": 6617.722,
"text": " Hey Kurt, you've spoken to so many people in the fields of theoretical physics, philosophy, and consciousness. What are your thoughts?"
},
{
"end_time": 6657.022,
"index": 272,
"start_time": 6644.957,
"text": " Also, thank you to our partner, The Economist."
},
{
"end_time": 6681.647,
"index": 273,
"start_time": 6659.275,
"text": " Firstly, thank you for watching, thank you for listening. If you haven't subscribed or clicked that like button, now is the time to do so. Why? Because each subscribe, each like helps YouTube push this content to more people like yourself, plus it helps out Kurt directly, aka me. I also found out last year that external links count plenty toward the algorithm,"
},
{
"end_time": 6691.51,
"index": 274,
"start_time": 6681.647,
"text": " Which means that whenever you share on Twitter, say on Facebook or even on Reddit, et cetera, it shows YouTube, hey, people are talking about this content outside of YouTube."
},
{
"end_time": 6716.459,
"index": 275,
"start_time": 6691.732,
"text": " which in turn greatly aids the distribution on YouTube. Thirdly, you should know this podcast is on iTunes, it's on Spotify, it's on all of the audio platforms. All you have to do is type in theories of everything and you'll find it. Personally, I gained from re-watching lectures and podcasts. I also read in the comments that hey, toll listeners also gain from replaying. So how about instead you re-listen on those platforms like iTunes, Spotify, Google"
},
{
"end_time": 6744.275,
"index": 276,
"start_time": 6716.459,
"text": " You also get early access to ad free episodes, whether it's audio or video."
},
{
"end_time": 6757.688,
"index": 277,
"start_time": 6744.275,
"text": " Thank you so much."
}
]
}No transcript available.