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Tim Maudlin Λ Tim Palmer: Superdeterminism vs. Bell's Theorem
July 25, 2023
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Tim, the whole paper is about free variables and a free variable is something that you can change in your theory. That's the whole basis of the paper. Free. What does free mean? If it doesn't mean you can't change it, then it has no meaning.
Welcome to Theories of Everything. My name is Kurt Jaimungal, and on the Toe Podcast, we explore theoretical physics, philosophy, and mathematics. In this episode, we have a theolocution with Tim Modellin and Tim Palmer, exploring Bell's theorem, and more importantly, the assumptions that go into that theorem. At times, it felt like the New Testament, like
Well, what does Bell say? Chapter two, verse four. So interpretations are bound and there's definitely room for a part two, especially with a blackboard, perhaps even filmed in person. So if you have questions or comments, please leave it below. Tim Palmer is a Royal Society research professor in the Department of Physics at Oxford. His PhD was in general relativity and he retains a strong interest in fundamental physics.
He's also an expert on climate physics and chaos theory, writing a popular book called The Primacy of Doubt, exploring the science of uncertainty in areas as diverse as the climate, economic forecasting, and quantum physics. He's a fellow at the Royal Society and an international member of the U.S. National Academy of Sciences. Tim Modelin is a professor of philosophy at New York University, specializing in the philosophy of physics.
He's penned several influential books, including Quantum Nonlocality and Relativity, as well as The Metaphysics Within Physics, simplifying Abstruse concepts for a broad audience. He's also the founder of the John Bell Institute, of which there's a GoFundMe in the description. As usual, every link, everything that's mentioned is in the description. Tim Modellin has been on before. The Theories of Everything podcast is in fact one of our most popular episodes where we discuss Bell's theorem, the philosophy of physics, and what concepts
All right, before we get started, there's a few pieces of terminology that may not be familiar to everyone and they're not expanded on in the podcast itself, primarily so we can just get to the meat of the discussion. But here's a recap in case you're interested. And if you know these terms, then feel free to skip
forward to the timestamp that's outlined either in the description or over here. So the terms are super determinism, a mix master universe, fractal cosmology, and an attractor. Super determinism is a class of quantum theories. It's not a single interpretation of quantum mechanics. In fact, it's not an interpretation at all. It's a class of quantum theories put forward by Gerard Tuft that don't have what's called statistical independence. So what is statistical independence? Well, it's one of the assumptions that go into Bell's theorem, at least that's
What is debated on today so much of the episode is on what is the definition of statistical independence the second terminology is mix master universe what is that well it's a solution to general relativity where the universe undergoes chaotic and turbulent transformations it was originally put forward to solve a problem that inflation ended up also solving and people seem to prefer inflation so you don't hear about the mix master universe.
Then there's fractal cosmology which says that the large scale cosmological structures are fractal like in their distribution now fractals don't always mean self similar though they do have infinite detail what it technically means is that there's one definition of dimension that we are.
Commonly told and then there's another definition of dimension and when these don't coincide and you have a fractal so ordinarily you've heard of RN so the real numbers to the end for instance we have three space so are to the three or four if we include time.
That's called the topological dimension. There's another definition of dimension called Hausdorff, and ordinarily these coincide for the objects that we think about, but sometimes they don't, and when they don't, specifically when one exceeds the other, that's called a fractal. Now attractors are used in chaos theory, and those describe the long term, long term in terms of time, dynamics of the system.
So that is, if you were to leave a system for a while, where does it tend to? Are there certain states or even trajectories that it moves toward? Now, there's a precise definition of what it means for there to be a long time, quote unquote, because that's vague. Also, it's vague to say tend to. So there's a mathematical definition of that as well. OK, so an example would be if there's a ball and it rolls down the hill like a U shaped hill, it will settle at the bottom. That bottom place would be called an attractor. And I don't like these
Ball and hill analogies, because they're overused in my estimation for physics, like the Mexican hat you show. Oh, there's a ball and it rolls down the hill. Or harmonic oscillator can be like a ball that just continually swings on the hill. Anyhow, attractor is used not in those scenarios, although that's technically an attractor. It's just generally used in chaos theory. Chaos theory is whenever you have a system where if you were to tweak it a tiny amount,
Then later, the future evolution deviates a large amount. So usually we have an input that if we were to tweak slightly in the input, the output is tweaked slightly. When that fails to be the case, it's chaotic. Okay, with those definitions out of the way, enjoy this Theolocution with Tim Palmer and Tim Modlin. Okay, professors, thank you. Welcome. It's an honor to speak with you for the first time, Tim Palmer and Tim Modlin. Welcome back.
For the viewers, both of you are named Tim, so I'm going to be referring to you all as Professor Modlin and Professor Palmer when appropriate. Why don't we get started with Professor Palmer? What have you been working on in the past few months and what excites you about it? Okay, it's a kind of difficult question because I split my time between two quite different
areas. So on the one hand I do a lot of work in climate physics and right now actually I'm preparing, I'm flying off to Berlin on Sunday for what I hope will be a really landmark meeting in climate physics. We're pushing for what I've been calling a CERN for climate change, so a kind of an
the type of modeling that we need to understand climate change at a much more detailed level than we can currently do, than we can currently have knowledge about by working internationally and creating international institutes. So the last month or so I've been preparing a kind of keynote talk on this, putting together some of the sort of scientific
Reasons why we need to work on climate change internationally. So I know that's not the topic for today. So I just wanted, but I want to just tell you about that because in a sense, I mean, what we will be talking about today is perhaps bringing ideas from fields like nonlinear dynamics, which plays a big role in climate change into, into quantum physics. So the other kind of half of my time is indeed on kind of fundamental physics. My PhD many years ago now was in general relativity.
I gave a talk a couple of weeks ago to the theoretical physics department on something I'm now calling rational quantum mechanics.
and the word rational is deliberately sort of ambiguous because it's an attempt to make some of the things like Bell's theorem which are traditionally viewed as kind of weird and incomprehensible more comprehensible but deliberately also using the other word rational which is that of in mathematics rational numbers are numbers which you know can be written as fractions like five over
The thing which people perhaps don't know about quantum mechanics unless you work in that area is that the continuum actually plays a vital role in the theory of quantum mechanics through what are called Hilbert spaces. So a Hilbert space is a vector space over a field of complex numbers and complex numbers are continuum is a continuum field. So despite the fact that we think of quantum as a sort of a discrete jump,
Continuum mathematics plays a key role in quantum mechanics. And my personal belief is that that is one of its problem areas. It's its strength in some respects, but it's also its problem. It's a problem in it creates it creates many of the interpretational problems that we have. So I've been developing a mathematical model where we sort of relax that
The idea is to see what that brings to the table, and I would argue it brings some pretty big, from a least conceptual point of view, pretty big consequences. So those are two different things, quite polar opposites in many respects, but that's what makes science fun, doing different stuff.
Great. Now, Professor Modlin, what have you been working on in the past few months, maybe even a year, and why does it ignite you? Well, this is going to be kind of ironic, the pair of things I'll mention. Maybe I'll do them in opposite order. That is first the theoretical thing. But, you know, this is not measured in the scale of months or even years. This is something I've been working on for several years, maybe a decade.
Which also has to do actually with getting rid of continuum, which is to develop theories of discrete spacetimes and to see how that changes the mathematical situation and whether you can get relativistic looking structures to emerge in a natural way from discrete underlying structures and so on. And that's kind of, I mean, I've had some very interesting results. I sort of got in two plus one dimensions, I got Minkowski spacetime to sort of drop out
without expecting it all of a sudden from a very, very, very different foundational picture. But that's been going on for years and years and years. What I've actually been spending my real time on recently is also institutional. That is, I'm sitting here right now in Croatia at the hopefully future home of the John Bell Institute. And what we're trying to do is set up a
a physical location to have workshops and summer schools on foundations of physics. And we're now at the point where we either fish or cut bait in terms of acquiring this location. We've built a lecture hall. We've built a lot of the infrastructure we've been running. There was a workshop on positronium about a week and a half ago.
but we have to figure out if we can actually get the financing. So anybody out there listening who wants to help us, you can, there's a GoFundMe or you can go to our website, which is www.johnbellinstitute.org and there's a link there to the GoFundMe and any support would be of great help to us in the immediate future. So those two things and
and teaching have pretty much taken up all my time.
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The link to the John Bell Institute will be written on screen right now. And I urge you, if you're watching while you'll be seeing it right now on screen as well, click on the link, browse it, donate what you can. If you believe in the cause, it's a great cause. OK, so Professor Modlin, what do you see as the main disagreements? I know there was a bit of a short stories between you two over the email exchanges, quite lengthy emails. If you could summarize for the audience what you believe the main disagreement is between you both. And then, Professor Palmer, I'd like to hear your comments.
Sir, I mean, I think it's actually pretty straightforward. Bell proved a theorem, actually is a theorem, it's a mathematical theorem, and it runs off of some assumptions as any theorem would, and draws some logical consequences from those assumptions. And the net output is a certain inequality
Where it says if your theory obeys these conditions, which I'll get to into in a second, then if you go into a lab and do experiments at far away from each other, ideally at space like separation relativistically, although that's kind of gilding the lily if you just put the labs far enough apart, there's an inequality, Bell's inequality, which if these assumptions hold,
Cannot be violated or anyway cannot be regularly or reliably or predictably violated. I mean, it could be violated by chance, but it's not the kind of thing any theory could predict a violation of. And so for over 50 years now, two things have been happening. One is experimentally.
The thing has been tested because quantum mechanics predicts violations and those violations have been found and they've been found just as quantum mechanics predicts and various experimental loopholes have been tightened up and at this point I don't think there's any actual dispute that in fact the inequality is violated by nature, by reality.
And if that's true, then one of the assumptions that goes into the derivation, of course, has to be false. Now, there are really only two mathematical. There's a lot of confusion about this. People say stuff like, oh, Bell assumes realism, which quite honestly, you don't even know what to make of it. I mean, it's a mathematical theorem. So anything he assumes, there has to be a clear mathematical statement of what it is.
There is no clear mathematical statement of realism or what the external world exists or something like that. It's hard to know even what to say about that. There are two mathematical assumptions that go into the theorem. One is called Bell locality and one is called statistical independence. The dispute is very simple. Bell felt and I feel
and the people I hang around with feel that it's not on the cards for any physical theory that we could possibly have reason to believe to violate statistical independence and therefore you just have to give up on the locality condition.
And we have theories that do that. We have several different theories of very different formulations that do that, that predict these violations. So you see how they predict the violations because they give up on locality. There have been people from the beginning who just really don't want to give up on locality. They just don't, you know, they're very adverse to it. And you're kind of painted into a corner at that point because the only other thing you could do is say, well, I'm going to give up on statistical independence.
And there have been various attempts at least, I mean, you see the logical situation and then the issue comes down to, okay, can you really in any plausible way produce an acceptable physical theory that violates this statistical independence condition? And I still don't think you can. I think, of course, logically it's possible, but I just don't see how it can be done in a way that's methodologically acceptable. And
The other Tim thinks the opposite, right? Wants to keep locality as far as I can tell. This is what Jared Tooft wants to do in his theory. He wants to keep locality in his automaton cellular automaton theory and give up statistical independence. Various people have tried to do that. Um, so that's, that's simply what the dispute is as far as I can tell. Professor Palmer, does that sound about correct? That sounds, uh, totally correct.
So I completely 100% agree with Tim on his summary. Maybe actually I could start by actually commenting on a couple of points where I think Tim and I actually agree, because I don't want this to be entirely a kind of a big fight or something.
And the first point is actually to kind of endorse the John Bell Institute concept, because I personally think, you know, Bell's theorem and what it's telling us about physics is super important. And Bell's theorem deserves, you know, consider and the work of Bell, John Bell in general, deserves
the sort of attention, you know, that a separate institute in Croatia would give. So, you know, I think that's like really good. I'm super happy to see, you know, that that institute. And I just feel, you know, this is a really important question. Personally, I think it's an important question, not perhaps not everyone agrees with this, but I personally think resolving this question is going to be crucial for developing
our theories of quantum gravity or theories that synthesize quantum physics and gravitational physics, because, you know, it is a fact of the matter that the local causality, you know, underpins the theory of relativity, both special and general relativity, the light cone structure of space time is is just kind of fundamental to general relativity. And the fact that it and of course, general relativity is is deterministic. It's
It's geometric, it's nonlinear. It's kind of most of the things that quantum mechanics isn't, you know, Schrodinger equations linear, it's kind of, you know, you're sort of struggling a bit to put a strong geometric interpretation on quantum mechanics. And it's, you know, it's nominally indeterministic, the collapse is sort of seen as an indeterministic problem. And of course, Bell's theorem raises this issue of
the causal structure of quantum mechanics. So I personally think that that kind of understanding Bell's theorem will be a crucial step to satisfactorily quantizing gravity, which we haven't really done. So at least there's no consensus in the community. As a brief aside, you both seem to be nodding at that. So you both are in agreement. Is this a consensus in the foundations of physics? I don't know. No, I kind of sense that it isn't people just kind of gloss over a little bit. I think
Bell's theorem they it's an it's an you know because if you know if you take the standard approaches to quantum gravity which is string theory and loop quantum gravity people just shrug their shoulders and say well Bell's inequality is violated and just kind of that's it but there's no real no real focus going into what that's telling us about physics
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There's no real focus going into what that's telling us about physics. The other thing I would say is I totally agree with Tim to kind of focus on these two issues of locality and so-called statistical independence. If we get time, it's not a phrase I'm actually super keen about because I don't
I think it necessarily says anything about statistics, but that's something we can come to. But in particular, I agree, for example, that issues about, well, realism, as Tim said, and the other one that's often racist, free will or free choice or something like that, is a kind of a bit of a red herring. And actually, this kind of brings me to, well, it kind of brings me to the point where I disagree with Tim, because
I got interested in Bell's, in a quality Bell's theorem back in the 1980s. I did my PhD in general relativity in the late seventies and kind of left the field. And it was actually a chance reading of a big volume that Stephen Hawking had edited on the, I think it was the 400th anniversary of Newton's Mathematica Principia, Principia Mathematica.
Which had an article on bells inequality and I kind of made a mental note to myself. I've got to get I've got to really understand this. I've been kind of putting it off for most of my life. I got to understand it. So that led me. Actually, that led me to read the paper that Tim said nails the argument against what's called super determinism, which is the violation of
Bell's, sorry, the violation of statistical independence. So that was actually one of the very first papers. I've still got my volume of Bell's book, which I bought in... I've got the newer volume. I have the old one too, but it's... But I bought that probably in the early 90s. But anyway, and that was pretty much one of the first papers I read.
The free variables and local causality and what i'd like to do you know what i'd really like to do in this session we have is kind of talk about that paper in particular because i think you know that that is as close as we're going to get to what bell thought about essentially this issue of
If you like the statistical independence assumption, which is, you know, which by the very title of his paper is to do with. What freedom do we have in the laws of physics to change parameters and change variables, you know, from one value to another? I mean, that's kind of the that's the underlying theme of the paper. We'll go into that. And so I think the reason, you know,
The reason I perhaps emailed you originally, Kurt, was that I watched and listened to the original debate with Tim. And I felt that, I mean, I totally agree with Tim that his example of a kind of conspiracy in the lab where, you know, rats are tested for whether they catch cancer or not in a smoky environment, I mean,
Any introduce the concept you could you could sort of, you know, you could. If you wanted to, you could distort the statistics coming out of that experiment in such a way as to kind of invalidate the seemingly obvious result that smoking did increase your likelihood of cancer. Now, I agree with Tim that that would indeed imply a violation of statistical independence in the kind of quantum mechanical context.
But where I disagree is that violations of statistical independence necessarily imply that type of conspiracy. And my view is that, and I'd be, you know, we can talk, in fact, I want to talk about it, that there is a, I think a mathematically rigorous, robust process that would violate
such statistical independence that does not have any connection whatsoever to do with this type of conspiracy. So my claim is that violating statistical impedance does not necessarily imply this kind of gross conspiracy. And I actually think reading, I mean, this is now reading between the lines to some extent, and Tim may disagree. And in a sense, I can't totally defend my position here, but I kind of sense reading John Bell's words
He was actually slightly equivocal about his position. He in the paper, he he kind of outlines what he calls a reasonable or a likely type of situation that that's likely to be the case in physics. But at the end, he kind of says, well, I'm not not actually sure. And I might be wrong about this. So far from sort of nailing it, as I think Tim said in the original interview, I kind of feel
This actually shows John Bell's sort of questioning a little bit what could be a viable process that would actually lead to a violation of statistical independence without implying the type of kind of grotesque conspiracy that Tim correctly raised with his example.
So I can talk a bit more about that, of course, but perhaps I should shut up for a second and we'll come back. To summarize, the disagreement is to whether or not super determinism is conspiratorial. And then number two, what did John Bell mean in his paper? That's right. I have a question about these questions. Why do we care what John meant? It's like exegesis. Oh, what did Wittgenstein mean in the tractatus? Who cares? Let's just talk about the first point, whether super determinism is conspiratorial.
Professor Marlin, why do we care about what Bell meant or didn't mean? The main reason to pay very close attention to whatever Bell wrote was that he was a really clear thinker and a really clear writer.
had extremely good judgment. And so that's the reason to pay attention to anybody doesn't mean that he was a, you know, a god and he didn't, you know, even Homer nods and he can make mistakes. I might say that that Bell's slight equivocation is just a bit of politeness. You know, and as you say, I'm not really sure we're going to get very far trying to get too deep into his head. The real question before us is just
the exact significance of this mathematical assumption that goes into the theorem. And maybe I can kick it off a little bit by saying, I don't think because this comes up a lot, this idea of evaluating counterfactual assertions, what would have happened had something been different, right? What would have happened had
Bob said his detector this way rather than that way. Is there a fact about that? Which, of course, in order for there to be a fact like that, you kind of have to believe you're doing a deterministic situation. If you have an indeterministic physics, fundamentally indeterministic physics, then right off the bat, you're going to say, well, there's no fact about what would have happened had
had things been different. In fact, there's no fact about what would have happened if things had been exactly the same up to a certain point, right? That's what indeterminism is. It says the physics allows you to be exactly the same up to a certain time and then diverge. So there's been a whole lot of literature for decades of people claiming that Bell's theorem tacitly presupposes something called counterfactual definiteness.
Bell clearly denies that, and he's right. I don't think it does. And I don't think that these mathematical conditions really have anything at all to do with counterfactuals. I think they're purely statistical statements about frequencies and that discussing counterfactuals is just off topic.
So if that's true, you know, I mean, it may very well be if we both agree about that, I'm not sure. And then I'm not even sure exactly what we're debating about. My feeling from the interchange is that Tim Palmer thinks that things about counterfactuals and what would have happened and so on are very important to this discussion. I don't think they are. And I'll just kick this off by saying the actual mathematical condition
Has a row in it, right? It has the symbol row that is supposed to be in the mathematical sense of probability measure. But the question is, I mean, you can use probability measures for lots of things for lots of different purposes. And here I think that that row is merely a statistical measure. It's a measure of frequencies.
