Quantum Mechanics Explained FROM SCRATCH

But notice the deep problems were about spooky action at a distance, not particularly about determinism. I'm really going to try to do this once [music] properly from beginning to end. What's going on with EPR? What's going on with Bell?

This is Tim Mlin, professor of philosophy at New York University and one of the world's leading philosophers of physics. Today, I'm thrilled to bring you a lecture with the breathing room. It requires to explain quantum physics and what Bell did with zero background knowledge. [music]

>> I've been told I have an unlimited amount of time. On this channel, I, Kircha Mungle, interview researchers regarding their theories of reality with rigor and technical depth.

>> Unfortunately, most people haven't understood the EPR paper. This is to set the record straight once and for all on what the great ironic reversal at the end is that Bell undermines Einstein's fundamental thesis that there's no [music] action at a distance but he undermines it using Einstein's own tools.

Professor, welcome. I'm super excited. Thank you for coming.

>> Um I'm very glad to be here. So, this title, okay, as far as I can see, EPR Bell, the completeness of the wave function, spooky action at a distance and all that. That's the title of this. Take it away. The title of the YouTube video may be something that can fit into the character >> count of the YouTube video and I went to all that trouble.

>> Uh, okay. So, let me explain to anybody watching this what this is.

>> It's not a kind of normal back and forth conversation designed that way. It it was supposed to be a real careful presentation uh a century of Bell's theorem and then a little bit on the problems that arise because of Bell's theorem. And in preparing for this I thought all right I have a kind of I've been told I have an unlimited amount of time which is unlike what I normally have. Usually you have to squeeze it down. And I thought, all right, if I really do have a lot of time, I'm really going to try to do this once properly from beginning to end. What's going on with EPR? What's going on with Bell? What Einstein was thinking? What Bell was thinking? Other things that happened in the meantime, the logic of Bell's argument, and the conclusions of it. So that's what this is all about. I should say that because I want this to be ab absolutely clear. Uh I've essentially written everything out.

>> Perfect.

>> And it's going to be a little boring because I'm going to be more or less reading what's on the screen. Uh unless I I riff on something or Kurt has some something he wants to interrupt me about and ask me about which is fine. Uh but don't be surprised that that's what's going on. Okay. So should we begin please?

Okay. So this comes in various acts, historical acts. I think there'll be some history here that almost nobody listening to this is aware of. Historians of physics are aware of it, but it's not usually talked about. So we're going to start in 1905. The honest moralists when Einstein develop proved that there were atoms and developed the special theory of relativity and proved equals MC² and on top of that really began quantum theory with his paper on the photoelectric effect. So let's just begin there.

So although plank is usually credited with being the originator of quantum theory because of work he did on uh thermal radiation in black body radiation in 1900. I think it's really not fair to say that began what became what we now think of as as quantum theory. Why? He was doing some statistical calculations in a normal way for a classical physicist doing statistical calculations. He knew what he was trying to get. He was trying to get a certain spectrum of radiation for black body radiation. He found that he could get the right answer out if instead of taking a limit going to zero, which is what you'd normally do, he stopped at a certain point. And so he stopped. And that point had little finite regions of phase space which were characterized by this plank constant h. He knew that gave him the result he wanted. It's not clear that he thought that what he was doing was quantizing anything. It's not clear that he had any real physical hypothesis about what he was doing. He just noticed that it worked. So when you really ask who really proposed quantization of a classical quantity, it's Einstein in 1905.

Now what was Einstein worried about? He wasn't worried about black body radiation. He was worried about the photoelectric effect. And the photoelectric effect was a known property of certain metals that when light fell on it, it created a current, an electrical current. And it was known how that current was related to the light. And it's a very surprising way that it's related to the light. I mean, it's not surprising from a classical perspective that light on a metal might start a current. It's obviously delivering energy to the metal. And you need to deliver energy to the metal intuitively to knock electrons free and get a current going. But the way that that depend that that that energy translated into current was very surprising. So let's go through the surprise. Classically you think of light as an electromagnetic wave and it's characterized by a frequency and an amplitude. The frequency tells you essentially what the color of the light is and the amplitude tells you what the brightness of the light is. And classically when you attribute energy to an electromagnetic wave, it depends on both the frequency and on the amplitude. So you can increase the energy by increasing the frequency and you can increase the energy by increasing the amplitude by making it brighter. So you would think that if light falling on a metal is creating a current, you could increase the current either by changing the frequency and making it higher or by changing the amplitude and making it brighter. But it actually turns out it doesn't work like that.

Um the dependency of the current doesn't go like that. Instead, what happens? Well, there's a critical frequency of light. Uh a critical color as it were. And as long as the light is below that frequency, no current flows at all, no matter how bright the light is. And as soon as it goes above that frequency, you start to get current. Uh so the current isn't just a function of the delivered energy, right? If you make it brighter, if it's below the frequency and you make it bright brighter, you do deliver more energy and the and the metal will heat up. But what you won't get is this electrical current. Once you get above that frequency, as you increase the brightness, you increase the current. So the classical model of light as an electromagnetic wave doesn't have any obvious way of making sense of that kind of data.

So Einstein noticed that you can make sense of it if you have a kind of really quantum hypothesis or discretetization hypothesis. You say it looks like the light is delivering energy to the metal in discrete small packets and the amount of energy in each one of those packets is a function of the frequency. As you increase the frequency, you increase the energy of each packet. And as you increase the brightness, you increase the number of packets. So to that extent it looks like the light is delivering energy more like particles would more like a set of particles. If the particles don't individually don't have enough energy if none of them has enough energy to dislodge an electron as it were then it doesn't matter how many of them you throw at it. It's not going to get a current. And as soon as you have even one that's above that threshold then you will start to get a current. Uh so this picture of energy being delivered in quanta or packets in discrete units is suggested by the way the photoelectric effect works and the hypothesis of how the frequency of the light is connected to this energy of these quanta is given by the famous formula E= H new. So there we have plank's constant again. plank. The one plank discovered in his calculations is now showing up and connecting together the frequency of the light to the energy of these quanta, right? quant of energy and then you would say that would explain why below a critical new you just don't get any current at all because because the quanta are not delivering each each individual quantum is not delivering enough energy to dislodge an electron and that is that is the quantum hypothesis as it appears here.

Now notice what's quantized here isn't really energy. A photon or a quantum of light can have any energy you like. You just have to pick the right new. Right? There's a continuum of different frequencies and each frequency gives you an energy that gives you a continuum of en possible energies of photons. It's rather that at a fixed frequency the energy is seems to be delivered in these discrete packets each of which has an energy that's determined by the frequency. Okay.

So what's this kind of like? Um, this would was a tremendous surprise for people who thought of light as a wave because if you think if light's like a wave like a water wave hitting the beach that of course carries energy and as it hits the beach it distributes that energy but it distributes the energy equally across the beach. If the beach is made of pebbles and a ra wave crashes on it, all the pebbles get jostled a little bit. But this is like a wave comes in and a few pebbles get shot way up, get a whole lot of energy, and the other one's nothing. Like the energy is not being equally distributed across the beach. And it's more like people are shooting bullets to the beach, right? So imagine a bunch of people with guns firing bullets at the beach. then if a pebble gets hit it will jump up and if it doesn't it won't and you don't expect the energy be distributed evenly. Um, so you get this kind of particulate model that seems to be connected with this behavior and uh as I say the the model is like this bullet model and you can go further you can say well if you're shooting bullets and it takes a certain amount of energy minimum amount of energy to dislodge a pebble then if your ammunition is too weak and individual bullets don't deliver that you'll get no effect. But as soon as you upgrade the ammunition, which would be the equivalent of upgrading the frequency, now they do have enough. Once you get beyond the critical threshold, suddenly the rocks will start to jump. Um, and the more bullets that are being shot, the more rocks will jump. That's like the brightness. So what happens is in this in this 1905 paper when Einstein tries to account for the photoelectric effect he introduces a kind of wave particle duality. Right? It certainly he says that the energy of the wave seems to be delivered more the way energy would be delivered by a particle than it would be by a classical a classical wave. Um, now there are still wave characteristics and there were wave characteristics in Einstein's theory. The actual calculation is rather complicated but part of it was these particle like this particle-like behavior of the light. Um, you still of course need some wave characteristics of light because light does behave like a wave. It refracts, it interferes. It does all sorts of things that when there was the original debate between the corpuscularians like Newton and the wave theorists, the wave theorists won that debate, classical debate because light does display wavelike characteristics of interference and refraction and so on. Uh, so then you have this idea of wave particle duality already is there in 1905. Light is in a certain respect behaving like a wave and in some other respect behaving like a particle.

All right. I'm sorry. Would you say that it's a wave particle duality or would you say that it's more like the quantum object has wave characteristics and particle characteristics, but that duality isn't quite the correct term in the way that we use dualities in math and physics otherwise. Like a co- vector is dual to a vector or something.

Yeah, it's yeah, it's certainly not a technical notion of duality as would be used in math. So yeah, that's the the the word isn't supposed to conote that when I when I'm using it here. And I think when people started talking about it, I don't think they had a a strict mathematical understanding. Um, all they meant was somehow this thing is in certain ways behaving like a wave and in other ways behaving like a particle. That's all.

One of the ways that it could be saved is if this is true that it either is going to behave like a particle or it's going to behave like a wave. It never behaves like both. That whenever it's behaving like a particle then it's behaving like a particle but not a wave. So I've heard some people say that. And I'm sure the audience have heard other lecturers say that or popularizers of science. Is that correct?

>> No, I would say I I would say nobody takes would would take that. That's a kind of Jackal and Hyde picture, right? I mean, there's one guy and sometimes he behaves like Jackal and other times he pa behaves very differently like Hyde. Um, and and he switches between the two, right? It's really quite dramatic when he switches between Jackal and Hyde. I don't think anybody thought that was going on, that it sometimes is just a particle and at other times is just a wave and it somehow switches between the two. It would just be crazy to try to make such a theory. Um, the the the the claim that I made which is that in certain ways you have a single thing and in certain ways its behavior is characteristic of waves and in other ways of particles. that is going to be true at all times. It's not like there's a trigger that switches it from particle mode to wave mode, right? I mean, you could imagine such a theor I can't imagine anybody taking it seriously. I mean, that's just kind of crazy, right? What would the trigger be?

Some people heard that from the double slit. I'm just trying to cuz I know the audience may be thinking but but I've seen other popularizations or other animations of this and that that if you look if you have the which way information then it starts to act like a particle and if you don't then it starts to act like

>> okay so I'll I'll even dunk a little bit on my friend

>> I want to preempt what the audience may be thinking just so that you can dispel any incorrect notions from popularization

>> no no this is fine this is good look I can dunk a bit on my friend Sean Carol who tried to do something which you shouldn't try to do which is reduce quantum theory to five words [laughter] and his five words were don't look wave look article and that sort of suggests this jackal and hyde thing but the trigger is being looked at and that's just of course lunacy right because what do you mean looking at a you know looking at what do you mean by looking at a particle I mean the the whole thing makes no sense and I'm sure Sean would not defend it he you know trying to reduce any theory to five words is not a great idea. Um, the the this this thing about which way information and so on and double slit and why the interference goes away. All of that is explained in a perfectly comprehensible manner just by looking at Schroinger evolution of the wave function and the Schroinger evolution is always wave. Schroinger's equation is a wave equation and it governs the wave function as a wave. and it explains why the interference goes away when you change the physical situation in certain ways. I subscribe to The Economist. Their science and their AI coverage is among the best I found anywhere. And I say that as someone who reads plenty of it. I'll give you some examples. They just ran an analysis on how attitudes towards science are changing in American politics and what this means for research and funding in scientific institutions moving forward. This sort of highquality reporting is fantastic. They even covered how dark energy may be weakening over time. Now, if that holds up, it completely changes our understanding of the universe's fate. If you watch this channel, those are exactly the kinds of questions that we explore every week. I subscribe to The Economist because their science and their AI reporting regularly surprises me with how deep it goes. And they're also of course known for global affairs, both political and economic reporting. They are top tier. And interestingly and flatteringly, TOE is one of the only podcasts that The Economist partners with. So as a listener, you get an exclusive 35% off. That's not a deal that they have just anywhere. Head to economist.com/toe to subscribe. That's economist.com/toe for 35% off. People characterize those ways as giving me which way information or whatever. That's just it that that just leads you in the wrong direction. You make certain physical changes to the situation. You plug Schroinger's equation in. You see what happens and you notice that in a in in fact in a continuous way the interference slowly degrades which if you thought either it's a particle or it's a wave. Well, how can there be this kind of continuum between the two behaviors? Right? There's a continuum between the behavior where you have sharp interference bands and you have don't have interference bands. Um, so no, that that jackal and hyde kind of picture is clearly incorrect and I don't think anybody would defend it who was serious about it. Um, I should say it puzzled Belle and he said he was always puzzled about once they noticed that there was both this wavelike behavior and this particle-like behavior and then they started worrying well is it a wave or is it a particle or is it a wavele or whatever that it didn't occur to them he says the obvious solution maybe there's both a wave and a particle right it the thing behaves somewhat like a wave because there is a wave and it behaves somewhat like a particle because there is a particle and they're both there. Um, that's the pilot wave picture that we're going to talk about later and it's an obvious way of explaining why you have both of these sorts of characteristics. Um, not the only way but that's an obvious way to do it.

