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

Episode Date: July 27, 2026

I personally subscribe to The Economist. TOE listeners get 35% off the annual subscription. No other podcast has this! https://economist.com/TOE This is a careful lecture that can be followed with zero background knowledge. Einstein thought he'd caught quantum mechanics in an act of spookiness — this podcast asks whether he was even worried about the right thing. Tim Maudlin, professor of philosophy at NYU and a leading philosopher of physics, delivers a rare full lecture tracing Einstein, EPR, and the road to Bell's theorem. The central claim: Einstein's real objection was never determinism — "God does not play dice" is a red herring — but non-locality, which he inferred rather than assumed. Maudlin traces the argument from Einstein's overlooked 1927 Solvay objection through the EPR paper's criterion of reality, showing why Bohr's famous reply never actually answered it. FOLLOW: - Spotify: https://open.spotify.com/show/4gL14b92xAErofYQA7bU4e - Substack: https://curtjaimungal.substack.com/subscribe - Twitter: https://twitter.com/TOEwithCurt - Discord Invite: https://discord.com/invite/kBcnfNVwqs - Crypto: https://nowpayments.io/donation/TOE - PayPal: https://www.paypal.com/donate?hosted_button_id=XUBHNMFXUX5S4 TIMESTAMPS: - 00:00:00 - Einstein's Quantization Hypothesis - 00:07:20 - Photoelectric Effect Implications - 00:12:30 - Wave-Particle Duality Myths - 00:20:40 - De Broglie's Matter Waves - 00:26:40 - Copenhagen's Completeness Doctrine - 00:34:10 - Solvay 1927: Two Conceptions - 00:41:20 - Pinhole Diffraction Problem - 00:48:00 - Collapse and Relativity Violations - 00:56:00 - Epistemic vs. Ontic Collapse - 01:05:00 - Ontological vs. Dynamical Locality - 01:14:00 - Configuration Space Objections - 01:25:00 - EPR's Criterion of Reality - 01:32:40 - Analyzing the Reality Criterion - 01:40:50 - Causal Isolation and Locality - 01:48:45 - Entangled Momentum Eigenstates - 01:56:45 - Logical Core of EPR - 02:04:40 - Position-Momentum Simultaneous Reality - 02:14:00 - Inferring Determinism from Locality - 02:26:30 - Conservation Laws and Information - 02:37:40 - Counterfactual Definiteness Debunked - 02:44:00 - Bohr's Incoherent Response - 02:52:00 - Schrödinger's Entanglement Confession LINKS MENTIONED: - Quantum Non-Locality and Relativity [Book]: https://amazon.com/dp/1444331272?tag=toe08-20 - On a Heuristic Point of View About the Creation and Conversion of Light [Paper]: https://sites.pitt.edu/~jdnorton/lectures/Rotman_Summer_School_2013/Einstein_1905_docs/Einstein_Light_Quantum_WikiSource.pdf - The Ghost in the Atom [Paper]: https://vdoc.pub/download/the-ghost-in-the-atom-a-discussion-of-the-mysteries-of-quantum-physics-1guq071e2ukg - Collected Papers on Wave Mechanics [Paper]: https://mwolf.pracownicy.uksw.edu.pl/MK/Schrodinger_Collected_Papers_on_Wave_Mechanics.pdf - Quantum Theory at the Crossroads [Book]: https://amazon.com/dp/0521814219?tag=toe08-20 - Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? [Paper]: https://journals.aps.org/pr/pdf/10.1103/PhysRev.47.777 - Bohr's EPR Critique [Paper]: https://journals.aps.org/pr/pdf/10.1103/PhysRev.48.696 - The Present Situation in Quantum Mechanics [Paper]: https://personal.lse.ac.uk/robert49/teaching/partiii/pdf/SchroedingerPresentSituation1935(1980trans).pdf - Bertlmann's Socks and the Nature of Reality [Paper]: https://cds.cern.ch/record/142461/files/198009299.pdf - On the Einstein Podolsky Rosen Paradox [Paper]: https://journals.aps.org/ppf/pdf/10.1103/PhysicsPhysiqueFizika.1.195 - Quantum Theory and Measurement [Book]: https://amazon.com/dp/0691613168?tag=toe08-20 - Tim Maudlin [TOE]: https://youtu.be/fU1bs5o3nss - Sean Carroll [TOE]: https://youtu.be/9AoRxtYZrZo - Robert Sapolsky [TOE]: https://youtu.be/z0IqA1hYKY8 - Jenann Ismael [TOE]: https://youtu.be/7kvXihDAOi0 - John Norton [TOE]: https://youtu.be/Tghl6aS5A3M Guests do not pay to appear. #science Learn more about your ad choices. Visit megaphone.fm/adchoices

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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 properly from beginning to end, what's going on with EPR, what's going on with Bell. This is Tim Maudlin, 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.