And that the statistical independence condition is just a claim about frequencies and nothing else and a claim about frequencies, actual frequencies, not counterfactual anything, just actual frequencies. If that's true, then all the talk about counterfactuals just doesn't even shouldn't even come into the discussion as far as I can tell.
So, I mean, I could go into more detail of how I understand that condition, and I guess Tim can go into more detail about how he understands the condition. But I think that would be kind of the crux of it. All right. Would it be okay if I was to summarize and then you tell me if my summarization is approximately correct and fill in any gaps? So, a counterfactual is this large word, which is scary, but it means contrary to fact conditional, which is another large word, but is
Simple it means that there's an if then statement and if your if is contrary to reality, then well, what would it have been like? So is that correct? Yeah. Okay. Now can you give an example in terms of something simple like a pair of glasses or a cup? So I say, uh, you know, here I am holding on to this, to this scissors. I didn't let go of it, but we all believe it is true that had I let go of it a second ago, it would have fallen, right?
That's what would have happened it didn't happen but it would have. Why do you believe that i'll do well whenever i do you know whenever i do drop it does fall and that gives me some word for believing if i had let go of it would fall anyway there's a huge philosophical logical literature on counterfactual conditions.
And it's very complicated, but I don't think it's relevant. So I would, you know, I would prefer not to have to get into the fine details of modal logic, which is really what you're doing there, because I don't think the condition has to do with counterfactual conditionals. Okay. And so Professor Palmer, what is counterfactual definiteness? And then can you please go into what you agree with what Tim Marlin said, or what you disagree with? Well,
I fundamentally disagree, but, you know, we have to be careful about words and maybe, you know, we might mean different things by the same word. So such as counterfactual. I mean, Bell's I mean, look, I do want to I mean, I agree with you. We don't we don't need necessarily to talk about Bell and what he wrote, but it's it's I think it's a useful it's useful to refer to this paper free free variable
Free variables and local causality. And what did Bell, what Bell is saying in that paper, and of course it's the title of the paper, is that how you interpret his theorem, how you interpret the experimental violation of his inequalities, depends on what are the free variables in, in the, in
A putative theory that you have to explain the violation of bell inequalities. So I just want to, I just want to pick up Tim on the example that you had where you dropped or you didn't drop. Let's say that in reality, you didn't drop the scissors and you know, you said, well, okay, I can infer that had I, uh, open my fingers, the scissors would have dropped because
You know if I do that experiment in in you know in 10 seconds time or tomorrow or the next week it will drop. But of course that you're doing the experiment at a different time and as and as Bell said actually in the paper you know the the moons of Jupiter will have changed the position of the clocks of the hand will have changed and you are not actually
You're not actually doing the experiment where the only thing that happened was you chain, you opened your fingers. Now, the point is, the point is, however, that we have, you know, Newton's laws of motion, you know, Newton's theory of gravity. And we can appeal to the theory and say, if I had changed the initial conditions of that pair of scissors in such a way that it was now
You know, no longer constrained by the frictional force of my fingers. I can solve the equations and indeed the scissors would drop to the to the desktop. So you can and in that in that theoretical calculation, you can assume that the moons of Jupiter are the same as they were in the real world where the scissors didn't drop.
So you can just change in your theory that one variable, if you like, which is your whether your fingers are gripping the scissors or not. And your theory will tell you that the scissors will drop if your fingers aren't gripping them. So. So that is a counterfactual. The fact that at that time, when the moons of Jupiter were such as they are,
In reality the scissors didn't drop the appeal to the theory to predict that the scissors would have dropped had the fingers been different is is a counterfactual and it's it's it's supported by the theory of you know Newtonian physics in this case that says yeah the the laws of physics do not
prevent or do not deny or do not contradict a counterfactual world where your fingers release the scissors and the scissors dropped. And really that's the point Bell is making. This is the crucial question. What things can we assume can be changed keeping everything else in the world fixed?
what things can't we? And that's where we come to his famous, and I'd like to discuss it, example where we set a quantum measuring system with a pseudo random number generator. I think this is a really important example. It's a nice example and we should come to that, but let me again just
I mean, I'm gonna allow myself to drift into this for a minute, but I do want to go back and say and insist.
In my view, counterfactual conditions have nothing to do with anything here. As a philosopher who's worked on this stuff, I can't avoid wanting to comment, but I'm a little scared of getting drawn into a dispute that I think is just a red herring. But let me give that. The only theories that would support counterfactuals are deterministic theories. If you want to say, gee, things actually went this way, what if they had been different?
If your theory is fundamentally indeterministic and says, well, if they've been different, there are various ways it could have gone like in a collapse theory in a fundamentally indeterministic collapse theory or something like that, then there's just no fact about what would have happened had things been different. The theory doesn't doesn't pick out a particular physical history that would have occurred under different conditions. Now, what Bell actually says a little bit in another paper
And he's clearly frustrated. He says, oh, people think my theorem presupposes determinism. And he says it doesn't. He says to the limited amount that determinism appears in his original argument, it's a theorem and not a supposition. It follows from certain perfect correlations and the other assumptions.
I would say the same thing. If you have an indeterministic theory, counterfactual definite is not on, but determinism is not required for the theorem. The CHSH form of the inequality makes that absolutely clear. In the case of the scissors, I said
I believe, and we all believe, in fact, had I just let them go, they would have fallen. Why do we believe that? Well, I said, because whenever I let them go, they do fall. And furthermore, I can let them go, as it were, whenever I want. There's no particular pattern to them being let go.
So if someone were to say, no, no, no, no, it really depends on the moons of Jupiter being in such and such a position that the scissors fall. I'm going to say, so wait, you're telling me whenever I happen to let go of my fingers, the moons of Jupiter just happened to be in exactly the right position so that they don't prevent. Oh, okay. Just a moment. So Tim modeling, if you can hear us, I don't know if you can hear, but you've just frozen for the past 20 seconds or so we're going to.
Sorry folks, that new one didn't work either, so now I'm back. I'll just pick that up, I know exactly what I was saying. Quite apart from theory, you could have reasons, everybody would take it to be reasonable to think that
Yeah, the moons of Jupiter have nothing to do with this thing falling when I let go of it. Why? Because it falls whenever I let go of it, irrespective of anything about it. And if you say, no, no, when the moons of Jupiter are just in this form, which they never happen to be when you let go of it, gosh, then the thing would float in the midair. You just wouldn't take that seriously for a second, right?
I mean, you wouldn't take such a thing. You can't say I have empirical evidence against it at the sense that because it's only making weird claims about counterfactual conditions, about what would have happened had things been different. I just want to get away from that. I think that's not the assumption, the assumption. And I do want to insist. Bell uses a certain phrase in this paper. He says, or at least effectively free for the purpose at hand.
Okay, and he insists that that's the careful formulation of the assumption of the theorem, which is that, say, Bob and Alice, who can set their devices in one of two ways each, that that setting is effectively free for the purpose at hand, which means something very different than that they have free will or this or that or even I don't think it has anything to do with
Right. And when he refers to things being free, he's referring to a property of the laws of physics. What he's saying in this paper is if we want to understand, you know, my theorem, this
experimental violation we've got to get down and look carefully at putative theories that may explain the experiments and the crucial the crucial issue will be what are what things can be varied and still satisfy the underlying laws of that theory that is the crucial that's the crux of the matter
That's why he says we cannot repeat an experiment changing just one variable. The hands of the clock will have moved and the moons of Jupiter. This is Bell talking. Physical theories are more amenable in this respect. We can calculate
The consequence of changing free elements in the theory be they only initial conditions and so can explore the causal structure of the theory i insist that my theory is primarily an analysis of certain kinds of physical theory i.e. what are the free variables in that theory so when i talk about counterfactuals i'm just referring to the question or counterfactual definite this is the question. If i have a theory of physics.
Is it justified or is it permitted to change one variable in that theory and with that variation continue to evolve the universe as a physically meaningful construct. So that's really what counterfactual definiteness is.
Can I give you Tim can I guess give you the because I don't want to talk too much in in sort of vague and abstract terms I want to give you the model that occurred to me when I read Bell's paper back in the whenever it was in the late 80s or early 90s because I'd been working in chaos theory you know for many years and
Maybe the viewers will be familiar with Ed Lorenz, Ed Lorenz was a meteorologist from MIT who put forward these amazing three differential equations. What's amazing about them is that they generate a kind of geometry in this three dimensional state space. So the three variables, so the state space is three dimensional. Run the model just for a long time from any old initial condition and you find
the equations trace out this geometry. It took actually quite a few years after Bell, Lorenz's paper for mathematicians to rigorously prove that this geometry was a fractal geometry in the three dimensional Euclidean state space. So the dynamical model that occurred to me was let's just imagine
We have a dynamical, by the way, the whole thing is deterministic. There is no indeterminism anywhere in the equations. It's totally 100% deterministic. Let's imagine we have a dynamical system which is evolving on this. It's called an attractor, strange attractor or fractal attractor. Let's imagine it's evolving on this attractor and we just freeze it. We just take a point on the attractor.
And we're going to write out and the reason for saying this will come to in a minute. We'll write out the values of the three variables at some instant in time where we've kind of frozen the evolution. We'll write the variables out to a million decimal places. Okay. And now let's ask the question. Because this goes to this question of freedom. What is the freedom in this particular dynamical model? What I'm going to ask is.
What would have happened to the future evolution of the state if I change the millionth digit of one of those three variables, keeping the other two variables fixed at what they were? So I'm just going to take a point on the attractor and take one variable, change it by one part in a million. You can make it one part in a billion if you like, doesn't really matter.
keep the other two variables fixed. The question is, how would that state evolve into the future? The thing is that that seemingly tiny, tiny perturbation, keeping the other two variables fixed is enough to take the state off its attractor into one of the gaps in the fractal geometry. There's kind of gaps which go down, you know,
smaller and smaller scales you can prove that that would take you off the attractor so if your dynamical system is defined by the geometry of the attractor then you've taken it to a point where it has the dynamical system is undefined because the dynamical point the points on the attractor are only defined on the attractor you've taken it off the attractor so you've done something to
tiny perturbation which is taking you from a completely deterministic system to a totally just undefined it's an undefined point okay now you could with your you could take that point that perturbed point back onto the attractor by also perturbing the other two variables so you could you know maybe add a little bit to x2 and a little bit to x3
and it would take the point back on the attractor. And then you could indeed say, OK, that point would evolve deterministically on the attractor. But the point is you've had to you've had to add perturbations to the other two variables. You can't keep those two very the other two variables fixed. And that idea really resonated with me when I first thought about it, because I thought this is exactly a counter example
to what Bell thought was a reasonable, you know, his reasonable assumption that we'll come on to this experiment in a minute, perhaps about pseudo random number generators. And he makes a key assumption, which is kind of reasonable, but this dynamical system would actually provide a counter example to that.
So then I got thinking, what would you need to actually scale this up to the universe? And the answer is simple. You just treat the whole universe as a, as a dynamical system evolving on some precisely on some, you know, chaotic attractor. And the interesting thing is there are cosmologies, you know, the famous mix master cosmology, which has, which have chaotic attractors. So this is not completely daft idea, but it provides a,
It provides an example of happy to happy to talk about this in more detail. It provides an example of how statistical independence can be violated without going anywhere near statistics. And I just just before I finish in one second, just just slightly counter the point that Tim Maudlin said. The statistical independence assumption does indeed mathematically refer to a probability
function on hidden variables and so on but that doesn't itself imply anything statistical you know so just to give you an example if i said that two plus two equals four that's not a statistical so nothing to do with statistics if i said that two plus two equals five i mean that's an incorrect statement but also nothing to do with statistics but i can equally say
two plus two equals four with probability one and two plus two equals five with probability zero. So I can easily inject probability distributions or probabilities into what are basically deterministic statements. And I think that is the sense in which this particular model would
Again, I need to start by signposting that I think
Everything I'm about to say is actually irrelevant to the discussion, but a lot of things were brought up and I have some things to say about them. I'll say them, but I hope to bring us back to what I think the main point is. Look, the theory of chaotic systems is very interesting. The theory of systems that have a very, very, very, very, very infinitely maybe sensitivity to initial conditions is very interesting. You don't need
three dimensions. You can do this with a logistical map and essentially one dimension is a standard example that you use and some of these systems have attractors. What does that mean? It means that if you start anywhere, the system will evolve toward the attractor. That's why it's called an attractor. Sometimes you get into a chaotic regime where there are no attractors. Okay, but there are regimes where there are attractors. Of course, you never get to the attractor.
I mean, if you start off it, you never get there. It's just, it's just in the long term, you get ever closer to it. So I don't even understand what it means to say it's probability one, the systems on the attractor systems are not going to be on attractors. They're going to be getting closer to attractors. They're off attractors, right? I mean, the chance of it being on the attractor is in some sense zero.
Um, but it's still at a tractor because the, the, the flow lines tend, tend toward this point. And this is easy to illustrate with these standard examples of the logistical map and so on. But again, this stuff about counterfactuals, I mean, I really want to insist that the statistical independence condition is a condition essentially about statistics. So let me at least say what I say it is, and you'll see that there's nothing about counterfactuals or what would happen or anything in it.
Alice and Bob are in two different labs far away from each other. I make a whole many, many, many pairs of entangled electrons, say in a singlet state, and I send one to Alice and one to Bob. And they collect them in these boxes labeled so they know which goes with which, right? Which of Alice's electrons was paired with which of Bob's electrons. Let's just imagine
that we have created a million of these. So Bob and Alice now have in their control, in their labs, an actual collection of a million electrons. Good. Now we assume that those electrons have some state. Call it lambda. What is lambda? Lambda can be anything you want. I mean, this is, Bell says, lambda just stands for whatever. You know, you make up the theory and tell me what lambda is.
And there will be an actual statistical distribution of the lambda in those million electrons. So maybe there's some characteristic, I don't know, squishiness that some electrons have and some electrons don't.
A certain percentage of Alice's electrons will be squishy, a certain percentage of Bob's electrons will be squishy, nothing to do with counterfactuals, it's just a statistical description of their state. Good. Now, so there's this row of lambda which comes up in this theory and that row, which is a probability measure, is not anything about probability, it's about these statistics. What percentage
What Bob and Alice are going to do is they're going to make selections. Each one is going to decide for each electron in their control whether they're going to send it through a device oriented this way or device oriented that way. It's a binary choice they make.
And when they're done, what they will have done is subdivide this big collection into four small collections, exhaustively. Namely, if we call them, say, measuring X spin and Y spin, the collection where both Bob and Alice have measured X, where Alice has measured X and Bob Y, Alice Y and Bob X and both Ys, right? You know, they're doing two binary choices. You're subdividing each
of the of the collections will now be subdivided into four and the statistical independence assumption is just that row of lambda that is the distribution of every of these characteristics with respect to the whole thing equals or you know it should be a little wiggly thing approximately equals row of each of those sub distributions right that is the set
that both Bob and Alice measure in X has some distribution. The set where Alice measures X and Bob measures Y has some distribution. If they're doing this kind of 50-for-fee, then each of these will have, I don't know, 250,000 members. So each of those subsets has a row. And the statistical independence assumption is just that the rows of the subsets are equal to or approximately very closely equal to
The row of the whole thing. Now, that statement that I just gave you says nothing about counterfactuals. Nothing. It just doesn't say anything about it. It says the statistics of this big set are very close to the statistics of each of the four smaller subsets.
And that's it. Now, why would you think that? Well, because Bob and Alice are just flipping coins. Why would the subset that gets picked out when Alice and Bob's coins come up both heads be fundamentally different than the subset picked out when one comes up heads and one tails? Or they're doing the digits of pi, or they're using a lottery machine, or they're using whatever you like to make that sorting.
You don't want to get stymied by this and there's something else that's the main point.
I see. It's hard to see how they could be because how could the theorem be about counterfactuals? Well, let's hear. So my view is that, Tim, you have described only part of what that we'll call it statistical independence, but I don't think it's a good word because I think that call it whatever you are. Yeah, okay. I mean, some people call it lambda independence, which I sort of prefer.
i just want to sorry before i get into that i just want to just make the point that there is nothing illogical or wrong or any other word you want to use to posit a dynamical system where the states are evolving on the attractor
I mean what you have described say with the logistic map or could be Lorenz's model is what people do in practice which is they start from any old point in state space and run the thing you know for as long as they can and as you say you get closer and closer to the attractor but mathematically you can just say my dynamical system is determined by those differential equations but where points
are on the attractor are on the invariant set i use the word invariant set by the way because once you're on the invariant set you're always on it and you always have been on it so it's just it's a it's a perfectly um you know it's a perfectly found dynamical system and i'm saying that dynamical system uh is pertinent to what we're discussing and this would be a good point to actually bring up the example that bell himself
raised in that paper because I think this makes it quite clear why counterfactuals are important and why Tim is actually focusing on only part of that of that assumption of the row of lambda and yeah row of lambda given the measurement settings is independent of the measurement settings so the example is we could I mean we Tim probably referred it to it
In the last interview, but it's worth going back over it. Bell imagine and he partly did this to to sort of keep humans out of the picture and free will and all that stuff. He said, imagine that Alice and Bob's measurement settings are determined by a pseudo random number generator. So we're taking the human out of it altogether. And
These particular so the pseudo random number generator will set will output a zero or one and that will determine the set the setting and the input is some number you give it and and Bell makes the statement that the that output of zero one is sensitive to the millionth digit of the input number. It could be pie if you like or anything else but the millionth digit is is
is a crucial piece of information in determining whether it's a zero or a one. I mean, maybe the billionth digit is not important, but the millionth is. Oh, can I just stop you here? I don't think that the example, as you say, you want a random sequence, statistically random sequence of zeros and ones. The idea is you, okay, take pi, start at the millionth digit, and then put a zero or one depending on whether it's odd or even.
And then go to the millionth and first, then go to the millionth and second, then go to the millionth and third. So that, uh, uh, the millionth, the parody of the millionth digit completely determines one of the entries. Right. Right. And then has nothing to do essentially with, with the ones that came before or after. So of course the billionth one will come up eventually. Yeah, yeah, yeah, yeah. No, but we're focusing on one particular run of the experiment and the,
You know, the claim is that the output was zero one is dependent on the millionth digit. Now, the crucial the crucial statement that Bell makes is that fixing says a or a prime. This is the this is zero one. This is the output that determines the measurement setting.
