Theories of Everything with Curt Jaimungal - Tim Maudlin: Quantum Nonlocality Explained FROM SCRATCH

Starting point is 00:00:00 Most of what you hear about quantum mechanics is wrong. The subjectivity, the thing about observation, even the indeterminism. None of that is forced on you. All this talk about how in quantum mechanics, the observer can't be left out. You've heard it a million times. No, this is so outrageous. This is Tim Modlin, Professor of Philosophy at New York University, founder and director of the John Bell Institute,

Starting point is 00:00:24 and one of the world's leading philosophers of physics. Today, I'm thrilled to bring you a lecture explaining Bell's theorem and non-locality in quantum physics with zero background knowledge required. The proof of non-locality is the most astonishing proof of any physical fact in the history of mankind. Facts are facts and proofs are proofs. On this channel, I, Kurtzimungle, interview researchers regarding their theories of reality with rigor and technical depth. Modlin is an expert elucidator, and you're in for a treat. Bell uses Einstein's own tools to prove that.

Starting point is 00:00:57 Einstein was wrong. Locality is dead. All right, this is the continue of the previous lecture, which went obscenely viral for some reason on quantum mechanics. How do you feel about that? Well, I'm happy. I mean, I've been trying to explain this stuff for my entire career. So, so quite honestly, to be able to get it presented to so many people at once is very exciting for me. It's kind of a capstone to all of this. Hopefully, it's a... make a little difference. Many of the comments, and I'll place them on screen, they say this was one of the best explanations of quantum mechanics ever from someone who doesn't know much quantum mechanics, but they've heard quantum mechanics explained 20 times. There were many people who

Starting point is 00:01:41 recently came out of graduating from physics, so they have their bachelor, some have their graduate degree, and they said this was the clearest explanation of EPR. And that was just part one. Now we're on to part two. So thank you so much, Professor, for giving me such a treat and the audience such a treat. Well, thanks for giving me the chance to do it. And my apologies for it going so long, but that's what it takes. So I'm going to begin, if people didn't watch the first one, they might want to watch it. If you did, here's just a really fast summary of the main points of what was proven in the EPR paper. So that was more or less where we got to by the end of last time. And so all of this is things I've said before, including slides that were before, but just so they're fresh in mind. So the EPR paper asks the question whether quantum mechanical description of reality, meaning the wave function is complete.

Starting point is 00:02:45 And so these are now just direct quotes from the paper. It's a very short paper and a very clear paper. And they tell you what they're after, right? So I'm just going to read it again. In attempting to judge the success of a physical theory, we may ask ourselves two questions. First, is the theory correct? And second, is the description given by the theory complete? It's only in the case in which positive answers may be given to both of those questions

Starting point is 00:03:14 that the concepts of the theory may be said to be satisfactory. The correctness of the theory is judged by the degree of agreement between the conclusions of the theory and human experience. So again, this is what we would call empirical adequacy. Is this theory making good predictions as far as we can tell? This experience, which alone enables us to make inferences about reality, in physics takes the form of experiment and measurement. It is the second question, the completeness question, that we wish to consider here as applied to quantum mechanics. So they're nowhere questioning the accuracy of the quantum mechanical predictions. That wasn't the issue. But then, what do you mean by a complete theory? Whatever the meaning assigned to the term complete, the following requirement for a complete theory seems to be a necessary one. Every element of the physical reality must have a counterpart in the physical theory. So think of the physical theory as the mathematical apparatus, together with all the commentary and so on, that you're given when you're given the mathematical apparatus so that it becomes an attempt to represent physical reality. We should call this the condition of completeness.

Starting point is 00:04:26 The second question is thus easily answered as soon as we're able to decide what are the elements of the physical reality, right? If we know something's real, we can then ask, is that represented in this formalism? What they're going to give us is a criterion for the existence of an element of physical reality. And again, you have to remember a criterion is not a definition. It's not something that will cover every case. It is just a sufficient condition. If the criterion is met, then they say there must be an element of physical reality. Why? Because, of course, how do we get our hands on elements of physical reality?

Starting point is 00:05:03 So the elements of physical reality cannot be determined by a priori philosophical considerations, but must be found by an appeal to the results of experiments and measurements. A comprehensive definition of reality is, however, unnecessary for our purpose. We shall be satisfied with the following criterion, which we regard to the, as reasonable, and this is the main point. If, without in any way disturbing a system, we can predict with certainty, that is, with probability equal to unity, the value of a physical quantity, by which they really mean the outcome of an experiment, the outcome of a measurement, or something like that, then there exists an

Starting point is 00:05:43 element of physical reality corresponding to this physical quantity, right? If I can predict the outcome of a momentum measurement on a system, predict it with certainty, completely accurately, then there is some element of physical reality in that system that corresponds to that. It seems to us that this criterion, while far from exhausting all possible ways of recognizing a physical reality, at least provides us with one such way whenever the conditions set down and it occur. And notice they're very stringent conditions. You have to be able to predict with certainty the outcome of your measurement without in any way disturbing the system. regarded not as a necessary, but merely as a sufficient condition of reality, this criterion is

Starting point is 00:06:26 an agreement with the classical as well as the quantum mechanical ideas of reality. Now, that criterion you have to pay attention to because part of the criterion is that you're able to make this prediction without in any way disturbing the system that you're predicting the outcome of. and his main complaint, Einstein's main complaint about the Copenhagen presentation or understanding of quantum theory from the beginning, and we went back last time to 1927 in the Solve conference, was that it seemed committed to non-locality. It seemed committed to the idea that something happening at one place could immediately disturb and change physically the physical situation

Starting point is 00:07:11 far away instantaneously. And that he called spooky action at a distance. Why did Einstein object to spooky action at a distance? Well, first of all, in itself, it struck him as a strange thing. It struck Newton as a strange thing, too. And secondarily, because it's supposed to be an instantaneous action, it would be a threat to relativity, because in relativity, nothing counts as instantaneous.

Starting point is 00:07:39 There's no way to define an instantaneous. instantaneous action because there's no absolute simultaneity. And Einstein just thought, look, you just don't want a theory where what happens in one region of space can suddenly and instantaneously affect the physical conditions in distant, especially arbitrarily distant regions of space. Now, one could worry, in addition, if you had it, is that change mediated by something going from the one to the other? If something I do here has an effect over there, is there some physical item that goes from one to the other, something we would call a tachion if this has to be faster than light, that's yet another issue, right?

Starting point is 00:08:23 You know, you might be even more upset if this action at a distance wasn't mediated. But that's not the issue here. It's just, is there such a thing? Einstein's worry was not about indeterminism. It wasn't about this issue of God playing dice. it's also not about signaling. He never expresses any concerns that the Copenhagen understanding of quantum theory

Starting point is 00:08:47 would allow superluminal signaling. If he thought that, he would presumably have said, okay, show us, right? If he said, you know, according to you, not only is there this spooky action at a distance, but I can use it to send signals, he presumably would have said,

Starting point is 00:09:02 now go into the lab and show I can do this. But he never asked them to do that. He never thought you could do that. In fact, he thought it was manifest in the examples he was talking about that you can't do it. And that's what's so upset him, right? He's saying, okay. So it wasn't an issue about superluminal signaling. This also is just to emphasize, Einstein thought if you accept what Copenhagen says, that's a threat to relativity.

Starting point is 00:09:29 He did not think it implies superluminal signaling. That's proof that Einstein didn't think of relativity in terms of signaling, right? He didn't think the essence of relativity was you can't send superluminal signals. He couldn't have, or else he wouldn't have saw these examples he gave as worrisome for relative. What he's objecting to is in this fundamental picture that Bohr and Heisenberg are presenting, that picture just commits you to this kind of spooky action at a distance, the action, the change, the physical dependency of what happens over here on what happened way over there. In the EPR argument, they only look at perfect correlations, at situations where when you're looking at the outcomes in these two distant labs, the correlations between them are perfect so that knowing the outcome in one lab allows you to predict with certainty, the outcome in the other. That's part of the criterion of reality, when you can predict with certainty and so on.

Starting point is 00:10:31 So they do use that case. Then having done that, you can additionally derive as a theorem that if you rule out spooky action at a distance, if you have a local theory in Einstein's sense, it must also be a deterministic theory. So you do get conclusions about determinism, but not from assumptions about determinism. You get conclusions about determinism from assumptions about locality. I've been called. I've been called. I've been called. these perfect correlations, EPR correlations, because they first appear in the EPR argument, and they're essential for the application of the criterion of reality that they give. I also argued in the first part that the perfection of those correlations isn't the point you could relax from perfect correlations to high correlations in otherwise similar circumstances and make little adjustments to the argument, and the argument. would still go through, right? You'd still have the argument that if you rule out spooky action at a distance, then the quantum mechanical description is not complete, which is the main point that

Starting point is 00:11:45 they were trying to make. Just to, again, I had this last time, but just to repeat it, because he always says things in the right way. Here's Bell talking about the logic of the EPR argument. It is important to note that to the limited degree to which determinism plays a role in APR argument, it is not assumed, but infer. What is held sacred is the principle of local causality or no action at a distance. Of course, mere correlation between distant events does not imply action at a distance, but it only implies needs to imply that there's a correlation between the signals reaching the two places. These signals, in the idealized example of bone, which we're going to talk about in a minute, must be sufficient to deterred.

Starting point is 00:12:31 whether the particles go up or down, so there you get an inference of determinism, for any residual undeterminism could only spoil the perfect correlation. It is remarkably difficult to get this point across that determinism is not a presupposition of the analysis. There is a widespread and erroneous conviction that for Einstein, determinism was always the sacred principle, the quotability of his famous God does not play dice, has not helped in this respect, among those who had great difficulty, this Einstein's position was born. And then in the first part I gave, went on with the quote,

Starting point is 00:13:07 but I'm not going to go on with it here. So where does this locality assumption, this no action at a distance assumption, come into the EPR argument, what role does it play logically? Well, it plays a role when you look at the reality criterion, and it says, if you can predict with certainty,

Starting point is 00:13:27 without any way disturbing a system, how the system will behave, then you have an element of reality. How do you know you're not disturbing the system, right? You do something to make the prediction. What assures you that what you do didn't, in fact, disturb the system, right? And it's there that what Einstein, Podolsky, and Rosen simply tacitly assume, I mean, they don't make a big deal of it. They think it's just something you wouldn't question is that separating,

Starting point is 00:13:59 Alice and Bob's labs far apart from each other, arbitrarily far apart, running the experiments at what we call space-like separation so that not even light could get from one to the other in the course of the experiments, that ought to be sufficient to assure you don't have a disturbance, that nothing Alice does or nothing that happens in her lab disturbs Bob's situation, nothing that Bob does, or anything that happens in Bob's lab, disturbes. Alice's situation. That's where the locality assumption plays a role in the logic of EPR. And if you grant them that, the argument goes through. So the claim is the argument is perfectly if you grant them no spooky action at a distance. Now, this is, again, what I'm saying

Starting point is 00:14:52 here, right, what happens in Bob's lab should not physically depend in any way on what Alice decides to do in her lab, and vice versa. And if there's some especially indeterministic interaction analysis lab that could come out different ways, then which way it actually comes out should not have any influence on Bob's lab, right? How could that information about how it came out? Supposing it was indeterministic, supposing there were different possibilities it could have occurred, how could the information about which one did occur get to Bob in time to have any influence on his outcome? Okay. If you grant that that this spatial isolation of the labs creates causal isolation, then everything in the logic goes through and what they conclude

Starting point is 00:15:50 are two things. The main thing they conclude is what the whole paper was about. Then the a mechanical description given by the wave function is not complete. There's more to the system than is represented there. Because the correlations are perfect, you could also and additionally imply that in a local account of all this would have to be deterministic, because that's the only way you could assure these perfect correlations. So that's where we were last time. Great. Now we have a little interlude between Act 2 and Act 3, which is not anything new. but it is very important nonetheless historically. And it was what happened when David Bohm wrote his textbook called quantum theory.

Starting point is 00:16:39 And he gave the EPR argument but changed the physical details in a way that does not at all affect the logic of the argument, but was nonetheless absolutely essential for allowing Bell to do what he did. So we just have to talk about what Bome did. And because you might ask yourself, why didn't Einstein himself come up with Bels theorem? In a way, you know, you get to Bell's theorem by reflecting on EPR. Certainly Einstein reflected on EPR. Why didn't he make the moves Bell made? And the answer is that because Bell had been thinking about Bome's way of,

Starting point is 00:17:24 Boehm's example. And we have no reason particularly to believe that Einstein, certainly before even reading Boehm in 1950, thought about the example reformulated in this way. Okay. So what did Boehm do? So he wrote this textbook. It gets published in 1951. Boehm is an assistant professor at Princeton. Bowen's own education was more or less Copenhagen-ish, and he was not out to undermine the Copenhagen approach in this textbook. It was just the opposite. He was out to try to express it in a very clear way so people would understand what quantum theory was, according to Copenhagen. And he worked hard at the pedagogy, and he worked hard at working out a lot of detailed examples. applications of the theory and so on. Of course, because he also was interested in the basic concepts,

Starting point is 00:18:27 he was interested in the EPR argument, and he wanted to present the EPR argument. What he did was he changed it from the specific example that EPR used, which had to do with momentum measurements and position measurements made on these distant particles, to spin measurements. And the result of that was twofold. One was there's just some technical mathematical issues that go away. They get a little messy in the EPR case because formerly there are no position eigenstates and no momentum eigenstates. And okay, you could you could think there's something problematic about that, but all that's completely cleaned up. The math is just pristine. And then we'll see something else happens that it's not clear bone even recognized, right? It seemed to be bell.

Starting point is 00:19:20 was the guy who recognized it. So we have to start with spin. We have to now understand what we mean by making a spin measurement. And in particular, we're going to talk about measuring spin in the way it was originally measured using what's called a stern garlock apparatus. People have probably heard these terms. Very easy to understand the physics here. I mean, the experimental situation is actually quite straightforward.

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Starting point is 00:21:35 Nobody would try to use the original EPR state anymore. Actually, that's what I was going to say is that most of the time when you're taught what EPR is, look up in a YouTube video, the majority of the time, it's about spin, spin up, spin down, separated. Yeah. And again, I mean, it's fine because the logic is identical, but it's worthwhile knowing that that's not the historical case. As I say, especially if he asked, but why didn't Einstein see all this?

Starting point is 00:22:00 The answer is he was thinking about the way he was thinking, the kind of experimental situations he was thinking about, it would never have occurred to him to do what you've. would be the analogous thing that you can do in the spin case, as we'll see. So it's just, you know, to understand the trajectory of the history, it's important to see that. Again, logic is the same. I gave the original EPR argument in terms of perfectly correlated momentum between the particles. Logic is exactly the same. So none of that changes because you're dealing with a spin state of a pair of particles,

Starting point is 00:22:39 an entangled spin state of a pair of particles, where the quantum mechanical formalism does predict perfect EPR correlations between the outcome in Alice's lab and the outcome on Bob's lab, because those are perfect again, as soon as Alice sees her result, she can perfectly predict Bob's result.

Starting point is 00:23:00 If you grant that what she did didn't disturb Bob's particle, then you're off to the races, right? So in a causally local theory, all of this, you know, all the same apparatus is there. And what I said last time that you could really run the argument with less than perfect correlations with certain little changes. It goes through just as well, it seems to me. However, there is something really new here. and I don't know that Bome realized it.

Starting point is 00:23:38 I think Bome just thought, I mean, as a guess, I have no historical data about this. He just thought spins easier to work with. It's simpler, easier to understand the things you write down. I mean, if you remember the EPR state, it's this integral over all possible momentum, blah, blah, blah, and then you've got an integral, and it's, you know, it's kind of, you know, a little scary.

Starting point is 00:24:04 As we'll see, the analogous spin state is very easy to write down. You don't have any integral. You just hold it in your hands and you see what it is. I don't know that Bome also saw that he was opening up the door to something that Bell will then take advantage of later. Okay. In the EPR case, again, the only situation you discuss is, when both Alice and Bob make a momentum measurement, or when both Alice and Bob make a position measurement.

Starting point is 00:24:43 And that's it. And if you were to ask, you could ask, well, what if Bob makes a momentum measurement and Alice makes a position measurement, right? I mean, in that situation, you could ask that.

Starting point is 00:24:56 And the theory would give you an answer, and the answer is now there's zero correlation between the outcomes. Then what happens in Bob Lab, gives you no information about what's going to happen in Alice's lab and vice versa. So it's of no use for anything in the neighborhood of this kind of argument. So if you check the same thing on both sides, you get these perfect correlations. If you check different things, you get no correlations. And that's going to change once we have spin.

Starting point is 00:25:26 If you try to do formally analogously in terms of position and momentum, what bone does in terms of spin and what Bell does in terms of spin, you wouldn't even know what kind of experiments to do. I mean, they would be mathematically formally defined operators, but if you ask, well, what kind of an experiment do I do to measure that? You would say, you know, it doesn't have any obvious experimental meaning. What we're about to see that with spin, it does. And it's very simple to understand. Okay. Um, In the case of spin, as we'll see, on Alice and Bob, each actually have an infinite number of different measurements they could make. Easy to describe what they do.