>> Great. But as I say, if someone were to try to really make physics out of the idea that that a photon at sometimes is in particle mode and at other times is in wave mode. and they then would have to give you an account of when it does what and good luck with that. I mean, that's really that's not going to be a serious theory. Anyway, you you had both of these characteristics and and and Einstein solves the problem of the photoelectric effect by attributing particle-like behavior to things that were classically waves. So, it occurs to De Bruyne, very young guy. Well, turnabouts, fair play. Um, why don't we think maybe things we think of classically as particles can display wave behavior, right? Just and that then he started talking about matter waves. Um, so again, you have an electron classically it's a particle. Classically, it's always somewhere. It moves around in some continuous way. It's not like a wave. It's not spread out. It doesn't interfere or anything like that. And De Bruyne says, "Well, if you took classical electromagnetic waves and gave them particle-like behavior, why don't I take classical particles and give them some wavelike behavior?" Uh, and he then made some you you then need a way again to link what will the wave behavior be? What kind of wave should I associate with these particles? And de Bruy as we'll see taking Einstein as his model said all right I can make that linkage using plank's constant. So one of them is this lambda equals h over p lambda if if something's going to be a wave it has to have a wavelength lambda and de bruy said okay a classical particle has a momentum p so let me just say that lambda equals h over p. There's planks constant again. Right now I can say if class if in a classical situation I would say this particle has such and such a momentum. I can say well then I expect it to to display wave behavior that would be associated with a wave of wavelength lambda. And what about but a wave has both a wavelength and a frequency. I needed new. So there he used the same one that Einstein used. E equals H new of course um Einstein was going the other direction. Einstein was saying well I know my light has frequency new what is the energy of these quant and de is saying well my particle has energy like 12 mv^2 classical energy

>> mhm

>> if I want to associate a frequency with it what will it be I'll use the same equation right but now I'm putting in the e and deriving the new so he he says if I take a classical particle which would have a momentum and an energy I have two equations that will give me a frequency and and a wavelength and then I can think about the the behavior of waves with that frequency and wavelength, right? Um, and that then led to people actually looking for interference behavior, wavelike behavior of electrons. And you sort of see how de got there. So let's just recap where we are, right? We're only in 1924. This is actually before what's normally called the birth of the new quantum theory which is 2526. And already de Bruy and Einstein back in 1905 have laid the foundations of the new quantum theory. What's called the breakthrough of Heisenberg which is now 1925 was the matrix mechanics. And what I've given you has no matrices in it in any obvious way. And it's just very different from what Heisenberg was doing. And I don't want to go into what Heisenberg was doing. I mean, it was clear and it was something else. Uh, but I'm telling trying to tell a reasonably smooth story. And the story gets smooth when after Heisenberg develops the matrix mechanics, Schrodener develops what's called wave mechanics 1926. And then there were various proofs that at least in certain circumstances, the two theories gave the same predictions. So they were generally considered to be just different mathematical presentations of the same theory. And furthermore, because people with classical training were very good at working with waves and really hadn't learned to work with matrices, pretty much everybody started working with Schrodener's presentation in terms of wave mechanics um rather than with the matrix mechanics. So we're now in 1927. The new quantum theory is certainly in place and people are talking about it. We have Schroinger's wave mechanics which which involves the introduction of the wave function that we're all familiar with which is a complex valued function which he didn't like using complex values. He was a little upset that he had to do it but he was forced into it. a complex valued function over the configuration space of a system. So that's what the mathematically what the wave function is and Schrodener specified its dynamics in what we call Schrodener's equation and that dynamics is a wave dynamics. So the wave function governed by Schroinger's equation is going to evolve in a wavelike way. There'll be interference. There'll be spreading uh there'll be refraction essentially refraction-like behavior. All the things you would associate with wave behavior. Nobody quite knew what to do with this wave function until Bourne came along and gave it this probabilistic interpretation where he said, well, what we're going to do with the wave function is square it and then treat those numbers as probabilities for measurement outcomes. Mhm. Um, that's where the probabilism comes into standard quantum mechanics. The failure of determinism. You say the theory no longer gives strict predictions about what's going to happen. It merely gives you different possibilities and assigns probabilities to them. And during this period, Bore and Heisenberg are working together to lay down principles of what's usually called the Copenhagen interpretation or the Copenhagen school. And the main principle of that school we want to focus on is the insistence that the quantum mechanical description the wave function of a system is complete. It tells you everything there is physically about the system and that this randomness or probability that's introduced by Bourne's rule reflects an actual failure of determinism in nature. Nature itself is not deterministic. And Boore was very insistent that they had passed a threshold from classical physics that you couldn't go back over. You're giving up determinism. You're giving up uh the ability to visualize what's going on. What Bore was very insistent on that. And in so far as you think you need to visualize things to understand them, you're giving up on understanding. But Bour kept saying, "But we've reached the end of the road. I mean, this theory is the final theory, and the reason you don't have a good time understanding it is your problem, not nature's problem."

>> For Schroinger, he proposes this wave function equation.

>> Most students when they're taught quantum mechanics, they're taught the Borne rule along with the Schroinger equation. So it's difficult to think what what would the Schroinger equation be doing without the Borne rule like what did Schroinger think the wave function was and then did Borne only invent that because of single particles cuz then you have to make sense of dots that are appearing on the screen or like how could those two ever be separated?

>> I mean, that's a that's a very good question. Schrodener I believe didn't particularly like Bourne's suggestion when he made it. Um, I if you if you're if you're tracking the development and you follow the development I gave you where De Bruy makes this suggestion that we ought to start treating matter particles using these wave characteristics and then we have wave equations for them. Um, what what really happened is that if you if you read Schroinger's big paper, it's a four-part paper when he introduced the m the uh wave mechanics and what he does in the first three parts is all stationary or static situations. Okay, so they're the kinds of situations where nothing is changing in the environment and you're looking for what we call iigen states or certain kind of stationary solutions to these equations. For what purpose? Well, in the case of, for example, the one that that really got this going for bore, in the case of atoms, you wanted to know what are the energy levels of the different that are available to electrons because the picture was that electrons in an atom can only be in certain energy states. And if they jump up from a lower one to a higher one, they have to absorb a certain amount of energy. And if they decay down, they emit energy in terms of light. And that was supposed to explain the atomic spectra that you could see, right? You just see that the light coming from the sun or the light coming from, you know, a neon tube or whatever um is not a uniform spectrum. It has very definite bands where the light is being produced. and the old quantum theory which is what preceded 1925 and so on. This is 1915. Bore is laying down these rules for the orbits that electrons can be in thinking of the orbits as planets as really little little particles in planetary orbits. and you restrict the orbits in certain ways that have to do with wave getting waves to fit around these orbits. That gives you a set of orbits and that gives you these transitions what these transitions are possible and that gives you the spectra of light. Okay, that's essentially for what they're doing a static situation. You're just solving for stationary solutions to your equations. And then what's important about the equations is what energies you associate them with. Right? [snorts] Now you can do all that without using Borne's rule. Nothing about Bourne's rule, nothing about probabilities there at all. It's just can I get the spectra right? So that's a kind of example of what you could do uh in a you know in a static situation what are their probabilities of anyway as it were in a static situation nothing's changing. Um, right right so there is a lot that you could do now in fact what what Schroinger does in that paper is the first three sections he's just dealing with these stationary solutions and the wave function he uses is real it's not complex it's a real valued function and then he says well what happens if the situation isn't stationary what happens if there's something that's being changed if I've got some electric field or something magnetic field and it's it's it's varying. Then he said, I'm he's forced into it more or less. He's unhappy about it. He's explicitly unhappy about it. He says, well, I'm going to now use a complex function. I'm going to the values of the function are not going to be real numbers anymore. They're going to be complex numbers. It was the only way he could think of to deal with this this non-stationary situation. Um, when we learn quantum mechanics, as you say, when a student learns it, the first thing they're told is a wave function is a complex function.

>> So, we start at a position where Schrodener just barely got to and wasn't happy about. He was hoping to replace that complex function with a real function. Uh, he says so, he just couldn't figure out how to do it. So you know the the Bourne's coming into this and suggesting squaring this complex function first of all why why square it squaring the complex function and then treating that those numbers as probabilities that's kind of completely out of left field. Um, but of course for many purposes it worked. So that's why the situation was so confusing. Nobody really understood what was going on. And and and when I don't know what Borne exactly thought, but when when when certainly Bore insisted that these probabilities when you got them were fundamental that they reflected indeterminacy, innate indeterminism in nature itself and Schroinger was upset about that. I think Powi was upset about that. This that did not go over well.

>> [sighs and gasps]

>> Um, so it it was a very confused situation. Okay. So there we are in 1927. This stuff has come out and at the fifth SV conference all the big shots as we know get together and have a nice photograph taken of them all together. And there was a lot of discussion of the quantum theory. And in that discussion, Einstein first raises objections to the quantum theory as it's being exposited by Boore and Heisenberg. And these objections are very important. They tell you what was on Einstein's mind from the beginning. So we're 1927. People knew you could use Bourne's rule together with the wave function together with the Schroinger equation and make some statistical predictions, right? You use the Schroinger equation to evolve the wave function. You squared the wave function to extract some probabilities. You use those probabilities to make statistical predictions. And it worked. Um, and even though the new quantum theory again is attributed to Heisenberg in the matrix mechanics really even by 1927 I think people were mostly working with this Schroinger wave mechanics picture and so Einstein is focused down on the wave function because this is now if you use the Schroinger presentation the central object you're using to describe your system is a wave function. So he's very focused down on the wave function and he notices that one in the same mathematical object can be used to represent a physical system with different physical meanings, right? With different physical interpretations or understandings of what's being represented. And he's very clear about it. And he says sometimes when we describe something the description is a merely statistical one. That is we're not describing an individual system. We're describing an ensemble usually a kind of ideal infinite ensemble of systems. And he thought that that's the natural way to understand this Schroinger wave. and he was worried but he was very worried about about how bore was trying to understand it. Um, and so he was he really is focused down on this very simple question. When I write down a wave function, is that supposed to describe a single particle or only a collection of particles? A large collection of particles, right? So the second would be a statistical understanding. And he raised some problems about this with an example which in which I think most people don't know but if you don't understand this example you won't see where Einstein is coming from that involved a pinhole and a hemispherical detector. Okay. So at the SV conference and we have records of the discussions at the conference. So this was not you know Einstein giving a formal presentation. It's just him him raising objections. And so he imagines this situation where you have a a a beam of say electrons and they're being shot at a barrier with a pinhole in it with a very small hole in it and beyond the pinhole there's a screen and not just a screen but a hemispherical screen. So the picture is you've got this screen with a hole in it and then around centered around that hole is a large hemispherical screen where the screen is the same distance in all directions. Okay, that's going to be kind of important. And we all know that that the idea was from De Bruy that gee the particles the electrons have associated wave behavior. They have frequencies and they have wavelengths and they'll behave the way water waves or you know electromagnetic waves do. Well, what do they do? Um, when you shoot a a wave through a small hole, it defracts. What comes out the other end is a wave like a semic-ircular wave or an expanding wave in water. A semic-ircular wave in another dimension you get a a growing hemispherical wave because the wave defracts and as it were comes out of the pinhole going in all the different directions. So here's a transcript of that discussion. This is a transcript in a recent book by Anthony Valentini and uh Guido Baktia about the SV conference. And I'm just going to read this right if I can. So Einstein, despite being conscious of the fact that I've not entered deeply enough into the essence of quantum mechanics, nevertheless, I want to present here some general remarks. One can take two positions toward the theory with respect to its uh postulated domain of validity, which I wish to characterize with the aid of a simple example. Let S be a screen provided with a small opening. O figure two, we'll see figure two in a minute. And P, a hemispherical photographic film of large radius. Electrons impinge on S in the direction of the arrows. Some of these go through O. And because of the smallness of O and the speed of the particles are dispersed uniformly over the directions of the hemisphere and act on the film. Both ways of conceiving the theory now have the following in common. There are de boy waves which impinge approximately normally on s and are defracted at o. So this is again de br introduces this idea that even electrons will exhibit wave behavior. Behind s there's a sphere there are spherical waves which reach the screen p and whose intensity at p is responsible for what happens at p. So there's the picture. There's figure two. You see the electrons coming in. You see the little hole o. You see the arrows going out in all directions toward the hemispherical screen which is equal distance away. Right? We can characterize the two points of view as follows.

So Einstein says look what we're agreed as it were mathematically that part of the description. But physically what what are we talking about here? What what exactly does this wave function represent? And he gives you two conceptions. Conception one, the De Bruyne Schroinger waves do not correspond to a single electron. Right? The Deceer waves is what we would call the wave function, but to a cloud of electrons extended in space. The theory gives no information about individual processes, but only about the ensemble of an infinity of elementary processes. So you imagine, you know, you're shooting these electrons at this pinhole and imagine that it they just each one gets somehow defracted or shot off out of the pinhole in different directions. But if I shoot a million of them and I just follow that cloud of electrons as it were, then the whole cloud will then spread out hemispherically. Right? That's conception one. Conception two, the theory claims to be a complete theory of individual processes. Notice the word complete there.

>> Mhm.

>> Right. Of and notice the word individual, right? That the theory purports to tell us everything about the individual processes about an individual electron. Each particle directed toward the screen so far as can be determined by its position and speed is described by a packet of the de Schroinger waves of short wavelength and small angular width. This wave packet is defracted and after defraction partly reaches the film T in a state of resolution by which I think he means by a state of resolution that it's been thinned out as you would imagine. You you shoot this wave in it comes out in all directions and it thins out as it as it goes out and by the time it hits this hemispherical screen it's rather thin, right? and it'll get thinner and thinner the further the screen is. Okay. According to the first purely statistical point of view, size squared expresses the probability that there exists at the point considered a particular particle of the cloud. For example, at a given point of the screen. So again, you now have s squared at the screen. You can you you square sigh. It's actually going to be pretty uniform across the screen. And you say, but what is that number? You know, Bourne tells me it's a probability. The probability of what? And Einstein says, well, if I have this large collection of particles and you just as it were arbitrarily pick a particle, you can think of that as the probability that that particle is somewhere there near the screen. Right? According to the second conception two s^ squ expresses the probability that at a given instant the same particle is present at a given point for example on the screen right so he's saying you just shoot a single particle through in the second conception as this spreads out it represents the particle itself that single particle in some sense spreading out and the probability is the probability of some kind of action of that particle on the screen. Here the theory refers to an individual process and claims to describe everything that is governed by laws. So again the two points in conception two the wave function describes a single individual system and furthermore is a complete description of it. It describes everything about it. So if the wave spreads out then the particle spreads out. The second conception goes further than the first in the sense that all the information resulting from one results also from the theory by virtue of two that the converse is not true. It is only by virtue of two by the second conception right that the wave function describes individual systems and is complete. It's only by virtue of two that the theory contains the consequence that the conservation laws are valid for the elementary process. It's only from two that the theory can derive the result of the experiment of Geigger and Boa and can explain the fact that in the Wilson cloud chamber the droplets stemming from a alpha particle are situated on very nearly on continuous lines. Why? Because you're you're trying to explain single continuous lines through a cloud chamber then you're talking about a single particle and what it's doing. You're not talking about a collection. You're talking about what a single particle is doing. Mhm.

>> But on the other hand, and this is the main point, on the other hand, I have objections to make to conception 2. The scattered wave directed toward P does not show any privilege direction. If size squared were simply regarded as the probability that at a certain point a given particle is found at a given time, it could happen that the same elementary process produces an action in two places on the screen. Right? Why? Well, you've got this single particle. Send it through. It's spreading out. Okay. So, suppose I I say this this wave completely describes a single particle. The wave goes through the hole and spreads out uniformly in all directions toward the screen. And that's supposed to represent that it is physically possible for that single particle to interact with all these different points on the screen where where the wave is reaching. Right? But then he says, "But then why can't the particle interact at more than one place? Why can't it interact over here because the wave got there and interact over here because the wave got there?" Right? How could you avoid if if the particle itself is, as it were, thinning out and spreading out in all different directions, how can you avoid it acting at different points on the screen? And again, if you're talking about a collection of particles, then you have no problem because you say, well, some of them can interact over here and some of them can interact over here. But for a single particle, what could that mean?