Fixing A or A' indeed fixes something about the input, i.e. whether the millionth digit is odd or even. Now this is the crucial statement, but this peculiar piece of information is unlikely to be the vital piece for any distinctively different purpose, i.e. it is otherwise rather useless. So the point is this, that we're doing this experiment in a world where
Moons, to use the example again, the moons are going around Jupiter and various other things are happening. You know, people are going for a walk in the park and stuff is happening. His point, which is a kind of, you know, it's a reasonable point. I'm not saying it's not reasonable, but I'm claiming that in the context of quantum mechanics, it is questionable. But his point is that
all these other things the moons of jupiter the people going for a walk in the park the value of the millionth digits irrelevant they just carry on their lives and of course that's a that's a perfectly that's the sort of thing that you would expect to be true if the world was governed say by newtonian physics because or indeed by most simple dynamical systems because you can
take an initial condition where you know somebody's about to go into the park where the moon is about to take in a particular phase of the orbit keep all that stuff fixed and vary the millionth digit and that's a perfectly reasonable perturbed initial condition and you can carry on solving your newtonian equations with that slightly different initial condition so that is a kind of scientific
statement if you like or scientific justification for Bell's what he calls his reasonable assumption that the millionth digit is is unlikely to be the by the way note the word unlikely not definitely not unlikely to be the vital piece of for any distinctively different purpose. So already there's kind of an implicit
reference to the fact that this millionth digit is a free variable in the sense it can be twiddled it can change you can keep everything else fixed you can just twiddle that thing and the world will will continue but i want to come back to my example where do you see twiddling in this i mean he says
It's unlikely to be the vital piece for any distinctively different purpose, i.e. otherwise rather useless. I take it what he means there is that conditioning on that fact, not asking what would have been the case if it had been different,
But just conditioning on that gives you no information, no useful information about anything else. It'll tell you a very important thing in the physical world. Namely, did Alice pick X or Y in that run? It'll absolutely tell you that important physical fact, but it just won't give you any information. It doesn't really have to do with determinism. It won't change the likelihood that Jupiter's
Moons are in any particular phase. It won't change the likelihood that people are walking in the park. It won't change the likelihood in that or have any effect on anything else in terms of the statistics. But Tim, this is the whole point I'm trying to make. I can and I do claim to have a mathematical model where and it's just a generalization of the example that I
Discussed with Lorenz's attractor where you can't change the millionth digit of one of the variables and keep the others fixed but he doesn't say it doesn't it doesn't it leads you to an advantage doesn't say you can do that.
That's what it says. It's it says it's not a useful piece of information for any distinctive other thing really different purpose. In other words, if you change that information, you know, I'm trying to keep saying in other words, but he doesn't talk about changing it. He just says it's not useful information for any other purpose.
The whole paper is about free variables and a free variable is something that you can change in your theory. That's the whole basis of the paper. Free. What does free mean? If it doesn't mean you can't change it, then it has no meaning. Can you tell us what's meant by or what you interpret as being meant by effectively free for the purposes at hand, at least in terms of subdivisions? Effectively free for the purpose at hand means precisely that making choices
subdividing your ensemble on the basis of those things will give you sub ensembles that are statistically similar. Let me just reread the paragraph. Row of lambda equals row of lambda conditioned on A and B. There's nothing about counterfactuals in that claim. Tim, let me just reread this. Just a moment, just a moment. Please reread, yes. We're kind of, I don't want to sort of like say I'm
What Bell says is, in that previous quote, we cannot repeat an experiment changing, note the word changing, just one variable, the hands of the clock will have moved and the moons of Jupiter. Physical theories are more amenable in this respect. We can calculate the consequence of changing free variables in a theory, be they only initial conditions. So he is talking about
Is it reasonable to, to assume that if I changed the parity of that millionth digit, the rest of the world would just carry on functioning as if nothing had happened. And I'm claiming I have a perfectly mathematically rigorous, you know, theory. I don't know whether it's correct or not, but it's a, it's a candidate theory where that assumption is false. That assumption is incorrect. Yeah.
Look, we're at cross purposes here. We could go into fine analysis of the pros, but at the end of the day, it's a mathematical theorem. It follows from certain mathematical assumptions. And the relevant mathematical assumption is what I said, that rho of lambda equals rho of lambda conditioned on any collection of the settings that you like, right?
role of lambda equals role of lambda conditioned on Alice and Bob Joe both choosing X or Alice choosing X and Bob choosing Y. That is the mathematical condition that's used to derive the inequality. And that condition says nothing about counterfactuals. Okay. I agree with your mathematical statement of the condition. I disagree with your interpretation of it.
And I'll just give you how I see the violation of statistical independence applying to that chaos model that I described. Rho, we have some lambda, we have some factor of the matter where Alice and Bob measure the spin of particles with their measurement settings.
oriented in a certain way so by construction that that occurred we can assign it a probability of one we can normalize it by some factor if you want to but essentially that occurred in reality that's a probability of one my claim would be that therefore that the real world this is an manifestation of the real world evolving on the on the attractor now what i want to in testing the statistical
independence assumption i want to ask the question what is that probability is it one or is it zero so this is a very deterministic approach to probability when i keep lambda fixed but i change let's say either alice or bob's measurement setting from a b to a b prime or something like that and i would claim that this model can under certain circumstances
Return the value zero for probability in other words. When you change and bells paper is about changing things when you change Bob setting from B to B prime say keep Alice's fixed today and keep lambda fixed then when that state if that state gets perturbed off this attractor the probability goes from one to zero.
And your measurements, your your lambda independence or your statistical independence is violated. So it's a counterfactual world where you varied B to B prime and. Your theory says that's that's an undefined state.
So I violated so-called statistical independence. I violated that mathematical condition, but it's got nothing to do with statistics. It's got nothing to do with your million particles. It's one particular pair of particles. So, so yeah, I mean, look, we don't agree about what the mathematically the theorems about that. That's just that simple word. I mean, it's not, you can't test Bell's inequality with a single pair. It makes it, it's only an inequality that can be tested statistically.
You have to do experiments on many, many, many, many pairs. And the condition is that the sub-ensemble that are subjected to this test condition and the sub-ensemble that's subjected to a different test condition and so on, that those sub-ensembles are all statistically similar to one another.
And that's just not a claim about what would have happened had you made a different. I mean, let me go to the Brad example, just to make sure everybody listening is following this. Right. So I know you think this is a bad analogy, but let me at least. No, I don't think it's a bad analogy. Okay. What I'm saying is it only tests part.
This is for the audience. You're interested in a question like, does smoking cause cancer? We all know that correlation is not causation. That is, you can have correlations between things where there's no direct causal connection between them. Yes, smoking is correlated with getting cancer, but having ashtrays in your house is also correlated with getting cancer.
But not because the ashtrays are dangerous, right? Because that's due to a common cause. And the way you try and tease out the causal connections, the gold standard experimentally is to do a randomized controlled trial where you take a set of test subjects and this is essentially statistical. You need many, many test subjects. You know, I need a thousand, a million, you know, 10,000 rats. And you then
Randomly sort them, as we say, into the experimental and control group. You treat the two groups the same except with respect to the condition you're worried about, like subjecting them to smoke, and then you see whether you get more cancer in one group rather than the other. Now, why do you do that? Well, you say, I don't know what causes cancer. I mean, maybe cancer can be caused by genetic defects, cancer being caused by whatever. Maybe there's stuff I have no idea. This is not about a theory. I don't even know what causes cancer.
Suppose there's some unknown X factor that will make a rat more likely to have cancer. And suppose 8% of the rats have it. The assumption is, well, because I randomly sorted them into two groups, if 8% of the big group has it, then about 8% of each of the subgroups will have it. Why? Because my sorting was random, because my sorting was something like I sorted them on the parity of the digits of pi, right?
I mean, why would sorting on the parity of the digits of pi tend to push the ones with X factor this way rather than that way? That's the logic of random controlled experiments, that the randomness, and this is where the freedom comes in, or effectively free for the purposes at hand, the physical randomizing, I mean, Bell talks about physical randomizing devices like auto balls that are bouncing around.
What are they for? They're for producing random sequences. And then you use those random sequences to sort the things, and as a result, you're highly confident that the groups that they get sorted into are statistically like each other, even in respects you have no nothing about, even in respects you have no theory about.
Even with respect to this X factor that we don't have a clue about, still whatever percentage have the X factor in the control group will have the X factor in the experimental group. So it's a very important assumption for experimental science on statistics. And as I said, mathematically, that is the mathematical assumption of the theory. Now, I mean, Tim keeps saying that's only part of the assumption, but I kind of don't understand because it's a mathematical claim and it says this row
is equal to the row conditioned on the choices that are made that's just what it is to say there's more to it mathematically there's no more to it well is it okay um there is tim and um i mean your your example certainly violates um statistical independence
and you know if that if that was the way if there was some conspiracy like that that was needed to um to somehow you know uh understand bell serum i i'd be with you this is this is this is crazy i mean nobody would would postulate that but my claim is that you don't you can't go in the other direction that
Violating the statistical independence condition, what we call statistical independence, does not imply that the statistics of Bell experiments are somehow skewed in a conspiratorial way. And I tried to give this example, I mean, and it's very close to the example that Bell talks about in that paper. This is why we're having this
conversation is because my reading of that paper was just so completely different to yours this is why i felt i've got to come on and say i don't agree that because bell never talks about in that paper he doesn't talk about statistics of uh of anything he's talking about one particular run of the experiment where the measurement setting has been determined by the millionth digit and the claim is that
That millionth digit is unlikely to be the vital piece for any distinctively different purpose. And I would say in the light of all the previous discussion in the paper about the fact that the whole theorem is about whether certain variables can be changed, you know, is permitted to change variables. What he's basically saying is it seems reasonable that we could change that millionth digit without affecting anything else in the world. And
I'm claiming that there's based on geometric theories of chaos. There are models where that idea is wrong and the way that impacts on the statistical independence assumption is just something which has probability one when you're on the attractor.
suddenly goes to probability of zero when you're off the attractor so it's nothing to do with the statistics of many many many particles it's about one particular you know you take one at a time particle and that's of course you know that is that is a crucial um if you go through the the proof of of bell's theorem you know you have you have your some deterministic function which outputs spin
Given a lambda and a measurement setting, you have all the different possible measurement settings, zero, one, so on, and then you integrate over lambda. And if your theory says actually no, this variation that you've done of the measurement setting, keeping lambda fixed,
This hypothetical measurement setting that you didn't actually do, but you might have done that violates the conditions of your theory. Then you can't derive Bell's inequality and you can't derive it because you violated this. You violated statistical independence, but nothing to do with statistics. Why statistical independence is not a good phrase in my view. Well, OK, so I think I'm not sure if we're going to. I mean, I'll just cite a passage.
Because, as I said, the theorem is a mathematical theorem. So if you want to say, there's such and such an assumption made, you have to point to where that shows up in the mathematics. Now, Bell, on the first page of free variables and local causality, gives the assumption, which is he has this V, which is, I would say, a statistical claim about
Distribution of hidden variables conditioned on and then a, b, c, a prime, b, c prime, the v conditioned on all these different things is the same. And what does he say about it? He says, for me, this means that the values of such variables, that is the settings of the instruments, this is explaining the phrase, it has been assumed that the settings of instruments are in some sense free variables. Let's see if it has anything to do with counterfactuals.
For me, this means that the values of such variables have implications only for their future light cones. They are in no sense a record of and do not give information about what has gone before. Now, I mean, let's just pause for a second. If you're making these settings on the on the parodies of the digits of pi, starting with the millionth digit, that obviously is not a record of nor does it give any information about anything that's gone before.
Because it's fixed by pi. That's a thing that can't be changed independently of the physical history of the universe. Whether Alice set her device this way or that way, if it depends on whether the millionth digit of pi is even or odd, that obviously gives no information about anything that came before.
In particular, they have no implications for the hidden variables V and the overlap of the backlight cones, and then he gives this condition. Now, I have to certainly say it is not true that this theorem mathematically assumes that the function from lambda and the settings to the outcome is deterministic. It doesn't. And the CHSH version of it explicitly doesn't.
In the particular case of singlet electrons where you have perfect correlations, perfect correlations. So if I check the Z spin in the same direction, they're always anti-correlated. Then Bell says, well, the only thing that could get that right in a local theory would be a deterministic theory, because if it was indeterministic in a local theory,
Then, of course, on this side it could come out either way, and in a local theory that can't have any influence on the other side, so there's no way it could guarantee these perfect correlations. But the inequality doesn't require perfect correlations. The inequality, the CHSH version, assumes no perfect correlations. There are still statistical restrictions on local theories.
So the talk about determinism just that that's that it and this is a bit dangerous because many people thought that Bell assumed determinism. And then they thought, well, I can get out of Bell's theorem just by saying the world's not deterministic. And that's if it was that simple, it would be no big deal. It's not true. Well, I mean, this is this is tangential. I mean, I'm not I'm assuming
For simplicity, determinism, but the future is is entirely there's nothing in deterministic about the model. You know, I mentioned Lorenz's equations. They are 100% deterministic. If you given an initial state, you can determine the future state by the equations or the equations determine the future state. So I don't want to, you know, just bringing in concepts of indeterminism here seems to just muddy the waters because we're not talking about indeterminism. I don't think.
What I'm talking about is the notion that variables that you might think are free, and I come back to that millionth digit, the assumption is that it's a free variable in the sense that it has no bearing on anything else in the world, can be questioned. And it can be false in the sense that changing that millionth digit
Can produce a state of the world which is just inconsistent with your deterministic laws of physics and the fractal attractor example I think illustrates that perfectly change the millions digit of one of the three Lorentz variables keep the other two fixed you moving off the attractor. And that is a violation of statistical independence because you've taken a row equals one situation on the attractor to a row equals zero situation off the attractor.
I think we see what the disagreement is here. For me, these rows are essentially statistical information about collectives. You have to do experiments on collectives to test this theory and they're about
the distributions of sub ensembles within a large ensemble. To me, that's just what it says. Now, Tim thinks it says something else. I'm not sure how we can. I mean, it seems to me we're just repeating these two sides at this point. I don't think we're making any contact and I'm not sure how we could usefully go on. I can say, as I've said before, I don't see how you look at the mathematical condition.
and say, gee, here's a claim about counterfactuals or what would happen if that's implicit in the mathematical condition. I would just like to see it pointed out. Well, because medical condition is that this row equals that row equals that row equals that row. Right. But if row if you in this model that I have, if you have the real world, the real world happens once.
A particular hidden variable, a particular run of the experiment has a particular hidden variable. Alice and Bob measure with a particular set of settings. So if you've got a good theory, it better describe that situation. So it better assign a probability that's non-zero to rho of lambda given what Alice and Bob actually measured.
Because that's just a fact of the world, right? So that row is non zero of row of lambda. I don't know what that means. The measurement, the probability of row of land. Oh, sorry. The row of lambda given, let's say, let's say Alice measured zero in the zero direction and Bob measured in the zero direction for a particular lambda, then row of lambda given zero, zero, given the zero zero setting.
Better be non-zero. If you've got a theory of physics which describes what happens in the real world, then it better give a row that's non-zero. So that row of lambda given zero zero. Yeah, we're just at a point of mutual incomprehensibility. Since I think of these rows as describing actual statistical distributions, actual statistical distributions,
Right, but let's say on a single run, there's no distribution. I mean, there's a trivial distribution. The probability is one. If you haven't, that's why you don't care about that. That's why you have to look at if take take a million runs, the the for a particular, uh, let's say the distribution is is uniform on those million lambdas, then the over that distribution, the probability is like one over a million.
Right, because you did a million runs. You mean one over a million. No, I'm not. I'm not. I'm sorry. I'm just not interested. So in the example of rats, I said there's this X factor, 8% of the total population of the rats have it. So probably about 8% of the subpopulations do. Now, if your subpopulations are only one rat, then of course it can't be 8%. That doesn't make any sense. You know, your chosen subpopulations have to be pretty big.
So when you say go down to a single case, I mean, the way I'm understanding this, the rows make no sense. Yes, well, I'm just saying if you go down essentially claims about statistics, actual statistical distribution. Professor Palmer, can you frame this in terms of ensembles? Well, I if you like, I thought I was trying to do you can imagine a uniform distribution of of on on your ensemble of lambdas. And then for any particular, let's say you have a million,
Then the row for a particular lambda and a particular pair of measurement settings, zero zero, will be one over a million. That will be a kind of a normalized probability on your ensemble. The point is it's non zero. I don't care whether it's one over a million or one over one or one over 10 or any number you like, as long as that's not zero. What I'm saying is if you have a theory
Which has certain conditions, mathematically defined conditions, like being on your attractor. I couldn't name other types of theories where you take a particular lambda. Okay, whether in the real world, the zero zero measurement was made and you say, what is the value of that row for that lambda, keeping that lambda fixed when
I replace zero zero by say zero one. What do you mean by keeping lambda fixed? Sorry? I don't see what you mean by lambda. I mean if lambda is fixed then you know the relevant row is a point distribution. I've got a million, sorry I'm getting confused, I've got a million values of lambda I'm just going to put a
Maybe it would be easier if you use just four values of lambda than a million. Suppose whenever they produce these pairs of electrons in the singlet state, which according to standard quantum mechanics,
every pair is physically absolutely identical to every other pair so there's no you know every the the distribution is a hundred percent singlet state right that's that's what row is some of these pairs are different than others we're unaware of and they're
The lambdas will be different on each. But you mean they'll be unique to every single. Let's make them. You can't say anything general at all. No two pairs. No two pairs of electrons have any physical similarity to any other pair. Is that what you're suggesting? I'm saying that there's no reason that they should not have distinct lambdas. I mean you and I
share lots of similarities. We have two eyes and a nose and all the rest of it, but our DNA is different, is unique. Each of us has unique DNA, so I don't see what's the big deal about that. Each electron pair has a different lambda. Why not? It's no big deal. It would be awfully odd if that were true, that there would be any reliable statistical predictions that could come out of such a theory.
I don't see why it should be. I mean, you just draw lambdas from a distribution such that each one is unique. But they're all going to behave differently. I mean, I don't understand how you would... I mean, the reason why we can say a certain percentage of human beings have typo blood is because actually their DNA is exactly similar in that respect.
But it's not. I mean, it's similar in terms of what determines their blood type. Right. But it's but each of our DNA, all the people who have typo blood have the same genes for typo DNA is unique. So sorry, Professor Palmer, please. So what I want to do is take one of these lambdas and change what actually happened zero zero to something that might have happened, but didn't happen, say zero one. And I'm going to ask my theory
What right? What row am I going to? What row does my theory predict for that counterfactual measurement setting zero one? And what I'm saying is there are situations where that returns the identical value of zero. So that's a violation of statistical independence, which has got nothing whatsoever to do with statistics of anything. It's just it's just. It's just a statement that one
that with a measurement setting that occurred in reality if i vary the measurement setting to something that let's say might have happened that didn't happen my theory says that that counterfactual violates certain conditions in the theory and therefore returns a row that's identically zero so we you know we can normalize the rows of the actual experiment it can be one over four or one over million doesn't really matter but it's not zero
But the theory returns a value of zero. And what I'm saying is that I think that is the type of thing that was at the back of Bell's mind, you know, when he wrote that paper, because he wasn't talking about statistical similarities between sub ensembles. He was asking this question, does the millionth digit matter for any distinct distinctively different purpose? That was the key point of his paper.