Starting point is 00:26:13 Easy to describe what the outcomes would be. We can do this all the time. We do this all the time in the lab. So what is spin? Well, there is this physical characteristic we call spin. formally, when we have an object as a particle with spin, instead of the wave function being a complex function,

Starting point is 00:26:37 it's called a spinorial function. We could go into the math. It doesn't really matter. Physically, people often say, a particle with spin acts as if it has a magnetic moment, if it's like a little bar magnet. And then sometimes they say, well, if it's a charge particle, if you imagine a classical charge particle, a classical charge

Starting point is 00:27:00 ball of charge, literally spinning, it would create a magnetic field. And then, I mean, there's actually kind of a funny meme where they say, yeah, so spin, to understand spin, it's like there's a little ball, a charge ball that's spinning, except there's no ball and nothing is spinning, which is about right. I mean, you have this kind of classical. system that you're using and then, but none of the classical features that make it relevant do you think exist. So it's a weird situation. All you really need to know is that it behaves as if it has, it's like a little bar magnet with a north and south pole. It has a magnetic moment. And if you have something with a magnetic moment like that, and again, this is purely classical,

Starting point is 00:27:47 and you shoot it through an in homogeneous magnetic field. So a magnetic field that's changing how strong it is in a certain direction, then the prediction is that the object will be deflected. It could be deflected up, it could be deflected down. Yeah. I have a quick question. Sure. Okay, use the phrase, it behaves as if. Now, when we're speaking about something fundamental, the electron is supposedly fundamental. When someone says the electron behaves as if it has charge, let's imagine that. We just say the electron has charge. So what's the as if doing here? Well, the as if here is, at the end of the day, all we really are going to care about is doing certain experiments and getting certain outcomes. And the outcomes will be spots on

Starting point is 00:28:42 screens that either appear up here or down there. Now, if it were a classical spinning charged object with a magnetic moment and you shot that thing, according to classical physics, shot it through this magnetic field. Classical physics would predict that it will be deflected, and it will hit the screen, it could hit the screen in different places and be deflected either up or down. And it'll tell a whole story of it going through and the forces on it and blah, blah, blah. Here what we're saying is, well, I'm not saying that it really is a spinning object.

Starting point is 00:29:19 I'm not saying it really does go through. I'm not even saying it goes through on a definite trajectory. All that's really going to matter is that the spots flow on the screen. So when I say it behaves as if, I mean, behaves with respect to the actual observable outcome, right? It's the same kind of observable outcome you would get from such a classical system. That's the only respect in which I'm claiming it's behaving like that. Got it, right? So this is very paired back from, you know, the classical form.

Starting point is 00:29:55 physics would attribute all kinds of physical characteristics to such a system that would lead to this behavior. We're not claiming that it has all of those characteristics, all of them, or anything like all of them. We're just claiming that with respect to the outcome of this experiment. Okay? So in the classical case, if I take my little bar magnet and throw it through this field, it'll tend to be deflected. How much and in what direction will it be deflected? Well, that's depends on how this bar magnet is oriented. If we imagine the field is changing in this direction, depends on how the bar magnet is oriented with respect to that axis, that direction. It'll get a maximum deflection in one way. If it's oriented this way, say with the north here and the south

Starting point is 00:30:43 here, I'll get the maximum deflection in the other way if I flip it over and now the north is at the bottom and the south is at the top. If I oriented at right angles, there'll be no deflection, it'll go straight through. If I oriented at some angle, it'll still, it'll be deflected, but less than it would be if it were exactly oriented, right? So this is the range of outcomes the classical theory would predict, given this inhomogeneous magnetic feel. Okay? And so, again, to do this, classically, again, it's very easy. You just need to make an in homogeneous magnetic field. So the field lines, if you kind of picture the magnetic field by field lines, the density of field lines is changing. It's not constant. And the easy way to do that and the way

Starting point is 00:31:36 they did do it is just to take your magnet that has a big magnet that has a north and a south pole and you make them geometrically different. You make one of them, say, the North Pole very pointy and the one on the bottom very flat or even concave. And from that, geometrical difference when you draw the magnetic field lines, you see the density changes from top to bottom. And that's what, that classically is what would give you a net force on this bar magnet and deflected. But as we just saw, classically, if you asked, well, how is it going to be deflected? You could say, well, it depends on the exact orientation of my bar magnet. There's, there's a range of cases. There's a continuous range of cases from a maximum downward to a maximum

Starting point is 00:32:21 upward deflection. What happens when you treat this quantum mechanically, and again, it's now, if you ask, but why does it do that? We're not in the business right now of saying why it does that. This is just what quantum mechanical formalism predicts. It says, well, that range of possible outcomes gets discreetized. There are only two. There will be only one of two possible outcomes for a spin-half particle. It'll either be deflected. it up a certain amount or deflected down a certain amount. You can think of those as corresponding to the maximum and minimums that you had in the classical case. And it'll never go straight through, and it'll never go just deflected halfway up or anything. It'll either go up or down.

Starting point is 00:33:06 Binary outcome. That's for a spin half particle. For a spin one particle, it would be three. It would be of deflected up or go straight through or be deflected down. So then you would have three outcomes. That discretization is characteristic in certain cases of quantum mechanics. Not always, not everything is discretized in quantum mechanics, but sometimes it is.

Starting point is 00:33:29 This is a case where it is. Again, that makes this very easy to describe the experimental data, because in each run of the experiment, the outcome is either it went up or it went down, and there's no further but how much, right? Here's a

Starting point is 00:33:44 picture that just illustrates everything I just said. My stern Garlock magnet has this pointy north end and this flat south end. I have a particle source that's shooting the electrons through the magnetic field. The classical prediction, which is this blacked in eye, says the particle could end up anywhere there. Now, you might ask, why is it this eye shape? And the answer is because as you move, the strongest effect is right straight down the center. And as the particle drifts off to one side or the other, the magnetic field is no longer as in homogeneous, and the effect then just damps down. So the eye kind of goes like that. Whereas in the quantum mechanical case,

Starting point is 00:34:30 all that black middle is gone, right? Things, that's, the particles will not show up in the middle. They'll either all be, each one will either be deflected up or it'll be deflected down. Again, the eye shape for the same reason, because the magnetic field is going down. down. So there's the quantum mechanical prediction. Very different than the classical prediction, if you want to say, what's a good experimental reason to think that quantum mechanics is doing something right here, that classical mechanics wasn't doing? And now I want to show you, and I love, I like to do this because this is a wonderful thing. This is the actual data. This is the data that Stern and Gerlock got

Starting point is 00:35:15 when they first did this experiment this was printed on a postcard and sent to bore himself and the you know you have the original handwriting interesting of the experimenters and you exactly see on the left with no magnetic field everything's just you have a straight line everything's just going through straight

Starting point is 00:35:35 and on the right that eye shape and again you'll notice the white the white in the middle. The particles are not, none of the particles are going straight through in the middle. They're either going to this side

Starting point is 00:35:47 or to that side. So, and you know, you shows what the sizes are and everything. So this is stuff really going on. I see a little dagger coming out of the right side. I don't know if that's just

Starting point is 00:35:57 an artifact of the printing. I, yeah, that little thing at the top, I assume it's, you know, look, this is real experiments.

Starting point is 00:36:07 Yeah, yeah. You have experimental effects. I couldn't tell you why that occurs. But there's no reason to think that that indicates something went drastically wrong. We've done this enough now to know that those predictions were right. Okay. So when we do these spin experiments, what's the situation? Well, in the EPR case, as I said, there are only two quantum.

Starting point is 00:36:40 that people ever talk about measuring, which are position in momentum. And as far as that goes, in terms of the outcomes they could get, that's a continuous spectrum. They could get any momentum, and the particle could show up at any position. There's no quantization there. In the spin case, on the one hand, instead of an infinite number of possible outcomes, you always have one of two possible outcomes when you do the experiment. So it simplifies in that way. But in the other direction,

Starting point is 00:37:13 instead of only having one or two possible experiments you can do, you have an infinitude of possible experiments you can do because you orient your stern-Garlock magnet, and you can twist that magnet however you want. You can have it this way or this way or 45 or 30 or 60. And so you now have an entirely new palette of practically doable experiments from which you can get this data. And that's, that second part is what's going to lead us to Bell's theorem.

Starting point is 00:37:49 What just as in the original EPR case, the experimenters can by their own, whatever way they want, decide whether to measure position or momentum. Here are two experimenters, Alice and Bob, can, in whatever way they like, orient, determine the orientation of this stern garlock magnet. So all of those orientations are available to them. They can use any choice procedure they want to pick on a particular run of this experiment how the magnet should be set. So when we indicate a spin experiment, one thing we have to do is indicate the direction

Starting point is 00:38:27 of the magnet. We have to give a direction. This doesn't come in the original EPR case because that wasn't any, they weren't orienting anything. And so we speak of X spin or Y spin or Z spin or 45 degrees between X and Y spin, where all of those just indicate a direction in space. And that's going to be the direction that points from, say, the south to the north pole of my magnet. And it can be anything.

Starting point is 00:38:52 And no matter how I orient the magnet, I'll always either get one of these two outcomes, which are typically called spin-up or spin-down outcomes. either the particle is deflected toward the North Pole or away from it. So in a way, we get a conceptual simplification because we no longer have a continuous spectrum, we have just two possible outcomes. And so that makes it very easy

Starting point is 00:39:23 to talk about what the data out of one of these experiments is going to be, because you just, on every run, tell me which way was each, was the magnet pointed and did it come out up or down? That makes the analysis very easy. Theories of Everything is brought to you by Mod. Mod prescribes a once or twice daily medaphanal drink that can keep you energized and alert throughout the day.

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Starting point is 00:40:21 planet. Soldiers and pilots use it, as well as astronauts aboard the space station, where full concentration is required. It's now available at modmod.com to qualifying patients. Visit mod.com, that's mOD.com, for a free consultation and get 10% off your first order plus free shipping with the promo code T-O-E. That's promo code tow at mod.com. See their website for important safety information, and we thank Mod for sponsoring the pod. Now, quantum mechanics treats spin, as I said, by changing the wave function from a complex valued one to a so-called spinner valued one. We don't need to go into any of the mathematical details of that, but we can just talk about what possible spin states, quantum mechanical spin

Starting point is 00:41:13 states, a single particle, spin-half particle like an electron, can be it, according to the theory. There's a palette, as usual. There's a state. space. And if you have a state that is guaranteed according to quantum mechanical formulas, to give a certain result, if you check the spin in a certain direction, then we say, that is say X spin up. That particle is an X spin up, meaning if you orient your magnet in the X direction, the prediction is 100%, it'll be deflected up. And it's X-spin down if 100% according quantum mechanics, it's going to go down. Notice those are, again, perfect predictions, the kind that you needed to apply the EPR criterion of reality. You needed to be able to make

Starting point is 00:42:11 perfect predictions. You can prepare particles, as it turns out, so that they will all go up in the X direction. You can compare them, you can prepare them so they'll all go down in the X direction. You can prepare them so they'll all go up in the Y direction. If you twist the magnet, they'll all go this way or they'll all go that way. If you twist the magnet of 45 degrees, they'll all go this way, they'll all go that way. So you have all of that state space of spin states available to a single spin half particle. So there's just an easy way that you can just look at it and see what's being said to represent these possible spin states. And that's what we use. Typically, you'll see it on the screen, these so-called kets. So bar X arrow up.

Starting point is 00:42:59 Angle bracket just means it's been prepared. So if you check the spin in the X direction, it's sure to go up. Y arrow down. If you check in the Y direction, it's sure to go down. And you now, we would have to go into how you mathematically represent these. But it, it, It just turns out, interestingly, if you're able to perfectly predict what a particle will do if you check in the X direction, then you will be completely uncertain what it will do if you check in the Y direction, in an orthogonal direction, if you check at right angles, or the Z direction, anything at right angles. The more certain you are about what it'll do in the X direction, the less certain you are about

Starting point is 00:43:46 what it'll do in the Y direction and vice versa. And that fact, and that just falls right out of the quantum formalism, that's an example of what's called the Heisenberg uncertainty relation that everybody's heard of and nobody disputes that. I cannot prepare a particle in a way that I can predict if you check X, it'll say go up, and if you check Y, it'll go up, right? There is no such quantum mechanical state. So for a single particle, it's kind of easy. You say, well, what spin state is it in? Normally what you'd say is, well, there's some direction in which it's spin up or spin down.

Starting point is 00:44:30 You have to tell me that direction. You're to tell me whether it's up or down. Then you've nailed it down. That's the spin state it's in. Now, what if I have two particles? what if because we're now going to deal with sending a two-particle system we're going to send one particle to alice and one to bob what kind of spin states can a pair of particles be in well the first thing you want to say which is kind of obvious is they they ought to be in these states

Starting point is 00:44:56 if i can prepare a single particle x spin up and i can prepare a single particle y spin down then i can prepare a pair of particles the first one is x spin up and the second one's y spin down send this one to Alice and that one to Bob, right? So those are easy and you expect them and you can do that. And those are called product states where the spin of one particle has nothing to do with the spin of the other. They're just, they are independent of each other. Doing an experiment on one gives you zero information about what any experiment done on

Starting point is 00:45:27 the other would come out. Okay. So you would expect there to be those states and there are those states. And they're called product states. and you can kind of make any product state you want by giving one particle or particular spin and the other particle, whatever spin you like. And then how we represent that, and if you just look at the bottom here, again, it's very intuitive. We just put the A for the particle going to Alice, B for the particle going to Bob, and that first state would represent Alice's has been prepared

Starting point is 00:46:00 X-Spin-Up and Bob's has been prepared X-SPen up. And the second one, Alice has been prepared X-SPen-up, and Bob's has been prepared X-spin-down. And in the third one, Alice has been prepared Y spin-up, and Bob's has been prepared X-spin-up. All of those are possible. They have to be. They're there. But what we know is that what's really special about the EPR state,

Starting point is 00:46:23 the one that was used to run the EPR argument, was that it was entangled. It had this new feature, this very non-classical feature that Schrodinger recognized and gave the term that we, translate entanglement to. And these really have no classical analogs, right?

Starting point is 00:46:42 And that's why Schrodinger said it is entanglement rather than anything else. It's entanglement rather than, say, indeterminism that forces a departure from classical lines of thought. And so you can have entangled spin states between two particles. and oh, that's what I just said. The particular entangled state, the analog to the EPR state

Starting point is 00:47:12 in the EPR paper, is what we call the singlet state for a pair of spin-half particles. And it can be written now that I've told you, if you haven't even ever seen this before, you can kind of look at it and say, oh, I kind of see what that's going to do.

Starting point is 00:47:29 Or it's not that hard to read. which is nice. So it's the single state, and it's this. It is not, it is one over root two, so you have this weighting factor times the state where Alice's particle is X spin up and Bob's has X spin down, minus one, equal weighting factor one over root two, the state where Alice's is has spin down and Bob's has spin up. So as it were, one over root to this, minus one over root to that, where the this and the that are the product states. But we're not taking, we don't have a product state anymore because we're taking this some of them. We're adding them up, because these are vectors, and we're doing vector addition on them. And what happens in the

Starting point is 00:48:18 entangled state is, if you ask, but what state is just Alice's all alone in? It really isn't in a state anymore. I mean, you just can't characterize Alice. particle without somehow referring to Bob's, and you can't really characterize Bob's particle without referring to Alice's. They really have become, that's why the word entanglement, right? Their physical situation has become interwoven between the two of them in a way that mathematically you can't separate them and just have a product of this times that. So if I were to say, even if you didn't know any quantum mechanics,

Starting point is 00:49:00 okay, I have a pair of particles. I'm going to send one to Alice and one to Bob. Here's the spin state. What predictions would you make about what this will do? Now, if you just look at it without knowing any quantum mechanics or just a tiny bit of few hints, you might say, well, suppose Alice and Bob both decide to orient their magnets in the X direction. they don't have to, but suppose they decide to.

Starting point is 00:49:26 Sure. And then you'd say, well, the first part of that expression, that is a state where alices will go up and bobs will go down. And the second part is a state where alices will go down and bobs will go up. So you might say, well, probably I'll get one of those two outcomes, right? It looks like those are the only components that go into this thing, right? And that would be right. just by looking at it, you could say, yeah, there are two possible outcomes here.

Starting point is 00:49:57 Alice up, Bob down, and Alice down, Bob up. You'll never get both of them up. You'll never get both of them down. And you can even say a little more. There's our state again at the top here. You can say a little more because you've got one over Route 2. And that's the key to making probabilistic predictions here. So what you do and why you do this, okay, there's a long story one might or might not be able to tell about why you do it, but what in fact you do is you square that. And you take, well, one over two squared, that's a half. The other one over root two or minus one over root two squared, that's a half. A half and a half is one, which it better be. Those are probabilities. And your predictions will be statistical. They'll not be surefire about exactly what will happen and you would say, well, probably according to the theory, 50% of the time you'll get up down this way and 50% of the time you'll get down up that way. And you can just kind of read it right off. That is in fact what quantum mechanics predicts. So it would say there's a 50% chance of Alice up and Bob down and a 50% chance of Alice down, Bob up. Importantly,

Starting point is 00:51:15 essentially there is zero chance of both Bob and Alice getting up and zero chance of them both getting down. Therefore, you know, even though you don't know from that state, whether if you do this experiment, you get this or this, you know for sure from that state, whatever Alice gets, Bob will get the opposite. The results will be anti-correlated. That's an EPR prediction. That is, that's a perfect prediction. That's a 100% prediction. They will get opposite results. And now we can run the EPR argument, right?