>> Right? He says but that interpretation according to which s^ squ expresses the probability that this particle notice that this we're talking about a single particle is found at a given point assumes an entirely peculiar mechanism of action at a distance which prevents the wave continuously distributed in space from producing an action in two places on the screen. That peculiar mechanism of action in a distance is what we call collapse of the wave function. That is in that theory you say all right if a spot forms here on the screen that's one thing but that formation of the spot also has an effect of destroying eliminating the wave function everywhere else at every other point of the screen where it had reached right and according to this theory it did reach there right even for a single particle the wave function got to the other parts of the screen. Why don't they ever create a second spot? Because as soon as the first spot forms, something happens that annihilates the rest of the wave function. That's collapse of the wave function. And he says that's action at a distance, right? Because the formation of the spot over here is causing the physical wave over here to go to zero instantly and globally. Because if that change didn't happen instantly and globally, then sometimes we'd get two spots or three or more etc.

>> or three or four. Exactly. And you never do.

>> Yeah.

>> Right. You only ever get one spot. In my opinion, one can uh remove this objection only in the following way. One does not describe the process solely by the Schroinger wave but at the same time one localized the particle uh sorry during the during the propagation I think that Mr. De Bruyne is right to search in this direction. If one works solely with the Schroinger waves, interpretation two of SI squared implies to my mind a contradiction with the postulate of relativity. And that's because of the spooky action at a distance, right? Because you need this instantaneous change in the wave function. The collapse is global and instantaneous and that violates relativity. So Einstein already in 1927 is worried about spooky action in a distance. He's worried about the completeness of the wave function and he's sympathetic to De Bruy who says the wave function isn't complete. The wave function doesn't tell you everything. In addition to the wave function, there's this particle and the particle is always somewhere and it's always moving in some direction and therefore if the particle is headed in this direction to the screen, no spot will form on the other part of the screen.

>> So this demonstrates an understanding of quantum mechanics. But the first sentence he said, if I could read it correctly, had said something like despite the fact that I haven't ventured deeply into the essence of quantum mechanics, like what did Einstein mean? Was he just being humble or what?

>> But I I couldn't say I think my this is a guess. My guess is you know Heisenberg especially the matrix mechanics this was very unfamiliar mathematics. You know Schroinger was less unfamiliar because they were used to dealing with wave equations and solving them. My guess is that you know he just hadn't felt like he had mastered what Eisenberg had done and so on.

>> I see. Uh, but you know, whatever you maybe it was just being humble but you can see his worry is already there in 1927.

>> Mhm.

>> And the worry is against a conception in which a the wave function is complete. It tells you everything about B an individual system. It's not a statistical description description of an individual system and it's complete. And in order to avoid problems, it has to collapse, right? In order for this thing to work, it has to collapse. And the collapses look like they violate relativity and they're uh because they would have to be instantaneous and global, faster than light. At least that's what I assume he means by that. So again, this this is an episode that everybody should know, and I don't think that many people do. I mean, historians know about it, but it doesn't get the play that other episodes do. And it just shows how quickly Einstein grasped the fundamentals of Bour's understanding of quantum theory and had deep problems about it. But notice the deep problems were about spooky action at a distance. Not particularly about determinism. I mean, he doesn't mention that he doesn't like indeterminism. What he mentions

Is he doesn't like this instantaneous weird collapse of the wave function.

Mhm. Okay. Notice this example involves only a single particle, not a pair of particles or anything. And so there's nothing about entanglement and so on, but he's already on to this idea that that that this wave function could not provide a complete description of the individual system. Uh if it did, as I say, the collapse of the wave function would then have to be a real physical change. It would have to be instantaneous and it would have to violate relativity. So we have again spooky action at a distance. Already 1927. He's worried about that.

Now, all of these worries about action at a distance, violations of relativity, and so on are connected to conception two, not to conception one. So, he again he's saying, I've got a mathematical formalism here, sure, but that doesn't tell me how to understand it as a physical theory. And Bohr is pushing conception two explicitly. The wave function is complete and it does describe an individual system and Einstein Einstein is very worried.

Now notice this very important point. Einstein's worry about relativity here has nothing to do with super luminal signaling. You only have a single particle and in this situation there's no suggestion that somehow anybody could use this collapse of the wave function to send signals. I mean in this case the collapse would be associated with just a spot forming somewhere on the screen. That's it. And nobody has any control over where that's going to form. So the issue of signaling isn't there. And so Einstein isn't thinking of relativity as about signaling, which it isn't. So people who think, "Oh, I can solve all the problems of relativity by just proving that you can't send super luminal signals miss the point. If Einstein thought that was the problem, he wouldn't thought thought there was a problem in 1927 with this single particle example." Right?

And there are also people who somehow think oh action at a distance has to be some very special thing and you have to take action very seriously and so on. But this when Einstein really talks about action at a distance here and again the action is just the sudden change of the wave function itself. That's the you know that the fact that the spot forming here has the collateral instantaneous effect of annihilating the wave function elsewhere. That for Einstein is action at a distance and nothing to do with super luminal signaling but he says it looks like it's incompatible with relativity which you see why because in relativity you can't even define an instantaneous change because there's no such thing as as an instant of time.

In relativity there's no objective simultaneity. When people worry so when you just look at the collapse of the wave function and you say well let me take that collapse seriously which you would have to if you thought the wave function was complete. Immediately you're going to say, "Gee, that looks spooky. That looks that looks non-relativistic." The the normal reaction to that is people say, "No, no, no, no. The collapse of the wave function isn't the physical change. It's just an updating. It's like Bayesian updating. It's changing not the physical world, changing your beliefs about the physical world because you got new information about it, right? And this has been a standard thing of of people trying to defang the collapse by interpreting as merely epistemic as updating. But Einstein's very clear here. This is a complaint about conception two. And in conception two, it can't be updating because you said the wave function was complete. And if the wave function is complete, there's no new information to update on what's you know what saying the wave function is complete provides a complete description of the individual electron means there are no other facts about the individual electron that you could come to know right because if you know the wave function the wave function's complete you know everything. So it is the nature of conception two that precludes thinking of collapse merely epistemically. And of course what Einstein is really objecting to is is conception two.

Now, here's something De Broglie said. Well, no, not something De Broglie said. Okay, so he praises, right? We saw that Einstein knows that De Broglie has been playing with a theory, the pilot wave theory, where there is a wave and there is a particle. And that was Bell says at one point he doesn't understand why everybody was worried about wave or particle, wave or particle, and why they just didn't think wave and particle, which is what De Broglie thought. Yes, there is a wave and it follows a wave equation and also there's a particle and the wave guides the particle. The wave determines where the particle goes. Right? That's the basic idea of the pilot wave theory.

If you take that view then rel you're not in any issue about relativity because it's essentially when the when the spot forms on the screen you do get new information. You get information about where the particle was. The particle was going in some direction from the pinhole to the screen all the time. It's going the the entire time it's following some trajectory and you don't know what it is. And you can't figure out just from the wave function what it is. So if you want collapses to just be epistemic updating, then you need new information you can update on. And if you have both a wave and a particle, then even if you know the wave, you can update on the position of the particle. And and none of that requires spooky action at a distance or anything mysterious. When a spot forms somewhere on the screen, it's because a little bit before it formed, the particle was very near that location headed in the direction of the screen. That's not mysterious. And that doesn't involve spooky action at a distance. It just involves particles forming spots where they actually hit the screen. It's because you don't know that location of the particle that you can update on it without that being a physical change. Right? And then the fact that the the chance of a spot forming elsewhere immediately is reduced to zero. Again, that's not a physical change. It's just you realizing that in fact because the particle was headed this way, it had no chance of forming a spot over that way. There you can make the collapses merely epistemic or merely updating or Bayesian. But the point is if you want to do that with collapses, you got to have something to update on. And if the wave function is complete, you don't have anything to update on because you already know everything. So you can take De Broglie's route which Einstein was impressed with and he thought he was on the right track but to do it you have to deny the completeness of the wave function and therefore you have to deny the entire Copenhagen approach because that's what Bohr and Heisenberg were insisting that the wave function was complete and that the theory could not be improved upon by adding any more physical structure what were called hidden variables. Right? And if they do that, then they're stuck with the collapses as real physical changes, which is the way it comes out in von Neumann's mathematical principles of quantum mechanics. Um, and that sudden collapse which is in that book is instantaneous and global. And so you see why Einstein would think it violates relativity in independently of anything about sending signals or anything else. Any physical change that's instantaneous and global, you can't make sense of in relativity.

Well, of course, what Einstein saw was that if you think of that actual experiment where you're just shooting these electrons and these spots are forming, there's nothing in the phenomena that suggest anything like that going on. There's nothing in the phenomena that demand any kind of spooky action at a distance. The natural assumption is just the particles are going through the hole and different ones are going off in different directions. And so we could give and anybody could do this off the top of their head. What we would call a local relativistic no action at a distance model of the experiment um which is that yes, a particle gets shot. It's traveling along a definite trajectory. Maybe it's accompanied by a wave that's guiding it. Fine. When it gets to the pinhole, some of the particles go through and their waves interact with the pinhole somehow. And the result of that is to shoot the particle off in different directions in different experiments. And then the distribution over many experiments is a spots forming in all these different places. Uh and this is the kind of thing that Bell would have said, why didn't they why didn't they all jump on that idea? You don't have to decide between particle and wave. You just postulate there's both particle and wave.

Mhm. 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. And also remember to hit subscribe.

At this point, would positing a particle and a wave also entail a preferred foliation or a time slice that's preferred? It at this point it wouldn't because we're only dealing with a single particle and a single particle wave function is just defined on regular physical space and the Schrödinger equation which would govern the dynamics of that wave that single particle wave that doesn't have to violate or you can use the Dirac equation I mean they they knew you could have relativistic versions of the Schrödinger equation, right? You had the Dirac equation. So you can do that relativistically. And if if you just have this particle that's as it were accompanying the wave that's accompanying the particle and sort of guiding the particle, all of that can be local and you don't need any spooky action at distance to do that. So for a single particle system, there's no obvious threat at all to relativity in this picture. Now we're going to get to multiple particle systems soon. Then there is going to be you know but for the single particle and again you start with the single particle example of the pinhole.

So Einstein thinking about that wouldn't have thought gosh if I put in a particle that's moving that's going to be a threat to relativity. Why would it be? Okay. Um so anyway I'm I'm not going to read I mean I have this all written out but now I'll just people can go read it. You know the steps are you shoot the particle at the spin it's at the pinhole. It's following a definite trajectory. When it reaches the pinhole, it either goes through or doesn't. And the the little wave with it maybe interacts, but that can all be local and nice. And then it comes out the other end. If it goes through, it comes out the other end and can be refracted or shot off in different directions. Then from the pinhole to the screen, it pretty much propagates classically inertially straight line trajectory to the screen. Why think anything else, right? Um, and then when it gets to the screen, okay, the particle hits the screen, interacts with the screen, and forms a dot where it hits it. But where it hits it is already decided as soon as it comes out of the pinhole, right? Where it where it hits is not decided at the last moment when it gets there. Where it hits is decided when it leaves the pinhole, it's headed in some direction. It just goes that way. And that kind of theory would account for all the phenomena without any spooky action at a distance anything like that right. Um, it would give the the pinhole would essentially randomize the direction of the outgoing particle probably because of the fine dynamics of the interaction with the pinhole. Maybe you could add something stochastic there. It doesn't matter. Then it just travels off along the hem along to the screen and then it forms dots where it hits. And so none of these interactions would require any non-locality action at a distance. No threats are raised to relativity. All right?

So that's just what we were talking about. This word local and non-local has come up many times. Are there different kinds of locality such that Einstein would have been okay with non-locality of a type B but not of a type A or what have you or does local always refer to the same thing?

I mean there are you can make fine distinctions between different types of locality Einstein does so u and he likes all of them. [laughter] Okay. I mean, uh, okay. Um, and and he says, so, so let me just make two two distinctions. One, we might call ontological locality, which means the physical state of the world can be completely expressed if you just give me the physical state of each of take the entire universe and break it down into tiny little regions that slightly overlap. Okay? But tiny regions as small as you like. And for each little region, tell me what's going on there. So you tell me what's going on here, what's going on here, what's going on here. And they slightly overlap so you can match them up around the edges. For those people who know general relativity, this is like having a chart, an atlas of charts to cover it. If a if a theory is ontological local then by telling me what's going on in each individual little region without mentioning anything else outside that region but by covering the entire thing with these little [clears throat] regions I then nail down the entire physical state. Okay. So that the whole the entire physical state of the universe is as it were nothing and over and above the little physical states of the little pieces. So we can call that ontological locality. All of classical physics had that right? I mean you think of a a a Maxwellian electric field. How do I specify the state of the field? I tell you what it is here. I tell you what it is here. I tell you what it is here. Right? For all the little regions I just tell you how strong is the electric field and in what direction is it pointing. And if I tell you that for all the little regions I've nailed it down. That's it. There's nothing else to say. Okay. So, Einstein recognized that the field theory as developed by Maxwell and so on was a really ontological local theory. These fields were local objects that had local quantities and you could ask you could point your finger in space and say what is the value of it here? What is the value of it here? Okay. And that's all there was to it.

Einstein certainly believed that he also believed in what we can call dynamical locality. This is the no action at a distance point which is that if something happens in this little region, the only way it can have an influence elsewhere is for something to propagate at some speed less than the speed of light in relativity. Something to propagate with some speed from here to where it's going to have its effect, >> right? It can't have an instantaneous effect far away. That's the no action at a distance. That's a different kind of non-locality. That's dynamical non-locality. That's the one I'm talking about here. When he worries about action at a distance, he's worried about dynamical non-locality. He sort of took on locality for granted. He I don't know that he even talks about it that much, but there's a a wonderful um place where Einstein is talking very explicitly about how in the field theory things get more and more local because you can as it were take a microscope and focus into smaller and smaller regions of spacetime and in each little region it not only has its own little physical state but the laws themselves apply just in that region. You can just check in that region. Do the laws apply? Why? Because the laws are given by differential equations.