I've been told I have an unlimited amount of time. On this channel, I. Kurchai Mungle, interview researchers regarding their theories of reality with rigor and technical depth. Unfortunately, most people haven't understood the EPRP. This is to set the record straight once and for on what? 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. Professor, welcome.

I'm super excited. Thank you for coming. 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 account of the YouTube video. And I went to all that trouble. 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 was supposed to be a real careful presentation, 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 absolutely clear, 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 unless I riff on something or if Kurt has something he's, something he wants to interrupt me about and ask me about, which is fine. 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 mirabalus when Einstein developed and proved that there were atoms and developed the special theory of relativity and proved equals mc squared and on top of that really began quantum theory with his paper on the photoelectric effect so let's just begin there

so although plonk is usually credited with being the originator of quantum theory because of work he did on thermal radiation in black body radiation in 1900 i think it's really not fair to say that onk began what became what we now think of 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 plant 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 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 the 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. The dependency of the current goes and go like that. Instead, what happens? Well, there's a critical frequency of light, 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. 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 brighter, you do deliver more energy 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 discretization 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 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. 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 equals H-new. So there we have Planck's constant again. The one Plank discovered in his calculations is now showing up, connecting together. the frequency of the light to the energy of these quanta, right, these quanta 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 the quanta are not delivering, 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 possible energies of photons. It's rather that, at a fixed frequency, the energy is seen. 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? This was a tremendous surprise for people who thought of light as a wave, because if you think if lights 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 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, hit, it will jump up. And if it doesn't, it won't. And you don't expect the energy be distributed evenly. So you get this kind of particulate model that seems to be connected with this behavior. And as I say, 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. 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 wave. Now, there's still wave characteristics, and there were wave characteristics in Einstein's theory. the actual calculation is rather complicated, but part of it was this particle-like behavior of the light. 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. does display wave-like characteristics of interference and fraction and so on. 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 certainly not a technical notion of duality as would be used in math. So, yeah, that's, the word isn't supposed to connote that when I'm using it here. And I think when people started talking about it, I don't think they had a strict mathematical understanding. 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.

I'm sure the audience have heard other lecturers say that or popularizers of science. Is that correct? No, I would say nobody would take that. That's a kind of Jekyll and Hyde picture, right? I mean, there's one guy, and sometimes he behaves like Jekyll and the other times he behaves very differently like Hyde.

And he switches between the two, right? It's really quite dramatic when he switches between Jekyll 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.

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 theory. I can't imagine anybody thinking it's 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, because I know the audience may be thinking, but I've seen other popularizations or other animations of this and 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 a way. Yeah, okay. So 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, no, this is fine. This is good.

Look, I can dunk a bit on my friend, Sean Carroll, who tried to do something which you shouldn't try to do, which is reduce quantum theory to five words. And his five words were, don't look, wave, look, particle. And that sort of suggests this Jekyll 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 it? What do you mean by looking at a particle? I mean, the whole thing makes no sense, and I'm sure Sean would not defend it. You know, trying to reduce any theory to five words is not a great idea.

The, 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 Schrodinger evolution of the wave function, and the Schrodenger evolution is always wave. Schrodinger'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've 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

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So as a listener, you get an exclusive 35% off. That's not a deal that they have just anywhere. Head to Economist.com slash T-O-E to subscribe. That's economist.com slash T-O-E for 35% off. People characterize those ways as giving me which way information or whatever. That just leads you in the wrong direction. You make certain physical changes to the situation. you plug Schrodinger's equation in, you see what happens, and you notice that in a, 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. So no, that Jekyll and Hyde kind of picture is, clearly incorrect, and I don't think anybody would defend it who was serious about it. I should say it puzzled Bell, and he said he was always puzzled about once they noticed that there was both this wave-like 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 waivocal or whatever, that it didn't

occur to them, he says, the obvious solution, maybe there's both a wave and a particle. particle, right? 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. 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. 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 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. That's not going to be a serious theory.

Anyway, you had both of these characteristics and Einstein solves the problem of the photoelectric effect by attributing particle-like behavior to things that were classically waves. So it occurs to DeBroy, very young guy, well, turnabout's fair play. Why don't we think maybe things we think of classically as particles can display wave behavior, right?