Starting point is 00:51:54 Because now, if I prepare a pair of particles in the singlet state and send one to Allison, one to Bob, and they're both going to measure in the X direction, just from the preparation, neither knows what they're going to see. But both know that they will see the opposite of what the other. sees. So once Alice does her experiment and sees her outcome, she can predict with certainty and correctly what Bob will see. And now if what she did did not disturb Bob's system, now we can apply the EPR criterion of reality and say, well, something in Bob's particle, when it got to Bob, already had to predetermine it in what it was going to do.

Starting point is 00:52:43 And whatever that is, that's not represented in the wave function, because the wave function doesn't tell you that. The wave function only gives you this probabilistic prediction. So then we can conclude the wave function is incomplete. Same EPR argument runs perfectly, okay? And you would say, if you want it to be a local theory, no spooky action at a distance, again, just as with EPR, It must be a deterministic theory.

Starting point is 00:53:10 The two particles must have had either their tendency to do up-down or their tendency to do down-up from the beginning. All Alice does is reveal a fact that was already there. Once that fact is revealed to her, she can then update in a usual Bayesian manner on that information and say, ah, now not only do I know something about my particle, I know something about Bob's particle, right? Bob's particles, the other one. It's like the dollar bills that you tear in half. So you can, again, run exactly the EPR argument. If there's no spooky action at a distance, the wave, the singlet state is not a complete description. In a complete description, you would have to, it would have to be deterministic, and the complete description would tell you exactly which way

Starting point is 00:54:01 each particle was going to go. Now, you might have noticed, and you might have wondered, it might occur to you to wonder, if I go back for a second to the singlet state, I said if you square the one over root two, you get 50%, so you get 50% predictions 50% this and 50% that. And you might say, but why that minus sign? I mean, the same would be true if you put a plus sign there, right?

Starting point is 00:54:28 I mean, is that minus sign doing some work for you? Why did you decide that? The answer is, yes, it is doing some work. If I put a plus sign instead of a minus sign, I would get a different state called the M equals zero triplet state, has different characteristics, not for X spin. It does not have different characteristics for that experiment, but for other experiments it has different characteristics. And the one we want is the singlet state with the minus sign.

Starting point is 00:54:54 Why? Because it has a symmetry. And the symmetry, I mean, well, I can go even further. To run the EPR argument, all we needed to know is that for sure they'll get opposite results. It didn't really matter that half the time it's this and half the time it's this. It could be that, you know, 25% of the time it's this and three quarters of the time it's that. As long as they're always opposite, that's all I need to run the argument. So the half and half sort of didn't really play a role.

Starting point is 00:55:23 But now the mind, you could have all these. states, the special thing about the singlet state, among all of these different superpositions you could write that have this perfect correlation, is that if you change from expressing it in terms of X spin to expressing it in terms of Y spin or Z spin or 45 degree spin or whatever, it has exactly the same mathematical form up to a constant. So there's a symmetry that the singlet state has that, say, the M equals zero triplet state does not have. The M equal zero triplet state is not the same for all directions. That's why you put the minus sign in. That's why we want it there for anybody interested. We're actually going to use that symmetry in the argument. It makes

Starting point is 00:56:12 things easy. Because it tells you, yes, if Alice and Bob both check in the X direction, one will get up and the other will get down. Also, if they both check in the Y direction, one will get up in the other get down. If they check in the Z direction, if they check in any direction, as long as they're checking in the same direction, one up and one down, 100% perfect correlation, perfect anti-correlation. Okay. So that's just what I say here. If I rewrite, which I can do, the singlet state, instead of expressing it in terms of X spin, I express it in terms of Y spin, or in terms of Z spin or in terms of 45 degrees spin up to a constant, it always takes exactly the same mathematical form. And therefore, the EPR argument can be run in exactly the same way for all directions.

Starting point is 00:57:02 That's going to be important. Now, suppose we had a causally local theory. Again, suppose it nothing that Alice does, nothing about which direction she decides to orient her magnets, makes any difference at all to what happens in Bob's lab. Then I can run the EPR argument for all of these directions and say, well, in a local theory, it must be that the outcomes are predetermined in all directions. Because, remember, the EPR criterion of reality is just if you can make the prediction without disturbing the system. And Alice can make a prediction in any direction, whatever direction she wants. If she wants to predict Bob's in the X direction, she just checks the X direction in her lab. If she wants to predict Bob's in the Y direction, she checks the

Starting point is 00:57:51 Y direction in her lab and so on. So she can do it in any direction. And if you say there's no spooky action in a distance, none of those things she can do would disturb Bob's particle. Therefore, Bob's particle has to be predetermined in its behavior in any direction. It has to, as we sometimes say, come with an instruction set that tells it what to do if it encounters a stern garlock magnet, no matter how that stern garac magnet happens to be oriented. That's the only way a local theory could make these predictions. It's the only way. Now, this is an as I say, in 1951, boom. who started out as kind of a Copenhagenist, wrote this textbook. He appreciated the EPR argument.

Starting point is 00:58:47 I mean, he appreciated it was an interesting argument. He reformulated it for spin instead of the way it was done or written. What happens? As I said, Bohm is an assistant professor at Princeton, young guy. He's very interested in what Einstein would think about his book. And he doesn't know Einstein and he's a little scared. He's apparently asking around to be. at Princeton, do you know Einstein? Could you go, you know, could you ask him what he think? And as he's doing this, Einstein sends him a message. I don't know, calls him or sends him a message or something.

Starting point is 00:59:22 He says, hey, I read your book. Really good book. Would you like to come talk about it? Out of the blue. Wow. And, you know, Einstein is over at the Institute for Advanced Study. And Bohm goes there. And Bohm at the time, I don't know if his roommate.

Starting point is 00:59:38 He was some very close connection to Murray-Dell-Man. because Gelman tells this story. He says, okay, so Bome goes to talk to Einstein about the book. And Einstein really appreciated the clarity of the book. Anyway, the story is he goes to talk to Einstein and comes back after a few hours and tells Gilman, I'm back to square one. Einstein has talked me out of the whole thing. Einstein has convinced me this whole Copenhagen approach can't work.

Starting point is 01:00:06 which is that that's pretty impressive it's impressive it's impressive both on Einstein's and on Boem's part right Einstein had the arguments and Boem recognized they were good arguments and decided

Starting point is 01:00:24 even though he tried the best he could to make Copenhagen work he couldn't make it work and that's 1951 right and then in 1952 Boem says, all right, I need to do something more acceptable. And he starts working on a so-called hidden variables theory and he finds it. It turns out to be essentially what DeBroy had already presented it in Solvay in 1927. As far as I know, there's not any indication that Boehm knew about DeBroi's work.

Starting point is 01:00:59 I don't know that people had paid much attention to it. it certainly fell out of favor very quickly, and DeBroy himself did not pursue it. Anyway, in 1927, DeBroy wasn't really prepared to answer technical questions, and he kind of fumbled a bit in Solve, and apparently was kind of embarrassed. Young guy, you can imagine, among the great physicists of the time. You can imagine that Bohm, having just written an entire textbook on quantum theory, was in a much better position

Starting point is 01:01:31 to see how to make this theory work and how it would work in various well-known circumstances. And so, Bome, again, within the course of a year, writes these two papers come out in physical review, a suggested interpretation of quantum theory

Starting point is 01:01:50 in terms of, quote, hidden variables, parts one and two. And now you have, again, a deterministic theory with no collapse of the wave function that makes all the same predictions as standard quantum theory. And that's what we call, again,

Starting point is 01:02:10 the pilot wave theory, sometimes people call it DeBroy Bone Theory. They both certainly get credit. Pilot wave is a nice descriptive way of talking about it. And it's a theory in which you have particles. Part of the ontology is there are particles, by which I mean particles, by which I mean little objects that always have positions that follow continuous trajectories, and therefore at all times have configurations. So there's always a fact, physical fact about what the configuration of a set of particles is. And in this theory, the wave function is part of the theory. It evolves by Schrodenger Revolution. It plays a role in guiding the configuration.

Starting point is 01:02:55 by something called the guidance equation, which does not appear in Copenhagen or in standard quantum mechanics. Standard quantum mechanics doesn't have a guidance equation because it doesn't have anything to guide. It doesn't accept that there are particles that always have positions. And what it does by this equation,

Starting point is 01:03:14 which is a deterministic equation, is it determines how the configuration of the particles evolves in time. Are particles defined by following continuous trajectories? I don't know if they're defined that way. Of course, this is now a bit of a semantic question. If you had a particle and you said it could, as it were, be moving along over here, then suddenly disappear and then reappear way over here without moving continuously from one to the other, of course, that would raise a certain number of questions, like, well, how do you know it's the same one?

Starting point is 01:03:50 I mean, usually the idea is that because a particle follows a continuous trajectory, you can tell which particle at time one is which particle at time two by just seeing how it got from, you know, how it got from here to there. Now, one could say, no, no, no, I think there are particles. They always have positions, but I think they can jump around. Nonetheless, remain the same particle. You could do that. It would involve, you know, some adjustments. It's obviously simpler.

Starting point is 01:04:20 It's not, when I say a classical particle, of course, classical physics had this idea going back to democratists and democracy and atoms. And they didn't pop out of existence and pop back into existence somewhere else, right? They just moved around. I was more thinking, well, what if it turns out that spacetime or whatever, quote unquote, gives rise to space time, the space time's emergent from, has a discrete structure. than necessarily as you move along in that discrete structure you would be discontinuous. Okay, that I think, the answer to that, that's a different question.

Starting point is 01:04:57 Okay, that's a good question, a different question. I'll tell you a little story about Einstein here. If I have a discrete space time, and you're going to have to stop me because this is what I'm working on. If I have a discrete space time

Starting point is 01:05:09 so that for every location, there is a definite set of nearest neighbors, of next-door locations, Right? Yes. Then what you mean by a continuous motion, or what you ought to mean by a continuous motion, is one that always goes to a nearest neighbor.

Starting point is 01:05:26 Got it. So it could still move continuously in that sense. It's, in that discrete setting, that's what counts as a continuous motion. Now, Einstein in one of his books, I think maybe the popular book on relativity, He's trying to give people everyday folk the idea of what continuity means. And he exactly says, well, continuous motion is, as it were, where you always go from a point to a near next point to a nearby point to a nearby point. Now, of course, in a continuum, there is no next point over, right?

Starting point is 01:06:03 So in a continuum, it turns out that defining what is a continuous motion and what's a continuous curve, that's actually very tricky. and the standard definition is actually kind of weird and has strange examples of, okay, I mean, we could spend forever on that, what counts as a continuous function. In a continuum, it turns out those are really complicated. In a discrete structure, I would say,

Starting point is 01:06:26 what you mean by a continuous motion is always a motion to a nearest neighbor. Bump, bump, bump. What would be discontinuous to jump from here to here without going through any of the intermediate ones. So, something just happened recently. The Economist sat down with Elon Musk, who told them that AI will surpass human intelligence within five years, and then in ten, humans won't be running the world.

Starting point is 01:06:51 It went viral, and I recommend you check it out. See, The Economist is more than a magazine. Actually, I subscribe to the Economist's annual subscription. Their science and AI coverage is among the best that I found anywhere, and I say that as someone who reads plenty of it. They even covered how dark energy may be weakening with time. If that holds up, it completely changes our understanding of the universe's fate. Those are exactly the kinds of questions that we explore every week on this channel.

Starting point is 01:07:17 Now, the Economist is, of course, known for global affairs, both political and economic reporting. Interestingly and flatteringly, Toe is one of the only podcasts that the Economist partners with. So as a Toll listener, you get their exclusive sale, 35% off the annual subscription. This is not a deal they have just anywhere. Head to Economist.com slash T-O-E to subscribe. That's Economist.com slash toe for 35% off. So you have particles. They always have a configuration.

Starting point is 01:07:46 Configuration evolves in time. It does so by the guidance equation. The wave function, again, if we go back to Einstein's question, does the wave function represent something about the individual system, even a system with many particles? Or is it a statistical description of an ensemble of many systems? The answer is, no, the wave function in the pilot wave theory is a feature, a physical feature of the individual system. And it guides the individual particles in that system. And it determines how the configuration of those particles changes with time.

Starting point is 01:08:26 It itself is not a statistical description. It is a real physical characteristic of an individual system. and what does it do? It always evolves deterministically, so you certainly don't have a problem with collapse of the wave function, that was always an issue because it doesn't collapse.

Starting point is 01:08:48 The wave function always evolves by Schrodenger evolution, the configuration of particles always evolves deterministically in accordance with the guidance equation, whole theory is deterministic, returns all the predictions of standard non-relativistic quantum mechanics.

Starting point is 01:09:05 So that was the theory that Bome published in 1952 in response to Einstein talking to him. Einstein didn't like the theory. You might say, oh, was Einstein pleased at what Bome did? Nope, he wasn't pleased, which shouldn't really surprise you too much because it was pretty much with DeBroy had done in 1927 and Einstein did not jump on the DeBroy bandwagon either. It's a deterministic theory. So if you thought, gosh, Einstein's issue was determinism, you'd say, why didn't he jump on? This is what he wanted.

Starting point is 01:09:41 Well, we'll see why. It's easy to see why. Because what bothered Einstein wasn't the indeterminism. It was the spooky action at a distance, right? It was the non-locality. It was the idea that something going on in Alice's lab could influence the stuff going on in Bob's lab, right? That's what I've been saying all along since 1920. That's what bothered him.

Starting point is 01:10:06 That's what bothered him in the EPR example. And in the pilot wave theory, it is a non-local theory. It is clear, and it's very easy to see it because you have a complete theory. You can analyze what would happen under different experimental conditions. It's very easy to see that the way this theory works, the way the guidance equation works, is non-local in your face, right? whether Bob's particle goes up or down in his lab can depend on whether Alice has oriented her magnet this way or that way in her lab, even though her lab is 100 million miles away.

Starting point is 01:10:48 So if you're worried about the non-locality, you are not happy with this theory. And Einstein wasn't happy with. Someone had a question from the last episode, which will again place a link on screen. they wanted to know why isn't configuration space already perfectly local? And if I are reading the question, it says, in configuration space, the entire system is located at one single point. So, trivially, everything is local, and this is where Bell started from after studying pilot wave theory.

Starting point is 01:11:20 What do you make of that? Well, you see, the locality that Einstein was worried about, the spooky action at a distance that he was worried about, clearly was always in his mind associated with physical space, right? Spooky action at a distance meant doing something here in physical space had an instantaneous physical effect somewhere else in physical space, right? I mean, the locality is physical locality for him was locality in physical space. Now, configuration space is not physical space.

Starting point is 01:11:57 It has way too many dimensions and it doesn't have the geometry of physical space and it's not this, as it were, the space in which we have laboratories with magnets that point in directions and, you know, we orient the magnets in physical space and the dots are up and down in physical space and so on. It's true that if you write down the dynamics of the pilot wave theory, you can write it down formally all of it in a way in configuration space. both the wave function, and then what happens is because the configuration space has so many dimensions, the configuration of, say, 10 to the 23rd particles, a very complicated configuration in physical space, gets represented by a single point in this very high-dimensional space. And as the configuration changes, and it's changing in all sorts of ways, that gets represented by the motion of this single particle in this high-dimensional space. But that high-dimensional space is not considered to be physical space. That's just a formal mathematical trick, right? That's just a formal representation of a collection of particles in physical space. If you try to tell me, no,

Starting point is 01:13:15 no, I just don't believe there are many particles in a low-dimensional physical space. I believe that all there really is is a single particle in a extremely high dimensional space. Then you get a theory that Shelley Goldstein, I mean, David Albert kind of presents this as if this were the pilot wave theory, which it isn't. Shelly Goldstein gave it the name, The Marvelous Point Theory, because the ontology of this theory is that there's only one particle, the marvelous point. and all it does is wander around in this very high-dimensional space. And somehow all the stuff you think of is going on in physical space is somehow produced by the motion of this particle, this single particle in this high-dimensional space,

Starting point is 01:14:10 without there really being configurations, because you only have one particle. If you only have one particle, it doesn't have an interesting configuration. It's very, you know, it's really, it's thinking of it in that way does allow you to say the physics would be local in this high dimensional space. But then how any of this stuff connects up with dots going up or down in labs, with magnets being oriented this way or that way in a lab, the magnet's made of lots of particles, right? I mean, it's made a lot of particles. It becomes very obscure how you connect that theory to experience. And if you can't connect your theory to experience, it can't be an empirical theory.

Starting point is 01:14:59 Right. I mean, Shelly would say things like, well, you've described a world, but how could that be our world? Right. And it's cheating. It's absolutely cheating to say, oh, it's our world because that point, that really is a configuration of 10 to the 26 particles. No, it isn't. You just told me it isn't. You told me there aren't 10 to the 26 particles. You told me there's only one particle. And then you're saying, by the way, you know, if that one particle wanders over here,

Starting point is 01:15:29 you better watch out because over in this region, that represents you having broken your leg. Yes. It's going to hurt. Whereas if it wanders over here, you're having, you know, a lemonade by the sea, and that's going to be nice. And you say, wait, this one particle, you know, How is it? Now, you can't answer that by saying, but that's because that single particle merely is a representation of a configuration, because you told me there isn't a configuration. So there's a bunch of cheating that goes on here. If you want to postulate that physical space has very, very, very high dimensions, you can do that. I mean, the string theorists went higher than three. They didn't go to 10 to the 26th or anything like it, right? They went to 22 or the 10

Starting point is 01:16:14 or do 11. The string theorists added a few dimensions to physical space. Okay, that's fair, fair play. Then we want to ask you things like, but why does it seem to only have three? And then you say, oh, they're compactified and it's a claw by yow manifold and blah, blah, blah. That's fair play. You need to work it all out. It's not fair play to say, well, really, there's essentially infinite number of dimensions and there's only a single particle. And when I say, but then, you know, why does it look like there's a rectangular table in front of me? Well, because think of that particle as if it represented a configuration, which doesn't really exist,

Starting point is 01:16:53 but would be the configuration of a table. That's just cheating, right? That's just cheating. And I don't see any way to make sense of a theory where the physical space is this high dimensional space and there's only a single particle in it. So at that point, if you care so much about locality, you're trying to save it, then the cure is worse than the disease?