>> Mhm. >> Local differential equations, right? The the the laws of of uh electromagnetism explain how the electric field right here is going to change merely in terms of the nearby electric and magnetic fields. Nothing else. So you can you can just focus down on little pieces. And not only do they have their own physical states, but but in that little region, you can check, do the laws of physics hold there? And there's nothing for the laws of physics to hold everywhere except for it to hold in all the little regions. Now, if there were action at a distance, that wouldn't be true. Right? If I if by snapping my fingers, I could make something happen far away by law. Then if I'm watching far away and suddenly that thing happens and I say, "Gee, I wonder if if that happened by the laws of physics," I'd say, "I don't know. I have to check far away and see if somebody snapped their fingers." Right. I have to check everywhere.

>> Right. Right. Right. >> Because the laws themselves would postulate this spooky action at a distance. So to know if the laws are being satisfied, I'd have to check everywhere. That That's a problem. And Einstein saw that as a problem. He didn't he didn't deny that that kind of action in a distance was logically possible. But he did think that you couldn't do science in such a world because there would be nothing like an isolated system you could experiment on or quasi-isolated system. We can isolate little systems because they're local and because we can kind of shield them from outside influences coming from the outside which have to come in continuously through the walls. Right? So Einstein really believed in both of those kinds of locality but the one of interest here is the dynamical one. This you know so we have this like very modest little theory that can explain the phenomenon which is that these spots form all over the screen one by one. Uh in in a very everyday way. Maybe we involves a little wave that goes along with the particle. We we need to explain the diffraction that happens at the at the pinhole, but everything else is just the particle going this way and then and then it shoots out that way or that way or that way. And uh and and certainly there's nothing that would even vaguely threaten relativity and all that.

So what about this wave that's traveling out in all directions, right? That's not the whole story. That's not complete. On. If if we do this over and over again many many times and we have an ensemble of particles and not a single particle then if we were to watch that ensemble as it were all of their trajectories overlaid on each other exactly what we would see is a whole bunch of particles going in hitting the pinhole and then spreading out in a hemispherically uh uh expanding way, right? And so that would kind of look like what the wave function does. So that would suggest that the wave function is not really uh a description of an individual system but it's some kind of statistical description of a large collection ideally infinite collection infinite collection of systems. Um but if you say that then immediately you're going to say the wave function's not complete right it's certainly not doesn't give you a complete description of an individual particle it's just a kind of averaged out description of a whole collection of particles and so in the case of the pinhole we get this moral which is that even though it seems to Einstein that Bohr and Heisenberg have committed themselves to this weird action at a distance associated with wave collapse and they've committed themselves to that by insisting the wave function is a complete description of an individual system. Uh that you don't need to do anything like that, right? That that commitment of that that that they're getting spooky action at a distance not out of the phenomena at all. They're getting it out of this dogmatic attachment to the idea that quantum mechanics as it as it existed at that time was the end of physics was the final theory right and of course he he thinks you know that's silly right he's you know why would you do that why would you adopt convention two and get this weird consequence when you don't have to do that um and I I Think what if you want to understand Einstein what happened to Einstein afterwards was that he just couldn't con I think he thought in 1927 these are powerful powerful objections to what Bohr and Heisenberg were pushing and they didn't pay any attention they didn't they didn't stop them they didn't say oh yeah we made a mistake they continued to insist that the wave function is complete they continued to insist you know um

Now there's another worry that Einstein has about this which comes in the record right after what I read. So this is the next thing he says and I just want to note it here. It involves systems that have not a single particle which everything we've done up until now is a single particle but systems with two particles. So he says I should also like to point out briefly two arguments which seem to be to speak against the point of view too. This view is essentially tied to a multi-dimensional representation parenthesis configuration space since only this mode of representation makes possible the interpretation of size squared peculiar to conception two. Now it seems to me that objections of principle opposed to this multi-dimensional representation.

So again let's stop for a minute. He says once you move I I said before if you have only a single particle the wave function is just defined on physical space and it kind of behaves like a water wave or an electromagnetic wave familiar from classical physics. When you have two particles, mathematically the wave function psi is not defined on physical space anymore. It's defined on configuration space. And whereas phys if physical space has three dimensions, the configuration space for two particles has six dimensions and for three particles has nine dimensions and for four particles has 12 dimensions. Mhm.

>> A single point in configuration space represents the entire configuration of that set of particles. A single point in configuration space specifies where each of the particles is. And so if you only have one particle, okay, you're just pointing out a point in space. If you have two, you need two points. If you have three, you need three points and so on. Now, conception two wants the wave function to be complete. and that that's really giving you the deep physical picture of the of the system. So he says it seems to me that objections of principle can be opposed to this multi-dimensional representation. In this representation indeed, two configurations of a system that are distinguished only by the permutation of two particles of the same species are represented by different points in configuration space. Okay, that's a that's a technical issue we could go into and there are ways around that but it's the second one I want to point out which is not accord with the new results in statistics. I mean this has to do with Bose Einstein statistics but let's not worry about that. The furthermore part is interesting. Furthermore, the feature of forces acting only at small spatial distances finds a less natural expression in configuration space than in the space of three or four dimensions.

So again, what's he worried about there? He's again has this idea of locality that forces only act between nearby things, right? Forces don't act immediately between distant things. But distant what? Distant in physical space.

>> Uhhuh. >> But he says if you're not doing this in physical space, but you're doing it in configuration space, it's harder to even specify what you mean by forces acting only at a small spatial distance. It's as if spooky action at a distance in physical space is almost going to be hard to avoid if your theory is stated in configuration space. Einstein seems to see that and that's going to be the key to what's going to happen. And briefly speaking, what's the difference between a configuration space in quantum mechanics versus a classical configuration space of Hamiltonian dynamics? Mathematically nothing at all.

>> Nothing. You have a configuration space. You can write down Hamiltonian dynamics in configuration space. That's just a mathematical trick. That is instead of specifying say where eight particles are in three-dimensional space, you represent that configuration by a single point in a 24-dimensional space. Why? Because I need 24 numbers. I need three numbers for each of my eight eight particles. Configuration space is a classical notion. Was used all over classical mechanics. It was used all over Hamiltonian mechanics and the configuration space. Well, the mathematical thing they used in quantum mechanics was the classical configuration space. It wasn't phase space. I should mention that in phase space, a point in phase space specifies not only the positions but also the momenta of all the particles. So, it has six dimensions for every particle. But configuration space has only three. But it it is that very configuration space mathematically that Schrödinger put his wave function on. Right? The wave function was a complex function on classical configuration space.

What I mean to say is is there something in particular about the way that configuration space is being used in the quantum case where Einstein's objections bite more so than in the classical case? Is it because the classical case can then be translated back to Newtonian dynamics on 3D whereas the quantum one doesn't seem I mean let me just say this look in in classical physics the use of these high-dimensional abstract spaces was merely a mathematical convenience. The real physics was stated in physical space. The Newtonian force laws. I mean take take Newtonian force of gravity 1/r^2. What's r? The distance between these two particles in physical space, right? In physical space. So, of course, you have these force laws and they're stated in terms of things being near or far from each other in physical space. That's this kind of locality, dynamical locality. You can take those laws and then express them on a single high-dimensional space mathematically, but that's just a different mathematical way of presenting the very same theory. You're going from this theory initially stated in physical space to a high-dimensional abstract representation. The problem in quantum mechanics is that you're starting with a high-dimensional abstract thing, but you're not sure what's an abstract representation of.

>> Got it? >> Right. And the question is, can I go back down and and give myself a picture of things going on in physical space?

>> And the answer is it's not obvious how you do that. And it's certainly not obvious given what they're doing that if you do that you're going to end up with a dynamically local theory where where the only effects are by nearby things in physical space. So Einstein was worried about that too. Einstein had this worry in 1927. He saw as soon as I go from one particle to two, things get really screwy here because I'm treating the wave function as fundamental and not just as a convenience to represent something that's better represented on physical space. Okay, I'm now saying what I just said. Of course, you know, these configuration spaces as abstract objects were used all the time in classical mechanics. People knew all about them and they were used to using them. Hamiltonian mechanics was stated was was written in terms of functions on configuration space on phase space really but that it was just considered to be a mathematical convenience. When conception two takes the wave function seriously as fundamental and complete right then that's a new situation. The space it's defined on would seem to take on an entirely new significance than it does in classical mechanics where you understand that the real physics is all can be specified just in terms of things going on in physical space. Okay.

So after the Solvay conference where are we? Um Einstein is frustrated clearly with Bohr and Heisenberg with conception two. He thought he'd given very powerful arguments against conception two but Copenhagen didn't change their minds. Right. Um, he of course never claimed to show that the Copenhagen interpretation was inconsistent or made the wrong predictions or anything. What he showed in 1927 was that it was unnecessarily committed to spooky action at a distance, right? Instantaneous changes in the state of a particle because you had instantaneous changes in the wave function and the wave function was supposed to be a complete representation of the state of the particle. Um, the 1927 argument involves only a single particle, but already Einstein's worried about multiparticle systems. Um, now this is a very quick thing. Notice his complaint against conception two was about spooky action at instantaneous action at distance, threat to relativity. He didn't mention indeterminism there. Einstein popularly is presented as if what really worried him about quantum theory was indeterminism was really you know I mean he talks about spooky action at distance but then also fundamental indeterminism this god plays dice stuff but notice if you start in 27 you don't really see him complaining about indeterminism you see him complaining about spooky action in a distance and he does that just with this simple example um

Now you could promote the argument in 27 into a conclusion of indeterminism and this is just an aside by using what's called Curie's principle. Pierre Curie and Curie said look suppose I have a system that has some symmetry and the laws respect the symmetry that if it has a symmetry at any time it has a symmetry at all times and here we're assuming if we assume the wave function is complete in the pinhole situation the entire situation the physical situation has a symmetry around on this axis that goes through the pinhole and the wave function would also have that symmetry or could have that symmetry and that would tell you that it if it evolves deterministically it always has to have that symmetry I mean Curie's principle is for deterministic theories but we know that at the end of the experiment we break the symmetry that is a spot forms here or forms there or forms there and that breaks the symmetry so then by Curie's principle you could say if you want to maintain that the wave wave function is complete, you have to be committed to indeterminism. Um, and then God would have to play dice. Now, Einstein doesn't make that argument. You could make that argument and you can see how some of these considerations might lead you to see the role of indeterminism in the standard theory. End of act one.

Okay. Act two, eight years later, EPR argument. Again the Einstein I think if you read Einstein's comments they're very powerful as far as I know they didn't have a lot of effect then what happens in 1935 Einstein Podolsky and Rosen produce a paper which is making basically exactly the same points that Einstein was making in 27 but in a way that appeared to them to be rhetorically sharper. Um, and it involves now a system of a pair of particles rather than a single particle. So this issue of the wave function being on configuration space sort of does come into it. Um, at least you know this is something that's going to be used to make this more powerful. So now I'm just repeating what we said for a single system the configuration for a single particle configuration space is three-dimensional because the configuration of a single particle is just indicating where it is in space. So you just point to a point in space. If space is three-dimensional that's what you got. If you have a pair of particles then you indicate the configuration by telling me where both particles are. So now I have to give you two points. I have to give you six numbers as it were. You have a six-dimensional space. Not only is the wave function in the EPR paper defined on this six-dimensional space, it is a highly entangled wave function. What we would call an highly entangled wave function between the two particles. Um Einstein doesn't say that because the term entanglement had not yet been invented. It was invented by Schrödinger later in 1935 after he reads the EPR paper. But but [clears throat] that is a fact about that particular thing and we'll talk about that.

>> What's the advantage of having two particles? Well, one advantage is that I can take one particle and send it to Alice over here and another particle and send it to Bob way over there. And because Alice and Bob now each have a particle to play with and they can be put in their labs arbitrarily far apart, this worry about spooky action at a distance is very easy to understand. Can it be that anything that happens in Alice's lab influences the state of affairs in Bob's physically or the other way around? Right? That would be clearly spooky action at a distance in Einstein's mind.

Now, there are three parts of the EPR argument. I want to triage this and keep them separate. There's the conceptual part where they introduce some terminology and they lay out what they mean by words and they lay out some principles. Right? I think all of that is exactly right. There's then a logical aspect. How does the argument unfold? What steps do they go through? I think the argument was unnecessarily complicated. I think you can give a simpler, more direct argument to the conclusion they come to. and I will do that and I'll mention how they I think make it more complicated than it needs to be. I think it can be improved in that respect.

>> Then there are some technical aspects because of the particular example they use that are mathematical problems. I'm not going to go into those at all. Um, but they're there. I'm just mentioning it later. We're going to change the example in a way that gets rid of those technical problems so they won't bother us. That the the the experiment the the EPR argument is not affected by these technical considerations. Okay, let's start at the beginning. We want to understand EPR again. What's the title? Can quantum mechanical description of physical reality be considered complete? The very same question Einstein raised in 1927 still on that. Is the wave function complete? Right? That's the focus of the paper. The quantum mechanical description he referring to there is the wave function. The setting of this whole thing again is in Schrödinger's wave mechanics. The issue of completeness was already raised in 27. And now they're even more careful to explain what they mean by a complete description. This is part of the conceptual being conceptually clear. I think Einstein was just frustrated because he tried to get these points across and they wouldn't go across. So they're trying to be very careful.

So here's the quote now. Some quotes from the paper. "In attempting to judge the success of a physical theory, we may ask ourselves two questions. One, is the theory correct? And two, is the description given by the theory complete? It's only in the case in which positive answers may be given to both of these questions 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 that's what we would call empirical success, right? Fitting experiment, fitting the data, getting the data right, making correct predictions, that's correctness. This experience, empirical experience, which alone enables us to make inferences about reality in physics, in physics takes the form of experiment and measurement. It is the second question, not the one about correctness. Right? So they're not questioning the predictions of standard quantum mechanics. It is the second question which we wish to consider here as applied to quantum mechanics. Is it complete? Then they have to define what they mean by completeness. "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." Right? Think of the mathematical theory or whatever. "We shall call this the condition of completeness." Right? If there's an if there's something in physical reality that's not represented in your theory, then your theory is not complete. Right? You haven't [laughter] you haven't your theory doesn't describe all of physical reality. They said you that has to be right.

The second question is this easily answered as soon as we're able to decide what are the elements of physical reality. Now you see you have another problem right to be complete the theory has to describe every piece of physical reality. How do I know I've got a piece of physical reality? So they're going to answer that question by providing a criterion of physical reality. And again many people I think do not understand what a criterion is although they're perfectly clear about this. Okay, so let's just again go slowly. A criterion is not a definition, right? A definition is supposed to give you necessary and sufficient conditions for something. A criterion just gives you sufficient conditions. Not ne not necessary conditions. It's just if something meets the criterion, you know it's of that sort. But if it doesn't meet the criterion, you don't know it isn't of that sort, right? But it's enough, right? Meeting the criterion is enough.