Okay. How do you all feel progress can be made if there's such a large interpretive differences at the bedrock? Right. Okay. So I, again, I think we're, I think we've reached the point I predicted at the beginning. I said, I think counterfactuals have nothing to do with this. It's a red herring. I didn't want to get too much into counterfactuals because I understand what the condition is as a purely statistical condition about the actual statistics of actual ensembles and actual sub ensembles that are defined by the
choice of measurement setting, that statement just doesn't have to do with what would have
particular piece of information is otherwise rather useless. The way I read that is he says, well, that's a really important piece of information if you want to know what Alice chose. That'll tell you what Alice chose. Why? Because she was choosing on the basis of the output of this algorithm and that particular output determined on the nth run, whether she chose this way or that way. But he says for any other distinctive purpose, it's a rather useless piece of information.
I don't hear any counterfactuals in that. I don't hear any claims about... I don't even know how to evaluate the claim. What would the world have been like if the millionth digit of Pi had a different parity than it actually has, right? That's a counter-mathematical. I don't even know how to make sense of it. I don't think it has to do with what Bell has in mind when he says this information is not useful for any other purpose. But we're just now going back and forth over the same territory, and I just don't think we're making any progress here. So I guess I feel like I've stated
okay i think i think people can go look at the theorem they can look at mathematics they can look at the mathematical condition and see what they see in it right i just going to finish i mean we can finish but let me just reread you know what bell wrote he wrote we can calculate the consequences of changing free elements of a theory be they only initial conditions
And so can explore the causal structure of the theory. I insist that be his beables paper is primarily an analysis of certain kinds of physical theory. Now, why would he have written that if the central point wasn't about whether your physical theory had had three elements that could be changed? He uses the word change is clearly your ability to change
variables in your putative physical theory is central to Bell's theorem and that's what he says and and I'm just coming up with a model where what might seem reasonable actually turns out to be wrong and I think that model can be a useful way of understanding Bell's the violation of Bell's inequality without having to resort to non-locality which is very anti-relativistic and so difficult therefore to
I hope one day, Tim, you'll invite me to Croatia. It sounds like a fantastic institute. I'd love to spend a few days with you chatting over a glass of wine and, you know, a wonderful wine here.
I'm sure it's great wine, great local wine. I'm sure it's absolutely wonderful. So, um, yeah, who knows? All right. Well, thank you all. And again, if you have any thoughts afterward and you're like, you know what? I think that we can make some ground, some headway. Actually, can I, can I just make a tangent? I'm not going, I promise I'm not going to go back to the, to what we've just been fighting over. Sure. But there is a kind of conceptual point I would like to make. Um,
That is, Tim ended up saying, look, this non-locality really doesn't seem to be consistent with relativity. And yeah, that's right. I mean, that's why Einstein hated standard quantum mechanics, the spooky action at a distance. He hated it from the beginning. He hated wave collapse because it seemed to be instantaneous. Absolutely. But I do think it's worth pointing out that
Special relativity was developed by reflecting on classical Maxwellian electrodynamics, which is a local theory and could not violate Bell's inequality. And general relativity was developed by taking that and then trying to make it give back to good approximation Newtonian gravitational phenomena. And that's also a local theory and could not violate Bell's inequality. Well, if we let the gravity go at the speed of light,
So GR and SR were perfectly good reactions to what Einstein had before him. But what he had before him were theories that could not violate Bell's inequality. That is that he had theories that could perfectly well be local. And it seems to me that
The question is how do you react when you find out there is this thing Bell's inequality and it is in fact violated and that would have shocked Einstein to his core. But it does seem to me a reasonable thing is to reassess and say, well, what if I could give you a theory?
That isn't relativity, but does give relativity to good approximation or relativistic structures. Let me put it this way. Relativistic structures are in it or emerge from it either to very good approximation or even precisely. But they have more than general relativity. They have more structures, say they have a preferred foliation.
Is it unreasonable to say, well, why do you want this preferred foliation? The answer is, well, if you give me that, I can easily write down dynamics that will violate Bell's inequality. And I don't have to violate statistical independence or anything else. This can be done. It's kind of easy to do. It just seems to me that the goal of maintaining relativity as the last word in space-time structure
I don't understand because those theories were developed in ignorance of violations of Bell's inequality and they were developed in a setting where there was no pressure to be able to violate Bell's inequality at space like separation because nobody knew you could. So I think physicists do have this deep attachment to relativity. It's a beautiful theory. GR is a beautiful theory.
Unlike quantum mechanics, it's an understandable theory. The more you work with it, the better you understand it. You work out all these models and you see what's going on. I have a deep aesthetic appreciation for it, but it just seems like trying to work violations of Bell's inequality into it, there's a really
I don't want to
You know, I mean, good on you and good luck with your theory. But I just want to respond to that. The general point. I mean, Maxwell's equations are basically linear equations, so they wouldn't they wouldn't exhibit any of the sorts of things that I've been talking about. So, you know, you can run you can run Maxwell's equations from a slightly perturbed initial condition and you'll get a another perfectly good solution of Maxwell's equations.
So there's no way Maxwell's equations would ever violate this notion of counterfactual definiteness or what I would call violate statistical independence. But GR is actually a different kettle of fish because it is nonlinear. And as I think I mentioned earlier, you can, Misner did this years ago, concoct cosmologies, which are chaotic and
You can envisage a situation where you have a cosmological solution of GR, which exhibits the kind of fractal invariant set structure. So then the question of counterfactual definiteness really is relevant in this scenario because you can perturb off the invariant set of something like the Mixmaster universe and
I mean, if you were going slightly beyond what we're discussing, but this for me,
brings into focus what I think is the real message behind Bell's theorem. And I think it's a really profound one. And it's not to do with non-locality, but it's to do with the kind of holistic structure in the laws of physics that we don't have at the moment, for example, in the standard model. Because if this idea about, you know, fractal attractors and stuff, geometry of these attractors is right, these are very holistic structures. These are not things that you'll see by just looking at the Planck scale.
You'll only see them by looking at the structure of the universe as a whole. So this may be telling us that the whole kind of direction that physics is contemporary theoretical physics is trying to go by just kind of going down to smaller and smaller scales, hopefully to the plank scale. So people say this is probably not going to solve our quantum gravity problems. That's my view. And that's what that for me is the big message behind behind Bell's theorem.
Thank you all for being so generous with your time. The book that Tim Palmer has written is a great
Popular science book on the subjects that we've just spoken about is called The Primacy of Doubt. The links to that will be in the description. The links to the John Bell Institute, especially the GoFundMe, because there isn't a place to go. Well, there's a place we don't own it. OK, there's a place they would like to own it. There's a place and we built stuff here, but we don't own it. And so if we if we can't buy it, we're going to lose everything we've put into it.
Thanks for having us. Thank you very much. Thank you.
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▶ View Full JSON Data (Word-Level Timestamps)
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"text": " Tim, the whole paper is about free variables and a free variable is something that you can change in your theory. That's the whole basis of the paper. Free. What does free mean? If it doesn't mean you can't change it, then it has no meaning."
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"text": " Welcome to Theories of Everything. My name is Kurt Jaimungal, and on the Toe Podcast, we explore theoretical physics, philosophy, and mathematics. In this episode, we have a theolocution with Tim Modellin and Tim Palmer, exploring Bell's theorem, and more importantly, the assumptions that go into that theorem. At times, it felt like the New Testament, like"
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"text": " Well, what does Bell say? Chapter two, verse four. So interpretations are bound and there's definitely room for a part two, especially with a blackboard, perhaps even filmed in person. So if you have questions or comments, please leave it below. Tim Palmer is a Royal Society research professor in the Department of Physics at Oxford. His PhD was in general relativity and he retains a strong interest in fundamental physics."
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"text": " He's also an expert on climate physics and chaos theory, writing a popular book called The Primacy of Doubt, exploring the science of uncertainty in areas as diverse as the climate, economic forecasting, and quantum physics. He's a fellow at the Royal Society and an international member of the U.S. National Academy of Sciences. Tim Modelin is a professor of philosophy at New York University, specializing in the philosophy of physics."
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"text": " He's penned several influential books, including Quantum Nonlocality and Relativity, as well as The Metaphysics Within Physics, simplifying Abstruse concepts for a broad audience. He's also the founder of the John Bell Institute, of which there's a GoFundMe in the description. As usual, every link, everything that's mentioned is in the description. Tim Modellin has been on before. The Theories of Everything podcast is in fact one of our most popular episodes where we discuss Bell's theorem, the philosophy of physics, and what concepts"
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"text": " All right, before we get started, there's a few pieces of terminology that may not be familiar to everyone and they're not expanded on in the podcast itself, primarily so we can just get to the meat of the discussion. But here's a recap in case you're interested. And if you know these terms, then feel free to skip"
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"text": " forward to the timestamp that's outlined either in the description or over here. So the terms are super determinism, a mix master universe, fractal cosmology, and an attractor. Super determinism is a class of quantum theories. It's not a single interpretation of quantum mechanics. In fact, it's not an interpretation at all. It's a class of quantum theories put forward by Gerard Tuft that don't have what's called statistical independence. So what is statistical independence? Well, it's one of the assumptions that go into Bell's theorem, at least that's"
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"text": " What is debated on today so much of the episode is on what is the definition of statistical independence the second terminology is mix master universe what is that well it's a solution to general relativity where the universe undergoes chaotic and turbulent transformations it was originally put forward to solve a problem that inflation ended up also solving and people seem to prefer inflation so you don't hear about the mix master universe."
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"text": " Then there's fractal cosmology which says that the large scale cosmological structures are fractal like in their distribution now fractals don't always mean self similar though they do have infinite detail what it technically means is that there's one definition of dimension that we are."
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"text": " Commonly told and then there's another definition of dimension and when these don't coincide and you have a fractal so ordinarily you've heard of RN so the real numbers to the end for instance we have three space so are to the three or four if we include time."
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"text": " That's called the topological dimension. There's another definition of dimension called Hausdorff, and ordinarily these coincide for the objects that we think about, but sometimes they don't, and when they don't, specifically when one exceeds the other, that's called a fractal. Now attractors are used in chaos theory, and those describe the long term, long term in terms of time, dynamics of the system."
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"text": " So that is, if you were to leave a system for a while, where does it tend to? Are there certain states or even trajectories that it moves toward? Now, there's a precise definition of what it means for there to be a long time, quote unquote, because that's vague. Also, it's vague to say tend to. So there's a mathematical definition of that as well. OK, so an example would be if there's a ball and it rolls down the hill like a U shaped hill, it will settle at the bottom. That bottom place would be called an attractor. And I don't like these"
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"text": " Ball and hill analogies, because they're overused in my estimation for physics, like the Mexican hat you show. Oh, there's a ball and it rolls down the hill. Or harmonic oscillator can be like a ball that just continually swings on the hill. Anyhow, attractor is used not in those scenarios, although that's technically an attractor. It's just generally used in chaos theory. Chaos theory is whenever you have a system where if you were to tweak it a tiny amount,"
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"text": " Then later, the future evolution deviates a large amount. So usually we have an input that if we were to tweak slightly in the input, the output is tweaked slightly. When that fails to be the case, it's chaotic. Okay, with those definitions out of the way, enjoy this Theolocution with Tim Palmer and Tim Modlin. Okay, professors, thank you. Welcome. It's an honor to speak with you for the first time, Tim Palmer and Tim Modlin. Welcome back."
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"text": " For the viewers, both of you are named Tim, so I'm going to be referring to you all as Professor Modlin and Professor Palmer when appropriate. Why don't we get started with Professor Palmer? What have you been working on in the past few months and what excites you about it? Okay, it's a kind of difficult question because I split my time between two quite different"
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"text": " areas. So on the one hand I do a lot of work in climate physics and right now actually I'm preparing, I'm flying off to Berlin on Sunday for what I hope will be a really landmark meeting in climate physics. We're pushing for what I've been calling a CERN for climate change, so a kind of an"
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"text": " the type of modeling that we need to understand climate change at a much more detailed level than we can currently do, than we can currently have knowledge about by working internationally and creating international institutes. So the last month or so I've been preparing a kind of keynote talk on this, putting together some of the sort of scientific"
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"text": " Reasons why we need to work on climate change internationally. So I know that's not the topic for today. So I just wanted, but I want to just tell you about that because in a sense, I mean, what we will be talking about today is perhaps bringing ideas from fields like nonlinear dynamics, which plays a big role in climate change into, into quantum physics. So the other kind of half of my time is indeed on kind of fundamental physics. My PhD many years ago now was in general relativity."
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"text": " I gave a talk a couple of weeks ago to the theoretical physics department on something I'm now calling rational quantum mechanics."
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"text": " and the word rational is deliberately sort of ambiguous because it's an attempt to make some of the things like Bell's theorem which are traditionally viewed as kind of weird and incomprehensible more comprehensible but deliberately also using the other word rational which is that of in mathematics rational numbers are numbers which you know can be written as fractions like five over"
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"text": " The thing which people perhaps don't know about quantum mechanics unless you work in that area is that the continuum actually plays a vital role in the theory of quantum mechanics through what are called Hilbert spaces. So a Hilbert space is a vector space over a field of complex numbers and complex numbers are continuum is a continuum field. So despite the fact that we think of quantum as a sort of a discrete jump,"
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"text": " Continuum mathematics plays a key role in quantum mechanics. And my personal belief is that that is one of its problem areas. It's its strength in some respects, but it's also its problem. It's a problem in it creates it creates many of the interpretational problems that we have. So I've been developing a mathematical model where we sort of relax that"
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"text": " The idea is to see what that brings to the table, and I would argue it brings some pretty big, from a least conceptual point of view, pretty big consequences. So those are two different things, quite polar opposites in many respects, but that's what makes science fun, doing different stuff."
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"text": " Great. Now, Professor Modlin, what have you been working on in the past few months, maybe even a year, and why does it ignite you? Well, this is going to be kind of ironic, the pair of things I'll mention. Maybe I'll do them in opposite order. That is first the theoretical thing. But, you know, this is not measured in the scale of months or even years. This is something I've been working on for several years, maybe a decade."
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"text": " Which also has to do actually with getting rid of continuum, which is to develop theories of discrete spacetimes and to see how that changes the mathematical situation and whether you can get relativistic looking structures to emerge in a natural way from discrete underlying structures and so on. And that's kind of, I mean, I've had some very interesting results. I sort of got in two plus one dimensions, I got Minkowski spacetime to sort of drop out"
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"text": " without expecting it all of a sudden from a very, very, very different foundational picture. But that's been going on for years and years and years. What I've actually been spending my real time on recently is also institutional. That is, I'm sitting here right now in Croatia at the hopefully future home of the John Bell Institute. And what we're trying to do is set up a"
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"text": " a physical location to have workshops and summer schools on foundations of physics. And we're now at the point where we either fish or cut bait in terms of acquiring this location. We've built a lecture hall. We've built a lot of the infrastructure we've been running. There was a workshop on positronium about a week and a half ago."
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"text": " but we have to figure out if we can actually get the financing. So anybody out there listening who wants to help us, you can, there's a GoFundMe or you can go to our website, which is www.johnbellinstitute.org and there's a link there to the GoFundMe and any support would be of great help to us in the immediate future. So those two things and"
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"text": " and teaching have pretty much taken up all my time."
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"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."
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"text": " The link to the John Bell Institute will be written on screen right now. And I urge you, if you're watching while you'll be seeing it right now on screen as well, click on the link, browse it, donate what you can. If you believe in the cause, it's a great cause. OK, so Professor Modlin, what do you see as the main disagreements? I know there was a bit of a short stories between you two over the email exchanges, quite lengthy emails. If you could summarize for the audience what you believe the main disagreement is between you both. And then, Professor Palmer, I'd like to hear your comments."
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"text": " Sir, I mean, I think it's actually pretty straightforward. Bell proved a theorem, actually is a theorem, it's a mathematical theorem, and it runs off of some assumptions as any theorem would, and draws some logical consequences from those assumptions. And the net output is a certain inequality"
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"text": " Where it says if your theory obeys these conditions, which I'll get to into in a second, then if you go into a lab and do experiments at far away from each other, ideally at space like separation relativistically, although that's kind of gilding the lily if you just put the labs far enough apart, there's an inequality, Bell's inequality, which if these assumptions hold,"
},
{
"end_time": 841.237,
"index": 33,
"start_time": 819.735,
"text": " Cannot be violated or anyway cannot be regularly or reliably or predictably violated. I mean, it could be violated by chance, but it's not the kind of thing any theory could predict a violation of. And so for over 50 years now, two things have been happening. One is experimentally."
},
{
"end_time": 863.712,
"index": 34,
"start_time": 842.005,
"text": " The thing has been tested because quantum mechanics predicts violations and those violations have been found and they've been found just as quantum mechanics predicts and various experimental loopholes have been tightened up and at this point I don't think there's any actual dispute that in fact the inequality is violated by nature, by reality."
},
{
"end_time": 892.824,
"index": 35,
"start_time": 865.196,
"text": " And if that's true, then one of the assumptions that goes into the derivation, of course, has to be false. Now, there are really only two mathematical. There's a lot of confusion about this. People say stuff like, oh, Bell assumes realism, which quite honestly, you don't even know what to make of it. I mean, it's a mathematical theorem. So anything he assumes, there has to be a clear mathematical statement of what it is."
},
{
"end_time": 917.534,
"index": 36,
"start_time": 893.183,
"text": " There is no clear mathematical statement of realism or what the external world exists or something like that. It's hard to know even what to say about that. There are two mathematical assumptions that go into the theorem. One is called Bell locality and one is called statistical independence. The dispute is very simple. Bell felt and I feel"
},
{
"end_time": 938.729,
"index": 37,
"start_time": 918.046,
"text": " and the people I hang around with feel that it's not on the cards for any physical theory that we could possibly have reason to believe to violate statistical independence and therefore you just have to give up on the locality condition."
},
{
"end_time": 967.551,
"index": 38,
"start_time": 939.326,
"text": " And we have theories that do that. We have several different theories of very different formulations that do that, that predict these violations. So you see how they predict the violations because they give up on locality. There have been people from the beginning who just really don't want to give up on locality. They just don't, you know, they're very adverse to it. And you're kind of painted into a corner at that point because the only other thing you could do is say, well, I'm going to give up on statistical independence."
},
{
"end_time": 994.36,
"index": 39,
"start_time": 968.08,
"text": " And there have been various attempts at least, I mean, you see the logical situation and then the issue comes down to, okay, can you really in any plausible way produce an acceptable physical theory that violates this statistical independence condition? And I still don't think you can. I think, of course, logically it's possible, but I just don't see how it can be done in a way that's methodologically acceptable. And"
},
{
"end_time": 1022.807,
"index": 40,
"start_time": 995.435,
"text": " The other Tim thinks the opposite, right? Wants to keep locality as far as I can tell. This is what Jared Tooft wants to do in his theory. He wants to keep locality in his automaton cellular automaton theory and give up statistical independence. Various people have tried to do that. Um, so that's, that's simply what the dispute is as far as I can tell. Professor Palmer, does that sound about correct? That sounds, uh, totally correct."