Starting point is 01:17:21 Yes. Or, yeah, the cure is much worse, right? Much, much worse than what you're trying to cure. Einstein wouldn't have bought that either. No, because Einstein says, you know, he says explicitly even in the quotes I gave in the EPR paper when he says, the correctness of the theory depends on how the predictions of the theory connect to our experience.

Starting point is 01:17:44 And he wants that connection to be principled, right? He wants there to be a principled link between what the theory says there is and what our everyday experience says about, you know, oh, you know, a needle went this way or that way or a dot formed here or there, so on, a principled one. Now, it could be a little unusual, right? I mean, again, I think the string theorists were okay in saying, well, maybe at microscopic level there are more spatial dimensions than we're aware of at macroscopic level. Yeah, that's why we call it microscopic, because we can't see.

Starting point is 01:18:22 Maybe, but of course, they had only three big dimensions. So how you would connect their theory of things going on in these 11 dimensions to things that we would represent. port as going on in three dimensions, that's straightforward. Those are the three big dimensions. I think Einstein, you know, he would be okay with a move like that, but not with this other one. And I'm with Einstein there. I want, you know, I want my, if I want to take the ontology presented by a physical theory seriously, I want to be able to comprehend how it could be a theory of the world I'm familiar with. And, you know, the connection there ought to be somewhat comprehensible.

Starting point is 01:19:15 Got it. All right. Good. So, as we know, Einstein's worry was non-locality. The pilot wave theory is really obviously plainly non-local. Because it's deterministic, it will give you truth values for counterfactual claims. Because in a deterministic theory, if you tell me enough about any situation, theory will tell me what would happen in that situation, right? In an indeterministic theory, it might say, I don't know, different things might happen. But in a deterministic theory, it'll say, well, if that had been, you know, two pounds heavier, the thing would have broken. And that's a, you know, so you can evaluate all these counterfactuals. What would have happened if changed the situation? What would the result be? So because it's that, you can do all that.

Starting point is 01:20:02 And it's just clear. It's an absolutely non-local theory in an EPR spin kind of case. there are situations where as things were Bob got his result, his particle went up. But the theory said, if Alice had simply oriented her magnet in a different direction, Bob's particle would have gone down. Or if Alice had delayed, if she'd gone on a coffee break and not done her experiment at the time she did, but a little later, Bob's particle would have gone down. There's a clear dependency on the behavior of Bob's particle on what happens in Alice's life. lab so that the non-locality of the theory is just manifest. One more time, that doesn't mean you can signal. That doesn't mean there's some way of building a superluminal signaling device with

Starting point is 01:20:56 the theory. But everybody agrees it's a non-local theory, which tells you non-locality is not the same as signaling. Okay. So the problem Einstein had with Copenhagen quantum theory, sorry, if the problem he had with Copenhagen were indeterminism, which is what Pauley was trying to explain to Bourne, that's not his problem. Einstein would have embraced Bowman 52 and already would have embraced DeBroy in 27, since his real problem was non-locality. Rather than indeterminism, he couldn't accept the pilot wave picture, right? He says it, he said earlier on he thought DeBroi was thinking along the right lines, but he never liked what DeBroi did. And presumably, This is why.

Starting point is 01:21:40 We know that Einstein was fooling around with similar theories. And presumably he was never satisfied because whenever he wrote something down, the natural thing to do, it ended up being non-local. And that is how things stood until Einstein died in 1955. As far as we know, you know, that was he went to his grave, believing that every version of quantum theory he ever saw had spooky action at a distance and it didn't need it, and you needed a theory that got rid of it.

Starting point is 01:22:14 And certainly the EPR phenomena did not require it, right? The perfect correlations in the EPR argument do not require spooky action at a distance, easy to reproduce those without it. Now, finally. All right. Final act. Where we've been going this whole time,

Starting point is 01:22:38 1964 Bell's theorem. So Bell's is going to take up the thread. What's Bell's background? He had a kind of standard sort of Copenhageny introduction to quantum theory as far as I know. He was puzzled, he says he was puzzled by the theory, as sort of everybody is. Nobody reads their first quantum mechanics, takes their first quantum mechanics course and says, oh, yeah, obviously. It goes like that. everybody's kind of trying to understand it.

Starting point is 01:23:10 And he had the same thought that Einstein did that maybe these statistical predictions, these probabilistic predictions, really are just because you're dealing with ensembles and you don't have all the details of the individual systems as it would be so in thermodynamics or in statistical mechanics. Any approach like that is called a hidden variables approach just because it denies the completeness of the wave function, which was Einstein's whole point. point, right? Wave function isn't complete. If it's not complete, there are additional variables. Those additional variables were called hidden variables for bad reasons, but that's the name that's

Starting point is 01:23:47 stuck. And so Bell himself also thought, well, why don't we add some additional variables here and make things more rational? Now, he reports that when he was studying, he raised this possibility with his professors, and actually he says he was reading Born's book, and he'd been told, actually, in the quote, he says he read this in Bourne's book, that that possibility, the idea that you could add additional variables to the standard quantum formalism and still keep the same predictions, the same empirical predictions, had been ruled out mathematically by von Neumann. You know, I guess he even has a bit of a quote from Bourne's book.

Starting point is 01:24:32 and that von Neumann had proven that no such theory could return the same predictions as standard quantum mechanics. Oh, so now, this is in his paper on the impossible pilot wave, which is about the pilot wave theory. I actually have the quote here. When I was a student, I had much difficulty with quantum mechanics. It was comforting to find even Einstein had such difficulties for a long time. Indeed, they led him to the heretical conclusion that something was missing in the theory. and this is now the quote from Einstein, I am in fact rather firmly convinced

Starting point is 01:25:08 that the essentially statistical character of contemporary quantum theory is solely to be ascribed to the fact that this theory operates with an incomplete description of physical systems. So we're back at incompleteness. More explicitly, in a complete physical description, the statistical quantum theory,

Starting point is 01:25:24 this is again, Einstein speaking, would take an approximately analogous position to the statistical mechanics within the framework of classical mechanics. Einstein did not seem to know that this possibility of peaceful coexistence between quantum statistical predictions and a more complete theoretical description had been disposed of with great rigor by J. von Neumann, right? This is, Bell actually, he's being funny here, okay? I mean, you have to understand. It's dry humor. Bell knew perfectly well that Einstein was aware of von Neumann's supposed

Starting point is 01:26:02 was proof and also aware of the errors in it, which was known even at the time shortly after von Neumann published his book was pointed out by the philosopher Greater Herman, who had the double unfortunate condition of being a philosopher and being a woman, and so was completely ignored. She pointed out errors in the logic of what von Neumann claimed. Einstein clearly saw them, He knew all along. Anyway, is it a distraction to go into that? Well, what we know, let me tell you what I know. We know that Greta von Herman noticed this because she published about it, okay?

Starting point is 01:26:47 But again, she was a woman, she's a philosopher. She didn't get, you know, she didn't get the credit she deserved for doing that. There's a story that someone, I can't remember who. I mean, I should have looked up the diesel story. Went to Einstein in Princeton, in his home in Princeton. And he was talking about quantum theory, and I guess talking about a hidden variables theory, because he had been playing with these theories all along. And whoever he was talking to said, but what about von Neumann?

Starting point is 01:27:18 Didn't von Neumann prove you can't do this? And the report is, Einstein went to his shelf, pulled von Neumann's book off the shelf, opened it to a page, pointed to a... a specific line and said, there's no reason to believe this, which was an assumption that von Neumann had made, the same assumption that Greta von Hermann pointed out. So we know Einstein knew

Starting point is 01:27:45 that von Neumann had not proven such a thing. I mean, I could try to go into the details, but I do think it would take us too far afield. Yeah, that's fine. I mean, I will say one other little thing. There's an interview that somebody did with Bell and Bell says to the interviewer, he says, you can write this down, that Von Neumann's assumption was not merely wrong. It was foolish. It was foolish. Von Neumann made an assumption

Starting point is 01:28:14 about if certain operators, which are what you use in quantum theory to make predictions, and the operators form a vector space, so you can add them and so on. They have algebraic, they can have algebraic relations between them, that if the operators have certain relations, then the outcomes, the observed outcomes have to obey those same relations. And that's just not true. And there's no reason to assume it has to work that way. And in the pilot wave theory, it doesn't work that way. And there was never a reason to believe it would work that way. And if you deny that, then von Neumann's proof falls apart. I mean, Bell also says at some point, once you get your hands on the theorem, it falls apart in your hands. The story is, well, let me

Starting point is 01:28:57 read this and then say a little more about Bell. myself, he says, did not know von Neumann's demonstration at firsthand. For the first time, it was, for at that time, it was available only in German, which I could not read. However, I knew of it from the beautiful book by Bourne, natural philosophy of cause and chance, which was in fact one of the highlights of my physics education. Discussing how physics might develop, Bourne wrote, and now this is born, I expect that we shall have to sacrifice some current details to use still, and to use still, and to use still, more abstract methods. However, these are only opinions. A more concrete contribution to this question

Starting point is 01:29:37 has been made by J. van Neumann in his brilliant book, Mathematica, Gunglangen the Quantum Mechanic. He puts the theory on an axiomatic basis by deriving it from a few postulates of a very plausible and general character about the properties of, quote, expectation values, averages in their representation by mathematical symbols. The result is that the formalism of quantum mechanics is uniquely determined by these axioms, in particular, and here's the main point of what Born is claiming, no concealed parameters, no additional variables, no hidden variables, can be introduced with the help of which the indeterministic description could be transformed into a deterministic one. Hence, if a future theory should be deterministic, it cannot be a

Starting point is 01:30:25 modification of the present one, but must be essentially different. How this could be possible without sacrificing a whole treasure of well-established results, I leave to the determinists to worry about. So notice, it's not only, it's determinism here. Born is claiming that von Neumann has mathematically proven that no deterministic theory can make the same predictions as standard quantum mechanics. And then Bell, now this is Bell again reporting. Having read this, I relegated the question to the back of my mind and got on with more practical things. What else could he do? He couldn't check the proof. Proof was in German. He didn't read German. Later on, when that book gets translated into English and Bell gets a

Starting point is 01:31:14 copy and looks at it and looks at the proof, he has the same reaction Greta von Herman had and the same reaction Einstein had and said, Van Neumann, why are you making this assumption? No reason to make it. Silly assumption. Foolish assumption. Kurt here, note that if you'd rather listen to Toe, we're on Spotify, iTunes, everywhere with a podcast catcher. You can just search my name or theories of everything.

Starting point is 01:31:41 And also, remember to hit subscribe. Okay. But Bell didn't get it that way. How did he get there? Now he says, in 1952, I saw the impossible Donovan. It was in papers by David Bone, the ones I just talked about. Boehm showed explicitly how parameters could indeed be introduced into non-relativistic wave mechanics, with the help of which the indeterministic description could be transformed into a deterministic one,

Starting point is 01:32:08 just what had been claimed to be shown impossible by von Neumann. More importantly, in my opinion, more important than the determinism, and Bell is very clear about this, he's, not wedded to determinism. More importantly, in my opinion, the subjectivity of the orthodox version, the necessary reference to the observer could be eliminated. So all this talk about how in quantum mechanics, the observer can't be left out. And unlike classical fizz, blah, blah, blah, you've heard it a million times. No, that is not forced on us. Okay. Moreover, he says, the essential idea was one that had been advanced already by DeBroy in 1927 in his pilot wave picture. Now, the last of this quote, and I love this.

Starting point is 01:32:58 I mean, anybody, if you ever read, Parted Bell, this is just a wonderful paragraph. But then why had Bore not told me of this pilot wave, if only to point out what was wrong with it? Why did von Neumann not consider it? More extraordinarily, why did people go on producing impossibility proofs, after 1952, that is, after you have this explicit thing in your hands, and as recently as 1978, when even Pauley, Rosenfeld and Heisenberg could produce no more devastating criticism of Boe's version than to brand it as metaphysical and ideological. And, you know, you'll see all the footnote numbers if you want to know what he's referring

Starting point is 01:33:39 to. This is in on the Impossible Pilot. Why is the Pilot Wave picture ignored in textbooks? should it not be taught, not as the only way, but as an antidote to the prevailing complacency to show that vagueness, subjectivity, and indeterminism are not forced on us by experimental facts, but by deliberate theoretical choice. That is a very powerful statement that most of what you hear about what quantum mechanics reveals to us about the world that we weren't expecting from classical

Starting point is 01:34:17 physics is wrong. It's not forced on you, right? The subjectivity, the thing about observation, the thing about measurement, the thing about, you know, the centrality of subjectivity, even the indeterminism. None of that

Starting point is 01:34:33 is forced on you by any experimental results in the sense that you have a theory, at least for the non-relativistic theory, you have a theory that gives you all those same results and doesn't have any of those features. Like it or don't like it. Maybe you don't like the theory. Okay, but it exists. Don't pretend it doesn't exist. That was Bell's point. Okay. So,

Starting point is 01:35:00 1952, Bell has Bones' theory in hand, and he has, therefore, DeBroes' theory in hand. He knew that determinism could in principle be reconciled with the standard predictors. of quantum mechanics. He also knows that the usual conceptual problems that you associate with Copenhagen, the role of observation, collapse of the wave function, that could be overcome. Again, in this theory, there's no collapse of the wave function, so you don't have to worry about that. But as we saw, Einstein's main issue is still there. What about the spooky action at a distance that he was complaining about in the Copenhagen view in 1927, since the pilot wave theory did not attempt

Starting point is 01:35:47 to uphold the completeness of the wave function, right? So it agrees that wave function's not complete. You have to add the particle positions. Those are the additional variables. There was no issue about that. But even so, the non-locality remained in the theory, arguably even more obvious and in your face in this theory than in Copenhagen.

Starting point is 01:36:07 because kind of in Copenhagen, you're not quite sure what the theory says. I mean, you're just really not sure quite what the theory says. And in this theory, you know what the theory says. So now we're in the last act. So it occurs to Bell, as it would have occurred to Einstein. Okay, I know I can get back determinism if I want it. I know I can get rid of the measurement problem if I want to do that. I know I can get rid of the collapse of the wave function if I want to do that

Starting point is 01:36:33 and still get all the same statistical predictions in the non-relativist equine. theory. Can I do it without spooky action at a distance? Can I get rid of that feature? That is not settled by Baum and DeBreuth. Now Einstein, as we know, always assume it could be. In principle, you ought to be able to do all this without spooky action at a distance. He certainly knew of no experimental phenomena that seemed to require it. It just showed up theoretically in the theory, right? It didn't show up, as it were, in the data. And that's what Einstein presumably was looking for when he died in 1955. He was still looking for a local theory.

Starting point is 01:37:18 Certainly the perfect EPR correlations that they used to argue against the completeness of the wave function, those could be accounted for without spooky action at a distance. That's the kind of Burtleman-Sox example. You just predetermined things at the source. So Bell was interested in this question. He eventually gets a sabbatical, and he decides to now he can spend his time instead of just doing it on the weekends for fun.

Starting point is 01:37:46 He's really going to look into this. He clears the ground in a paper, which is Bell, 1966, which is going to puzzle you. You're going to say, wait, I thought the main theorem was 1964, but now you're saying he cleared the ground. And the fact is he wrote the 1966 paper first and then he wrote the one. So their appearances were switched

Starting point is 01:38:08 from the order in which they were written. So Bell on this sabbatical says, okay, I know von Neumann's supposed no hidden variables proof is no good. There are a bunch of other proofs out there that claim to be no hidden variables proofs that show that somehow the predictions of quantum mechanics

Starting point is 01:38:30 cannot be reconciled with additional variables. And so he decides, I'll go through those. I'll check them all, all the ones he could find. And that's that he finds problems with every single one. We could, you know, it would be, again, off to the side what those problems are, but they're there. And of course, there have to be problems, right? He knew, why? Because he had BOM's theory in his hands.

Starting point is 01:38:57 And he said, but this theory makes all the right predictions. And it is a hidden variables theory. So you can't have a proof that a hidden variable's theory. theory can't make these predictions. Because, you know, it can be done. Here's how it can be done. So in a way, it was much easier for him to diagnose where these proofs go wrong. So he goes

Starting point is 01:39:12 through and he does that. And it eventually gets published in 1966 in this paper called On the Problem of Hidden Variables in Quantum Mechanics. The main theorem that we're going to talk about had already come out in 1964. But out of, okay, so this is out of order.