And then he started talking about matter waves. 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 DeBroy 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 wave-like behavior? And he then made some, 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 DeBroy, as we'll see, taking Einstein as his model, said, all right, I can make that, linkage using Planck's constant. So one of them is this lambda equals H over P. Lambda, if something's going to be a wave,

it has to have a wavelength, lambda. And DeBroy said, okay, a classical particle has a momentum P. So let me just say that lambda equals H over P. There's Planck's constant again, right? Now I can say, if in a classical situation, I would say this particle has such and such a momentum, I can say, well,

then I expected 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, Einstein was going the other direction.

Einstein was saying, well, I know my light has frequency new. What is the energy of these quantum? and DeBroy is saying, well, my particle has energy, like one half mv squared, classical energy. 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 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 a wavelength. And then I can think about the behavior of waves with that frequency and wave length, right? And that then led to people actually looking for interference behavior, wave-like behavior of electrons. And you sort of see how DeBroy 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 DeBroy 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. but I'm trying to tell a reasonably smooth story. And the story gets smooth when after Heisenberg develops the matrix mechanics, Schrodinger 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 class, training were very good at working with waves and really hadn't learned to work with matrices, pretty much everybody started working with Schrodinger's presentation in terms of wave mechanics, 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 Schrodinger's wave mechanics, 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 the system. So that's what the map, what the wave function is. And Schrodinger specified its dynamics in what we call Schrodinger's equation. And that dynamics is a wave dynamics. So the wave function governed by Schrodinger's equation is going to evolve in a wave-like way.

They'll be interference, they'll be spreading, 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. 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, Boer and Heisenberg are working together to lay down principles of what's usually called the Copenhagen interpretation of 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 Bohr 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

the ability to visualize what's going on, what Boer was very insistent on that, and insofar as you think you need to visualize things to understand them, you're giving up on understanding. But Boer 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 Schrodinger, he proposes this wave function equation. Most students, when they're taught quantum mechanics, they're taught the BORN rule along with the Schrodinger equation. So it's difficult to think what would the Schrodinger equation be doing without the BORN rule?

Like, what did Schrodinger think the wave function was? And then did BORN only invent that because of single particles? Because 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 very good question. Schrodinger, I believe, didn't particularly like Bourne's suggestion when he made it.

If you're tracking the development and you followed the development I gave you where DeBroy makes this suggestion that we ought to start treating matter particles using these wave characteristics

and then we have wave equations for them. What really happened is that if you read Schrodinger's big paper, it's a four-part paper when he introduced the wave mechanics, and what he does in the first three parts is all stationary or static situations. Okay? So there's,

are the kinds of situations where nothing is changing in the environment. And you're looking for what we call eigen states or certain kind of stationary solutions to these equations. For what purpose? Well, in the case of, for example, the one 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 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, Bohr is laying down these rules. for the orbits that electrons can be in, thinking of the orbits as planets, as really little particles in planetary orbits,

and you restrict the orbits in certain ways that have to do with 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. Now, you can do all that without using Bourne'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 in a static situation, what are their probabilities of anyway? As it were, in a static situation, nothing is changing. Right, right.

So there is a lot that you could do. Now, in fact, what Schrodinger 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 varying. Then he said, 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. 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 non-stationary situation. When we learn quantum mechanics, as you say, when a student learns it, the first thing they're told is the wave function is a complex function. So we start at a position where Schrodinger just barely got to

and wasn't happy about. He was hoping to replace that complex function with a real function. He says so. He just couldn't figure out how to do it. So, you know, the Borns coming into this and suggesting squaring this complex function, first of all, why square it? Squaring the complex function and then treating those numbers as probabilities, that's kind of completely out of left field.

But, of course, for many purposes, it worked. So that's why the situation was so confused. using. Nobody really understood what was going on. And when I don't know what Boren exactly thought, but when certainly Bore insisted that these probabilities when you got them were fundamental, that they reflected indeterminacy innate indeterminism in nature itself. And Schrodinger was upset about that. I think Pauley was upset about that. That did not go over well. so it was a very confused situation. Okay.

So there we are in 1927. This stuff has come out, and at the fifth Solve 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 Bohr and Heisenberg.

And these objections are very important. They tell you what was on Einstein's mind from the beginning. So we're in 1927. People knew you could use Bourne's rule together with the wave function, together with the Schroden's equation, and make some statistical predictions. You use the Schroden's 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. And even though the new quantum theory again is attributed to Heisenberg in the matrix mechanics really even by

1997 I think people were mostly working with this Schrodinger wave mechanics picture. And so Einstein is focused down on the wave function because this is now, if you use the Schrodinger 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 Schrodinger wave. And he was worried, but he was very worried about how Bohr, was trying to understand it.