},
{
"end_time": 1044.735,
"index": 41,
"start_time": 1022.944,
"text": " So I completely 100% agree with Tim on his summary. Maybe actually I could start by actually commenting on a couple of points where I think Tim and I actually agree, because I don't want this to be entirely a kind of a big fight or something."
},
{
"end_time": 1075.162,
"index": 42,
"start_time": 1045.947,
"text": " And the first point is actually to kind of endorse the John Bell Institute concept, because I personally think, you know, Bell's theorem and what it's telling us about physics is super important. And Bell's theorem deserves, you know, consider and the work of Bell, John Bell in general, deserves"
},
{
"end_time": 1103.763,
"index": 43,
"start_time": 1075.623,
"text": " the sort of attention, you know, that a separate institute in Croatia would give. So, you know, I think that's like really good. I'm super happy to see, you know, that that institute. And I just feel, you know, this is a really important question. Personally, I think it's an important question, not perhaps not everyone agrees with this, but I personally think resolving this question is going to be crucial for developing"
},
{
"end_time": 1134.36,
"index": 44,
"start_time": 1104.599,
"text": " our theories of quantum gravity or theories that synthesize quantum physics and gravitational physics, because, you know, it is a fact of the matter that the local causality, you know, underpins the theory of relativity, both special and general relativity, the light cone structure of space time is is just kind of fundamental to general relativity. And the fact that it and of course, general relativity is is deterministic. It's"
},
{
"end_time": 1161.971,
"index": 45,
"start_time": 1135.043,
"text": " It's geometric, it's nonlinear. It's kind of most of the things that quantum mechanics isn't, you know, Schrodinger equations linear, it's kind of, you know, you're sort of struggling a bit to put a strong geometric interpretation on quantum mechanics. And it's, you know, it's nominally indeterministic, the collapse is sort of seen as an indeterministic problem. And of course, Bell's theorem raises this issue of"
},
{
"end_time": 1191.186,
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"start_time": 1162.381,
"text": " the causal structure of quantum mechanics. So I personally think that that kind of understanding Bell's theorem will be a crucial step to satisfactorily quantizing gravity, which we haven't really done. So at least there's no consensus in the community. As a brief aside, you both seem to be nodding at that. So you both are in agreement. Is this a consensus in the foundations of physics? I don't know. No, I kind of sense that it isn't people just kind of gloss over a little bit. I think"
},
{
"end_time": 1216.971,
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"start_time": 1191.578,
"text": " Bell's theorem they it's an it's an you know because if you know if you take the standard approaches to quantum gravity which is string theory and loop quantum gravity people just shrug their shoulders and say well Bell's inequality is violated and just kind of that's it but there's no real no real focus going into what that's telling us about physics"
},
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"start_time": 1218.08,
"text": " If you'd like to learn about the topics in this video, then a great place to start would be Brilliant. Brilliant has courses on gravitational physics, electricity and magnetism, quantum objects, even quantum mechanics with Sabine Hassenfelder. It's a place where even if you're entirely new to a subject, you can come to understand via bite-sized interactive learning experiences these esoteric topics that underlie modern physics."
},
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"text": " On the Theories of Everything channel, there's plenty of technical talk on extended supersymmetry and symplectic geometry, which underlie some attempts to unify gravity with other interactions. Also soon to come, spacetime metric engineering, symmetric teleparallel gravity turns Simon modifications to general relativity, and a great place to ascertain the fundamentals of what was just said is brilliant."
},
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"text": " They even have courses on neural nets and statistics and sampling. Often, when I want to learn about a subject, I'll take courses even on those I feel like I've mastered, only for Brilliant to show me new ways of thinking about it. This happened with their course on knowledge and uncertainty, where information theory is taught and intuitive ways of thinking about the definition of entropy are shown to you."
},
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"text": " It's fruitful for me to know where certain unification attempts with gravity work and don't work. And Brilliant is a great place for me to patch up gaps in my knowledge, helping me conduct better podcasts to make more informed assessments. Visit brilliant.org slash toe. That's T O E for 20% off your annual premium subscription."
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"text": " As usual, I recommend you don't stop before four lessons. You just have to get wet. You have to try it out. And I think you'll be greatly surprised at the ease at which you can now comprehend subjects you previously had a difficult time grokking."
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"text": " Henson, a family-owned aerospace parts manufacturer, has ventured beyond the realms of the International Space Station and the Mars rover to redefine your shaving experience. Using aerospace-grade CNC machines, they've created metal razors with staggering precision"
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"text": " extending a mere 0.0013 inches. This translates to a secure, stable blade that's vibration-free. Henson's clog-free design incorporates built-in channels that bid farewell to annoying hair and cream clogs. Henson's shaving's all about providing the best razor, not just the best razor business."
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"text": " So let's say goodbye to plastics, subscriptions, proprietary blades, and planned obsolescence. Henson is the epitome of affordability and sustainability. It's time to bid adieu to subscriptions and embrace a razor that will last you a lifetime. Head over to hensonshaving.com slash everything. Choose the razor that suits your style and use the code EVERYTHING to snag two years worth of blades for absolutely free. It's time to elevate your shaving game with Henson Shaving."
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"text": " There's no real focus going into what that's telling us about physics. The other thing I would say is I totally agree with Tim to kind of focus on these two issues of locality and so-called statistical independence. If we get time, it's not a phrase I'm actually super keen about because I don't"
},
{
"end_time": 1441.903,
"index": 57,
"start_time": 1412.363,
"text": " I think it necessarily says anything about statistics, but that's something we can come to. But in particular, I agree, for example, that issues about, well, realism, as Tim said, and the other one that's often racist, free will or free choice or something like that, is a kind of a bit of a red herring. And actually, this kind of brings me to, well, it kind of brings me to the point where I disagree with Tim, because"
},
{
"end_time": 1467.671,
"index": 58,
"start_time": 1442.705,
"text": " I got interested in Bell's, in a quality Bell's theorem back in the 1980s. I did my PhD in general relativity in the late seventies and kind of left the field. And it was actually a chance reading of a big volume that Stephen Hawking had edited on the, I think it was the 400th anniversary of Newton's Mathematica Principia, Principia Mathematica."
},
{
"end_time": 1495.247,
"index": 59,
"start_time": 1468.285,
"text": " Which had an article on bells inequality and I kind of made a mental note to myself. I've got to get I've got to really understand this. I've been kind of putting it off for most of my life. I got to understand it. So that led me. Actually, that led me to read the paper that Tim said nails the argument against what's called super determinism, which is the violation of"
},
{
"end_time": 1524.002,
"index": 60,
"start_time": 1496.391,
"text": " Bell's, sorry, the violation of statistical independence. So that was actually one of the very first papers. I've still got my volume of Bell's book, which I bought in... I've got the newer volume. I have the old one too, but it's... But I bought that probably in the early 90s. But anyway, and that was pretty much one of the first papers I read."
},
{
"end_time": 1550.418,
"index": 61,
"start_time": 1524.514,
"text": " The free variables and local causality and what i'd like to do you know what i'd really like to do in this session we have is kind of talk about that paper in particular because i think you know that that is as close as we're going to get to what bell thought about essentially this issue of"
},
{
"end_time": 1580.606,
"index": 62,
"start_time": 1552.568,
"text": " If you like the statistical independence assumption, which is, you know, which by the very title of his paper is to do with. What freedom do we have in the laws of physics to change parameters and change variables, you know, from one value to another? I mean, that's kind of the that's the underlying theme of the paper. We'll go into that. And so I think the reason, you know,"
},
{
"end_time": 1610.367,
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"start_time": 1581.357,
"text": " The reason I perhaps emailed you originally, Kurt, was that I watched and listened to the original debate with Tim. And I felt that, I mean, I totally agree with Tim that his example of a kind of conspiracy in the lab where, you know, rats are tested for whether they catch cancer or not in a smoky environment, I mean,"
},
{
"end_time": 1639.94,
"index": 64,
"start_time": 1610.811,
"text": " Any introduce the concept you could you could sort of, you know, you could. If you wanted to, you could distort the statistics coming out of that experiment in such a way as to kind of invalidate the seemingly obvious result that smoking did increase your likelihood of cancer. Now, I agree with Tim that that would indeed imply a violation of statistical independence in the kind of quantum mechanical context."
},
{
"end_time": 1668.712,
"index": 65,
"start_time": 1641.186,
"text": " But where I disagree is that violations of statistical independence necessarily imply that type of conspiracy. And my view is that, and I'd be, you know, we can talk, in fact, I want to talk about it, that there is a, I think a mathematically rigorous, robust process that would violate"
},
{
"end_time": 1697.398,
"index": 66,
"start_time": 1669.394,
"text": " such statistical independence that does not have any connection whatsoever to do with this type of conspiracy. So my claim is that violating statistical impedance does not necessarily imply this kind of gross conspiracy. And I actually think reading, I mean, this is now reading between the lines to some extent, and Tim may disagree. And in a sense, I can't totally defend my position here, but I kind of sense reading John Bell's words"
},
{
"end_time": 1724.787,
"index": 67,
"start_time": 1698.507,
"text": " He was actually slightly equivocal about his position. He in the paper, he he kind of outlines what he calls a reasonable or a likely type of situation that that's likely to be the case in physics. But at the end, he kind of says, well, I'm not not actually sure. And I might be wrong about this. So far from sort of nailing it, as I think Tim said in the original interview, I kind of feel"
},
{
"end_time": 1744.087,
"index": 68,
"start_time": 1725.742,
"text": " This actually shows John Bell's sort of questioning a little bit what could be a viable process that would actually lead to a violation of statistical independence without implying the type of kind of grotesque conspiracy that Tim correctly raised with his example."
},
{
"end_time": 1772.551,
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"start_time": 1744.497,
"text": " So I can talk a bit more about that, of course, but perhaps I should shut up for a second and we'll come back. To summarize, the disagreement is to whether or not super determinism is conspiratorial. And then number two, what did John Bell mean in his paper? That's right. I have a question about these questions. Why do we care what John meant? It's like exegesis. Oh, what did Wittgenstein mean in the tractatus? Who cares? Let's just talk about the first point, whether super determinism is conspiratorial."
},
{
"end_time": 1785.879,
"index": 70,
"start_time": 1772.944,
"text": " Professor Marlin, why do we care about what Bell meant or didn't mean? The main reason to pay very close attention to whatever Bell wrote was that he was a really clear thinker and a really clear writer."
},
{
"end_time": 1811.92,
"index": 71,
"start_time": 1786.254,
"text": " had extremely good judgment. And so that's the reason to pay attention to anybody doesn't mean that he was a, you know, a god and he didn't, you know, even Homer nods and he can make mistakes. I might say that that Bell's slight equivocation is just a bit of politeness. You know, and as you say, I'm not really sure we're going to get very far trying to get too deep into his head. The real question before us is just"
},
{
"end_time": 1840.998,
"index": 72,
"start_time": 1812.722,
"text": " the exact significance of this mathematical assumption that goes into the theorem. And maybe I can kick it off a little bit by saying, I don't think because this comes up a lot, this idea of evaluating counterfactual assertions, what would have happened had something been different, right? What would have happened had"
},
{
"end_time": 1865.111,
"index": 73,
"start_time": 1841.527,
"text": " Bob said his detector this way rather than that way. Is there a fact about that? Which, of course, in order for there to be a fact like that, you kind of have to believe you're doing a deterministic situation. If you have an indeterministic physics, fundamentally indeterministic physics, then right off the bat, you're going to say, well, there's no fact about what would have happened had"
},
{
"end_time": 1894.684,
"index": 74,
"start_time": 1865.64,
"text": " had things been different. In fact, there's no fact about what would have happened if things had been exactly the same up to a certain point, right? That's what indeterminism is. It says the physics allows you to be exactly the same up to a certain time and then diverge. So there's been a whole lot of literature for decades of people claiming that Bell's theorem tacitly presupposes something called counterfactual definiteness."
},
{
"end_time": 1923.456,
"index": 75,
"start_time": 1895.503,
"text": " Bell clearly denies that, and he's right. I don't think it does. And I don't think that these mathematical conditions really have anything at all to do with counterfactuals. I think they're purely statistical statements about frequencies and that discussing counterfactuals is just off topic."
},
{
"end_time": 1953.319,
"index": 76,
"start_time": 1924.667,
"text": " So if that's true, you know, I mean, it may very well be if we both agree about that, I'm not sure. And then I'm not even sure exactly what we're debating about. My feeling from the interchange is that Tim Palmer thinks that things about counterfactuals and what would have happened and so on are very important to this discussion. I don't think they are. And I'll just kick this off by saying the actual mathematical condition"
},
{
"end_time": 1977.824,
"index": 77,
"start_time": 1954.104,
"text": " Has a row in it, right? It has the symbol row that is supposed to be in the mathematical sense of probability measure. But the question is, I mean, you can use probability measures for lots of things for lots of different purposes. And here I think that that row is merely a statistical measure. It's a measure of frequencies."
},
{
"end_time": 1998.439,
"index": 78,
"start_time": 1978.251,
"text": " And that the statistical independence condition is just a claim about frequencies and nothing else and a claim about frequencies, actual frequencies, not counterfactual anything, just actual frequencies. If that's true, then all the talk about counterfactuals just doesn't even shouldn't even come into the discussion as far as I can tell."
},
{
"end_time": 2028.592,
"index": 79,
"start_time": 1999.258,
"text": " So, I mean, I could go into more detail of how I understand that condition, and I guess Tim can go into more detail about how he understands the condition. But I think that would be kind of the crux of it. All right. Would it be okay if I was to summarize and then you tell me if my summarization is approximately correct and fill in any gaps? So, a counterfactual is this large word, which is scary, but it means contrary to fact conditional, which is another large word, but is"
},
{
"end_time": 2058.319,
"index": 80,
"start_time": 2028.882,
"text": " Simple it means that there's an if then statement and if your if is contrary to reality, then well, what would it have been like? So is that correct? Yeah. Okay. Now can you give an example in terms of something simple like a pair of glasses or a cup? So I say, uh, you know, here I am holding on to this, to this scissors. I didn't let go of it, but we all believe it is true that had I let go of it a second ago, it would have fallen, right?"
},
{
"end_time": 2077.449,
"index": 81,
"start_time": 2058.643,
"text": " That's what would have happened it didn't happen but it would have. Why do you believe that i'll do well whenever i do you know whenever i do drop it does fall and that gives me some word for believing if i had let go of it would fall anyway there's a huge philosophical logical literature on counterfactual conditions."
},
{
"end_time": 2103.677,
"index": 82,
"start_time": 2078.029,
"text": " And it's very complicated, but I don't think it's relevant. So I would, you know, I would prefer not to have to get into the fine details of modal logic, which is really what you're doing there, because I don't think the condition has to do with counterfactual conditionals. Okay. And so Professor Palmer, what is counterfactual definiteness? And then can you please go into what you agree with what Tim Marlin said, or what you disagree with? Well,"
},
{
"end_time": 2133.66,
"index": 83,
"start_time": 2104.991,
"text": " I fundamentally disagree, but, you know, we have to be careful about words and maybe, you know, we might mean different things by the same word. So such as counterfactual. I mean, Bell's I mean, look, I do want to I mean, I agree with you. We don't we don't need necessarily to talk about Bell and what he wrote, but it's it's I think it's a useful it's useful to refer to this paper free free variable"
},
{
"end_time": 2161.886,
"index": 84,
"start_time": 2133.899,
"text": " Free variables and local causality. And what did Bell, what Bell is saying in that paper, and of course it's the title of the paper, is that how you interpret his theorem, how you interpret the experimental violation of his inequalities, depends on what are the free variables in, in the, in"
},
{
"end_time": 2191.391,
"index": 85,
"start_time": 2162.363,
"text": " A putative theory that you have to explain the violation of bell inequalities. So I just want to, I just want to pick up Tim on the example that you had where you dropped or you didn't drop. Let's say that in reality, you didn't drop the scissors and you know, you said, well, okay, I can infer that had I, uh, open my fingers, the scissors would have dropped because"
},
{
"end_time": 2214.309,
"index": 86,
"start_time": 2191.613,
"text": " You know if I do that experiment in in you know in 10 seconds time or tomorrow or the next week it will drop. But of course that you're doing the experiment at a different time and as and as Bell said actually in the paper you know the the moons of Jupiter will have changed the position of the clocks of the hand will have changed and you are not actually"
},
{
"end_time": 2242.551,
"index": 87,
"start_time": 2216.527,
"text": " You're not actually doing the experiment where the only thing that happened was you chain, you opened your fingers. Now, the point is, the point is, however, that we have, you know, Newton's laws of motion, you know, Newton's theory of gravity. And we can appeal to the theory and say, if I had changed the initial conditions of that pair of scissors in such a way that it was now"
},
{
"end_time": 2268.507,
"index": 88,
"start_time": 2243.166,
"text": " You know, no longer constrained by the frictional force of my fingers. I can solve the equations and indeed the scissors would drop to the to the desktop. So you can and in that in that theoretical calculation, you can assume that the moons of Jupiter are the same as they were in the real world where the scissors didn't drop."
},
{
"end_time": 2295.367,
"index": 89,
"start_time": 2269.206,
"text": " So you can just change in your theory that one variable, if you like, which is your whether your fingers are gripping the scissors or not. And your theory will tell you that the scissors will drop if your fingers aren't gripping them. So. So that is a counterfactual. The fact that at that time, when the moons of Jupiter were such as they are,"
},
{
"end_time": 2324.377,
"index": 90,
"start_time": 2297.568,
"text": " In reality the scissors didn't drop the appeal to the theory to predict that the scissors would have dropped had the fingers been different is is a counterfactual and it's it's it's supported by the theory of you know Newtonian physics in this case that says yeah the the laws of physics do not"
},
{
"end_time": 2350.282,
"index": 91,
"start_time": 2324.804,
"text": " prevent or do not deny or do not contradict a counterfactual world where your fingers release the scissors and the scissors dropped. And really that's the point Bell is making. This is the crucial question. What things can we assume can be changed keeping everything else in the world fixed?"
},
{
"end_time": 2371.869,
"index": 92,
"start_time": 2350.879,
"text": " what things can't we? And that's where we come to his famous, and I'd like to discuss it, example where we set a quantum measuring system with a pseudo random number generator. I think this is a really important example. It's a nice example and we should come to that, but let me again just"
},
{
"end_time": 2381.049,
"index": 93,
"start_time": 2373.08,
"text": " I mean, I'm gonna allow myself to drift into this for a minute, but I do want to go back and say and insist."
},
{
"end_time": 2410.964,
"index": 94,
"start_time": 2381.459,
"text": " In my view, counterfactual conditions have nothing to do with anything here. As a philosopher who's worked on this stuff, I can't avoid wanting to comment, but I'm a little scared of getting drawn into a dispute that I think is just a red herring. But let me give that. The only theories that would support counterfactuals are deterministic theories. If you want to say, gee, things actually went this way, what if they had been different?"