Starting point is 01:39:29 So he knew we could have a theory where the wave function is incomplete. We knew it could be a deterministic theory. We could retain all the predictions of standard quantum theory. But could it be made a low, could you make a local theory that had those characteristics? And so this is what is discussed in the paper, which this entire presentation is really about. This 1964 paper published in volume of, published in volume of the paper, one of a brand new journal that was being started by a friend of Bells

Starting point is 01:40:08 and that went out of business within the decade. I don't know. I didn't have that many. So an obscure journal with no track record such that it would be perfectly possible for this paper to disappear without a trace. Right. For those of you who want to, you know,

Starting point is 01:40:28 stay up at night worrying about what could have happened. It'd be on VIXRA. Yeah, I mean, Bell didn't try to get it published in one of the big physics journals, because it was his friend's journal. I mean, he said, here, here is a paper. Fortunately, preprints got into the hands of Abner Shimony, who's a philosopher and a physicist, a PhD, both in philosophy and physics. He understood the importance of the theorem. Bell did not go around making a lot of noise for himself. This could have been missed, but this is the paper you need to read. And it's a clear paper. It's a nice paper. And I'm just going to read you the beginning of it. Again, the title is on the Einstein-Padolsky-Rosen paradox. So this is just the quote. The paradox of Einstein-Pedolsky and Rosen was advanced as an argument

Starting point is 01:41:14 that quantum mechanics could not be a complete theory, but should be supplemented by additional variables. These additional variables were to restore to the theory causality and locality. Notice, both of them. Causality is determinism here. and locality. In this note, that idea will be formulated mathematically and shown to be

Starting point is 01:41:38 incompatible with the statistical predictions of quantum mechanics. So now we are going to have a theorem that says the predictions of quantum mechanics are not compatible with something, but with what exactly? It is the requirement of locality or more precisely that the result of a measurement on one system

Starting point is 01:41:56 be unaffected by operations on a distant system with which it has interacted in the past, that gives you the entanglement, that creates the essential difficulty. It is locality, the requirement of locality, that creates the essential difficulty. There have been attempts to show that even without such a separability or locality requirement, no hidden variable interpretation of quantum mechanics is possible. These attempts have been examined elsewhere, four, and four is this other paper. that I just mentioned, the 66 paper, and found wanting, right? All of those supposed no hidden

Starting point is 01:42:35 variables proofs, caution specker theorem, I mean, people may know that name, these things, Bell looked at them and said, no, no, they don't work. Moreover, a hidden variable interpretation of elementary quantum theory has been explicitly constructed. That, of course, is bones. He's referring there to bones. That particular interpretation has indeed a grossly non-local structure. this is characteristic, according to the result to be proved here, of any such theory which reproduces exactly the quantum mechanical predictions. But that means of any theory, period, that reproduces exactly the quantum mechanical predictions. It would be impot. So, again, now that, just you have to go read that and read that and read that.

Starting point is 01:43:23 Bell is as clear as he can be about what he's doing. He knows you can get determinism by adding hidden variables, additional variables. Shouldn't call them hidden, additional variables. He knows that you can get all the same statistical predictions. It is hoped by Einstein you could also restore locality, restore in the sense that classical physics is local. You can also restore locality. He's going to prove, nope, you can't get locality back. That one you can't get.

Starting point is 01:43:52 That one you're stuck with. Yeah. Did you say that Bell didn't think Colkin Speckers, contextuality held up or that Cochin Specker didn't disprove the viability of hidden variables theory? A hidden variables theory can be contextual. I mean, what he pointed out

Starting point is 01:44:09 is the kind of contextuality that you can use to get the caution specker phenomena is tame. It's fine. It's not even counter, it's not even counterintuitive. It basically, if

Starting point is 01:44:27 you translate that kind of contextuality into regular language, it says the way an experiment comes out depends on how it's done. Right. I mean, what Cochern and Schbecker, for people who know this and we don't have time to go into it, what they assume is that the same permission operator, I mean, the problem is you have different experimental, physically different experimental conditions that you associate the same permission operator with. And what they assume is that any experiment that's associated with that operator is physically identical to any other experiment that's associated with that operator, that they're all kind of physically interchangeable.

Starting point is 01:45:10 And why think that? No reason to think that. Absolutely. I mean, a good reason not to think that. I mean, Bell gives examples. So if you think in a very concrete way, how do I have... have to set up my lab to do this? How do I have to set up my lab to do that? That can give you a contextual theory. All that means is that, for example, two different apparatuses that are both

Starting point is 01:45:34 called, say, momentum measuring devices might give you different results because they're built differently. That's really not an amazing thing that might happen, that physically different pieces of equipment could give you different results. So the assumptions that go in to Cohen and Schrecker are made at a certain kind of abstract mathematical level that does not translate into a plausible physical principle. That's the right thing to say. Now, one way to think about, I'm going to say this, I can't. One way to think, you've got contextual hidden variables theories. Those are not puzzling. Where the context. is, I throw, I have some particles and the context is, okay, what experimental condition am I

Starting point is 01:46:26 putting them in? Am I putting this kind of magnetic field or this kind of magnetic field? Okay, that can affect how the thing behaves. What Bell does is says, yeah, but what if we separate them so that the relevant context for the outcome over here is the physical situation over here? Now that's different. That's spooky action at a distance. Bell really proves the quotient speckers. Anyway, it doesn't matter. This would take us, okay. Good.

Starting point is 01:46:56 So there's been all kinds of confusions about what Bell was trying to do, what he did do, what his assumptions were, and that confusion cannot be justified by any flaw in what Bell wrote. Bell wrote clearly, concisely, exactly. You have to read him carefully. You can't be sloppy in your reading, but that's on you. It's not on him. So once we're finished with the theorem, I'll talk about some of the misapprehensions of what Bell was doing, but he just told you what you're doing.

Starting point is 01:47:30 I'm going to check whether we can restore locality, get a local theory that makes all the same predictions as standard quantum mechanics. By putting in, of course, by putting in additional variables, I'm going to have to do that. We already know that from EPR. We know that what I'm going, if I want it to be local, it's got to be deterministic. And if it's going to be deterministic, I need to add these additional variables. Okay, you can do that. That's the only kind of theory that could work. He's going to show it can't work.

Starting point is 01:48:02 He's going to show it can't restore locality. So again, I just want to talk about the details here. First thing, the title of the paper on the Einstein-Fidolsky paradox, He assumes the reader has read the EPR paper. It's a short paper. It's also not a hard paper to understand. He assumes they've understood and have seen what EPR proved. What they prove is that if you have a local theory and what Alice does doesn't affect

Starting point is 01:48:31 Bob and what Bob does doesn't affect Alice, it has to be a deterministic theory. It has to have more variables than are in the wave function. It has to be an additional variables theory. Okay. So he makes clear he's picking up where EPR left off. He understands and expects the reader to understand that EPR had already proven something very important, but he said there's more work to do to achieve the sort of theory Einstein wanted, which we know Einstein was never satisfied. Let's again recall what EPR proved and on what precise premises.

Starting point is 01:49:07 nominal target is whether the quantum mechanical description, the wave function ascribed to an individual system is complete, that is whether the description contains, whether implicitly or explicitly, the representation of all the elements of physical reality, all the physical characteristics or facts in the system. EPR tacitly assumes a locality condition, namely the experiments carried out by Alice in no way disturb the physical state of Bob's particle in lab and vice versa when they apply the criterion of reality. If we grant the accuracy of the quantum mechanical prediction of the perfect EPR correlations, and that's never at issue, and although for momentum measurements, right, if we grant just that, and we don't really need to, but if we also grant it for

Starting point is 01:49:57 position measurements, EPR argue that if one rules out violations of locality condition, then the quantum mechanical description, that is the wave function, must be incomplete. Explicitly, if the predictions of quantum mechanics are accurate and the perfect EPR correlations are correct, then if there's no violation of locality, the quantum mechanical wave function is not complete, is incomplete. That's got an if and another if then, okay, that's kind of a complicated sentence, but it's just one sentence. I'm going to rewrite the last part of it.

Starting point is 01:50:33 So what I just wrote using what we call the confer positive is logically the same as this. If the predictions of quantum mechanics are accurate and the perfect EQR correlations are correct, then if there's no violation of locality, the quantum mechanical wave function is not complete. Sorry, that's what I just wrote. If we take the contra positive of the consequence, we now get, sorry, this is now what we get. If the predictions of quantum mechanics are accurate and the perfect DPR correlations are correct, then if the quantum mechanical wave function is complete, then there must be a violation of locality.

Starting point is 01:51:06 If the quantum mechanical wave function is complete, there must be a violation of locality. Because if there's no violation of locality, then it's incomplete. So now we just take the contra-positive. Yes? Just look at that. Now, that again, it's a little complicated,

Starting point is 01:51:23 but everybody grants the accuracy of the prediction. So the first thing says, if the EPR correlations hold, but everybody grants they hold. That's just the correctness. That's just the correctness of quantum mechanics in terms of making predictions. So that's not an issue. So the first part's okay.

Starting point is 01:51:39 So then we get the conclusion, if the quantum mechanical wave function is complete, then there must be a violation of locality. Trying to maintain the completeness of the wave function commits you to spooky action at a distance. That's what EPR proved. Now, since EPR assume that locality is not violated, that yields logically the conclusion that the quantum mechanical wave function is not complete, there must be so-called hidden variables or additional variables.

Starting point is 01:52:09 You can't get away without them if you want to maintain locality. Right? But the point is to maintain locality. The point is not, you know, the point is not just to put in extra variables to do something else. The point is to maintain locality. So one more time, EPR make only two fundamental assumptions. The quantum mechanical predictions,

Starting point is 01:52:32 the perfect EPR correlations are accurate, and the other is a locality assumption. What happens in Alice's lab does not disturb or change, the physical state of Bob's and vice versa. From those assumptions and only those assumptions, EPR derived the incompleteness of the wave function and hence, since this means the same thing, the existence of so-called hidden variables, additional variables.

Starting point is 01:52:56 Not hidden. Actually, hidden is bad because hidden suggests you can't see them. But in the pilot wave, theory, the additional variables are particle positions. And you can pretty well see where particles are, at least macroscopically, right? You can see that, oh, look, all the particles went this way rather than that way. That's seeing what the particles did. So they're not hidden, right? They're not like ghosty or, you know, as Bell says, it's really the wave function that's hidden.

Starting point is 01:53:22 You can't see the wave function very directly. You infer that the wave function exists, but you more directly see what the particles are doing. Right. Now, we have the additional fact, and I insisted from the beginning, this is an additional fact, logically additional fact. Because the EPR correlations are perfect correlations, you can infer the outcome of Bob's experiment with complete accuracy from the outcome of Alice's and vice versa. The EPR argument also proves if it's a local theory, if you have a local theory, the hidden variables must be deterministic. It also has to be deterministic. The states

Starting point is 01:54:02 the particles when they reach their respective labs must be sufficient to determine the outcomes of the momentum measurements and also the position measurements. And if you go back and read what I said before, there's another quote from Bell where he says, all the correlations prove is that the signals when they reach the labs in the Bohm experiment must be sufficient to determine the outcomes. He mentions Bohm there and I said, wait, well, you'll see what he means, because we hadn't gone through spin and all that. You can go back and read that now and understand it. But, as Bell insisted, determinism is not an assumption, right? Determinism is not an assumption of the EPR argument, EPAR proof.

Starting point is 01:54:39 It's a theorem. The basic assumption, the basic premise is a locality assumption. And since Bell is just picking up where EPR left off and from the very same assumptions they make, namely locality and the accuracy of the quantum mechanical predictions, he inherits the conclusions they properly came to, namely the incompleteness of the wave function and further that the additional variables must. If it's going to be local, at least in the experiment they discussed, be deterministic. The additional variables set at the source must fix the outcomes of the experiment's analysis in Bob's lab.

Starting point is 01:55:17 That's the price you're going to pay if you want to maintain locality. Okay? That EPR already proved and Bell is entitled to it. Because if you don't grant that, then in a local theory, if it was indeterministic, if what happens and Alice's lab is indeterministic, how in the world does Bob's particle always do the opposite thing? It would somehow have to be sensitive to how Alice's came out, right? This is Bertelman's socks again. So, as we've seen, Bell was frustrated by people who misunderstood the logical structure of the EPR argument,

Starting point is 01:55:51 and particular, he's frustrated with people who attribute to EPR an assumption of determinism. He stated explicitly how hard it was to get across that EPR do not, assume determinism, but infer it from the basic assumption of locality and, of course, the assumption of perfect correlations. In footnote 10 to the Bertelman-Sox paper, you might want to look at it, he reports that he himself has suffered the same fate, right? He was frustrated that people didn't carefully understand what EPR did. Then he's frustrated they didn't understand what he did. So here's footnote 10. And his, this is Einstein's followers. It doesn't matter what that says. My own first paper on this subject, i.e. on the Einstein-Podolsky-Rosen paradox, that paper, the one we're talking

Starting point is 01:56:37 about, started with a summary of the EPR argument from locality to deterministic hidden variables. But commentators have almost universally reported that it begins with deterministic hidden variables, right? That's an error. That's a logical error, and it's an important one. Because if Bell started with those as assumption, someone could say, oh, I just reject determinism. So I reject your assumption, so I don't care about your conclusion. If I don't accept your assumption, I don't care what you can prove from it. But that's not what he starts with. He starts with locality, because that's what EPR started with. Okay, so the real situation, so here's where we are. Bell's introductory section is pellucid, absolutely clear, just go read it. But just to make absolutely

Starting point is 01:57:27 clear what the logical situation is in his 1964 paper, like the EPR paper, is an investigation into the sorts of theories that could recover the predictions of standard quantum theory. Heinzheim was unhappy with both the fundamental indeterminism and the non-locality

Starting point is 01:57:43 of the Copenhagen view, but his main complaint from the beginning was the non-locality rather than the indeterminism. Copenhagen granted, even touted, right, they would say the indeterminism. They sort of like to say, oh, you know, you have to give up your classical intuitions and accept indeterminism.

Starting point is 01:58:01 But they never straightforwardly acknowledge the non-locality. And if you don't believe that, go read Boar's response to the EPR paper and see whether he straightforwardly says, yes, I believe in non-locality. I believe in spooky action and distance. He denies it. He says, no, there's no mechanical spooky action. It isn't. No, no, no.

Starting point is 01:58:21 Right? They were happy with the indeterminism, but they never embraced the non-locality, which was the thing Einstein always didn't like about their theory. Now, why is it? I understand why Einstein didn't like non-locality, but it seems like people of his generation also didn't like it, but why? Is it because of the reverence for Einstein or what?

Starting point is 01:58:42 I think, look, one thing Einstein explicitly mentions, and go back and look at what he says in 27, you can go back and look at the quotes from the Solvei conference, he sees, and I think he correctly sees, the non-locality doesn't seem compatible with relativity. Why? Non-locality is some kind of instantaneous action at a distance, but in relativity, the notion of instantaneous doesn't make any sense. It can't be defined. This is, this, it requires what we call a global foliation of space time or absolute simultaneity, and in relativity, you get rid of those. So I think Einstein saw correctly that if you

Starting point is 01:59:23 accept this spooky action at a distance, relativity itself is at risk. And he didn't want to put relativity at risk without good reason. And he couldn't see any reason to accept the spooky action at distance. Now, he may not have liked it for other reasons. I mean, Newton didn't like it, right? He says he says no rational person would believe in it. I mean, there are lots of people who find that just intuitively ugly or unacceptable or whatever. And to this day, there are people who don't want to accept non-locality and they'll more or less clutch it any straw to try to avoid it, as we'll see. The psychology of that, I can't quite explain. It's contrary to the idea that these physicists are all open-minded and willing to explore wacky ideas that you wouldn't imagine,

Starting point is 02:00:10 right, which they do all the time, but non-locality is somehow beyond the pale. Non-unitarity as well. Yeah. I mean, unit, I mean, people who think unitarity, I mean, my goodness, that's a very that's a very theoretically inflected property, which you would think you could give that up and not lose a lot of sleep over it, if you could gain a lot by giving it up, right? Yeah. So, you know, physicists are very strange

Starting point is 02:00:38 in what they pick and choose as, I will die on this hill rather than get this up. And, you know, for many of them locality just seems to be something they absolutely won't question. As I say, you can make an argument, which I personally believe, it's not a logical proof. I believe Einstein was right.

Starting point is 02:01:00 The easiest way to really, and I'll talk about this at the end, to really implement non-locality cleanly in a physical theory is to give up relativity, is to put back absolute simultaneity, is to put back a preferred foliation of space time. I think he was right about it. I think relativity has to give here, ought to give.

Starting point is 02:01:23 I don't know, has to. do is too strong, ought to give. We ought to have our minds open to that happening. We have good reason to believe it happens. That's my view. Einstein certainly was not going to accept the incorrectness of relativity on the basis of Boers version of Copenhagen quantum mechanics, which he thought was poorly argued and incoherent. Right. So what EPR have already shown that any local theory up to the task of recovering the predictions of quantum mechanics must be deterministic in order to recover these perfect distant correlations. And Bohm had proven that a deterministic theory could recover all the predictions of quantum

Starting point is 02:02:08 mechanics, standard quantum theory, but the pilot wave theory was manifestly non-local, right? He had to pay the price of non-locality for that. Bell wants to consider whether any local theory can recover all the predictions of standard quantum formalism, sorry, any local theory can recover all the predictions of standard quantum formalism. His only assumption, as with EPR, is locality. The locality already forces determinism on you, but that wasn't an initial assumption. The EPR argument, as we said, runs off perfect correlations between the outcomes in distant labs, and standard quantum theory does predict such perfect correlations for particular initial wave functions of the system. The situations to give you

Starting point is 02:02:52 these perfect correlations have to be ideal in certain respects, but these are standard predictions you'd learn in introductory quantum mechanics. However, what the standard quantum theory also makes predictions about correlations between outcomes of distant experiments, where the correlations are not perfect. They're not, if Alice gets up, Bob gets down, or if Alice gets down, Bob gets up, right? They're inherently statistical predictions. That, you know, quantum theory trades a lot in these statistical predictions. What Bell did, which is new, is he turned his attention from the perfect correlations to some weaker correlations for pairs of particles in the singlet state. So we've introduced the singlet state. We know it predicts perfect correlations if Alice and Bob measure in

Starting point is 02:03:46 the same direction, whatever it is. But now it occurs to you that you can ask a different question. Suppose I prepare a pair of particles in the singlet state, and Alice is going to make a measurement, Bob's going to make a measurement, which means they're going to orient their magnets one way or nothing. But suppose they don't happen to orient them in exactly the same direction. Suppose their directions are offset from each other. Okay. Now, this is just not the kind of condition you would ever get to if you kept with the EPR position momentum case. Because you just don't have these infinite number of possible measurements you can make. You can do position or you can do momentum and that's it.