"Again, from the paper, the elements of physical reality cannot be determined by a priori philosophical considerations, right? We can't figure out what the world is made of just by thinking, 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." So they're not going to try and define what it takes to be real. "We shall be satisfied with the following criterion which we regard as being reasonable." Here's the criterion and in in italics. "If without in any way disturbing a system, notice that that's absolutely essential. 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. Then there exists an element of physical reality corresponding to this physical quantity." So suppose I have a system and I can without any way disturbing the system I can somehow predict say the outcome of an experiment. I'm going to I'm going to weigh it or I'm going to you know uh do do a momentum measurement or whatever. If I'm able before that experiment is done to predict with absolute certainty and accuracy how that's going to come out, then there must be an element of physical reality in the system that corresponds to that, right? There must be something in the system that's resulting in it doing that. That seems really hard to deny.

"It seems to us that this criterion, while far from exhausting all the possible ways of recognizing a physical reality, at least provides us with one such way whenever the conditions set down and it occur regarded not as a necessary but merely as a sufficient condition of reality. This criterion is in agreement with classical as well as quantum mechanical ideas of reality." I'll say a word because he they go on to explain the second part when they say this is accepted even in quantum mechanics. What do they have in mind? They have in mind this everybody says if a system's in an eigen state of an operator like the momentum operator, the position operator, whatever. If the wave function is in an eigen state, which means you can predict with certainty what a a measurement of that will give you, then the system has that quantity, right? It has that momentum. Mhm. And he says that's true. That's as true in quantum mechanics as anywhere else. People take the ability from the from the theoretical description to make a perfect prediction to be a sign that the system itself has the corresponding property.

So let's just look at these. These are the pieces of the conceptual apparatus. And I think they're perfect, right? I mean, how could you deny when they say for whatever you mean by a complete physical theory, it better be that every aspect of physical reality is represented in the theory, right? If you've left something out, you left something out and then it's not complete. So I I think that again, how could you complain about that? Of course, you can give incomplete descriptions. When when we describe a a glass of water just by its temperature, that's not a complete description. It just gives you a statistical average, right? There are lots of different specific ways the glass of water could be at micro level that result in exactly the same temperature. So, that's an incomplete description. To get to a complete description, you have to go down to all the fine details and get all nail down everything that's there. Right? A fundamental theory purports to give a complete description. If you're if you admit that your theory is not complete, you're admitting it's not fundamental. You're admitting that somehow you're only describing this in a coarse grain way that maybe there are interesting things to say about it in this at this level of description, but it's not the end of physics because the physics has to go down into the details. People who don't like the conclusion of the EPR argument, and there are a lot of them, they have to find something to complain about, right? So often they pick on the criterion of physical reality. They say, "Oh, I'm going to get out of their argument by just denying the criterion." Um, but I think if you think about it, you can't coherently deny the criterion. It is in in a philosopher's terminology analytic. Um, it follows just from the meanings of the words in it. So let's see why the condition is if I can accurately predict the outcome of an experiment on a system without in any way disturbing the system. What does that mean? Without in any way altering its physical state. That's the criterion I whatever I do to make this prediction it cannot change the physical state of the system. So suppose I do this thing that doesn't at all disturb the system and now I can predict what it's going to do. Then you say all right there must be an element of physical reality in the system that's making it do that right how can you deny that I mean you know it's it's something's assuring it's going to do that it has to be its physical state. Um, but if I now suppose I do this without in any way disturbing the system that that means that before I did whatever I did the system was already in that state I didn't change the state even before I was able to make the prediction even before I did whatever it was that allowed me to make the prediction the system already had that property. Why? Because I know after I do it has the property and by definition I didn't disturb it. So by definition it had the property before I did it. Right? If it didn't have the property before, but it did have the property after then I disturbed it.

>> Right? This is just analytic. So I just don't see how one can question this criterion. Now notice the criterion doesn't even demand that I actually make the prediction. It's just that I be in a situation where I could make the prediction without disturbing it. If that's even possible, then there must be some element of reality in the system, right? Because you're saying that the system what its situation is independent of what I do. It's independent of my making the prediction or not making the prediction or whatever. If it's just possible for me to do this, then there must be an element of reality in the system. Um, I think that's correct. I think that's accurate. I think it works in modal logic. I think everything's okay with it. I don't think you can you're going to get out of this by denying the criterion of reality. And that's what I'm saying here. If it's if it's really an analytic criterion, you can't say I'm going to avoid the conclusion of this argument by denying the criterion. That's just incoherent. Um, what grounds could one possibly have for denying this criterion, right? That that heat they give.

Now, there is a place really throughout the EPR argument where they appeal to a a principle of no action at a distance, no spooky action at a distance. The appeal is tacit. They don't come out and say it, but it's clear that they use it. And so, I want to be explicit about it. So, again, we now have two particles.

>> Sure. >> Send one to Alice. Send one to Bob. Alice and Bob can do whatever experiments they want on their particles, right? And their labs can be situated as far apart as I like. They could be a hundred billion light years away as far as we're concerned, right? They're just they they they are separated. They're also separated in a way that uh Alice's experiment can be done at what we call space-like separation from Bob. So that even light couldn't get from one to the other in time to influence it. Okay. So that's the situation claim in such a case whatever Alice does or whatever happens in her lab does not disturb Bob's particle or the state of the sit physical state in Bob's lab and vice versa right if we separate these particles we put them in the separate labs we take them very far apart Alice can do whatever she wants Bob can do whatever he wants neither will disturb the other's physical state right okay now this is important cuz the listener may think well wouldn't Heisenberg listening to the previous slide raise his hand and say well Einstein your antecedent namely that if you don't disturb the system then so and so that will never obtain because of my uncertainty principle. Well that's not true if you're at different spacetime points.

>> Yeah, I'm not I mean the I mean I'm not sure why he would bring up the uncertainty principle here because we're just talking about two different particles, right? We're talking about Alice doing something to one particle and Bob doing something to an entirely different particle. So the the

The uncertainty principle doesn't even apply. That really applies to predictions about a single particle, right? I can't simultaneously predict accurately its position and its momentum, for example. And the better I can predict the one, the worse I can predict the other. But that's just a claim about individual particles. This is a claim about the goings on in one lab not disturbing the physical state in a very, very, very distant lab. So why, why, why would even the uncertainty principle come up here, right?

Um, I mean, it's true, the uncertainty principle was when people, when, when, when Heisenberg and Bohr talked about this, they always talked about, oh, if I do an experiment like an electron microscope or whatever, then when I probe the particle, I disturb the particle or something like that, right? I disturb the target. But we're not talking about whether Alice's actions disturb Alice's particle. Sure, maybe they do, or Bob's actions disturb Bob's particle. Probably they do. It's, do Alice's actions disturb Bob's particle [laughter] way over there?

>> Right. Right.

>> That would be spooky action at a distance.

>> Right.

This is the, this is the tacit assumption they're making that because they can separate Alice and Bob away from each other as far as they like, they are justified in saying that anything Alice does, any outcome in her lab, whatever, does not disturb Bob's physical situation. Anything Bob does, any outcome in his lab does not disturb Alice's physical situation. Now, you could blankly deny that, but then you would just have to say, "No, I do think what Alice does disturbs Bob's physical situation, and that is spooky action at a distance." Then you're just saying, "No, I'm, I'm, I'm down with spooky action at a distance." Right? You could do that. EPR don't even imagine anybody would do that. It never occurs to them that anybody would do that. [laughter] It seems crazy to them. And, and, you know, Einstein, I think, never, it never occurred to him that any of his opponents would simply blankly say, "Yes, we believe in spooky action at a distance." If you do, notice what happens. Let me finish it here.

So what EPR assume in their argument is that what we call space-like separation, or anyway, separating Alice and Bob very far from each other, ensures causal isolation of the experiments from each other. Right? Nothing going on in Alice's lab influences or changes the physical state in Bob's. Nothing going on in Bob's lab influences or changes the physical state in Alice's. You could just deny that, right, and sign on to it and say, "No, what Alice does messes up Bob, or what Bob does messes up Alice." Um, if you say that, then the EPR criterion of reality just doesn't apply. It's not that the criterion is wrong, it just doesn't apply because the criterion requires that you make the prediction without disturbing the system you're predicting about. What EPR assume is that anything Alice does will not disturb Bob's particle and anything Bob does will not disturb Alice's particle. Uh, if you deny that, then again, it's not that you're saying the criterion is wrong. You're just saying the criterion doesn't apply by signing on to spooky action at a distance.

>> Mhm.

>> Okay. Then you shouldn't deny it. Right? In other words, if that were Heisenberg's position, if Heisenberg said, "But wait, Einstein, I already believe that something Alice does here can influence Bob's thing way over there." Then he should just say, "No, I believe in spooky action at a distance, right? I accept it."

>> But that's one thing he never did and Bohr never did. They never just said, "Yes, we believe in spooky action at a distance."

I know you covered this earlier, but just to hammer the point home, many people think that, well, we get around Einstein's objections because you're not able to signal. You're not able to send information. So, you're saying no, Einstein still had objections even without—

>> Look, nothing he said has anything to do with signaling. And as I say, when he worried about, about this sudden change in the collapse of the wave function, even in 1927, the issue wasn't signaling. He didn't think, oh gosh, you could use that to signal. It has nothing to do with signaling. Signaling is a red herring and it's a dangerous red herring because people think that, oh, if you can't signal, then no problem. But Einstein's objections were never of the form, I think using quantum mechanics you could superluminally signal. I mean, if he thought that, he would say, "Look, go do this experiment and see if you could do it." That was never his worry. That's just, that's a straw man, right? Einstein does not require the ability to signal in order to say there's superluminal, there's action at a distance.

>> Now, what about this? What if someone says, "Okay, forget about Einstein himself, the man. What about special relativity, the theory as such? Does special relativity allow for superluminal non-signaling but disallow superluminal signaling?"

>> Look, this is a good, excellent question. Um, the first book I wrote, *Quantum Non-locality and Relativity*, is exactly on this question. Namely, everybody thinks relativity prevents something from going faster than light, or almost everybody. But what, what does it prevent from going faster than light? Does it prevent particles from going faster than light? Does it prevent energy from going faster than light? Does it prevent causation from going faster than light? Does it prevent signals from going faster than light? Or does it prevent nothing from going faster than light? I mean, I, in my book, I have a chapter on each of these positions.

>> And the answer is, there's no canonical answer here. But certainly, it is absolutely clear Einstein didn't think the issue was signaling. Because if he thought the issue was signaling, he wouldn't be worried about relativity in all these cases where there's no possibility of signaling. I mean, if the wave function collapse is a real physical process and by the spot forming here on the hemispherical screen, the physical situation everywhere else changes, for Einstein, that's spooky action at a distance. But you can't use that to signal because you have no control over anything, right? To signal, you have to control something. You have to, the sender of the signal has to have something under their free control, and the receiver of the signal has to have something they can observe that will go differently depending on what the sender does. That's just the definition of signaling. And none of that is at play here. There's no suggestion that's an issue here. But, but man, action at a distance is an issue here. That just proves that Einstein didn't think of it in terms of signaling. 100%, he didn't think of it that way. And you shouldn't. Got it? Okay? And therefore, even if you can prove you can't signal faster than light in a theory, that doesn't prove the theory is relativistic. Okay? That, that's what people, that's the mistake people make. And all these people doing quantum field theory and appealing to the equal-time commutation relations. I, I don't want to go into all that. That's all that same mistake. It's all that mistake. It's that mistake that they're saying, "Oh, gee, we can't signal, therefore this is relativistic." Nope. Doesn't follow. Just doesn't follow.

Anyway, in EPR, they write down a state for this joint system of two particles because it's of two particles. You notice, big sigh, that's the entire state of the joint system has an x1 and an x2. Those are two variables. Each three-dimensional, right? So it would be six-dimensional. X1 ranges over all of three-dimensional space. X2 ranges over all of three-dimensional space. The wave function is assigned, its values are assigned to pairs of positions, one for x1 and the other for x2, to configurations. That's why the wave function is defined on configuration space. So they write down this wave function. It's there in front of you. It's the integral from minus infinity to infinity to blah, blah, blah. I'll talk for a minute about this thing. You'll notice it's an integral dp. It's an integral over all possible momentum. All momentum from negative infinity to positive infinity. You'll also notice that it has in the, in the formula there's x1, x2, and then there's an x0. That's a little confusing because x0 isn't a variable, right? X1 and x2 are variables and x0 is just a constant. So they, he shouldn't have used x, right? They shouldn't have used x. That was a bad idea. Um, the constant is not going to play any important role here and I won't talk about it. This is where there are technical details about the mathematics of this that we could go into, but that they don't make any difference in the end. Okay. Uh, but x1 is a spatial variable pertaining to particle one. X2 is a spatial variable pertaining to particle 2, and x0 is just a constant. So we'll ignore it. So let's just, I mean, look at this state for those of you who know a little calculus, can integrate that sigma calculus thing is saying, add up all of these contributions, different contributions for different values of p, because you'll notice p is sitting there, it's e to the 2 pi i over h x1 minus x2 plus x0, that whole thing times p, and you're integrating that over all possible values of p.

Mhm.

>> Okay. So, you can think of that as adding a bunch of little pieces, one piece for each different possible value of p. So, uh, what is being added here? Well, if we just forget about the constant, I just don't want to deal with that x0. You're adding up a bunch of pieces that have this form that I have here, e to the 2 pi i over h x1 minus x2, that whole thing times p. And that, if you remember how exponents go, can more usefully be written just as a product. E to the 2 pi i over h x1 * p, E to the 2 pi i over h x2 * negative p, right? 1 * p, 1 * negative p. And that state that I just wrote there, that single state, is what's called a product state because you'll notice it's just taking a part of it that's merely a function of x1 and multiplying it by another part that's merely a function of x2, and that's it. So you can separate, as it were, the x1 part from the x2 part. And each of those pieces are what we call momentum states. So each piece is what you'd use to represent a particle that definitely has the momentum p in terms of x1 and definitely has the momentum minus p in terms of x2. Okay. So that state represents a situation where particle one quantum mechanically is in an eigenstate. It has definitely momentum p. The other particle, x2, definitely has momentum minus p. Therefore, that's a state where the total momentum of both particles is zero. Right? Because p plus minus p is zero. So that state is an eigenstate of total momentum zero. So I hope anybody who knows quantum mechanics can see that's, that's what that state is. But remember, the EPR state isn't that state. The EPR state is what you get when you integrate, I'll go back, when you integrate over all the possible values of p, states that look like that. So it's what we call a superposition. The EPR state is a superposition of all these different states, each of which has zero total momentum. Okay. So we see that this joint state has zero total momentum and the EPR state is built out only of states like that. So only out of states that have zero momentum. So the EPR state has zero, is an eigenstate of zero total momentum. If you know quantum mechanics, you're following what I'm saying. However, because of this integration, the EPR state is not an eigenstate for either particle one or particle 2. So, in, in the EPR state, we would say particle one has no particular momentum, no definite momentum at all. Particle 2 has no definite momentum at all. It's not in an eigenstate. Nonetheless, the joint system of one and two definitely has zero momentum. Okay, that's the standard way we would talk about that state.