},
{
"end_time": 2437.551,
"index": 95,
"start_time": 2411.391,
"text": " If your theory is fundamentally indeterministic and says, well, if they've been different, there are various ways it could have gone like in a collapse theory in a fundamentally indeterministic collapse theory or something like that, then there's just no fact about what would have happened had things been different. The theory doesn't doesn't pick out a particular physical history that would have occurred under different conditions. Now, what Bell actually says a little bit in another paper"
},
{
"end_time": 2462.927,
"index": 96,
"start_time": 2438.268,
"text": " And he's clearly frustrated. He says, oh, people think my theorem presupposes determinism. And he says it doesn't. He says to the limited amount that determinism appears in his original argument, it's a theorem and not a supposition. It follows from certain perfect correlations and the other assumptions."
},
{
"end_time": 2488.729,
"index": 97,
"start_time": 2463.677,
"text": " I would say the same thing. If you have an indeterministic theory, counterfactual definite is not on, but determinism is not required for the theorem. The CHSH form of the inequality makes that absolutely clear. In the case of the scissors, I said"
},
{
"end_time": 2510.23,
"index": 98,
"start_time": 2489.633,
"text": " I believe, and we all believe, in fact, had I just let them go, they would have fallen. Why do we believe that? Well, I said, because whenever I let them go, they do fall. And furthermore, I can let them go, as it were, whenever I want. There's no particular pattern to them being let go."
},
{
"end_time": 2539.889,
"index": 99,
"start_time": 2510.708,
"text": " So if someone were to say, no, no, no, no, it really depends on the moons of Jupiter being in such and such a position that the scissors fall. I'm going to say, so wait, you're telling me whenever I happen to let go of my fingers, the moons of Jupiter just happened to be in exactly the right position so that they don't prevent. Oh, okay. Just a moment. So Tim modeling, if you can hear us, I don't know if you can hear, but you've just frozen for the past 20 seconds or so we're going to."
},
{
"end_time": 2563.558,
"index": 100,
"start_time": 2540.418,
"text": " Sorry folks, that new one didn't work either, so now I'm back. I'll just pick that up, I know exactly what I was saying. Quite apart from theory, you could have reasons, everybody would take it to be reasonable to think that"
},
{
"end_time": 2589.07,
"index": 101,
"start_time": 2564.309,
"text": " Yeah, the moons of Jupiter have nothing to do with this thing falling when I let go of it. Why? Because it falls whenever I let go of it, irrespective of anything about it. And if you say, no, no, when the moons of Jupiter are just in this form, which they never happen to be when you let go of it, gosh, then the thing would float in the midair. You just wouldn't take that seriously for a second, right?"
},
{
"end_time": 2617.79,
"index": 102,
"start_time": 2589.343,
"text": " I mean, you wouldn't take such a thing. You can't say I have empirical evidence against it at the sense that because it's only making weird claims about counterfactual conditions, about what would have happened had things been different. I just want to get away from that. I think that's not the assumption, the assumption. And I do want to insist. Bell uses a certain phrase in this paper. He says, or at least effectively free for the purpose at hand."
},
{
"end_time": 2648.2,
"index": 103,
"start_time": 2618.626,
"text": " Okay, and he insists that that's the careful formulation of the assumption of the theorem, which is that, say, Bob and Alice, who can set their devices in one of two ways each, that that setting is effectively free for the purpose at hand, which means something very different than that they have free will or this or that or even I don't think it has anything to do with"
},
{
"end_time": 2678.08,
"index": 104,
"start_time": 2648.575,
"text": " Right. And when he refers to things being free, he's referring to a property of the laws of physics. What he's saying in this paper is if we want to understand, you know, my theorem, this"
},
{
"end_time": 2705.606,
"index": 105,
"start_time": 2678.933,
"text": " experimental violation we've got to get down and look carefully at putative theories that may explain the experiments and the crucial the crucial issue will be what are what things can be varied and still satisfy the underlying laws of that theory that is the crucial that's the crux of the matter"
},
{
"end_time": 2724.462,
"index": 106,
"start_time": 2706.135,
"text": " That's why he says we cannot repeat an experiment changing just one variable. The hands of the clock will have moved and the moons of Jupiter. This is Bell talking. Physical theories are more amenable in this respect. We can calculate"
},
{
"end_time": 2752.875,
"index": 107,
"start_time": 2724.462,
"text": " The consequence of changing free elements in the theory be they only initial conditions and so can explore the causal structure of the theory i insist that my theory is primarily an analysis of certain kinds of physical theory i.e. what are the free variables in that theory so when i talk about counterfactuals i'm just referring to the question or counterfactual definite this is the question. If i have a theory of physics."
},
{
"end_time": 2778.114,
"index": 108,
"start_time": 2753.456,
"text": " Is it justified or is it permitted to change one variable in that theory and with that variation continue to evolve the universe as a physically meaningful construct. So that's really what counterfactual definiteness is."
},
{
"end_time": 2804.565,
"index": 109,
"start_time": 2778.797,
"text": " Can I give you Tim can I guess give you the because I don't want to talk too much in in sort of vague and abstract terms I want to give you the model that occurred to me when I read Bell's paper back in the whenever it was in the late 80s or early 90s because I'd been working in chaos theory you know for many years and"
},
{
"end_time": 2835.213,
"index": 110,
"start_time": 2806.51,
"text": " Maybe the viewers will be familiar with Ed Lorenz, Ed Lorenz was a meteorologist from MIT who put forward these amazing three differential equations. What's amazing about them is that they generate a kind of geometry in this three dimensional state space. So the three variables, so the state space is three dimensional. Run the model just for a long time from any old initial condition and you find"
},
{
"end_time": 2861.886,
"index": 111,
"start_time": 2835.657,
"text": " the equations trace out this geometry. It took actually quite a few years after Bell, Lorenz's paper for mathematicians to rigorously prove that this geometry was a fractal geometry in the three dimensional Euclidean state space. So the dynamical model that occurred to me was let's just imagine"
},
{
"end_time": 2889.838,
"index": 112,
"start_time": 2862.278,
"text": " We have a dynamical, by the way, the whole thing is deterministic. There is no indeterminism anywhere in the equations. It's totally 100% deterministic. Let's imagine we have a dynamical system which is evolving on this. It's called an attractor, strange attractor or fractal attractor. Let's imagine it's evolving on this attractor and we just freeze it. We just take a point on the attractor."
},
{
"end_time": 2920.947,
"index": 113,
"start_time": 2891.101,
"text": " And we're going to write out and the reason for saying this will come to in a minute. We'll write out the values of the three variables at some instant in time where we've kind of frozen the evolution. We'll write the variables out to a million decimal places. Okay. And now let's ask the question. Because this goes to this question of freedom. What is the freedom in this particular dynamical model? What I'm going to ask is."
},
{
"end_time": 2950.708,
"index": 114,
"start_time": 2922.363,
"text": " What would have happened to the future evolution of the state if I change the millionth digit of one of those three variables, keeping the other two variables fixed at what they were? So I'm just going to take a point on the attractor and take one variable, change it by one part in a million. You can make it one part in a billion if you like, doesn't really matter."
},
{
"end_time": 2980.572,
"index": 115,
"start_time": 2951.186,
"text": " keep the other two variables fixed. The question is, how would that state evolve into the future? The thing is that that seemingly tiny, tiny perturbation, keeping the other two variables fixed is enough to take the state off its attractor into one of the gaps in the fractal geometry. There's kind of gaps which go down, you know,"
},
{
"end_time": 3009.036,
"index": 116,
"start_time": 2980.93,
"text": " smaller and smaller scales you can prove that that would take you off the attractor so if your dynamical system is defined by the geometry of the attractor then you've taken it to a point where it has the dynamical system is undefined because the dynamical point the points on the attractor are only defined on the attractor you've taken it off the attractor so you've done something to"
},
{
"end_time": 3039.087,
"index": 117,
"start_time": 3010.196,
"text": " tiny perturbation which is taking you from a completely deterministic system to a totally just undefined it's an undefined point okay now you could with your you could take that point that perturbed point back onto the attractor by also perturbing the other two variables so you could you know maybe add a little bit to x2 and a little bit to x3"
},
{
"end_time": 3069.155,
"index": 118,
"start_time": 3039.462,
"text": " and it would take the point back on the attractor. And then you could indeed say, OK, that point would evolve deterministically on the attractor. But the point is you've had to you've had to add perturbations to the other two variables. You can't keep those two very the other two variables fixed. And that idea really resonated with me when I first thought about it, because I thought this is exactly a counter example"
},
{
"end_time": 3092.79,
"index": 119,
"start_time": 3069.872,
"text": " to what Bell thought was a reasonable, you know, his reasonable assumption that we'll come on to this experiment in a minute, perhaps about pseudo random number generators. And he makes a key assumption, which is kind of reasonable, but this dynamical system would actually provide a counter example to that."
},
{
"end_time": 3121.681,
"index": 120,
"start_time": 3093.899,
"text": " So then I got thinking, what would you need to actually scale this up to the universe? And the answer is simple. You just treat the whole universe as a, as a dynamical system evolving on some precisely on some, you know, chaotic attractor. And the interesting thing is there are cosmologies, you know, the famous mix master cosmology, which has, which have chaotic attractors. So this is not completely daft idea, but it provides a,"
},
{
"end_time": 3152.705,
"index": 121,
"start_time": 3123.114,
"text": " It provides an example of happy to happy to talk about this in more detail. It provides an example of how statistical independence can be violated without going anywhere near statistics. And I just just before I finish in one second, just just slightly counter the point that Tim Maudlin said. The statistical independence assumption does indeed mathematically refer to a probability"
},
{
"end_time": 3181.681,
"index": 122,
"start_time": 3153.66,
"text": " function on hidden variables and so on but that doesn't itself imply anything statistical you know so just to give you an example if i said that two plus two equals four that's not a statistical so nothing to do with statistics if i said that two plus two equals five i mean that's an incorrect statement but also nothing to do with statistics but i can equally say"
},
{
"end_time": 3205.469,
"index": 123,
"start_time": 3182.5,
"text": " two plus two equals four with probability one and two plus two equals five with probability zero. So I can easily inject probability distributions or probabilities into what are basically deterministic statements. And I think that is the sense in which this particular model would"
},
{
"end_time": 3235.367,
"index": 124,
"start_time": 3206.34,
"text": " Again, I need to start by signposting that I think"
},
{
"end_time": 3263.131,
"index": 125,
"start_time": 3235.998,
"text": " Everything I'm about to say is actually irrelevant to the discussion, but a lot of things were brought up and I have some things to say about them. I'll say them, but I hope to bring us back to what I think the main point is. Look, the theory of chaotic systems is very interesting. The theory of systems that have a very, very, very, very, very infinitely maybe sensitivity to initial conditions is very interesting. You don't need"
},
{
"end_time": 3287.5,
"index": 126,
"start_time": 3263.131,
"text": " three dimensions. You can do this with a logistical map and essentially one dimension is a standard example that you use and some of these systems have attractors. What does that mean? It means that if you start anywhere, the system will evolve toward the attractor. That's why it's called an attractor. Sometimes you get into a chaotic regime where there are no attractors. Okay, but there are regimes where there are attractors. Of course, you never get to the attractor."
},
{
"end_time": 3307.483,
"index": 127,
"start_time": 3288.097,
"text": " I mean, if you start off it, you never get there. It's just, it's just in the long term, you get ever closer to it. So I don't even understand what it means to say it's probability one, the systems on the attractor systems are not going to be on attractors. They're going to be getting closer to attractors. They're off attractors, right? I mean, the chance of it being on the attractor is in some sense zero."
},
{
"end_time": 3337.551,
"index": 128,
"start_time": 3307.807,
"text": " Um, but it's still at a tractor because the, the, the flow lines tend, tend toward this point. And this is easy to illustrate with these standard examples of the logistical map and so on. But again, this stuff about counterfactuals, I mean, I really want to insist that the statistical independence condition is a condition essentially about statistics. So let me at least say what I say it is, and you'll see that there's nothing about counterfactuals or what would happen or anything in it."
},
{
"end_time": 3366.954,
"index": 129,
"start_time": 3339.121,
"text": " Alice and Bob are in two different labs far away from each other. I make a whole many, many, many pairs of entangled electrons, say in a singlet state, and I send one to Alice and one to Bob. And they collect them in these boxes labeled so they know which goes with which, right? Which of Alice's electrons was paired with which of Bob's electrons. Let's just imagine"
},
{
"end_time": 3396.937,
"index": 130,
"start_time": 3367.346,
"text": " that we have created a million of these. So Bob and Alice now have in their control, in their labs, an actual collection of a million electrons. Good. Now we assume that those electrons have some state. Call it lambda. What is lambda? Lambda can be anything you want. I mean, this is, Bell says, lambda just stands for whatever. You know, you make up the theory and tell me what lambda is."
},
{
"end_time": 3417.466,
"index": 131,
"start_time": 3397.602,
"text": " And there will be an actual statistical distribution of the lambda in those million electrons. So maybe there's some characteristic, I don't know, squishiness that some electrons have and some electrons don't."
},
{
"end_time": 3446.852,
"index": 132,
"start_time": 3417.961,
"text": " A certain percentage of Alice's electrons will be squishy, a certain percentage of Bob's electrons will be squishy, nothing to do with counterfactuals, it's just a statistical description of their state. Good. Now, so there's this row of lambda which comes up in this theory and that row, which is a probability measure, is not anything about probability, it's about these statistics. What percentage"
},
{
"end_time": 3470.708,
"index": 133,
"start_time": 3447.466,
"text": " What Bob and Alice are going to do is they're going to make selections. Each one is going to decide for each electron in their control whether they're going to send it through a device oriented this way or device oriented that way. It's a binary choice they make."
},
{
"end_time": 3498.695,
"index": 134,
"start_time": 3471.681,
"text": " And when they're done, what they will have done is subdivide this big collection into four small collections, exhaustively. Namely, if we call them, say, measuring X spin and Y spin, the collection where both Bob and Alice have measured X, where Alice has measured X and Bob Y, Alice Y and Bob X and both Ys, right? You know, they're doing two binary choices. You're subdividing each"
},
{
"end_time": 3527.363,
"index": 135,
"start_time": 3499.531,
"text": " of the of the collections will now be subdivided into four and the statistical independence assumption is just that row of lambda that is the distribution of every of these characteristics with respect to the whole thing equals or you know it should be a little wiggly thing approximately equals row of each of those sub distributions right that is the set"
},
{
"end_time": 3557.278,
"index": 136,
"start_time": 3528.063,
"text": " that both Bob and Alice measure in X has some distribution. The set where Alice measures X and Bob measures Y has some distribution. If they're doing this kind of 50-for-fee, then each of these will have, I don't know, 250,000 members. So each of those subsets has a row. And the statistical independence assumption is just that the rows of the subsets are equal to or approximately very closely equal to"
},
{
"end_time": 3580.06,
"index": 137,
"start_time": 3557.79,
"text": " The row of the whole thing. Now, that statement that I just gave you says nothing about counterfactuals. Nothing. It just doesn't say anything about it. It says the statistics of this big set are very close to the statistics of each of the four smaller subsets."
},
{
"end_time": 3611.493,
"index": 138,
"start_time": 3582.91,
"text": " And that's it. Now, why would you think that? Well, because Bob and Alice are just flipping coins. Why would the subset that gets picked out when Alice and Bob's coins come up both heads be fundamentally different than the subset picked out when one comes up heads and one tails? Or they're doing the digits of pi, or they're using a lottery machine, or they're using whatever you like to make that sorting."
},
{
"end_time": 3641.903,
"index": 139,
"start_time": 3611.971,
"text": " You don't want to get stymied by this and there's something else that's the main point."
},
{
"end_time": 3668.78,
"index": 140,
"start_time": 3642.5,
"text": " I see. It's hard to see how they could be because how could the theorem be about counterfactuals? Well, let's hear. So my view is that, Tim, you have described only part of what that we'll call it statistical independence, but I don't think it's a good word because I think that call it whatever you are. Yeah, okay. I mean, some people call it lambda independence, which I sort of prefer."
},
{
"end_time": 3693.234,
"index": 141,
"start_time": 3669.838,
"text": " i just want to sorry before i get into that i just want to just make the point that there is nothing illogical or wrong or any other word you want to use to posit a dynamical system where the states are evolving on the attractor"
},
{
"end_time": 3721.732,
"index": 142,
"start_time": 3694.002,
"text": " I mean what you have described say with the logistic map or could be Lorenz's model is what people do in practice which is they start from any old point in state space and run the thing you know for as long as they can and as you say you get closer and closer to the attractor but mathematically you can just say my dynamical system is determined by those differential equations but where points"
},
{
"end_time": 3750.776,
"index": 143,
"start_time": 3721.937,
"text": " are on the attractor are on the invariant set i use the word invariant set by the way because once you're on the invariant set you're always on it and you always have been on it so it's just it's a it's a perfectly um you know it's a perfectly found dynamical system and i'm saying that dynamical system uh is pertinent to what we're discussing and this would be a good point to actually bring up the example that bell himself"
},
{
"end_time": 3778.387,
"index": 144,
"start_time": 3751.186,
"text": " raised in that paper because I think this makes it quite clear why counterfactuals are important and why Tim is actually focusing on only part of that of that assumption of the row of lambda and yeah row of lambda given the measurement settings is independent of the measurement settings so the example is we could I mean we Tim probably referred it to it"
},
{
"end_time": 3803.968,
"index": 145,
"start_time": 3778.695,
"text": " In the last interview, but it's worth going back over it. Bell imagine and he partly did this to to sort of keep humans out of the picture and free will and all that stuff. He said, imagine that Alice and Bob's measurement settings are determined by a pseudo random number generator. So we're taking the human out of it altogether. And"
},
{
"end_time": 3832.705,
"index": 146,
"start_time": 3804.445,
"text": " These particular so the pseudo random number generator will set will output a zero or one and that will determine the set the setting and the input is some number you give it and and Bell makes the statement that the that output of zero one is sensitive to the millionth digit of the input number. It could be pie if you like or anything else but the millionth digit is is"
},
{
"end_time": 3859.599,
"index": 147,
"start_time": 3833.217,
"text": " is a crucial piece of information in determining whether it's a zero or a one. I mean, maybe the billionth digit is not important, but the millionth is. Oh, can I just stop you here? I don't think that the example, as you say, you want a random sequence, statistically random sequence of zeros and ones. The idea is you, okay, take pi, start at the millionth digit, and then put a zero or one depending on whether it's odd or even."