Starting point is 02:04:31 Those were the only ones people knew how to do, right? But with spin, okay, I can do spin this way or this way or this way or this way. I've got an infinite number of spins I can check. Again, I create a pair of particles. I have all the advantages of EPR that I send the particles out to these distant labs. One to Allison, one to Bob. They can be arbitrarily far apart. They can be so far apart and done at times where even light couldn't get from one to the other in time to influence it and so on.

Starting point is 02:05:00 And so here's our setup graphically. We have a source in the middle that produces a pair of particles, in this case in the singlet state. One is sent off in one direction to Alice's lab. One is sent off in the other direction to Bob's lab. Alice and Bob can set their magnets however the heck they want to set them. In this picture, Alice's is oriented in the Z direction, and Bob's is oriented in the 45 degrees between X and Z, given the axes I have here, right?

Starting point is 02:05:30 They can do whatever they want. And so there can be in the same direction or at any offset angles. And those variables about how the magnets are saying, are what we call free variables in the simple sense that the experimenters can set them however they want. They're variables under the immediate control of the experimenters. They can do what the heck they want with them. On each particular experimental run,

Starting point is 02:06:03 we're going to imagine at some signal, you produce these two particles, they go out to the two labs. On each run, Alice and Bob can, in whatever way they like, arrange for their magnets to be at whatever angle. And we know that no matter what angle it's at, they'll either get an up or a down outcome. Remember, the outcomes have been quantized, discreetized. So they'll either get spin up or down in whatever angle they set. So far, we've only talked about aligned angles when they're set in the same direction,

Starting point is 02:06:36 and then we get this perfect anti-correlation, one's up and the other's down. So that's offset zero, right? Zero degrees difference between their their orientations. What happens, right, and we get those perfect ante correlations, which are exactly what allow the EPR argument to be run, logic goes through perfectly. That gets us a deterministic, well, if it's a local theory, it must be deterministic. But what if they're offset? What if they're not perfectly aligned? So far, we haven't talked about that at all, right? What would the statistics be? What would you expect to see if they didn't pick the same direction to do their spin measurements in? And it's here that moving to the spin case comes into play.

Starting point is 02:07:23 The quantum formalism deals with this quite easily. It's not difficult. It can give you predictions for any offset angle between these two magnets. And what is that dependence? And again, I'm not going to prove this, but that's it. There it is. It's cosine squared theta over two, where theta is the angle between the two magnets, right? So if they're aligned to the same direction, whatever it is, theta is zero.

Starting point is 02:07:52 And it can be offset by five degrees or ten degrees or 90 degrees, whatever you like. Okay? So you take theta, you divide it by two, you take the cosine of that, and you square it. Okay? that anybody who's you know remembers what they did in high school should be able to do that um that will give you a number between zero and one and that'll be the probability have we gotten to the motivation what's the derivation of co squared theta divided by two or is that going to deflect us i can leave resources on screen if so i have not given you a motivation i'm just going to inform you at this point

Starting point is 02:08:33 That's how quantum mechanics makes this prediction, and I'll further inform you, it's a good prediction. Go into the lab and check. I mean, it really wouldn't matter if it came to somebody in a dream. It's checked. It's correct. This gives you the statistics. Again, these are probabilistic predictions now. So you might get, when you square that, you're going to get a number between zero and one, right? The cosine squared has to be a number between zero one. and that number will be the percentage of cases where the two results disagree, where one is up and the other's down. So if theta is zero,

Starting point is 02:09:14 Theta over two is zero, cosine or that is one, cosine squared is one, that tells you 100% of the time they'll get different results, right? They'll always get one up and the other down. If it's less than that, then maybe 90% of the time,

Starting point is 02:09:29 maybe 80% of the time. You'll get a statistical prediction. You can check that prediction by running the experiment over and over and over again with the same setup and seeing what the statistics are. And those statistics are correct. Now, again, why it should be cosine squared of Thade over two? Good question, but not going to help us to understand what Bell did to go into it, right? It is correct.

Starting point is 02:09:56 So for Theta equals 0, as I just said, the outcomes are certain to be different because cosine of 0 is 1, that squared is 1, 100%, they'll always be different. What if we go to Theta equals 90 degrees? So one's this way and the others at right angles. One's at X and the others at Y or the others at Z. Then, all right, we've got 90 degrees as Theta. Theta over 2 is 45 degrees, the cosine of 45. is one over root two, we square that, we get a half. So that tells us that there's no correlation

Starting point is 02:10:32 between the two outcomes, that no matter what Alice gets, half the time Bob will get up and half the time Bob will get down. And knowing what Alice gets gives you no information about that. Okay. They're uncorrelated. If the magnets are at right angles, the outcomes are completely uncorrelated. This is like what happened in EPR. If you decide to check position on one side and momentum on the other, you'll get a result, but they'll be uncorrelated, knowing the one result will not improve your prediction for the other. That's also true here if Alice and Bob happen to set their magnets at right angles to each other. Okay? No, there's no Shannon information.

Starting point is 02:11:19 The result of one gives you no Shannon information about the other. It doesn't allow you to improve your prediction about it. But we don't care about 90 degrees. We're not going to do 90 degrees here. We're going to do 60 and 120 degrees. Okay, we're going to use those offset angles. And again, if you just remember a little bit of your trig, the cosine of six, like if they're offset by 60 degrees,

Starting point is 02:11:44 cosine of 30 degrees is root 3 over 2, and I square that I get three-fourths. So if they're offset by 60 degrees, the results will disagree three quarters of the time. A quarter of the time, they'll both get up or both get down. Three quarters of the time, one will get up and the other will get down. That's just falls out of that formula. Okay? 75% disagreement.

Starting point is 02:12:12 What if we go to 120 degrees? Well, and now again, 120 degrees over 2, that's 60 degrees, the cosine of 60 degrees, the cosine of 60 is a half. I square that, I get a quarter. So Alice's result will disagree with Bob's only 25% of the time. Remember, originally they disagreed 100%. Now we're down to 25%.

Starting point is 02:12:33 That's what just falls out of that formula. That's actually correct. Go to the lab, check. Those are the numbers. Those are the predictions of phantom mechanics. They are right. Okay. Question. can any local theory predict that?

Starting point is 02:12:53 Can any local theory return these predictions? That's the question that's before us. What we want to do is ask whether we can recover locality by adding these additional variables. We know if we do, they have to be deterministic. We did that through the EPR argument. if you can do that in a way that will always get it right, that whenever Alice and Bob measure in the same direction, they get opposite results. You can do that locally? That's easy. But can you do it so that when they're offset, you get these statistics? That's the question. Can I recover these imperfect but non-zero correlations? This never occurred to Einstein. Because if you're thinking in terms of the EPR setup, it never would occur to you to even. ask that question. As soon as you switch to the spin case, it's a natural question to ask. What if

Starting point is 02:13:48 Alice and Bob are just arbitrarily setting their magnets and they're not always exactly lined up? What if they're off a little bit? This is what it predicts. Can I recover that with a local theory? That's what Bell proves the answer is no. No local theory, period. End of story. No local theory can make those predictions. Now, we want to see why, and I'm not going to ask you just to accept that because we can see why. There are easy proofs of this in particular cases. Bell proves it – Bell gives a very general proof that gives you a very general condition about when you can recover it locally and when you can't recover it locally. That's called Bell's inequality.

Starting point is 02:14:31 That can also be extended in various ways. But it's enough to see in a particular concrete case, why it can't be done. If you see that, you see that. And if that case is predicted by quantum mechanics, if it's one of the predictions of quantum mechanics, you're done. Because the question is, can I recover all the predictions of quantum mechanics with a local theory? And the answer is, no, you cannot. Locality is dead. It's out the window. Okay? All right. Let's see why. I want to simplify this as much as possible. So people see, there's not a lot of moving parts and I don't have anything. Look, no sleeves, nothing on my sleeves. So first, let's, you know, in principle,

Starting point is 02:15:14 Alice and Bob could pick any direction. They have an infinite number of directions for their magnets. Let's restrict that first. We'll restrict it that they either, we'll say there's the zero direction, say that's the z-axis, then there's plus 60 and there's minus 60. So you can go from the zero, either clockwise or counter-clockwise by 60 degrees. Those are your three options. bink, bink, bink. They can each do that. Now, we know that for the singlet state, if they happen to choose the same directions, you always get opposite results. 100% anti-correlation. Therefore, if it's a local theory, all of those results have to be predetermined at the source. There has to be, as it were, an instruction set given to the particle at the source. Here's what you do at this angle. Here's what you do at that angle. And the two have opposite instruction sets. for the same angle. So whatever one does, the other does the opposite. That's the only way to do that. Good. What if they're misaligned? Well, they can only be misaligned in two ways. They can be offset by 60 degrees, two different ways. Then we know that they're going to disagree not 100% of the time,

Starting point is 02:16:26 but 75% of the time. Or they can be offset by 120 degrees, in which case they disagree 25% of the time. Those are the statistics. because in any run of the experiment, they might choose the same angle. We need to have these predetermined outcomes if we want to maintain locality. Otherwise, you need action at a distance, and that's what we're trying to avoid. So, in this case, because of the perfect antichorrelations and the EPR reasoning, each particle must be produced with an instruction set of some sort that carries with it. The instruction set, coded in some physical property, would determine how the particle would behave,

Starting point is 02:17:05 were it to encounter a magnet set at any one of the three angles. That's the only hope you have of holding on the locality. It's the only hope already proven by EPR. And the instructions have to be exactly opposite because you want to maintain perfect anti-correlations. Okay? That's the only hope. Now, can you do it?

Starting point is 02:17:28 Again, when they're offset, we want to now, can we get these right predictions when they're offset, well, now the statistics allow to either agree or disagree. So on a single run, if you only do one run and the magnets are offset, you could get any result. You could do both up, both down, one up, the other down. They're all permitted. So on a single run, you're in no danger. But the point is the quantum mechanical predictions are statistical. They're the averages you should get over many, many runs, right? Like 75% on average, 25% on average. You have to do it lots of times to collect the statistics. Can any local theory recover those statistics? And that's what

Starting point is 02:18:17 we're asking. Can any local theory yield the right percentage of agreement and disagreement no matter how the magnets are set? And what he proves is that it is mathematically impossible to recover this 75%, 25% offset probabilities. Now, to prove this, I'm going to simplify even more. It was pretty simple because we got it down to Alice and Bob can only choose between three directions. We can actually even simplify it further. Alice can only choose between two directions. Bob can only choose between two directions.

Starting point is 02:18:53 For Alice, zero and 60, for Bob, zero and minus 60. So there are only four possible ways it can come out, Either they both choose zero, then they have to disagree, or they're offset by 60 degrees, then they have to disagree 75% of the time, or they're offset by 120. If Alice chooses 60 and Bob minus 60, then it's 120, then you need 25%. So, again, all of these will come up. And now I've just repeated what I just said. Here are the statistics we need for each of the. those four possible global experimental conditions. 100% when they're aligned, disagreement, 75% disagreement when they're misaligned by 60, 25% when they're misaligned by 120. All right, here's the proof, and I'm going to do it by trying to construct a local theory that gives me these statistics. And we just need, we're going to explain. in each run what this instruction set is going to tell Bob's particle to do if it's at zero or minus 60,

Starting point is 02:20:12 what Alice's particle should do if it's at zero or plus 60. Okay? So we need four rows, Alice zero, Alice 60, Bob zero, Bob minus 60. And this particular proof I personally learned from the book by Nick Herbert called Quantum Reality. So shout out to Nick Herbert. nice, clear proof. So let's just try and do it. Here's our chart, and we have all these runs of the experiment, because remember, these are statistical predictions. We need 75% on average and 25% on average, so we have to do it over and over again. We have all these runs. Thing would go on. We want to specify for each of these four experimental conditions what the particle would do. I'm going to start by filling in Alice's row for zero degrees. What the,

Starting point is 02:21:02 actual quantum mechanical prediction is, is that she'll randomly see up and down. Half the time she'll get up and half the time she'll get down. That's true for any direction, without any pattern. So the way I actually filled this in, by the way, is I literally flipped the coin. Okay, I wanted a random string of U's and D's, and it turns out people aren't very good at coming up with random strings. So I literally flipped the coin. And if it came heads, I put in a U, came tails, I put in a D. And so that, I filled in that row that way. It's not exactly 50%, but if I kept flipping, we know, you know, it would average to 50% using Ds and there'd be no pattern to it, right? Okay. Now, that's one row filled. As soon as that row is filled, I know what

Starting point is 02:21:49 Bob's zero row has to be, because if they both check at zero, they have to get opposite results. So we can immediately fill in Bob. Everywhere Alice gets a U, he gets a D. Everywhere Alice gets a D, he gets a U. We filled in two of the rows. Good. So far, so good. Now we have to ask, what about these 60-degree cases? What if Bob is set at zero and Alice is at 60

Starting point is 02:22:14 or Alice is at zero and Bob is at minus 60? We want those to disagree 75% of the time, not 100% of the time, but 75%. that means that when we look at Alice, the Alice Zero row, we have to change 25% of them when we go up to the Alice plus 60 row, right? Because they all disagree there. We want only 75% of them to disagree. So we have to choose, we have to change about 25% of them. So I flip two coins, right? I randomly chose which ones to change. And it comes out about 25%, not exactly. But I did it randomly. And by the same argument, when I go down from Bob Zero to Bob minus 60, I have to change about 25% of those. Because if they happen to check at Alice Zero and Bob minus 60, I want 75% disagreement instead of 100% disagreement. So I've got to change about 25% going from Alice's row up and about 25% going from Bob's row down.

Starting point is 02:23:22 and I decided which 25% literally randomly by flipping coins. So now I will just show you what I got. I got that. Okay? And if you look at it, you'll see that Bob zero and Bob minus 60 isn't quite the same. And Alice Zero and Alice Plus 60 isn't quite the same. They differ about 25% of the time. But now the thing is filled, right?

Starting point is 02:23:52 We have no more choices to make. But we still have another experimental situation to consider. What if Alice happens to choose plus 60 and Bob happens to choose minus 60? So we've got this 120 case. Then we wanted them to disagree only 25% of the time. Only 25%. But that can't happen. Why?

Starting point is 02:24:16 Well, in the middle two cases, they disagree 100% of the time. I changed only 25% going up and I changed only 25% going down. So the outer ones can at most disagree, at least have to disagree 50% of the time, right? There still have to be 50% that didn't get changed. Right? If I only change 25% going up and I only change 25% going down, at least 50% of the time, nothing changed. But if nothing changed, they still disagree. So I can't get 25% disagreement there.

Starting point is 02:24:52 Can't be done. You can't put use and ds into this chart in any way. Try it however you want where the statistics come out right. But that's what would have to happen to have a local explanation. So no local explanation can be correct. So there's non-locality. This is a statistical, a predictable statistical effect, which, you can check in the lab and which cannot be produced by any local theory. Now, at this point,

Starting point is 02:25:27 we're done. Now, again, you can then, Bell proves a more general kind of inequality calls Bell's inequality that covers, you know, many more cases. I mean, I just looked at a single case, and you can expand from there and cover, we'll see a different thing. But that's the proof. and I can't do anything except say it again more slowly but I'll save you that because you can rewind it and listen again okay but there's no there's no hidden

Starting point is 02:25:57 you know there's nothing going on here I'm not asking you to accept some weird you know high level mathematical anything right I'll even put up another animation of just a couple other trial runs on Monte Carlo simulation just to hammer the point home for people on screen you can do that

Starting point is 02:26:14 I mean, I'm going to do something in a minute that's even simpler. But it's not what Bell did. I wanted to start with what Bell did because Bell investigated the Singlet State and he got to the Singlet State from the EPR state via Boehm's reframing of it in terms of spin. So, again, this is three down means when I constructed that chart, it would be okay if you check, whenever you checked at zero zero, it would be okay if you checked at zero. 60, it would be okay if you checked at zero minus 60, but it wouldn't be okay if you checked it 60 minus 60, right? And if you just check on my chart, again, at 60 minus 60, you should

Starting point is 02:26:59 have a disagreement rate of only 25 percent on my chart at 68 percent. I mean, it's not even close. I mean, you do have to understand the way in which the numbers, the restraints on a local theory, the numbers are not even close to the quantum mechanical predictions. It's not like they're nearby. Yeah. There are huge differences. In this case, the best you could do would be 50%, but you'd have to get it down to 25%. And, you know, no, right? It would have to be half of what you could possibly do. And again, you can just think about it. You can't do it because you only change 25% going up. You only change 25% going down. At least, 50% have not been changed. So you still have 50% disagreement. Impossible. Impossible.