Now, pause for reflection. I'm giving you the Copenhagen story here, right? The Copenhagen story is systems only have physical features when they're in the appropriate eigenstates of the associated operators. That's a weird situation that I just described, right? Because you say, "Look, uh, because in the Copenhagen view, the only systems that have momenta at all are in eigenstates. If you're not in an eigenstate, you just don't have that property. If you're not in an eigenstate of position, you just don't have a position." Right? And the, we saw the reality criterion demands that if you are in an eigenstate, so you can predict the outcome of a momentum measurement, then yes, you have a momentum, right? There's an element of physical reality. Um, and if you could make that prediction without disturbing the system, you have, you know, you actually have a momentum. But according to Copenhagen, it's not merely that those particles have momenta, but that only those particles have momenta. The only particles that have momenta are ones that are in eigenstates. If you're not in an eigenstate, you just don't have a momentum. And therefore, according to Copenhagen, neither particle in the EPR state has a momentum.

>> And that, I say, is a curious state of affairs. Right? So if I'm Bohr, I'm going to have to say particle one has no momentum. Particle two has no momentum. But nonetheless, the joint system of particle one and particle two, taken together, does have a definite momentum, namely zero. Furthermore, you could say, well, we can verify that claim, verify, empirically verify total momentum zero. How? Have Alice and Bob both do momentum measurements. And what you'll find is that even though you can't predict what Alice will get and you can't predict what Bob will get, you can predict that Alice will get exactly the opposite of what Bob gets. If Alice gets p, Bob gets minus p, whatever p is. And when we add them up, we'll get zero, right? And that's true. That's, that's, that's a prediction of quantum mechanics. So that's a strange situation, right? That's a very weird situation of a large system, and in not just large, but remember this system consisting of particle one and particle two is spatially separated. Particle one's way over here and particle two is way over there. That the state of that joint system is not determined, according to Copenhagen, by the individual states of its parts. That's a strange situation. Now, we accept that. So we accept this prediction. If both Alice and Bob make position, make momentum measurements initially knowing the EPR state, we can't predict what either one will get, but we can predict they'll get opposite results. I say, what, what we've now noticed, and this is not controversial, is enough to reach the EPR conclusion. Right? We, we've done enough. When I say we've done enough, notice I haven't mentioned position at all here. I'm just talking about momentum. Why have we done enough?

>> Okay, so the logical situation is this. Um, and again, this is not the way they run the argument, but from their principles, you can run the argument this way, and I think they should have. Uh, once we know that the total momentum is going to always come out to be zero, right? Why didn't they run it this way? Okay, wait, make, I could make guesses, but let me not. Here's the argument. We create a pair of particles in the EPR state. We send them off. One to Alice, one to Bob. Alice and Bob are both going to make momentum measurements. Now, what we know, and they're going to carry out their experiments very far apart at space-like separation. Even light couldn't get from one to the other, and so on. They both know, Alice and Bob both know that the particles were prepared in the EPR state, right? They're aware of that. That's fine. We can tell them beforehand. Question.

>> Okay. Can Alice predict without in any way disturbing Bob's particle what the outcome of a momentum measurement on his particle will be? Can Alice, without disturbing Bob's particle, accurately predict the outcome of his momentum measurement? Well, we're assuming the accuracy of quantum theory. And certainly, we know that Alice can get herself in a position where she can accurately predict the outcome of Bob's measurement by measuring her own particle. Right? Whatever number she gets from momentum, she's going to say, "Well, Bob's going to get minus that because we know the total momentum is zero." So, in fact, she can, she certainly can get in a position to accurately predict the outcome of his experiment. The question now is, right, did she, in doing that, did she disturb Bob's particle? Remember, all she did was measure the momentum of her particle. Now, it's here where the locality assumption of EPR comes in. Tacitly, they think, "Of course, she didn't. She's way over there, he's way over there. Nothing she did changed his state." What she did put her in a position to make that prediction, but it didn't disturb his state.

>> Right?

>> But if that's true, then right here's where the fundamental tacit locality assumption of the EPR argument comes in. And it's so, it's so seems so obvious to them, they don't even mention it explicitly, right? That what Alice does in her lab can't disturb Bob's physical situation. That would be spooky action at a distance. If we accept that, then we say Alice is able to predict the outcome of Bob's experiment without disturbing his particle. So there must be an element of physical reality in his particle that determines what the outcome will be. Right? Then we just apply the reality criterion and we say there must be something in Bob's particle that determines the momentum that's going to come out. Right? But now we're done. Why? Because the EPR state doesn't tell me what that value is. It doesn't represent that. You know, I just argued there must be an element of reality which is the momentum of Bob's particle, but the EPR state doesn't tell me what that is. So it omits that. Right? Therefore, the EPR state isn't complete. There must be more to the world than is given by that wave function. Right? It, in fact, I mean, the Copenhagen view says something even weirder, in a way. The Copenhagen view says when we send these two particles out, one goes to Alice, one goes to Bob, neither has a momentum.

>> Now Alice makes her measurement and and and discovers, or anyway, gets an an outcome of some momentum for her particle. She can now predict Bob's.

>> Mhm.

>> Furthermore, because she did that, she collapsed the wave function and Bob's particle went from having no momentum at all to now having a momentum.

>> Right?

>> Because of what she did. That's spooky action at a distance in spades, man. I mean, that's as spooky as you can get as far as Einstein goes. He thinks that's crazy. So, if you just assume that Alice's experiment doesn't disturb the physical state of Bob's particle, then we get their conclusion. The quantum description is incomplete. QED.

>> Yes. Notice I never mentioned position from beginning to end. I was just working with momentum here. Just working with momentum. Argument over.

>> Mhm.

>> Now, they don't do it that. So, you know, the, the, you've got what went into this? The reality criterion, the assumption of no spooky action at a distance, and the accuracy of the quantum mechanical predictions. That's all we used. We derived the incompleteness of the quantum description. Since the reality criterion is analytic, you can't deny that. You have only two options: accept that quantum description is incomplete, or accept that Alice's operations in her lab do disturb the physical state of Bob's particle. That is, accept spooky action at a distance. Those are your two options. Either you admit it's incomplete, or you accept spooky action at a distance. Um, Einstein thought between those two, it's obvious spooky action at a distance is crazy. Just deny that quantum mechanics is complete. Now, that's not what I just did. That's not what EPR do. What do they do? They do what I just did, but they repeat it for position. They do it for momentum just the way I did it. And then they say, "By the way, if Alice, instead of measuring the position of her part, the momentum of her particle, decides to measure its position, then she can accurately predict the outcome of a position measurement that Bob will make." Uh, that the very same argument that proves that Bob's particle already had a momentum can be used to prove it already has a position. Right? And therefore, in reality, Bob's particle has both a momentum and a position. Right? That makes it even worse for Copenhagen because there is no quantum state that ascribes a definite position and a definite momentum at the same time to a particle. No such wave function exists. No wave function is simultaneously an eigenstate of the position operator and an eigenstate of the momentum operator. That's impossible. That's mathematically impossible. So if you think the wave function is complete and you think that the condition for having a property is that you're in an eigenstate, you can't accept that there are particles that have positions and momenta at the same time.

Now, you might wonder, I just, I gave you an argument for the correlation, momentum came because the total momentum is zero, right? The technical thing is, it's not obvious at all looking at the EPR state why it would have this feature that also, if Alice measures position at a moment and Bob measures position of his particle at a moment, that they'll be perfectly correlated. That each one from their result can accurately predict the other's result. That's true, but it's not obvious. And it's a little technically, it's even a little hard to get your hands around because you have to use, because there are no really position states. They're really delta functions, which aren't functions, they're distributions, and things get complicated. Okay? Uh, and I'm not going to go into any of that. It doesn't really matter. I'll give you a quick intuitive argument. I don't know if this is really how accurate it even is, but it's a way of thinking about it. Why would you expect that if Alice and Bob make position measurements at exactly the same time, that each can predict the position of the other's particle? Well, suppose these particles were shot out at Alice and Bob at some pre-pre-established moment, right? They were sent out from a central source, and Alice and Bob are equally far away. Then, if, if they, as it were, got very different distances from the source measuring their positions at the same time, they would infer that they had different momenta, right? That their momentum, total momentum wasn't zero. Why? Because you normally, actually, the way you measure momentum is by measuring the position at a time, knowing when the particle was released, taking distance over time and getting a velocity, and then multiplying by the, multiplying by the mass and getting a momentum.

>> So if the position measurements were like completely uncorrelated, then they would also say the momentums can't be as correlated as we claim they are. Right? So anyway, I think it's maybe not that surprising that somehow you would have this perfect correlation between position measurements taken at the same time. Um, anyway, what, what EPR do is they prove it for momentum and then they prove it for position and then they say, "Look, Bob's particle has to have both. There must be an element of reality of Bob's particle for its momentum and an element of reality for its position." And that's even impossible to represent quantum mechanically. Um, so here's what they say at the end of the paper. "Previously, we proved that either one, the quantum mechanical description of reality given by the wave function is not complete, or two, when the operators corresponding to two physical quantities do not commute, the two quantities cannot have simultaneous reality." And now what they think they've proven is that even though the momentum operator and position operator don't commute, the momentum and position *do* have simultaneous reality. Right? Starting then with the assumption that the wave function does give a complete description of the physical reality, we arrived at the conclusion that the two physical quantities with non-commuting operators can have physical reality. And again, tacitly, they're using the no action at a distance principle to say that what one experimentalist does does not disturb the other. Thus, the negation of one leads to the negation of the only other alternative, two. We are thus forced to conclude that the quantum mechanical description of physical reality given by wave functions is not complete. Bad QED, right? Quantum state is not complete. As I say, you could get there quicker and easier just focusing on momentum, but okay, they did it their way.

One could object to this conclusion on the grounds that our criterion of reality is not sufficiently restrictive. Indeed, one would not arrive at our conclusion if one insisted that two or more physical quantities can be regarded as simultaneous elements of reality only when they can be simultaneously measured or predicted. Right? That you have to be able, if you want to say they simultaneously exist, then you have to be able to simultaneously predict or measure them. On this point of view, since either one or the other, but not both simultaneously, of the quantities p and q can be predicted, they are not simultaneously real. Right? This makes the reality of p and q depend on the process of measurement carried out in the first system, which does not disturb the second system in any way. Notice again, their point is, what's real according to this criterion in Bob's lab depends on what Alice does. But they say, "What Alice does does not disturb the second system in any way." No reasonable definition of reality could be expected to permit this. So they just reject that. That's not the right way to think about things. It's not a matter of prediction. It's not a matter of what you can predict. It's a matter of what's there. And you can get a handle on what's there by figuring out what you can predict without disturbing. And if you, then you need a criterion for not disturbing, and that's no spooky action at a distance.

What about determinism in the EPR argument? And there's a reason I'm going into this, which will come up in a minute. As we said, Einstein usually, you associate two complaints about quantum theory to him: no spooky action at a distance and "God does not play dice," right? And we've seen exactly where the no action at a distance demand comes in centrally in the EPR argument, right? It's by appealing to no action at a distance that you argue there's no disturbance, and by arguing there's no disturbance, you argue there's an element of reality. So that's there. What about determinism? Somehow, do they tacitly assume determinism somewhere in this argument? The answer is no. And it's really important that the answer is no. So here's a quote from John Bell in this wonderful paper, *Bellman's Socks in the Nature of Reality*. "It is important to note that to the limited degree to which determinism plays a role in the EPR argument, it is not assumed but inferred. What is held sacred is the principle of local causality. No action at a distance. Of course, mere correlation between distant events does not imply action at a distance, but only a correlation between the signals reaching the two places. The signals in the idealized example of Bohr, which we'll get to in a minute, must be sufficient to determine whether the particles go up or down, for any residual undeterminism could only spoil the perfect correlation." But here's the important point. It is remarkably difficult to get this point across that determinism is not a presupposition of the analysis. There's a widespread erroneous conviction that for Einstein, determinism was always a sacred principle. The quotability of his famous "God does not play dice" has not helped in this respect. Among those who had great difficulty seeing Einstein's position was Bohr. Pauli tried to help him out in a letter of 1954. So here's the quote from Pauli's letter: "I was unable to recognize Einstein whenever you talked about him either in your letter or your manuscript. It seemed to me you'd erected some dummy Einstein for yourself which you then knocked down with great paw. In particular, Einstein does not consider the concept of determinism to be as fundamental as it is frequently held to be, as he told me emphatically many times. He disputes that he uses it as a criterion for the admissibility of a theory. The question is it rigorously deterministic? He was not at all annoyed with you but only said you were a person who will not listen." Right? And you can imagine he was annoyed, and he probably was annoyed. Right? He keeps trying. Einstein has been trying to explain for years what his objection is, and people keep attributing him positions he does not hold. Um, and this is one, the EPR argument nowhere assumes determinism. It infers it.

>> So is what you mean to say that, look, Einstein doesn't start with determinism. He ends with it as a conclusion, not as an ingredient in the input. It's deduced.

>> Well, no, that, no, that, no, that in the argument, okay, EPR given argument, it has certain premises. Among those premises is not that the theory must be deterministic. Okay? But at the end of the argument, you reach the conclusion that if the theory is to be local, it must be deterministic. From the assumption of locality, you infer the necessity of determinism. But you don't go into the game assuming determinism. Okay? I mean, we'll get to that in a minute. Here's the end of this quote. So, so again, there, the, the end of the quote from Bell. Bohr had particular difficulty with the Einstein Podolsky Rosen argument. Here's the summing up long afterwards when he edited the Einstein-Bohr correspondence. So, this is now a quote from Bohr: "The root of the difference between Einstein and me was the axiom that events which happen at different places A and B are independent of one another in the sense that an observation on the state of affairs B cannot teach us anything about the state of affairs A." So that's he thought Einstein held that, that if, if two events happen in different places, then seeing the one gives you no information about the other. And Bell says, "This is a classic line. Misunderstanding could hardly be more complete. Einstein had no difficulty accepting that affairs in different places could be correlated. What he could not accept was that an intervention at one place could influence immediately affairs in the other." Right? That's spooky action at a distance.