},
{
"end_time": 3889.753,
"index": 148,
"start_time": 3860.247,
"text": " And then go to the millionth and first, then go to the millionth and second, then go to the millionth and third. So that, uh, uh, the millionth, the parody of the millionth digit completely determines one of the entries. Right. Right. And then has nothing to do essentially with, with the ones that came before or after. So of course the billionth one will come up eventually. Yeah, yeah, yeah, yeah. No, but we're focusing on one particular run of the experiment and the,"
},
{
"end_time": 3915.145,
"index": 149,
"start_time": 3890.776,
"text": " You know, the claim is that the output was zero one is dependent on the millionth digit. Now, the crucial the crucial statement that Bell makes is that fixing says a or a prime. This is the this is zero one. This is the output that determines the measurement setting."
},
{
"end_time": 3944.77,
"index": 150,
"start_time": 3915.486,
"text": " Fixing A or A' indeed fixes something about the input, i.e. whether the millionth digit is odd or even. Now this is the crucial statement, but this peculiar piece of information is unlikely to be the vital piece for any distinctively different purpose, i.e. it is otherwise rather useless. So the point is this, that we're doing this experiment in a world where"
},
{
"end_time": 3971.544,
"index": 151,
"start_time": 3945.964,
"text": " Moons, to use the example again, the moons are going around Jupiter and various other things are happening. You know, people are going for a walk in the park and stuff is happening. His point, which is a kind of, you know, it's a reasonable point. I'm not saying it's not reasonable, but I'm claiming that in the context of quantum mechanics, it is questionable. But his point is that"
},
{
"end_time": 4002.432,
"index": 152,
"start_time": 3973.524,
"text": " all these other things the moons of jupiter the people going for a walk in the park the value of the millionth digits irrelevant they just carry on their lives and of course that's a that's a perfectly that's the sort of thing that you would expect to be true if the world was governed say by newtonian physics because or indeed by most simple dynamical systems because you can"
},
{
"end_time": 4030.384,
"index": 153,
"start_time": 4002.944,
"text": " take an initial condition where you know somebody's about to go into the park where the moon is about to take in a particular phase of the orbit keep all that stuff fixed and vary the millionth digit and that's a perfectly reasonable perturbed initial condition and you can carry on solving your newtonian equations with that slightly different initial condition so that is a kind of scientific"
},
{
"end_time": 4057.654,
"index": 154,
"start_time": 4031.493,
"text": " statement if you like or scientific justification for Bell's what he calls his reasonable assumption that the millionth digit is is unlikely to be the by the way note the word unlikely not definitely not unlikely to be the vital piece of for any distinctively different purpose. So already there's kind of an implicit"
},
{
"end_time": 4077.688,
"index": 155,
"start_time": 4060.623,
"text": " reference to the fact that this millionth digit is a free variable in the sense it can be twiddled it can change you can keep everything else fixed you can just twiddle that thing and the world will will continue but i want to come back to my example where do you see twiddling in this i mean he says"
},
{
"end_time": 4099.514,
"index": 156,
"start_time": 4078.063,
"text": " It's unlikely to be the vital piece for any distinctively different purpose, i.e. otherwise rather useless. I take it what he means there is that conditioning on that fact, not asking what would have been the case if it had been different,"
},
{
"end_time": 4126.049,
"index": 157,
"start_time": 4100.196,
"text": " But just conditioning on that gives you no information, no useful information about anything else. It'll tell you a very important thing in the physical world. Namely, did Alice pick X or Y in that run? It'll absolutely tell you that important physical fact, but it just won't give you any information. It doesn't really have to do with determinism. It won't change the likelihood that Jupiter's"
},
{
"end_time": 4155.162,
"index": 158,
"start_time": 4126.561,
"text": " Moons are in any particular phase. It won't change the likelihood that people are walking in the park. It won't change the likelihood in that or have any effect on anything else in terms of the statistics. But Tim, this is the whole point I'm trying to make. I can and I do claim to have a mathematical model where and it's just a generalization of the example that I"
},
{
"end_time": 4173.302,
"index": 159,
"start_time": 4155.572,
"text": " Discussed with Lorenz's attractor where you can't change the millionth digit of one of the variables and keep the others fixed but he doesn't say it doesn't it doesn't it leads you to an advantage doesn't say you can do that."
},
{
"end_time": 4191.578,
"index": 160,
"start_time": 4174.428,
"text": " That's what it says. It's it says it's not a useful piece of information for any distinctive other thing really different purpose. In other words, if you change that information, you know, I'm trying to keep saying in other words, but he doesn't talk about changing it. He just says it's not useful information for any other purpose."
},
{
"end_time": 4219.872,
"index": 161,
"start_time": 4192.244,
"text": " The whole paper is about free variables and a free variable is something that you can change in your theory. That's the whole basis of the paper. Free. What does free mean? If it doesn't mean you can't change it, then it has no meaning. Can you tell us what's meant by or what you interpret as being meant by effectively free for the purposes at hand, at least in terms of subdivisions? Effectively free for the purpose at hand means precisely that making choices"
},
{
"end_time": 4249.855,
"index": 162,
"start_time": 4220.469,
"text": " subdividing your ensemble on the basis of those things will give you sub ensembles that are statistically similar. Let me just reread the paragraph. Row of lambda equals row of lambda conditioned on A and B. There's nothing about counterfactuals in that claim. Tim, let me just reread this. Just a moment, just a moment. Please reread, yes. We're kind of, I don't want to sort of like say I'm"
},
{
"end_time": 4278.217,
"index": 163,
"start_time": 4250.555,
"text": " What Bell says is, in that previous quote, we cannot repeat an experiment changing, note the word changing, just one variable, the hands of the clock will have moved and the moons of Jupiter. Physical theories are more amenable in this respect. We can calculate the consequence of changing free variables in a theory, be they only initial conditions. So he is talking about"
},
{
"end_time": 4307.244,
"index": 164,
"start_time": 4279.019,
"text": " Is it reasonable to, to assume that if I changed the parity of that millionth digit, the rest of the world would just carry on functioning as if nothing had happened. And I'm claiming I have a perfectly mathematically rigorous, you know, theory. I don't know whether it's correct or not, but it's a, it's a candidate theory where that assumption is false. That assumption is incorrect. Yeah."
},
{
"end_time": 4334.667,
"index": 165,
"start_time": 4307.688,
"text": " Look, we're at cross purposes here. We could go into fine analysis of the pros, but at the end of the day, it's a mathematical theorem. It follows from certain mathematical assumptions. And the relevant mathematical assumption is what I said, that rho of lambda equals rho of lambda conditioned on any collection of the settings that you like, right?"
},
{
"end_time": 4364.36,
"index": 166,
"start_time": 4335.077,
"text": " role of lambda equals role of lambda conditioned on Alice and Bob Joe both choosing X or Alice choosing X and Bob choosing Y. That is the mathematical condition that's used to derive the inequality. And that condition says nothing about counterfactuals. Okay. I agree with your mathematical statement of the condition. I disagree with your interpretation of it."
},
{
"end_time": 4392.705,
"index": 167,
"start_time": 4364.821,
"text": " And I'll just give you how I see the violation of statistical independence applying to that chaos model that I described. Rho, we have some lambda, we have some factor of the matter where Alice and Bob measure the spin of particles with their measurement settings."
},
{
"end_time": 4422.176,
"index": 168,
"start_time": 4393.336,
"text": " oriented in a certain way so by construction that that occurred we can assign it a probability of one we can normalize it by some factor if you want to but essentially that occurred in reality that's a probability of one my claim would be that therefore that the real world this is an manifestation of the real world evolving on the on the attractor now what i want to in testing the statistical"
},
{
"end_time": 4452.005,
"index": 169,
"start_time": 4422.585,
"text": " independence assumption i want to ask the question what is that probability is it one or is it zero so this is a very deterministic approach to probability when i keep lambda fixed but i change let's say either alice or bob's measurement setting from a b to a b prime or something like that and i would claim that this model can under certain circumstances"
},
{
"end_time": 4477.585,
"index": 170,
"start_time": 4452.637,
"text": " Return the value zero for probability in other words. When you change and bells paper is about changing things when you change Bob setting from B to B prime say keep Alice's fixed today and keep lambda fixed then when that state if that state gets perturbed off this attractor the probability goes from one to zero."
},
{
"end_time": 4495.623,
"index": 171,
"start_time": 4478.336,
"text": " And your measurements, your your lambda independence or your statistical independence is violated. So it's a counterfactual world where you varied B to B prime and. Your theory says that's that's an undefined state."
},
{
"end_time": 4526.101,
"index": 172,
"start_time": 4496.374,
"text": " So I violated so-called statistical independence. I violated that mathematical condition, but it's got nothing to do with statistics. It's got nothing to do with your million particles. It's one particular pair of particles. So, so yeah, I mean, look, we don't agree about what the mathematically the theorems about that. That's just that simple word. I mean, it's not, you can't test Bell's inequality with a single pair. It makes it, it's only an inequality that can be tested statistically."
},
{
"end_time": 4547.841,
"index": 173,
"start_time": 4526.63,
"text": " You have to do experiments on many, many, many, many pairs. And the condition is that the sub-ensemble that are subjected to this test condition and the sub-ensemble that's subjected to a different test condition and so on, that those sub-ensembles are all statistically similar to one another."
},
{
"end_time": 4570.811,
"index": 174,
"start_time": 4548.626,
"text": " And that's just not a claim about what would have happened had you made a different. I mean, let me go to the Brad example, just to make sure everybody listening is following this. Right. So I know you think this is a bad analogy, but let me at least. No, I don't think it's a bad analogy. Okay. What I'm saying is it only tests part."
},
{
"end_time": 4600.452,
"index": 175,
"start_time": 4571.237,
"text": " This is for the audience. You're interested in a question like, does smoking cause cancer? We all know that correlation is not causation. That is, you can have correlations between things where there's no direct causal connection between them. Yes, smoking is correlated with getting cancer, but having ashtrays in your house is also correlated with getting cancer."
},
{
"end_time": 4629.377,
"index": 176,
"start_time": 4600.759,
"text": " But not because the ashtrays are dangerous, right? Because that's due to a common cause. And the way you try and tease out the causal connections, the gold standard experimentally is to do a randomized controlled trial where you take a set of test subjects and this is essentially statistical. You need many, many test subjects. You know, I need a thousand, a million, you know, 10,000 rats. And you then"
},
{
"end_time": 4659.428,
"index": 177,
"start_time": 4629.872,
"text": " Randomly sort them, as we say, into the experimental and control group. You treat the two groups the same except with respect to the condition you're worried about, like subjecting them to smoke, and then you see whether you get more cancer in one group rather than the other. Now, why do you do that? Well, you say, I don't know what causes cancer. I mean, maybe cancer can be caused by genetic defects, cancer being caused by whatever. Maybe there's stuff I have no idea. This is not about a theory. I don't even know what causes cancer."
},
{
"end_time": 4688.2,
"index": 178,
"start_time": 4660.265,
"text": " Suppose there's some unknown X factor that will make a rat more likely to have cancer. And suppose 8% of the rats have it. The assumption is, well, because I randomly sorted them into two groups, if 8% of the big group has it, then about 8% of each of the subgroups will have it. Why? Because my sorting was random, because my sorting was something like I sorted them on the parity of the digits of pi, right?"
},
{
"end_time": 4716.903,
"index": 179,
"start_time": 4688.558,
"text": " I mean, why would sorting on the parity of the digits of pi tend to push the ones with X factor this way rather than that way? That's the logic of random controlled experiments, that the randomness, and this is where the freedom comes in, or effectively free for the purposes at hand, the physical randomizing, I mean, Bell talks about physical randomizing devices like auto balls that are bouncing around."
},
{
"end_time": 4738.148,
"index": 180,
"start_time": 4717.705,
"text": " What are they for? They're for producing random sequences. And then you use those random sequences to sort the things, and as a result, you're highly confident that the groups that they get sorted into are statistically like each other, even in respects you have no nothing about, even in respects you have no theory about."
},
{
"end_time": 4767.927,
"index": 181,
"start_time": 4738.66,
"text": " Even with respect to this X factor that we don't have a clue about, still whatever percentage have the X factor in the control group will have the X factor in the experimental group. So it's a very important assumption for experimental science on statistics. And as I said, mathematically, that is the mathematical assumption of the theory. Now, I mean, Tim keeps saying that's only part of the assumption, but I kind of don't understand because it's a mathematical claim and it says this row"
},
{
"end_time": 4797.91,
"index": 182,
"start_time": 4768.217,
"text": " is equal to the row conditioned on the choices that are made that's just what it is to say there's more to it mathematically there's no more to it well is it okay um there is tim and um i mean your your example certainly violates um statistical independence"
},
{
"end_time": 4824.462,
"index": 183,
"start_time": 4798.507,
"text": " and you know if that if that was the way if there was some conspiracy like that that was needed to um to somehow you know uh understand bell serum i i'd be with you this is this is this is crazy i mean nobody would would postulate that but my claim is that you don't you can't go in the other direction that"
},
{
"end_time": 4851.493,
"index": 184,
"start_time": 4825.845,
"text": " Violating the statistical independence condition, what we call statistical independence, does not imply that the statistics of Bell experiments are somehow skewed in a conspiratorial way. And I tried to give this example, I mean, and it's very close to the example that Bell talks about in that paper. This is why we're having this"
},
{
"end_time": 4882.022,
"index": 185,
"start_time": 4852.108,
"text": " conversation is because my reading of that paper was just so completely different to yours this is why i felt i've got to come on and say i don't agree that because bell never talks about in that paper he doesn't talk about statistics of uh of anything he's talking about one particular run of the experiment where the measurement setting has been determined by the millionth digit and the claim is that"
},
{
"end_time": 4912.227,
"index": 186,
"start_time": 4882.585,
"text": " That millionth digit is unlikely to be the vital piece for any distinctively different purpose. And I would say in the light of all the previous discussion in the paper about the fact that the whole theorem is about whether certain variables can be changed, you know, is permitted to change variables. What he's basically saying is it seems reasonable that we could change that millionth digit without affecting anything else in the world. And"
},
{
"end_time": 4930.452,
"index": 187,
"start_time": 4912.91,
"text": " I'm claiming that there's based on geometric theories of chaos. There are models where that idea is wrong and the way that impacts on the statistical independence assumption is just something which has probability one when you're on the attractor."
},
{
"end_time": 4960.469,
"index": 188,
"start_time": 4931.015,
"text": " suddenly goes to probability of zero when you're off the attractor so it's nothing to do with the statistics of many many many particles it's about one particular you know you take one at a time particle and that's of course you know that is that is a crucial um if you go through the the proof of of bell's theorem you know you have you have your some deterministic function which outputs spin"
},
{
"end_time": 4986.92,
"index": 189,
"start_time": 4961.049,
"text": " Given a lambda and a measurement setting, you have all the different possible measurement settings, zero, one, so on, and then you integrate over lambda. And if your theory says actually no, this variation that you've done of the measurement setting, keeping lambda fixed,"
},
{
"end_time": 5016.084,
"index": 190,
"start_time": 4987.278,
"text": " This hypothetical measurement setting that you didn't actually do, but you might have done that violates the conditions of your theory. Then you can't derive Bell's inequality and you can't derive it because you violated this. You violated statistical independence, but nothing to do with statistics. Why statistical independence is not a good phrase in my view. Well, OK, so I think I'm not sure if we're going to. I mean, I'll just cite a passage."
},
{
"end_time": 5044.94,
"index": 191,
"start_time": 5016.544,
"text": " Because, as I said, the theorem is a mathematical theorem. So if you want to say, there's such and such an assumption made, you have to point to where that shows up in the mathematics. Now, Bell, on the first page of free variables and local causality, gives the assumption, which is he has this V, which is, I would say, a statistical claim about"
},
{
"end_time": 5075.196,
"index": 192,
"start_time": 5045.606,
"text": " Distribution of hidden variables conditioned on and then a, b, c, a prime, b, c prime, the v conditioned on all these different things is the same. And what does he say about it? He says, for me, this means that the values of such variables, that is the settings of the instruments, this is explaining the phrase, it has been assumed that the settings of instruments are in some sense free variables. Let's see if it has anything to do with counterfactuals."
},
{
"end_time": 5103.2,
"index": 193,
"start_time": 5075.708,
"text": " For me, this means that the values of such variables have implications only for their future light cones. They are in no sense a record of and do not give information about what has gone before. Now, I mean, let's just pause for a second. If you're making these settings on the on the parodies of the digits of pi, starting with the millionth digit, that obviously is not a record of nor does it give any information about anything that's gone before."
},
{
"end_time": 5125.503,
"index": 194,
"start_time": 5104.002,
"text": " Because it's fixed by pi. That's a thing that can't be changed independently of the physical history of the universe. Whether Alice set her device this way or that way, if it depends on whether the millionth digit of pi is even or odd, that obviously gives no information about anything that came before."
},
{
"end_time": 5153.37,
"index": 195,
"start_time": 5126.596,
"text": " In particular, they have no implications for the hidden variables V and the overlap of the backlight cones, and then he gives this condition. Now, I have to certainly say it is not true that this theorem mathematically assumes that the function from lambda and the settings to the outcome is deterministic. It doesn't. And the CHSH version of it explicitly doesn't."
},
{
"end_time": 5180.06,
"index": 196,
"start_time": 5153.78,
"text": " In the particular case of singlet electrons where you have perfect correlations, perfect correlations. So if I check the Z spin in the same direction, they're always anti-correlated. Then Bell says, well, the only thing that could get that right in a local theory would be a deterministic theory, because if it was indeterministic in a local theory,"
},
{
"end_time": 5202.619,
"index": 197,
"start_time": 5180.418,
"text": " Then, of course, on this side it could come out either way, and in a local theory that can't have any influence on the other side, so there's no way it could guarantee these perfect correlations. But the inequality doesn't require perfect correlations. The inequality, the CHSH version, assumes no perfect correlations. There are still statistical restrictions on local theories."
},
{
"end_time": 5231.459,
"index": 198,
"start_time": 5203.302,
"text": " So the talk about determinism just that that's that it and this is a bit dangerous because many people thought that Bell assumed determinism. And then they thought, well, I can get out of Bell's theorem just by saying the world's not deterministic. And that's if it was that simple, it would be no big deal. It's not true. Well, I mean, this is this is tangential. I mean, I'm not I'm assuming"
},
{
"end_time": 5259.804,
"index": 199,
"start_time": 5232.449,
"text": " For simplicity, determinism, but the future is is entirely there's nothing in deterministic about the model. You know, I mentioned Lorenz's equations. They are 100% deterministic. If you given an initial state, you can determine the future state by the equations or the equations determine the future state. So I don't want to, you know, just bringing in concepts of indeterminism here seems to just muddy the waters because we're not talking about indeterminism. I don't think."
},
{
"end_time": 5283.814,
"index": 200,
"start_time": 5261.869,
"text": " What I'm talking about is the notion that variables that you might think are free, and I come back to that millionth digit, the assumption is that it's a free variable in the sense that it has no bearing on anything else in the world, can be questioned. And it can be false in the sense that changing that millionth digit"
},
{
"end_time": 5314.309,
"index": 201,
"start_time": 5284.974,
"text": " Can produce a state of the world which is just inconsistent with your deterministic laws of physics and the fractal attractor example I think illustrates that perfectly change the millions digit of one of the three Lorentz variables keep the other two fixed you moving off the attractor. And that is a violation of statistical independence because you've taken a row equals one situation on the attractor to a row equals zero situation off the attractor."