Starting point is 02:27:49 And that's it, right? In a way, you could say that's it. Go into the lab and check whether the quantum mechanical predictions here are correct. And if they are, you have phenomena you've seen in a lab that cannot be reproduced by any local theory. So no local theory can return the quantum prediction, which is what Einstein wanted, right? He really wanted to get back locality. It's what Bell looked for. Can you get back locality? Answer, nope. Even if you wouldn't, you know, just admitting that the wave function is incomplete is not enough to say that you can recover locality and it turns out you can't. So again, you know, what I just showed was from Nick Herbert's book. Bell himself does a real mathematical, more general proof. His proof was then further

Starting point is 02:28:38 generalized into what's called the CHSH, Klausor, Horn, Shimoni-Holte inequality, which still involves pairs of particles. If you're interested in that, you can look at Appendix 2 of Bertelman's Sox. You can then say, well, what if instead of having two particles, I have three particles, or four particles,

Starting point is 02:28:56 or five particles, right? Other versions. Roger Penrose proves yet a different version in his book. I mean, there are all these different concrete situations over and over again what you're proving is the same thing. No local theory can make these predictions. And their predictions that quantum mechanics makes. And the important thing, their predictions that turn out to be correct. The real power of the theorem, as I say, isn't really in its generality. It's in its logic, right? Even if you only had proven it

Starting point is 02:29:30 for one single particular, precise case, if you can go in the lab and check, that could rule out locality. That single case could rule out locality and rule in non-locality, right? If you rule out locality, you rule in non-locality or spooky action at a distance. The very thing Einstein was trying to avoid, Bell proves you can't avoid. Look, it's an interesting situation. He uses the EPR setup. He uses Einstein's own tools to prove that Einstein was wrong. Now, of course, as Sean Carroll raises his hands, and a David Wallace raises his hands and says, yeah, but my theory retains locality, determinism, et cetera, with many worlds. Okay, so you were going to raise that question. You're raising it. Let me just say something. Sean Carroll will not say that many worlds is local. He'll say it's massively non-local. I know that, because I've asked him, and he says, no, it's a non-local theory.

Starting point is 02:30:29 and analyzing many worlds is of course made difficult because first you have to understand what the theory says. From the beginning it was often claimed that it was a local theory. And I will just say the following things. When you ask people, but why do you say that? They would say, oh, because the theory really runs on decoherence and anybody who's listened to these people, understands that you've got decoherence or approximate decoherence, and it leads to branching in many worlds and all the outcomes occur, right? And then they would say, but decoherence only takes place at the speed of light. That's how they're getting out of anything happening instantaneously.

Starting point is 02:31:18 And then if you ask them, but what makes you say it happens at the speed of light, they never had anything to say, because that doesn't even make any sense. Because decoherence is a feature of the wave function. And the wave function doesn't exist in physical space. So you can't say, how fast does it deco here? It's a global object. It is a global object. It is a universal object. If it decoheres it, as it were, decoheres everywhere all at once. It's not a local thing. So if someone, I don't know what David Wallace would say. I haven't asked him recently. Sean, and you can ask him, we'll say, no, it's a non-local theory. Nobody should be embarrassed by that. Why should you be embarrassed that your theory is non-local? Bell proved you need non-locality,

Starting point is 02:32:09 right? You should be embarrassed if you claim your theory's local because then you're going to say, well, how can you get the right predictions, right? Anyway, Sean will say, no, it's a, it's a, it's a very non-local theory. I mean, in quantum field theory, even the vacuum state is massively entangled. I mean, all of this non-locality is kind of driven out of entanglement, and entanglement is absolutely generic everywhere. So if you say, as the many worlds people want to say, all that exists is the wave function, and the wave function is massively entangled, you're going to have non-locality all over the place, which is what you do have.

Starting point is 02:32:46 Let me ask a simple question. If not for entanglement, because all of these proofs that I've seen of non-locality and bell and so forth, they all deal with entanglement. Are there any features of quantum mechanics, Heisenberg uncertainty, or some other odd feature that entails non-locality other than entanglement? no no that that's also a theorem any entangled pure state will violate some bell inequality any i mean sometimes the violations are very tiny because what the only states that don't violate any bell inequality or product states and it's easy to see that product states are fine because the two sides are uncorrelated but as soon as you have any amount of entanglement in a pure

Starting point is 02:33:33 state, you can find a bell inequality that that will violate, that no local theory could give you that. So this violation of locality is absolutely intimately tied to entanglement, not to uncertainty or anything like that. Okay. So what are the assumptions? So, again, presuppositions of the proof, one, the accuracy of the quantum predictions, two, EPR locality.

Starting point is 02:34:01 and there is a third thing that we use, which is this random sampling. So what I said is, you know, you have this big chart. Suppose I check in some of the cases at these two angles. Think of that as a random selection of rows, right? Random because I can, you know,

Starting point is 02:34:19 Alice and Bob can just do this kind of randomly in which times they happen to both get zero and which times they happen to one get zero and 160 is technically a random, random selection. If I take a random selection of rows, then by the law of large numbers, the statistics should be the same as the statistics for the entire chart. When I take random selections from big data sets, if they're really random selections, then the statistics of what I look at in that subgroup should be very, very, very close to the statistics in the whole group.

Starting point is 02:34:59 And the bigger the selection, the closer they get. That's basically the law of large numbers. That's how we do statistical sampling. So there is an assumption in the proof, which is that when Alice and Bob set their experimental conditions, they do so in a way that produces a random sample from all the pairs of particles they've been sent. Okay? That is an assumption and it's mathematic. You can point at that assumption when you look at the math.

Starting point is 02:35:29 of the proof and say that's where that's used. So those are the presuppenditions of the proof. Those are all the presuppositions of the proof. That's it. It's only one, two, and three. That's the totality of it. From one and two, from the accuracy of the predictions, which includes these perfect correlations, and from locality, we get the conclusion that there must be these predetermining elements of reality that determine the outcomes of the experiments on both systems. and then from three, from the random sampling, we say the observed statistics of the outcomes must be almost the actual statistical distribution

Starting point is 02:36:09 over all the cases. What we see is very close to the totality of what there was. We're just picking stuff randomly out and checking. So in the spin experiments, what we see is that when the magnets are misaligned by theta, then the particles yield different outcomes about cosine squared, over two of the time.

Starting point is 02:36:33 And so in the totality of the distribution, the particles should be anticoorrelated 100% of the time when the magnets are aligned, 75% of the time when misaligned by 60 and 25% by 120. If that is predetermined by an EPR local element of reality, then we would need a distribution on our chart that had those numbers.

Starting point is 02:36:57 But no such distribution exists. There isn't such a distribution. Can't be done. And the second assumption of random sampling, I just, I need to say a few words about it. It's called the statistical independence assumption. And the statistical independence there is just that the choice of experimental arrangement is statistically independent of the character of the incoming particles. that those have no interesting correlation between them.

Starting point is 02:37:35 And so you're taking a random sample. Each of these global experimental conditions is taking a random sample out of the totality of all the pairs that were created. Okay? Now, this assumption of statistical independence, that postulate is sometimes called as treating the variables

Starting point is 02:37:57 as free variables. That's just language. Unfortunately, and you would normally call these free variables, anybody would call them free variables, meaning they're just under experimental control, right? That's all that means. It's led to an unending and just painful confusion about what assumptions about it's making. because what people think is, oh, he says these are free variables, that means that Alice and Bob have free will. And now we have to consider under what conditions do people have free will. And now we say, if the physics is determinists, then people don't have free will. And then it just goes on and on and on. Painfully, if you have a philosophical training, because you first of all understand that free will has nothing to do with any of this. Okay.

Starting point is 02:38:50 And furthermore, determinism is compatible with free will, if you understand correctly. Okay, but the physicists who go run on about this haven't even read the philosophical literature. They haven't read Locke and they haven't read human. You know, it's just painful. It's just painful. Okay, that's free will is not an issue. Let me just show why. We want to ensure, what we want to ensure statistical independence.

Starting point is 02:39:17 Nobody ever thought Bob and Alice are sitting in their life. labs. And they say, oh, here comes a particle. What should I do? Oh, let me see. This time, I guess I'll do this. This time, I guess I'll do that. Right. I mean, that would be a really dumb way to run a lab, right? A really stupid way to run a lab. And furthermore, they couldn't make the decisions fast enough and so on. That's not what you do. Okay. In fact, this is a technical point. It's not in my slides. The magnets are actually too big to even move that quickly. What you really do is you have an optical switch. that will send your particles, if you're using photons, you have an optical switch that will send the particles

Starting point is 02:39:55 either to this setup or that setup. And it vibrates very quickly, and it randomly, this is what Aspe used, this is what Al-A-S-Bey-use when you wanted really quick, these really quick decisions to be made. Okay, that's not what you're doing. It would be a dumb way to run an experiment. It's not the way any experiment has been run.

Starting point is 02:40:13 Bob and Alice would get awfully tired very quickly about deciding, do I do this or do I do this? Okay. the right way to ensure this statistical independence assumption is to use what Bell calls a physical randomizing device, right? Those are his words, a physical randomizing device of a kind that's standardly used in randomized experimental protocols. What does you mean? And he talks about this, if anybody's interested, read the paper free variables and local causality. He spells all this out very beautifully. It has nothing to do with free will. Zero.

Starting point is 02:40:49 nothing. Okay? What is, he gives you examples of physical randomizing devices. I use, when I use coins to make my chart, and I did use coins, I did it as a physical animizing device. Why? Because it turns out if you ask people to make up a random string of use and z, Ds, or heads and tails, they're not very good at it. If you look at what they do, they typically don't produce random strings. They produce pattern strings. Like they'll say, oh, you know, they commit the gamblers fallacy. They say, oh, there have been three tails. There better be a heads next or something, right?

Starting point is 02:41:27 Humans are not good randomizers. But coins are good, right? Coins are good. They work. And when you choose lottery numbers and they have these fancy ping pong balls that are bouncing around, right? And you open a thing and a ping pong goals. That's a good randomizer.

Starting point is 02:41:44 That better be because that's a lotto machine. And, you know, you want to make sure that these are really random. random selections. Those are physical randomizers. They don't involve anybody's free will, right? The coin has no free will. The ping pong balls have no free will, but they're good randomizers, right? And you just check, do the strings that come out, do they have any patterns to them? And you can analyze them statistically and look for patterns. You don't find them. For the ping pong ball case, it's chaotic in a classical sense. That is very small differences

Starting point is 02:42:18 in initial conditions lead to different large-scale differences later. The differences scale up very quickly. And so it's unpredictable. Practically unpredictable, what ball will come next. That's what you want.

Starting point is 02:42:33 That's a good randomizer. That will produce a random selection of the experimental situations. Okay? Because it won't have any pattern to it. Is Conway's free will theorem relevant to this? Well, the fact that they call it the free will theorem is, because that's what's also ridiculous. All that's involved is statistical randomization.

Starting point is 02:42:58 Free will has nothing to do with anything. When Conway says, oh, if humans have free will, then electrons have free will, I mean, that's just lunacy. It's just crazy. What do you mean electrons have free will? Of course they don't have free will. They don't have will. If you don't have will, you don't have free will. They don't have volitions.

Starting point is 02:43:19 They don't have beliefs. They don't have desires. They don't decide to do things. Okay, this was, again, Conway was an interesting man. I mean, I and Shelley Goldstein and Roddy Tomoka spent many hours with Conway and with Sycoche and in their office. Interesting man didn't listen to people very much. And this was just a terrible, terrible mistake to call this the free will theorem.

Starting point is 02:43:43 and to say that it proves that electrons have free will. So what did he actually mean then? Or maybe he meant what he said and he was wrong. What's going on? He proved Bell's theorem. He proved Bell's theorem. What he proved was an instance of Bell's theorem. That's all.

Starting point is 02:44:00 Standard instance did nothing new. There is nothing new in what they did. They proved an example of Bell's theorem. From some, you know, reasonable premises. Okay, fine. There's nothing in that. There is nothing. There is nothing new in that, except a bunch of verbiage about free will that got thrown on top of it out of nowhere,

Starting point is 02:44:23 and then everybody perked up their ears and said, I mean, wouldn't you perk up your ears? If someone said, I just prove that electrons have free will? I guess I would perk up my ears, but I'd be pretty skeptical that anybody ever proved such a thing. Well, maybe he thought he proved that humans don't have free will. And you see, that's kind of an odd thing to prove, too. much of nonsense. I'm more interested in the if then, that he proved that if humans have free will, then electrons have free will. That's interesting.

Starting point is 02:44:49 That's what he claimed to prove. That's what he claimed to prove. But he proved no such thing. All he proved was balanced theory. Okay. I'm sorry. You know, that's the way it rolls. I mean, he was an interesting man, did a lot of interesting stuff, but this was not his finest hour.

Starting point is 02:45:09 Another kind of randomizing device that Bell talks about explicitly is a computer that produces what we call random strings. And he gives an example. Suppose you have a computer. It calculates the digits of pie, and then starting at the millionth digit, it puts out a one if it's even and a zero of its odd.

Starting point is 02:45:29 Okay? So it just runs on the parity of the digits of pie, starting in the millionth slot. That produces what we would normally call a random string of zeros and ones. It will be a string in which you notice no patterns. About half will be zeros, about half will be ones. Okay? It'll pass any statistical test you can think of for randomness.

Starting point is 02:45:51 But obviously there's no free will there. It's a mathematical fact what those are. The parity of the digits of pie is fixed by math. Nobody's exercising any free will. But if you make your decision about whether to set, whether to run it through this stern garlock or that stern garlock, on the basis of that string, that should be a random selection, and that should be statistically independent of the incoming particles. So again, free will has nothing to do with anything here. Now I'm just saying the same

Starting point is 02:46:29 thing. So Bell, and this, I'm using this case because Bell discusses it in the paper free variables and local causality, and he gives it an example of the physical randomizing device. doesn't involve anybody's free will. It's a computer calculating the parity of the digits of pie, right? This is just a red herring. This is just created an incalculable amount of confusion to no good purpose at all. So I'm going to quickly give you an analogy for the kind of thing we just proved. It's so simple you can just think it through, right?

Starting point is 02:47:10 You're on the street. Somebody is a gambling game. Here are the rules of the game. There are three cups. The person has two red balls and a blue ball. They're going to hide them under the three cups. And then you get to pick two cups, any two cups you want. You can put your fingers on any two cups you want, right?

Starting point is 02:47:26 Turn over the cups. And you can pick them, again, that's free in the sense that you can pick them any way you want, right? Flip coins, I don't care. Here's the payoff. You bet a dollar to play the game. if you whip the cups and they're of different colors, he keeps the dollar. But if they're the same color, right? In this case, they're both red.

Starting point is 02:47:48 You win $10. Right? That's the payoff schedule. Question, should you play this game? And imagine you can play over and over and over again. Should you play this game? Well, it's pretty easy to see that if the person isn't cheating, if this is a fair game, if it's really done the way it says, you should play the game.

Starting point is 02:48:09 game, right? Because two of the three ways you can pick two cups, which is the same as leaving one cup out, two of them he wins, but one of them you win. So you should win on average one out of three times. Every time you lose, you lose a dollar, but every time you win, you win $10. If I win one out of three times at those odds, I'm going to make money. I'm going to, I'm going to bankrupt this person. Right? The odds are. against the house. So sure, you should play, right? On this reasoning, you say, look, there are three cases. I'm choosing randomly. In one of the three I win, in two of the three I lose. I have a one and three chance of winning. And I, but I gain $10. I forfeit only $1. And suppose you play

Starting point is 02:49:04 this game now, imagine you start playing this game and you lose every time, every time. Every Every time you lose, you play 10 times, you play 20 times, you play 80 times, every time you lose. You can conclude something. Somebody's cheating. You can conclude that he's switching those balls around beneath the cups after you make your decision, right? He's somehow manipulating those balls. right? Anybody would conclude that and you should conclude that. He's running a scam on you, which you should expect because if it was up on the up and up, he's going to lose money.

Starting point is 02:49:51 Somehow when you pick which two, then the balls get moved or changed or something so that it's always a losing combination. Now here you don't exactly need action at a distance, but as I say, you do need action, right? It has to be that when you choose and lift a cup, merely reveal the color that was already there. It can't be working that way. The ball colors cannot be just pre-assigned at the beginning and merely revealed by lifting. And that's exactly what a local theory had to do for these outcomes. It had to pre-assign them at the beginning, and then those are just revealed when you run the particle through the machine. Right. So now, There is one way this might not be true, and this is the point I wanted to make.

Starting point is 02:50:43 Suppose this guy, no, it's really a good game, but he's a really good predictor of what you're going to do. He, you know, and there are people like this. They can like psychoanalyze you and say, oh, this time you're going to do this, this time. And he sets it up beforehand, right? It's like there are people who are really good at winning rock scissors paper because they like psychologically get into your head. Yes. And kind of. So that could be.