Now, the EPR argument runs logically on the existence of perfect correlations between the outcome of the experiment in Alice's lab and the outcome of the experiment in Bob's lab. And I will just call such perfect correlations EPR correlations because they're the correlations that show up in that paper. Given the definitions in the paper, they have to be perfect for two reasons, right? The first reason is that the criterion of reality requires Alice to be able to quote predict with certainty, that is with probability equal to unity, the outcome of Bob's experiment, and then with the condition, the writer, that she in no way disturbed the physical state in Bob's lab. So the criterion of reality, and again, it's not a definition, just a criterion, very, very narrow criterion, requires perfect predictability, and perfect predictability requires perfect correlation. It means that given the outcome in Alice's lab, there is only one outcome that could occur in Bob's lab, right? Um, and that's true because of the total momentum thing. Uh, but if you think about the logic of the argument, it's pretty clear that that perfect predictability, you could run the argument with a weaker condition. Right? If you just, if you just allow these correlations to go from perfect correlations to almost perfect correlations, or to strong correlations, the basic logic of the argument isn't going to change. Okay? Um, that, that, that you, you would still, Einstein would still say, "Look, something's wrong here if you think the wave function is complete."

Now, when you have these perfect correlations, so one thing to say is, when you have these perfect correlations, there is nothing weird about the correlations. They're everyday. They're obvious. They happen all the time. That's why when Bohr says Einstein couldn't accept that by finding out something in one location, you can, you can determine something about a different location. He says that, "Of course, Einstein accepts that." So we have these trivial examples. Everybody uses these. Take a dollar bill, tear it in half, shuffle them between your back, put them in two envelopes, send one envelope off to Alice, one off to Bob. Right? That's the preparation procedure. Alice and Bob both know the preparation procedure. They obviously have no idea when they get the envelopes which half is in their envelope. But of course, when Alice opens her envelope and sees the right half, she immediately knows that Bob is going to see the left half when he opens his envelope. Right? She can now perfectly predict what he's going to see. And in doing so, she doesn't disturb the state of Bob's envelope at all. Right? That's a trivial example. Um, Bell talks about the example of Bellman's socks. So Reinhardt Bellman, apparently, and this is true, he always wore socks of mismatching colors, different colors. You could never predict on a given day what color sock he would have on any foot. But as soon as you could see that his right sock was pink, you could immediately, this is by standard Bayesian conditionalization, infer that the other sock is not pink. Another trivial example of a perfect anti-correlation. And if you, obviously, seeing one sock doesn't affect the other, right? And if you think that that's all that's going on with collapse of the wave function is Bayesian conditioning, is updating on new data, then you say, "Of course, the collapse of the wave function is not a physical change. It's just an epistemic one. It's just a change in my knowledge. It's not a change in the world."

>> Sorry, quick question. Why did Bell have to go to Bellman's socks and not just regular socks? Was it because he wanted to show an anti-correlation?

>> No. Well, I think because Bellman was a funny guy and he was a friend of his.

>> [laughter]

>> >> I, I don't think there's any deep reason. Of course, you could, you could make the same point by saying every day Bellman puts on different colored socks, but you're never sure whether they'll both be red or both be green, right? It would make the same point. Uh, I think it's just Bellman was a funny guy, right? And he was a friend of—

>> I see. I think you know, he, there was a, this was actually, it may have been the conference was a tribute to Bellman. I'm not sure. Anyway, he even draws a little, a beautiful little drawing of Bellman in the paper. I mean, his own hand-sketched Bellman. I think he was just, just a friendly thing.

>> Um, what do these trivial examples show? They show nothing much of interest, right? Certainly they show that these kinds of perfect correlations between distant systems, uh, unlike what Bohr said, they don't show anything, right? [laughter] It's nothing wrong with them. Um, they don't suggest in any way that there's spooky action at a distance, just that there are correlations between different systems, between distant systems. Also trivial in these cases that the criterion of reality, uh, works here, right? Once you see one sock, you can predict about the other one. Once you, one half of the dollar bill, you can predict about the other one without in any way disturbing it.

>> What follows? It follows that there's an element of reality that determines the outcome, which is which half was actually in Bob's envelope all along, right? That's an element of reality. Or which color did Bellman's sock have all along, right? That's an element of reality. So, sure, you can apply the element. If you thought you had a description, a complete description, physical description of the world, and it didn't mention the colors of Bellman's socks, you're just saying, "No, it's not a complete description. You left something out." In these trivial examples, the preparation procedure, you can describe it, but it's incomplete, right? It doesn't tell you exactly what the preparation does. When you put the halves of the dollar bill in the envelopes, one half goes in one and one half goes in the other. And the preparation procedure doesn't tell you which goes in which. And when Bellman gets up, all you said is he puts on different colored socks, but you didn't say which colored sock goes on which foot. So those are incomplete descriptions. And that's why, because they're incomplete, that you can update on new information, because you start out without complete information. If you thought the wave function was complete, then if you knew the wave function, you have complete information and you can't update on anything because there's nothing to update on. So in the trivial cases, these correlations are already fixed at the source in an everyday way.

So is this a paradox? And again, this is, uh, uh, a point we'll see that Bell makes. People talk about the EPR paradox. Even Bell's papers on the Einstein on the paradox of Einstein, Podolsky, and Rosen. Is it a paradox? What does paradox mean? Usually a paradox is an argument whose conclusion is contrary to common opinions. In Greek, the *doxa*, or opinions of everyday folk. >> Or at least against some kind of reasonable expectation, right? It's only paradoxical if the conclusion is surprising. But you know that there are these correlations is not paradoxical between what Bob sees and Alice sees and the momentum. That's not paradoxical. And the actual conclusion of the paper is that the quantum mechanical description is, is incomplete. That the wave function is incomplete. That doesn't violate any widely held opinions or any common sense, right? I mean, most people have no views on that. It's not like they say, "Oh my god, we thought quantum mechanics was complete." Um, so to say that it isn't, that's not paradoxical. It's just an observation, right? [laughter] Calling it a paradox is very strange, right? It, it, what, what the conclusion violates is not common sense and not widely held opinion and not something that seems obvious. What it, the only thing it actually rejects is Bohr's Copenhagen school dogma. The dogma that the wave function is complete. That that's the end of physics. That there's nothing more to say. So it helps to call it a paradox because it sort of suggests that there's something paradoxical about it. What's paradoxical is actually the Copenhagen view that's paradoxical.

So here's again from Bellman's Socks. Bell says, "It is in the context of discussions like these that one must envision the discussions of the Einstein Podolsky Rosen correlations. Then it's a little less unintelligible that the EPR paper caused such a fuss and that the dust is not settled even now. It's as if we'd come to deny the reality of Bellman's socks, or at least of their colors when not looked at, and as if a child had asked, 'How come the socks always choose different colors when they are looked at? How does the second sock know what the first sock has done?'" Right? Right? I mean, this is just beautiful. There's nothing paradoxical about Bellman wearing different colored socks. There's something really paradoxical about saying before you looked at them, the socks didn't have any colors.

>> Mhm.

>> >> And you're [clears throat] looking at them brought the colors into existence. Right? That's weird in itself. But it's even weirder if the two socks looked at by two different people in two different places always choose different colors. How do they know? How does one sock know what the other sock has done? Paradox indeed, but for the others, not for EPR. EPR did not use the word paradox. They were with the man in the street in this business. Right? These correlations simply showed that the quantum theorists were hasty, too hasty in dismissing the reality of the microscopic world.

>> Which is of course what they like to do. In particular, Jordan had been wrong in supposing that nothing was real or fixed in the world before observation. For after observing only one particle, the result of subsequently observing the other, possibly very remote place, is immediately predictable. Could it be that the first observation somehow fixes what was unfixed or makes real what was unreal? Not only for the, the, the near particle, but also for the remote one, right? You see the spooky action at a distance in that view, that observation creates reality, which is what you hear about quantum theory all the time. Here's the end of this quote. For EPR, that would have been an unthinkable spooky action at a distance. To avoid such action at a distance, they have to attribute to the space-time regions in question real properties in advance of observation, correlated properties that predetermine the outcomes of these particular observations. Right? Since these real properties fixed in advance of observation are not contained in the quantum formalism, that formalism for EPR is incomplete. And it may be correct as far as it goes, but the usual quantum formalism cannot be the whole story. That's the argument, and it's absolutely right. And you'll notice where the determinism comes in. The determinism comes in because if the correlations are to be perfect, then the previous states of the of the objects have to determine the outcomes. If there was any chanciness there, then the two distant objects couldn't track each other in what they do. Okay.

Now, there's a comment that people often make here. I'll call it the conservation law gambit. And they say, "Look, um, we've got this correlation between the momentum measurements made by Alice and Bob, uh, and that's, there's an easy explanation for that. It's conservation of momentum, right?" [clears throat] Because we know the total momentum of the system is zero, and we know momentum is conserved. So obviously the system always has zero momentum. So obviously whatever momentum Alice gets, Bob will get the opposite. Right? And the explanation, as it were, is the conservation of momentum. Why is that a big deal? People, I've heard people say this, right? "What's so puzzling about that?" And that just misses the point, right? Because the, the global conservation law in this case does not follow from a local conservation law. In classical physics, global momentum is just the sum of local momenta. And what the global momentum is at all times is just the sum of all the local momenta of the particles. But here, if the wave function is complete, neither particle has a momentum. So you can't think that the total momentum is the sum of theirs. They don't have momenta, right? That doesn't happen in classical physics. So if they don't have pre-measurement momenta, then we have this puzzle, both of how you get any outcome on either side. It somehow has to be brought into existence. It's not discovered, it's brought into existence. Right? But then, in addition, the opposite momentum has to suddenly be brought into existence on the other side, 100 million miles away.

>> That's spooky action at a distance.

Now, as I say, these arguments, I'll go over this quickly. This is, uh, these arguments are running on perfect EPR correlations. Uh, you could relax them. We could demand not that you'd be able to perfectly predict, but I don't know, say, predict with 95% accuracy, something like that, and you could make equally plausible arguments. And it's not as if the perfection of the correlations is the logical backbone. You, you know, if you can go, what, what is the logical backbone of the argument? The perfect correlations, I say, are assumed in two places. One is where you say I have to be able to predict with certainty what happens. And the other is where we just said, because the correlations are perfect, if you have a local theory, it must be deterministic. It must be that the state of the particles entering the labs absolutely determines what the outcomes will be. And the reason for that is that if they didn't, then how could you be sure that the two outcomes will always give you opposite results? Suppose I have a stochastic theory, an indeterministic theory. Then you can kind of run the same argument. You don't require that by not obser-, not disturbing the system, you make perfect predictions. You just, uh, oh, anyway, this is Bell just makes this point here again. I'll repeat it about why you infer determinism, not assume it. "Sure, of course, mere correlation between distant events does not imply action at distance, but only correlation between the signals reaching the two. Uh, in the idealized examples of Bohr, they must be, the signals must be sufficient to determine whether the particles go up or down, for any residual undeterminism could only spoil the perfect correlation. You just wouldn't get the perfect correlation in a local theory if it wasn't deterministic." So, you do the inference to determinism only goes through in the case of perfect correlations.

The original EPR argument is formulated by appeal to perfect correlations between the outcomes that Alice gets and the outcomes that Bob gets, both for momentum and for position, although as I said, really momentum would do the job. One might think that, yeah, but that's very idealized. In a real-life situation, you'll never get perfect correlations. But if you think about the logic of the argument, you can see that you can reduce, reduce it to imperfect correlations in a pretty simple way and draw exactly the same conclusions. Because what's really going on is the question, can the wave function be complete if by doing something that in no way disturbs another system, I can at least make better predictions about it? Maybe not perfect predictions, but can I improve my predictions about it? Can I, can I say with more accuracy what

It might do? If I can, then again, if I haven't disturbed the system, then I didn't know something initially about the system. I've learned something that must have already been there about the system. So let's just walk through quickly this case of high but imperfect correlations.

You need to relax the reality criterion a bit and and you can make the argument go through. As I say, the key to the reality criterion is that whatever you do to improve your predictions has to not disturb the system you're predicting about. And the assumption is because Alice and Bob are so separated, nothing any either one does disturbs the physical state of the other. It's that distance between them and the timing of the experiments because they can do them at space-like separation so that not even light could send a signal from one to the other about what what was being done in the lab and what the outcome was. That's the worry that Einstein has about about relativity.

So we can reformulate this in terms of what we would in in modern information theory which didn't exist at the time in terms of Shannon information. Right? The real question is what Alice does and what she sees. Does that give her Shannon information about Bob's system? Which is really just a matter of saying does that allow her to improve her predictions about Bob's system. If she can do that without disturbing his system, then her initial representation of the system must have been incomplete. It could be improved. And you'll notice that if I put this in terms of Shannon information and just making better predictions, more accurate predictions, more precise predictions, even if they're not perfect predictions, then we don't have to worry about having these perfect EPR correlations.

Um, there must be I if she doesn't disturb his system in whatever she does, then she's learned something about his system. And if she's learned something about his system, then there must be stuff about his system she didn't know. But she knew its wave function, right? She knew its quantum state. So that the quantum state has to be incomplete. >> Right. Right. So in in in that case we again get the same conclusion of the incompleteness of the wave function without this very strong requirement of perfect prediction. Notice that what happens is because we don't require perfect prediction here, we also do not infer determinism. So this was part of Bell's point that EPR don't assume determinism, they infer it. And for that inference to go through, they needed perfect correlations. If you weaken it to less than perfect correlations, you still get the incompleteness of the wave function, but you do not you you are not able to infer that the underlying dynamics has to be deterministic. That's just to recover perfect correlations. Okay.

So again, the key to the whole argument is that the spatial separation between Alice's lab and Bob's lab affects a causal isolation between what's happening in those two labs during the courses of their experiments. Deny that. You can deny it, but if you deny it, you're just signing on to spooky action at a distance in in Einstein sense. And to repeat something we said a minute ago, none of that suggests that you can signal from one lab to the other. Doesn't require that any kind of signaling protocol exist. It's rather just the fact that you can improve the situation of your knowledge without disturbing the system. If you want to deny that, then you say, "I am disturbing the system." And if you're disturbing the system, that's spooky action at a distance. Whether or not that disturbance allows you to signal. So you have what we would call local and deterministic theories. They still obey no spooky action at a distance. They're still local, but they're not deterministic. So assuming locality, assuming determinism are different things.