},
{
"end_time": 5335.213,
"index": 202,
"start_time": 5316.459,
"text": " I think we see what the disagreement is here. For me, these rows are essentially statistical information about collectives. You have to do experiments on collectives to test this theory and they're about"
},
{
"end_time": 5361.715,
"index": 203,
"start_time": 5335.572,
"text": " the distributions of sub ensembles within a large ensemble. To me, that's just what it says. Now, Tim thinks it says something else. I'm not sure how we can. I mean, it seems to me we're just repeating these two sides at this point. I don't think we're making any contact and I'm not sure how we could usefully go on. I can say, as I've said before, I don't see how you look at the mathematical condition."
},
{
"end_time": 5390.026,
"index": 204,
"start_time": 5362.073,
"text": " and say, gee, here's a claim about counterfactuals or what would happen if that's implicit in the mathematical condition. I would just like to see it pointed out. Well, because medical condition is that this row equals that row equals that row equals that row. Right. But if row if you in this model that I have, if you have the real world, the real world happens once."
},
{
"end_time": 5416.51,
"index": 205,
"start_time": 5390.742,
"text": " A particular hidden variable, a particular run of the experiment has a particular hidden variable. Alice and Bob measure with a particular set of settings. So if you've got a good theory, it better describe that situation. So it better assign a probability that's non-zero to rho of lambda given what Alice and Bob actually measured."
},
{
"end_time": 5442.022,
"index": 206,
"start_time": 5416.8,
"text": " Because that's just a fact of the world, right? So that row is non zero of row of lambda. I don't know what that means. The measurement, the probability of row of land. Oh, sorry. The row of lambda given, let's say, let's say Alice measured zero in the zero direction and Bob measured in the zero direction for a particular lambda, then row of lambda given zero, zero, given the zero zero setting."
},
{
"end_time": 5471.766,
"index": 207,
"start_time": 5442.671,
"text": " Better be non-zero. If you've got a theory of physics which describes what happens in the real world, then it better give a row that's non-zero. So that row of lambda given zero zero. Yeah, we're just at a point of mutual incomprehensibility. Since I think of these rows as describing actual statistical distributions, actual statistical distributions,"
},
{
"end_time": 5500.93,
"index": 208,
"start_time": 5472.449,
"text": " Right, but let's say on a single run, there's no distribution. I mean, there's a trivial distribution. The probability is one. If you haven't, that's why you don't care about that. That's why you have to look at if take take a million runs, the the for a particular, uh, let's say the distribution is is uniform on those million lambdas, then the over that distribution, the probability is like one over a million."
},
{
"end_time": 5527.824,
"index": 209,
"start_time": 5501.442,
"text": " Right, because you did a million runs. You mean one over a million. No, I'm not. I'm not. I'm sorry. I'm just not interested. So in the example of rats, I said there's this X factor, 8% of the total population of the rats have it. So probably about 8% of the subpopulations do. Now, if your subpopulations are only one rat, then of course it can't be 8%. That doesn't make any sense. You know, your chosen subpopulations have to be pretty big."
},
{
"end_time": 5557.739,
"index": 210,
"start_time": 5528.609,
"text": " So when you say go down to a single case, I mean, the way I'm understanding this, the rows make no sense. Yes, well, I'm just saying if you go down essentially claims about statistics, actual statistical distribution. Professor Palmer, can you frame this in terms of ensembles? Well, I if you like, I thought I was trying to do you can imagine a uniform distribution of of on on your ensemble of lambdas. And then for any particular, let's say you have a million,"
},
{
"end_time": 5585.981,
"index": 211,
"start_time": 5558.114,
"text": " Then the row for a particular lambda and a particular pair of measurement settings, zero zero, will be one over a million. That will be a kind of a normalized probability on your ensemble. The point is it's non zero. I don't care whether it's one over a million or one over one or one over 10 or any number you like, as long as that's not zero. What I'm saying is if you have a theory"
},
{
"end_time": 5616.698,
"index": 212,
"start_time": 5588.404,
"text": " Which has certain conditions, mathematically defined conditions, like being on your attractor. I couldn't name other types of theories where you take a particular lambda. Okay, whether in the real world, the zero zero measurement was made and you say, what is the value of that row for that lambda, keeping that lambda fixed when"
},
{
"end_time": 5642.073,
"index": 213,
"start_time": 5617.108,
"text": " I replace zero zero by say zero one. What do you mean by keeping lambda fixed? Sorry? I don't see what you mean by lambda. I mean if lambda is fixed then you know the relevant row is a point distribution. I've got a million, sorry I'm getting confused, I've got a million values of lambda I'm just going to put a"
},
{
"end_time": 5672.159,
"index": 214,
"start_time": 5642.602,
"text": " Maybe it would be easier if you use just four values of lambda than a million. Suppose whenever they produce these pairs of electrons in the singlet state, which according to standard quantum mechanics,"
},
{
"end_time": 5693.131,
"index": 215,
"start_time": 5672.534,
"text": " every pair is physically absolutely identical to every other pair so there's no you know every the the distribution is a hundred percent singlet state right that's that's what row is some of these pairs are different than others we're unaware of and they're"
},
{
"end_time": 5722.415,
"index": 216,
"start_time": 5693.575,
"text": " The lambdas will be different on each. But you mean they'll be unique to every single. Let's make them. You can't say anything general at all. No two pairs. No two pairs of electrons have any physical similarity to any other pair. Is that what you're suggesting? I'm saying that there's no reason that they should not have distinct lambdas. I mean you and I"
},
{
"end_time": 5748.507,
"index": 217,
"start_time": 5722.875,
"text": " share lots of similarities. We have two eyes and a nose and all the rest of it, but our DNA is different, is unique. Each of us has unique DNA, so I don't see what's the big deal about that. Each electron pair has a different lambda. Why not? It's no big deal. It would be awfully odd if that were true, that there would be any reliable statistical predictions that could come out of such a theory."
},
{
"end_time": 5776.408,
"index": 218,
"start_time": 5750.009,
"text": " I don't see why it should be. I mean, you just draw lambdas from a distribution such that each one is unique. But they're all going to behave differently. I mean, I don't understand how you would... I mean, the reason why we can say a certain percentage of human beings have typo blood is because actually their DNA is exactly similar in that respect."
},
{
"end_time": 5805.725,
"index": 219,
"start_time": 5777.5,
"text": " But it's not. I mean, it's similar in terms of what determines their blood type. Right. But it's but each of our DNA, all the people who have typo blood have the same genes for typo DNA is unique. So sorry, Professor Palmer, please. So what I want to do is take one of these lambdas and change what actually happened zero zero to something that might have happened, but didn't happen, say zero one. And I'm going to ask my theory"
},
{
"end_time": 5836.425,
"index": 220,
"start_time": 5807.551,
"text": " What right? What row am I going to? What row does my theory predict for that counterfactual measurement setting zero one? And what I'm saying is there are situations where that returns the identical value of zero. So that's a violation of statistical independence, which has got nothing whatsoever to do with statistics of anything. It's just it's just. It's just a statement that one"
},
{
"end_time": 5865.094,
"index": 221,
"start_time": 5837.688,
"text": " that with a measurement setting that occurred in reality if i vary the measurement setting to something that let's say might have happened that didn't happen my theory says that that counterfactual violates certain conditions in the theory and therefore returns a row that's identically zero so we you know we can normalize the rows of the actual experiment it can be one over four or one over million doesn't really matter but it's not zero"
},
{
"end_time": 5890.896,
"index": 222,
"start_time": 5865.623,
"text": " But the theory returns a value of zero. And what I'm saying is that I think that is the type of thing that was at the back of Bell's mind, you know, when he wrote that paper, because he wasn't talking about statistical similarities between sub ensembles. He was asking this question, does the millionth digit matter for any distinct distinctively different purpose? That was the key point of his paper."
},
{
"end_time": 5920.879,
"index": 223,
"start_time": 5891.34,
"text": " Okay. How do you all feel progress can be made if there's such a large interpretive differences at the bedrock? Right. Okay. So I, again, I think we're, I think we've reached the point I predicted at the beginning. I said, I think counterfactuals have nothing to do with this. It's a red herring. I didn't want to get too much into counterfactuals because I understand what the condition is as a purely statistical condition about the actual statistics of actual ensembles and actual sub ensembles that are defined by the"
},
{
"end_time": 5931.869,
"index": 224,
"start_time": 5921.357,
"text": " choice of measurement setting, that statement just doesn't have to do with what would have"
},
{
"end_time": 5961.613,
"index": 225,
"start_time": 5932.398,
"text": " particular piece of information is otherwise rather useless. The way I read that is he says, well, that's a really important piece of information if you want to know what Alice chose. That'll tell you what Alice chose. Why? Because she was choosing on the basis of the output of this algorithm and that particular output determined on the nth run, whether she chose this way or that way. But he says for any other distinctive purpose, it's a rather useless piece of information."
},
{
"end_time": 5992.09,
"index": 226,
"start_time": 5962.108,
"text": " I don't hear any counterfactuals in that. I don't hear any claims about... I don't even know how to evaluate the claim. What would the world have been like if the millionth digit of Pi had a different parity than it actually has, right? That's a counter-mathematical. I don't even know how to make sense of it. I don't think it has to do with what Bell has in mind when he says this information is not useful for any other purpose. But we're just now going back and forth over the same territory, and I just don't think we're making any progress here. So I guess I feel like I've stated"
},
{
"end_time": 6013.251,
"index": 227,
"start_time": 5992.551,
"text": " okay i think i think people can go look at the theorem they can look at mathematics they can look at the mathematical condition and see what they see in it right i just going to finish i mean we can finish but let me just reread you know what bell wrote he wrote we can calculate the consequences of changing free elements of a theory be they only initial conditions"
},
{
"end_time": 6039.77,
"index": 228,
"start_time": 6013.899,
"text": " And so can explore the causal structure of the theory. I insist that be his beables paper is primarily an analysis of certain kinds of physical theory. Now, why would he have written that if the central point wasn't about whether your physical theory had had three elements that could be changed? He uses the word change is clearly your ability to change"
},
{
"end_time": 6068.66,
"index": 229,
"start_time": 6040.606,
"text": " variables in your putative physical theory is central to Bell's theorem and that's what he says and and I'm just coming up with a model where what might seem reasonable actually turns out to be wrong and I think that model can be a useful way of understanding Bell's the violation of Bell's inequality without having to resort to non-locality which is very anti-relativistic and so difficult therefore to"
},
{
"end_time": 6095.469,
"index": 230,
"start_time": 6069.582,
"text": " I hope one day, Tim, you'll invite me to Croatia. It sounds like a fantastic institute. I'd love to spend a few days with you chatting over a glass of wine and, you know, a wonderful wine here."
},
{
"end_time": 6122.381,
"index": 231,
"start_time": 6096.135,
"text": " I'm sure it's great wine, great local wine. I'm sure it's absolutely wonderful. So, um, yeah, who knows? All right. Well, thank you all. And again, if you have any thoughts afterward and you're like, you know what? I think that we can make some ground, some headway. Actually, can I, can I just make a tangent? I'm not going, I promise I'm not going to go back to the, to what we've just been fighting over. Sure. But there is a kind of conceptual point I would like to make. Um,"
},
{
"end_time": 6152.244,
"index": 232,
"start_time": 6124.07,
"text": " That is, Tim ended up saying, look, this non-locality really doesn't seem to be consistent with relativity. And yeah, that's right. I mean, that's why Einstein hated standard quantum mechanics, the spooky action at a distance. He hated it from the beginning. He hated wave collapse because it seemed to be instantaneous. Absolutely. But I do think it's worth pointing out that"
},
{
"end_time": 6182.875,
"index": 233,
"start_time": 6153.046,
"text": " Special relativity was developed by reflecting on classical Maxwellian electrodynamics, which is a local theory and could not violate Bell's inequality. And general relativity was developed by taking that and then trying to make it give back to good approximation Newtonian gravitational phenomena. And that's also a local theory and could not violate Bell's inequality. Well, if we let the gravity go at the speed of light,"
},
{
"end_time": 6209.258,
"index": 234,
"start_time": 6183.899,
"text": " So GR and SR were perfectly good reactions to what Einstein had before him. But what he had before him were theories that could not violate Bell's inequality. That is that he had theories that could perfectly well be local. And it seems to me that"
},
{
"end_time": 6227.824,
"index": 235,
"start_time": 6211.203,
"text": " The question is how do you react when you find out there is this thing Bell's inequality and it is in fact violated and that would have shocked Einstein to his core. But it does seem to me a reasonable thing is to reassess and say, well, what if I could give you a theory?"
},
{
"end_time": 6252.637,
"index": 236,
"start_time": 6228.677,
"text": " That isn't relativity, but does give relativity to good approximation or relativistic structures. Let me put it this way. Relativistic structures are in it or emerge from it either to very good approximation or even precisely. But they have more than general relativity. They have more structures, say they have a preferred foliation."
},
{
"end_time": 6277.5,
"index": 237,
"start_time": 6253.899,
"text": " Is it unreasonable to say, well, why do you want this preferred foliation? The answer is, well, if you give me that, I can easily write down dynamics that will violate Bell's inequality. And I don't have to violate statistical independence or anything else. This can be done. It's kind of easy to do. It just seems to me that the goal of maintaining relativity as the last word in space-time structure"
},
{
"end_time": 6301.374,
"index": 238,
"start_time": 6278.541,
"text": " I don't understand because those theories were developed in ignorance of violations of Bell's inequality and they were developed in a setting where there was no pressure to be able to violate Bell's inequality at space like separation because nobody knew you could. So I think physicists do have this deep attachment to relativity. It's a beautiful theory. GR is a beautiful theory."
},
{
"end_time": 6325.52,
"index": 239,
"start_time": 6301.834,
"text": " Unlike quantum mechanics, it's an understandable theory. The more you work with it, the better you understand it. You work out all these models and you see what's going on. I have a deep aesthetic appreciation for it, but it just seems like trying to work violations of Bell's inequality into it, there's a really"
},
{
"end_time": 6355.606,
"index": 240,
"start_time": 6326.681,
"text": " I don't want to"
},
{
"end_time": 6385.981,
"index": 241,
"start_time": 6356.391,
"text": " You know, I mean, good on you and good luck with your theory. But I just want to respond to that. The general point. I mean, Maxwell's equations are basically linear equations, so they wouldn't they wouldn't exhibit any of the sorts of things that I've been talking about. So, you know, you can run you can run Maxwell's equations from a slightly perturbed initial condition and you'll get a another perfectly good solution of Maxwell's equations."
},
{
"end_time": 6412.961,
"index": 242,
"start_time": 6386.459,
"text": " So there's no way Maxwell's equations would ever violate this notion of counterfactual definiteness or what I would call violate statistical independence. But GR is actually a different kettle of fish because it is nonlinear. And as I think I mentioned earlier, you can, Misner did this years ago, concoct cosmologies, which are chaotic and"
},
{
"end_time": 6441.852,
"index": 243,
"start_time": 6413.251,
"text": " You can envisage a situation where you have a cosmological solution of GR, which exhibits the kind of fractal invariant set structure. So then the question of counterfactual definiteness really is relevant in this scenario because you can perturb off the invariant set of something like the Mixmaster universe and"
},
{
"end_time": 6472.483,
"index": 244,
"start_time": 6442.671,
"text": " I mean, if you were going slightly beyond what we're discussing, but this for me,"
},
{
"end_time": 6500.862,
"index": 245,
"start_time": 6472.756,
"text": " brings into focus what I think is the real message behind Bell's theorem. And I think it's a really profound one. And it's not to do with non-locality, but it's to do with the kind of holistic structure in the laws of physics that we don't have at the moment, for example, in the standard model. Because if this idea about, you know, fractal attractors and stuff, geometry of these attractors is right, these are very holistic structures. These are not things that you'll see by just looking at the Planck scale."
},
{
"end_time": 6528.285,
"index": 246,
"start_time": 6501.493,
"text": " You'll only see them by looking at the structure of the universe as a whole. So this may be telling us that the whole kind of direction that physics is contemporary theoretical physics is trying to go by just kind of going down to smaller and smaller scales, hopefully to the plank scale. So people say this is probably not going to solve our quantum gravity problems. That's my view. And that's what that for me is the big message behind behind Bell's theorem."
},
{
"end_time": 6538.183,
"index": 247,
"start_time": 6530.077,
"text": " Thank you all for being so generous with your time. The book that Tim Palmer has written is a great"
},
{
"end_time": 6562.841,
"index": 248,
"start_time": 6538.49,
"text": " Popular science book on the subjects that we've just spoken about is called The Primacy of Doubt. The links to that will be in the description. The links to the John Bell Institute, especially the GoFundMe, because there isn't a place to go. Well, there's a place we don't own it. OK, there's a place they would like to own it. There's a place and we built stuff here, but we don't own it. And so if we if we can't buy it, we're going to lose everything we've put into it."
},
{
"end_time": 6588.814,
"index": 249,
"start_time": 6563.2,
"text": " Thanks for having us. Thank you very much. Thank you."
},
{
"end_time": 6616.323,
"index": 250,
"start_time": 6589.633,
"text": " The podcast is now concluded. Thank you for watching. If you haven't subscribed or clicked that like button, now would be a great time to do so as each subscribe and like helps YouTube push this content to more people. You should also know that there's a remarkably active Discord and subreddit for theories of everything where people explicate toes, disagree respectfully about theories, and build as a community our own toes. Links to both are in the description."
},
{
"end_time": 6632.005,
"index": 251,
"start_time": 6616.323,
"text": " Also, I recently found out that external links count plenty toward the algorithm, which means that when you share on Twitter, on Facebook, on Reddit, etc., it shows YouTube that people are talking about this outside of YouTube, which in turn greatly aids the distribution on YouTube as well."
},
{
"end_time": 6652.773,
"index": 252,
"start_time": 6632.005,
"text": " Last but not least, you should know that this podcast is on iTunes, it's on Spotify, it's on every one of the audio platforms. Just type in theories of everything and you'll find it. Often I gain from re-watching lectures and podcasts and I read that in the comments, hey, toll listeners also gain from replaying. So how about instead re-listening on those platforms?"
},
{
"end_time": 6682.056,
"index": 253,
"start_time": 6652.773,
"text": " iTunes, Spotify, Google Podcasts, whichever podcast catcher you use. If you'd like to support more conversations like this, then do consider visiting patreon.com slash Kurt Jaimungal and donating with whatever you like. Again, it's support from the sponsors and you that allow me to work on toe full time. You get early access to ad free audio episodes there as well. For instance, this episode was released a few days earlier. Every dollar helps far more than you think. Either way, your viewership is generosity enough."
}
]
}No transcript available.