Starting point is 02:51:07 but if you wanted to make sure that wasn't true, then what would you do? You'd use a physical randomizing device. You wouldn't use your free will. You'd flip coins. Right. You'd use the digits of pie. You'd use one of these other things

Starting point is 02:51:20 that exactly is not free will, but guarantees a statistically independent, right, that there's no pattern to what you do. And if there's no pattern to what you do, he can't predict what you're going to do. And if he can't predict what you're going to do, he can't set it up to win. So again, this whole free will thing,

Starting point is 02:51:37 is just off entirely in the wrong direction. You safeguard against failures of statistical independence by getting rid of free will and using randomizing. Okay. So we now have Bell's argument rests on two and only two assumptions. One is Einstein's locality assumption, no spooky action at a distance. The other is statistical independence assumption

Starting point is 02:52:04 that the choice of the experimental conditions can be made in a way that is statistically independent of the state of the particles when they're produced at this source. That's it. There are no other assumptions. And from those two, he derives mathematically that certain statistical outcomes cannot occur if those two assumptions hold. So your only choices are deny one of the two. Now, one of them is denying statistical independent. and there are people who've tried to deny it, and you've talked to some of those people. And this is just desperate, right?

Starting point is 02:52:43 You use the parody of digits of pie, and you're going to tell me that's not statistically random. I mean, this is just crazy. Furthermore, it's crazy in the sense that this is the way we do science. This is the way we do what we call randomized experiments. We try to be careful that when we do sampling, it's random sampling, and when we do controlled experiments, who goes into the control group and who goes into the experimental group is randomly decided.

Starting point is 02:53:10 And we assume that these kinds of procedures produce statistically independent and random selections. If we denied that, if someone says, I don't believe that experimental method is gone. You're throwing, talk about throwing out the baby with the bathwater, right? You're going to get rid of all of science in order to try to defend locality. that is not a rational thing to do. If you try to do that with a computer doing it on the, you know, digits of pie, good luck with that. You know, it's just crazy. So we only have two assumptions.

Starting point is 02:53:46 One is locality. One is statistical independence. You don't want to deny statistical independence. The only rational response is to give up a locality. Okay. You have to give up locality. Einstein would be unhappy. I bleed for him.

Starting point is 02:54:01 But, okay, it's very common sense locality, it's intuitive, classical physics is local. It's a big deal to abandon it. I personally think that the proof of non-locality is the most astonishing proof of any physical fact in the history of mankind. That's my view. But it's a proof, or good enough, right? Facts are facts and proofs or proofs. This is the only reasonable conclusion. the physics of the actual world is not low.

Starting point is 02:54:33 Now, I'm going to do something very quickly, then I'm going to respond to some things people said, and then we're done. Cool. The end is inside. So, having done all this, much later, 1989, there's a new example showing the same thing, discovered, well, what I've shown you now is what Bell did.

Starting point is 02:54:56 He was working with these singlet states. It gave rise to the experiments done by John Klauser-Laspe, Anton Zilinger. They got the Nobel Prize for those experiments. They showed violations of Bell's inequality from these pairs of particles. There is this kind of interesting thing that the violation only shows up statistically

Starting point is 02:55:17 over many runs, right? You have to collect a lot of statistics. Okay, but that's okay. If you only ran it once, you couldn't prove anything. You're not in any danger, as it were, on one run, as long as if they both pick zero, they give opposite results. That's the only ironclad thing. So for a single run of the experiment, you could be sure,

Starting point is 02:55:40 you could arrange things locally that you're not going to get into any trouble. But what happened was in 1989, Danny Greenberger, Michael Horn, and Zylinger discovered this so-called GHZ example, which has this another character. It only runs on non-probabilistic, 100% predictions, predictions for every run of the experiment. So it takes that statistical character out, and that was nice. I mean, Bell's proof should be convincing anyway,

Starting point is 02:56:17 but still, it's nice to see that you can get it even simpler, even more direct. it uses only perfect EPR correlations, where if you know two of the outcome, well, in this case, we're going to use three particles, send them to Alice, Bob, and Charlie. Any two outcomes determine the third. So that's a perfect kind of perfect EPR correlation. I can make a perfect prediction from what happened in these labs about what's going to happen in that lab. Okay? So it doesn't use these 75, 25, 25 things. It's all 100%. So the key innovation here is first that we're going to use three spin-half particles rather than two. They're created again in a specific entangled spin state. They're sent off to Alice Bob and now Charlie, three separate labs as far away as you like. Alice, Bob and Charlie, you do these experiments at space-like separation, so even light couldn't get from one to the other to influence their outcome.

Starting point is 02:57:18 and the free, again, the free variables are just the same orientation of the magnets. We're doing spin experiments. In each case, again, Alice, Bob, and Charlie each have two orientations they can choose. In this case, there are at right angles. So we call them the X and the Z direction. They're either going to orient it this way, orient it that way. They can decide on every run which to do anyway. random number generator, whatever the heck you want.

Starting point is 02:57:52 So there's the setup. You'll see in this case, two of them are oriented in the Z direction. One of them's oriented in the X direction. Again, the outcome will either be up or down, binary outcome space, up or down. So I hope we're happy since each experimenter has two choices, there are eight possible global experimental conditions, depending on what each of the three has done, two times two times two. and you can create an entangled state, the GHZ state,

Starting point is 02:58:26 where the quantum theory makes absolute perfect 100% predictions about four of these experimental arrangements, okay? Four of them. What happens in the other four doesn't really matter. It makes predictions, but the argument runs just on these four cases. So here are the predictions of quantum mechanics in this. case. And again, we could go through all the math, but it would just distract us. You just have to, one thing you can trust here is that math is correct. These are the predictions of quantum

Starting point is 02:58:56 mechanics. If it happens by chance that all of the three experimenters pick the X direction, then the prediction is with certainty there'll be an odd number of up outcomes. It's got to be odd. It might be one. It might be three. In fact, it's like 20, 25% it'll be one and 75 at the end. That doesn't matter. We don't care whether it's one or three. We just care whether it's even or odd. And it's 100% odd. And because it's 100% odd, if you know two, you know what the other one must be. Right? Because if you know what two are, you know whether the other one has to be up or down to make it odd. So you have the perfect EPR predictability from any pair to the third. Never zero and two, ever. On the other hand, If two pick Z and one picks X instead of all of them picking X, then there will certainly be an even number of up outcomes. Could be zero, could be two, doesn't matter, always even.

Starting point is 03:00:00 Again, if you know two, you know what the third one is, perfect DPR correlations. Now, there are obviously three different ways that can happen because it could be Alice who chooses X. It could be Bob who chooses X. It could be Charlie who chooses X. So there are three conditions like that. There's only one condition where they all choose X. So I've got four experimental conditions. If all three are X, odd.

Starting point is 03:00:24 If one is X and two or Z, even. That's all you have to remember. That's it. 100%. No exceptions. Those are the predictions of quantum mechanics. Now, what can we conclude? Well, again, suppose these detectors are set at random.

Starting point is 03:00:44 so there's no way for the preparation to know what's going to be out there, then if it's a local theory, all the results have to be predetermined. This goes back to the same EPR argument. You've got EPR correlations. You've perfect correlations. If it's a local theory, it has to be a local deterministic theory. So at the source, it has to be decided what Alice's will do if it's measured in the X direction, what it'll do in the Z direction, and the same for the other two. So that's our first conclusion. Nothing can happen by chance. If something happened by chance, how would the other ones always arrange that you always get the right parity? So same argument, same conclusion, just DPR again.

Starting point is 03:01:36 If none of them disturb any of the others, which is locality, it has to be predetermined. So here's our situation graphical. And you'll notice what we have here is each circle represents a particular experimental condition. X-1 is, I'm using one, two, and three here for Alice, Bob, and Charlie. X1 is Alice sets her magnet in the X direction.

Starting point is 03:02:05 X2 is Bob sets his magnet in the X direction. X3 is Charlie sets his in the X direction. Z1 is Alice sets her in the Z direction. Z2. Bob sets his in the Z direction. And Z3 is Charlie sets his in the Z direction. So each has two choices. So we've got these six.

Starting point is 03:02:26 And what you have to notice here, and I should give credit where credits do, I mean, I learned this from David Merman. I think he came up with this diagram. It's beautiful. It's just beautiful. Notice the lines. The dotted line represents the global configuration where they all pick X.

Starting point is 03:02:47 And the three solid lines represent the other three global possibilities where two pick Z and the other picks X. Okay? So if you just stare at that, you'll see, yeah. Okay, if they all pick X, it's along the dotted line. If two pick Z and one picks X, it's along one of the three solid lines. Question, can I predetermine these outcomes, which means write a U or a D in each of those six circles, such that no matter which of the global conditions occurs, it'll come out right? that is if they're all X's it'll come out odd number of views and if it's any of the other three it'll

Starting point is 03:03:30 come out even those are the predictions that's what we want to recover can i predetermine things so that will come out no matter how the experimental situation turns out that's our quest the nice thing about this i mean i always like to say look at it it would fit on a cocktail napkin this little diagram and the next time you're at a cocktail party and you want to prove that the world is non-local. Draw this diagram. Notice, in the case of the one we did at first, we needed these long sets of rows, right?

Starting point is 03:04:02 We needed 19 rows, and we were putting in 25% and 75%. No, no, no. This one, we just have this one. Just this one. I'm just going to run this once. I'm going to run this experiment once. Can you predetermine these outcomes such that no matter which of these four experimental outcomes is picked, it'll give me the right outcome. So let's just try. First, we'll just try once.

Starting point is 03:04:28 So we're going to start with the dotted row, all X's. We need an odd number of up outcomes. Could be one, could be three. Let's make it easy. We'll make it three. So then we know what to do in each case. I'll put you, a you, a you, all right? So that one's okay. Now we have to look at the other ones. They have to be even. Now, if we look at Z3, nothing forces it. I'm a little tired of writing U. So I'll just stick a D in there. Now our conditions bite. Why? Well, if we look at the row that goes X1 is U, Z3 is D, remember we need to have two, an even number of U along the solid lines. I have a U and a D. So that means that Z2 is forced to be a U. Yes. Has to be. So now we've got five out of six. All I have to do is.

Starting point is 03:05:20 has put a U or a D in the last one, but I'm screwed. Because if I make it even for one, I make it odd for the other. Right. Can't be done. Mathematically impossible. Now, you might say, oh, you just tried one way. Maybe there's some other way to do it. So Merman gives this argument, beautiful argument.

Starting point is 03:05:43 Merm, it's an argument by reductio. It says, let's assume you could, let's suppose there's some way. You could put U's and Ds in these six circles that satisfies all. four of these constraints simultaneously. Let's assume it can be done. Okay, you've done it. Now, pick up all the discs. We've got these discs. Pick all the discs along the dotted line and throw them in a hat. So you just picked an odd number of views because that has to be odd. Now, go along this solid line and pick them all up and throw them in the same hat. That has to be an even number. Then the other one, throw them in a hat. That has to be an even number. Then the

Starting point is 03:06:21 third one, throw them in a hat. Even number, right? Odd, even, even, even. That's what the constraints were. So, how many U's do I now have in the hat? Well, I have to have an odd number, right? Odd, even, even, even. It's an odd number. But I picked up every disc twice, because every disc lies at the intersection of two lines. Yeah. So I can't have an odd number of views. I don't care how you put use in these. You can't have an odd number of views. So that's just a proof. That is a absolutely ironclad mathematical proof that you cannot predetermine these outcomes in such a way as to satisfy these constraints. Quantum mechanics predicts that these constraints will be satisfied. Therefore, there's no local way to do it. Therefore, if in the lab this

Starting point is 03:07:13 is what you see, the physics isn't local, and this is what you see in the lab. Quantum mechanics doesn't make a mistake here. So that argument is so simple and has so few moving parts to it that anybody, anybody can assure themselves by working through it that no tricks have been played on them, no steps have been, nothing went underneath the radar. Locality, a local theory, cannot recover these predictions. So I find that to be an extremely beautiful thing.

Starting point is 03:07:56 And it just proves it, you can say it just proves what Bell already proved, which is true, but it's also nice and short and clear. It can't be done. That's been confirmed. So no locally causal theory can be correct.

Starting point is 03:08:11 Now we're at Einstein's problem. But if I violate local causality, if I have spooky action at a distance, seems to contradict relativity. Yeah, I think it does. I personally think it does. I think that's why we should be thinking about ways to replace relativity with a different account of space time, which allows for this, right, in which a theory that allows for this can be written, can be specified. That's my opinion. Okay, these are all predictions with certainty. The EPR criterion of reality applies, everything goes through, and notice that no matter what you do, every single individual

Starting point is 03:08:51 run, if you try to predetermine these things, in every single individual run, there'd be a chance you hit a bad combination of experimental conditions and give a quantum mechanically unacceptable result. So, if we assume that Alice, Bob, and Charlie select their experimental arrangements randomly, you'd expect, actually about one out of four or one out eight, you'd get a violation of quantum mechanics, of quantum mechanical predictions. So if you do this hundreds of times and it always comes out right, that's not. So once we take into account the actual experimental results, we get a conclusion. The physics of the world we live in is not local in nine signs and bell sense. That would have upset Einstein. I really would have. I mean, I

Starting point is 03:09:43 feel for him, right? He never liked the non-locality of quantum mechanics, but he also never had a proof that you couldn't get around it. Bell found the proof. And that distress, that upset, however strong it is, is not an argument. And it seems to me the right thing to do is just accept it and get on with your life, okay? This is something we really unlike the holographic hypothesis, right? How many, how many physicists think, oh, we have to accept? There's no proof, nothing like a proof that you need the holographic hypothesis for anything. Okay, there's a proof that you need non-locality and from experimental outcomes, right? I mean, it's nowhere near. Why? Anyway, you want to check, are there loopholes? Are there errors? Are there loopholes?

Starting point is 03:10:36 Something go long. So let me just talk about some of the loopholes. polls that people have talked about. We can call them, there are some that are implausible loopholes, right? Any empirical argument, of course, it's not absolutely certain. Because why? If you want to reject an empirical argument strongly enough, you can always reject that the experimenters were crooked, did they be paid off by, you know, Bell set up some kind of weird scheme where he paid off experimenters to report false conclusions or whatever, right? I mean, you can always make something up. You can always doubt it, but that's not always a reasonable doubt. We want a reasonable doubt, okay? Like, the flat, you know, think about flat earth society. It still exists,

Starting point is 03:11:25 and you can give them whatever empirical evidence you like, and they'll find some way around it, right? But that doesn't mean that what they're doing is reasonable. And if you look at what they're doing, it's manifestly unreasonable. So we want to talk about reasonable doubts and unreasonable doubts. So here's an unreasonable doubt you could raise. I'll call it the matrix scenario. So someone says, look, I just want to maintain locality. I just have to maintain locality. I will not give up locality. How do we know this isn't what's happening? Maybe all of my apparent experience of the world is illusory or misleading. Maybe as in the matrix, I've been kidnapped by aliens and my nervous system is plugged into a machine

Starting point is 03:12:08 and the machine is programmed, produce the appearance of a fictitious virtual world that behaves as if it were governed by quantum mechanics, right, that it would give these things. Maybe that's what's going on. And then they add the physics of the real world, the physics of the machines, is local in Einstein's sense. So can't I maintain locality by adopting this view?

Starting point is 03:12:33 and you want to say, look, it's a consistent objection. They didn't contradict themselves. It would, as it were, provide a way to square the appearances with locality, right? Would do that. And I want to say, I mean, I'm making this up. Okay, in a technical sense of confirmation, it's insane, right? It's crazy. Why?

Starting point is 03:12:56 Well, it's sort of like denying statistical independence. If you accepted that objection, then none of our apparent empiric, experience of the world provides reliable information of any sort about the physical world. So if the objection is accepted, the entire discipline of physics has to be abandoned. You would just have to say, well, we have no access to the physical world. It's the damn aliens. They're getting in our way and we can't get around it, right? So then you just give up physics. I mean, you don't say, I have vindicated local physics. Right, right, right. It's another instance of the remedies worse than the ailment.

Starting point is 03:13:32 yes right or throwing the baby out with the bath water sure so we don't want to do that right it's logically you know yes it is not logically self-contradictory but that's too low bar we don't want to do stuff so um i put denials of statistical independence condition in this thing you can say that you can say gosh i don't care if you use ping pong balls or the digits of pie or flip coins or anything you can never get a statistically independent selection. This is just, you know, it's just crazy. And furthermore crazy in a way that would undermine all of experimental physics and all of experimental science, the methodology of science. It's not a rational thing to do. Now, it did become popular to use the word real in the past couple of years, like in 2022.

Starting point is 03:14:24 I have a slide about that coming up. Oh, perfect. Okay. All right. Now I'm really getting to the end, and we're getting into some heavy rhetoric here. So people who don't like rhetoric, I'm sorry. But I can't spend this much time on it and not just finish strong. Okay. Okay. So Elizabeth Kubler-Ross famously described

Starting point is 03:14:44 the five stages of grief, denial, anger, bargaining, depression, and acceptance. And now's a great place for an intermission. Again, you just watched Part 2. The link to Part 1 is in the description, if you didn't check it out, I highly recommend you do. It covers quantum mechanics from scratch. Subscribe for Part 3, the final part, which will be released on my substack first at

Starting point is 03:15:09 Kurtjimungal.com. It may already be there, C-U-R-T, J-A-I-M-U-N-G-A-L. This is where Tim wraps it all up with hilarious derisiveness, and I even ask the questions that you all had in the comments section. If you're interested in supporting this channel so I can put out more lectures like this and more podcasts with great depth, then visit the three support. links in the description. One is PayPal, another is crypto, if you prefer that, and another is the substack itself.

Theories of Everything with Curt Jaimungal - Tim Maudlin: Quantum Nonlocality Explained FROM SCRATCH

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