What would happen in a local indeterministic theory? For example, you might say, well, when Alice does her experiment, there's some chance, 90% chance it turns out this way, 10% chance it turns out another fundamental chance. Same thing for Bob, but they're local because which way Alice's turns out has no influence or doesn't allow you to predict better what will happen to Bob's. Which way Bob's turns out does not allow you to improve your predictions about Alice. That would mean that these statistical spreads between the two systems are statistically independent of each other. Neither gives information about the other. That would be a local indeterministic theory. And that proves that the locality assumption is not per se an assumption of determinism. It only allows you to infer determinism if you have perfect correlations.

So in sum finally although the EPR argument from no action at a distance and perfect correlations to the incompleteness of quantum mechanic goal description uh is valid good argument. It's sound and it's simple right not very complicated. The same argumentative structure can be uh worked given no action at a distance and less than perfect correlations. If Alice's predictions for Bob can just be improved by her observations and if so then and the physics is local then the initial description she had must have been incomplete. That argument yields the conclusion that we want or that EPR wanted of the incompleteness of the quantum description from no action in a distance uh uh without entailing determinism that only follows if we have perfect correlations.

One thing that comes up a lot in discussions of Bell's theorem and EPR is a condition that's called counterfactual definitess or CFD. Sometimes. >> Mhm. >> People claim that that it is a fundamental assumption of EPR or a fundamental assumption of Bell at the beginning >> that things are counterfactually definitess. What definite? What does that mean? A theory supports counterfactual definitess if the theory allows you to assert with perfect confidence a counterfactual claim about what would have happened in a particular experimental situation had it been different from what it actually was. So counterfactual for those who don't know is short for contrary to fact conditional. A conditional is an if then and it's contrary to fact if the if part isn't what actually happened but what could have happened right if I had dropped the the bowl it would have broken that's a counterfactual claim >> if you did not step on the computer it wouldn't have broken yep >> exactly that >> that's an inside joke for those who are >> Yeah that one's true too uh we use these counterfactual conditionals all the time in everyday life we hate them to have definite truth values. When you say, "Gee, you could have saved that person if you, you know, if only you'd gotten up and and thrown them the rope." That's a that's a counterfactual conditional. It's saying if the if reality had been different in this way, it would have been different in that way. So, these are just kind of very common things. And it's it's sometimes asserted that there's a tacid assumption in the EPR argument or in Bell's argument that there's counterfactual definitess that all of these counterfactuals have definite truth conditions. Now what I want to point out here is that's not true. That's just not true. And then people say, "Oh, I can get out of these arguments by denying counterfactual definitess." It's not true. Neither argument assumes counterfactual definitess. In fact, counterfactual definitess is just the same as determinism, right? I can I can tell you what would have happened had things been different if I use a theory that's deterministic because then I say if I fill in the details enough, the theory will tell me what would have happened.

>> But if the theory isn't deterministic, if it's just probabilistic, the theory won't tell me what would have happened. It'll just tell me what might have happened. So the assumption of of counterfactual definitess is just a fancy way of saying they assume determinism. You said something super interesting. What could have happened is different than what might have happened. >> Sure. Because in I in well not what could have happened what would have happened is different from what might have happened. Okay. So suppose I have a deterministic theory and I ask well what would have happened if I had dropped the bowl and someone says well according to the theory it would have fallen to the ground and broken. Yeah that would have happened. Now suppose I have an indeterministic theory like I have coins that that have irreducible chances. 90% chance it comes heads and 10% chance it comes tails. I say well but I don't flip the coin right. I say but what would have happened if I had flipped the coin? >> Yes. Yes. Then the right thing to say is well I can't tell you exactly what would have happened. I said it might have come tails and it might have come heads right there's no definite fact if the fundamental dynamics is indeterministic about what would have happened had things been different. Usually there there's a range of ways it might have played out if things had been different because the indeterminism in the theory allows for different outcomes. Right? So the assumption of counterfactual determinatess is the assumption of determinism. But what I've argued and what Bell argued over and over is that EPR do not assume determinism. They infer it. So they don't assume counterfactual definitess in so far as they get it. They infer it from the perfect correlations. And so you can't defeat the argument by saying,"Well, I just don't believe in counterfactual definitess the way you can't defeat the argument by saying,"Well, I just don't believe in determinism." Because it never runs on determinism. It runs on no action at a distance. It runs on no spooky action at a distance. >> Yes. Yeah. We just I noticed verbiage. You just you said it runs on no action at a distance. And then you said dot dot. It runs on no spooky action at a distance. But to Einstein, isn't all action at a distance a spooky action? Spooky. The spooky is Yeah. The spooky is just a rhetorical. >> Okay. >> The spooky is just rhetorical. It's not as if Einstein would have said, "Oh, there's good action at a distance and there's spooky action at a distance." [laughter] And I'm okay with good action. No, no, it's a spooky spooky just his way of saying he thinks action at a distance is physically, you know, is not something he's willing to accept in a physical theory. >> Yeah. >> Got it. People bring up this counterfactual definitess and when they're doing it they're it's just a roundabout way using unfamiliar terminology to talk about determinism. And what they say is that the arguments assume presume counterfactual definitess which is just a roundabout way of saying they presume determinism and it's false. Neither argument the EP argument does not presume determinism. Bell's argument does not presume determinism because of the perfect correlations. EPR are able to infer determinism in a local theory. So that's just to keep people from being confused about this terminology that shows up in the literature a lot. It's just a distraction in some and I think we are almost there.

So the EPR argument from uh runs from causal locality again no action at distance to the incompleteness of the quantum mechanical description. That argument is valid good logical argument in response to it. Uh sorry Boore and company had only two logically pertinent responses. There were only two things they could do. Either they embrace the action at a distance as real novel unexpected physical discovery. They could do that or they could concede that the quantum mechanical formalism they use does not supply a complete physical description of a system. Those are the only options and for sure they didn't embrace that there was action at a distance. Actually they all and they also didn't say that the quantum mechanical description is incomplete. Right? So of the two logically possible responses they took neither. And it's very hard to understand what it is they were claiming. And particularly Bor writes a response immediately after the EPR paper comes out in 1935. He writes a response and it's an incoherent mess, right? Nobody understands that paper. I mean, there's a little story about I I've wasted so much time, but I'll tell you a little story. When I learned this stuff, everybody my my of my age, we got a big red book called quantum theor quantum theory and measurement that was edited by Wheeler and Zurich and it contained reproductions of all these foundational papers. They weren't retypet or anything. They were just copied and thrown into this big fat book. >> Interesting. >> And uh it contained the EPR paper, of course, it contained Boore's response and everybody read that. uh many years later after I had read it and so on, I was talking to Shelley Goldstein and Shel said, "By the way, did you ever notice that in that book two pages in Boore's response have been switched? They're out of order." And I said, "No, I didn't notice that." And I talked to other people and nobody noticed that. >> And if you try to read it, you turn the page and the sentence isn't even grammatical. [snorts] Um why didn't we notice? Because nobody's following it. Nobody. It's It doesn't have a logical flow. It doesn't have a clear through line. It just is words, right? It's just bore producing words that you can't follow. Um Bel Bell himself talks about not being able to understand bore in an appendix appendix one to to this paper um Erdleman socks.

So what we have is what does the EPR argument do? It assumes local causality, no action in a distance. It then argues that the that if you assume that the quantum mechanical description of a system cannot be complete, there's more actual physics that needs to be done. How did Boore and company respond to this? Well, one thing they could have done is just accept the spooky action at a distance. They could have said, "No, we think that Alice doing something in her lab does disturb the physical state of Bob in his lab." that would certainly answer the argument. Um, but they don't do that and the only other logically possible option for them is to admit that the quantum description of the system is incomplete and they don't do that either. The problem is they don't really do anything coherent. uh Boore in particular immediately tries to reply to the EPR argument and write something that gets published in the same journal that the EPR paper was nobody can understand it. The conclusion of the argument is that if you have a causally local theory and it predicts these kinds of distant perfect EPR correlations then inferred not assumed from the beginning it must be a deterministic theory and so if you want to maintain causal locality which is what Einstein wanted you better go for determinism it's the only thing that's going to work to return these perfect correlations, right? But if you say, "Look, I just don't believe they're perfect correlations. I don't think any of the correlations you see in the lab are perfect, even though quantum mechanics predicts perfect correlations here." That wouldn't even solve the problem because it's not that you need the perfect correlations to make trouble for the completeness of quantum theory. It's really enough that Alice can do something that improves her predictions for Bob. Uh it's it's not that you can it's certainly not that you can answer EPR by saying I believe in indeterminism because it was never an assumption of determinism in the thing.

Now how does the EPR paper get received? >> Um he's been Einstein has been complaining since 1927 about these very same things. quantum theory is not complete and so on. You might think it wouldn't have any effect. It's just people would say there's Einstein again making the same old complaints. But in fact, that's that that's not at all true. Switching from the single particle case that we saw in 1927 to the two particle cases where I can send one to Alice and one to Bob completely changed the rhetorical force of the argument. Um, Rosenfeld, who's Boore's associate, later reports the following. This is the quote. This onslaught came upon us as a bolt from the blue. Right? They weren't expecting anything like this. The effect on Boore was remarkable. As soon as he had heard my report of Einstein's argument, everything else was abandoned. We have to clear up such a misunderstanding at once. we should reply by taking up the same example and showing the right way to speak about it. In great excitement, Boore immediately started dictating to me the outline of such a reply. Very soon, however, he became hesitant. No, that won't do. We must try over again. We must make it quite clear." And so it went on for a while with growing wonder at the unexpected subtlety of the argument. Whatever Boore thought he had as an answer to this, when he himself tried to articulate it, he couldn't. Uh-huh. >> Bore later himself wrote, "Due to the lucidity and apparently incontestable character of the argument, the paper of Einstein pods and Rosen created a stir among physicists and has played a large role in general philosophical discussion. Certainly, the issues are of a very subtle character and suited to emphasize how far in quantum theory we are beyond the reach of pictorial visualization." Notice that pictorial visualization. Um, Boore loved that word visualization on shallow kite in German and probably because it's a a word that Kant used a lot. Kant was very worried about analikite and visualizing things and space is the form of outer intuition if you know your Kant. Um, but I think what should be clear is that the EP argu argument has absolutely nothing to do with visualization. Right? They don't ask you to visualize anything. All they ask you to is is accept that what Alice does in her lab doesn't disturb Bob's particle. What Bob does in his lab doesn't disturb Alice's particle. You don't have to visualize a thing. >> So this appeal to visualization again is Boore just falling back on a bunch of ideas that has been bouncing around in his head forever and not responding to the argument. Um, so Bore writes this response. It's it's it's published in Physical Review where the EPR one was published. He recycles in that paper some standard stuff that he'd said before about single particles and measuring position and momentum on single particles, which isn't to the point because you have two particles. And the issue isn't whether Alice measuring the position of her particle disturbs the momentum of her particle. It's whether Alice measuring the momentum of her particle disturbs the momentum of Bob's particle. That's a very different, you know, issue. A lot of what Boore writes in that paper is not to the point. Bell himself just tries to parse what Boore is saying at in appendix one to Bertman's socks and he gives up. He says I can't make any sense out of this. Boore himself says he was never satisfied with his own response and he was still working on it when Einstein died. Schroinger's response is really interesting >> in 1935. Schroinger writes a paper the present situation in quantum mechanics which everybody knows as the cat paper. That paper is written because of EPR in in footnote 7. Uh he writes Einstein Podilski Rosen he cites the paper and he says the appearance of this work motivated the present shall I say lecture or general confession. Very interesting response right? I mean, Schroer is responding to EPR and he's not saying, "I'm going to lecture you. I'm going to confess something." He appreciated the argument and he appreciated the role that entanglement plays in the argument, which I think even didn't really appreciate. In that paper, Schroinger introduces the term fer shrank, which we translate entanglement. So, everything to do with entanglement starts with EPR. the importance of it, the physical significance of it and so on come out of that paper. There we go. Okay, so we got to the end of act two. We'll now have a break and then we'll come back for a short interlude. >> Uh and then we'll get on to Belle's theorem, which is actually supposed to be the subject of this entire thing. But you can't understand Belle. You cannot understand Belle without understanding EPR. This is a great place to have an intermission. The audience will absorb all of this. I want you to say, let's imagine you were able to do also act three. So, this was all one long movie. >> This is to set the record straight once and for all on what I'm getting you to say this so that the audience as they watch act one and two since it's going to be its own video that they're watching right now that they can think, okay, given that that's where this is going, I also have a couple questions. Let me write them in the comments and maybe >> Tim would hopefully be able to answer that in act three as well. So our our main point what we're trying to get to is the significance of Bell's theorem but Bell's paper is called on the paradox of Einstein Pedulski and Rosen right so he starts his starting point is that you've read and understood the EPR paper unfortunately most people haven't read and many people who have read haven't understood the EPR paper so if you want to understand Bell you have to start by understanding EPR are. And you know where we're going to end up is seeing how Bell begins where Einstein left off and then ironically runs an argument to the conclusion that Einstein was wrong about spooky action at a distance that you can't get away from it that you need it that no local theory in Einstein sense can work can make the right predictions. So, you know, the the great ironic reversal at the end is that Bell undermines Einstein's fundamental thesis that there's no action at a distance, but he undermines it using Einstein's own tools out of EPR. And so you have to understand what they did and what their argument was based on because if you want to reject Bell's conclusion, you got to reject something. And people unfortunately think they can get out of Bell's conclusion by saying, "Well, I just don't believe in determinism or something like that." But that's no good because it was never an assumption. So that's where we're going with all this. Perfect. Thank you so much. I appreciate you spending so much time with me. I understand it's extremely late where you are. We'll finish up on another date. Thank you. >> Okay. >> Hi there, Kurt here. If you'd like more content from Theories of Everything and the very best listening experience, then be sure to check out my Substack at curtjongle.org. Some of the top perks are that every week you get brand new episodes ahead of time. You also get bonus written content exclusively for our members. That's c u r t j a i mu n g a l.org. You can also just search my name and the word Substack on Google. Since I started that Substack, it somehow already became number two in the science category. Now, Substack, for those who are unfamiliar, is like a newsletter, one that's beautifully formatted. There's zero spam. This is the best place to follow the content of this channel that isn't anywhere else. It's not on YouTube. It's not on Patreon. It's exclusive to the Substack. It's free. 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