And so 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? So the second would be a statistical understanding. And he raised some problems about this with an example, 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. So at the Solvei 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 raising objections. And so he imagines this situation where you have 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 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 DeBroy 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? When you shoot a wave through a small hole, it diffracts. What comes out the other end is a wave like a semicircular wave or an expanding wave in water, a semicircular wave, in another dimension, you get a growing hemispherical wave because the wave diffracts and as it comes out of the pinhole going in all the different directions. So here's a transcript of that discussion. This is a transcript in the recent book by Anthony Valentini and Guido Bakhtiwupi about the Solve 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 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 Bois waves, which impinge approximately normally on S, are diffracted at O. So this is again, DeBroy introduces this idea that even electrons will exhibit wave behavior. Behind us, there are spherical waves which reach the screen P and whose intensity at P is responsible

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please contact connects Ontario at 1-866-531-2,600 to speak to an advisor, free of charge. BetMGM operates pursuant to an operating agreement with Eye Gaming, Ontario. 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. All right.

we can characterize the two points of view as follows. So Einstein says, look, we're agreed, as it were, mathematically, that part of the description. But physically, what are we talking about here? What exactly does this wave function represent? And he gives you two conceptions. Conception one, the DeBroy Schrodinger waves do not correspond to a single electron. The DeBroy Schrodinger 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 they just, each one gets somehow diffracted 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 of one,

then the whole cloud will then spread out hemispherically. That's conception one. Conception two, the theory claims to be a complete theory of individual processes. Notice the word complete there. And notice the word individual, right? 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 in speed

is described by a packet of the DeBroy Schrodinger waves of short wavelength and small angular width. This wave packet is diffracted and after diffraction partly reaches the film P 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 shoot this wave in, it comes out in all directions and it thins out as it goes out, and by the time it hits this hemispherical screen, it's rather thin, right? And it'll get thinner and thicker 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 psi squared at the screen. You square psi. It's actually going to be pretty uniform across the screen. And you say, but what is that number? 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 2, size square expresses the probability that at a given

instant, the same particle is present at a given point, for example, on the screen. 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, but 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 Geiger and Boeha, and can explain the fact that in the Wilson Cloud Chamber, the droplets stemming from an alpha

particle are situated on very nearly on continuous lines. Why? Because you're trying to explain single continuous lines through a cloud chamber, then you're talking about a single particle in what it's doing. You're not talking about a collection. You're talking about what a single

particle is doing. But on the other hand, and this is the main point, on the other hand, I have objections to make, to conception two. 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 or several places on the screen, right? Why? Well, you've got this single particle,

send it through, it's spreading out. Okay, so suppose I say 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 the wave is reaching. But then he says, but then why can't the particle interact

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 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 size squared 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 stream. 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. 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 get two spots. Or three or more, et cetera. Or three or four.

Exactly. And you never do. Yeah. Right? You only ever get one spot. In my opinion, one can remove this objection only in the following way. One does not describe the process solely by the Schrodinger wave, but at the same time, one localizes the particle,

uh, sorry, during the, during the propagation, I think that Mr. DeBroy is right to search in this direction. If one works solely with the Schrodenger waves, interpretation two of size 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 at a distance,

he's worried about the completeness of the wave function, and he's sympathetic to DeBroy 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? I couldn't say. I think this is a guess. My guess is, you know, Heisenberg, especially the matrix mechanics. This was very unfamiliar mathematics.

Schrodinger was less unfamiliar because they were used to dealing with wave equations and solving them. My guess is that he just hadn't felt like he had mastered what Eisenberg had done and so on. I see. But whatever, maybe it was just being humble.

But you can see his worry is already there in 1927. 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 of an individual system and it's complete, and in order to avoid problems, it has to collapse. In order for this thing to work, it has to collapse, and the collapses look like they violate

relativity, and they're because they would have to be instantaneous and global faster than like. At least that's what I assume he means by that. So again, 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 Boer'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. Notice this example involves only a single particle, not a pair of 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 this wave function could not provide a complete description of the individual system. 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 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 Boer is pushing conception too explicitly. The wave function is complete, and it does describe an individual system.

And Einstein is very worried. Now, notice this very important point. Einstein's worry about relativity here has nothing to do with superluminal 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 is 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 superluminal signals miss the point. If Einstein thought that was the problem, he wouldn't have thought there was a problem in 1927 with this single particle example. 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, the fact that the spot forming here has the collateral instantaneous effect of annihilating the wave function elsewhere. That for Einstein is actually in a distance. Nothing to do with superluminal 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 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 non-relativistic.

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've got new information about it, right? And this has been a standard thing 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 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, too, that precludes thinking of collapse merely epistemically. And of course, what Einstein is really objecting to

is conception too. Now, here's something DeBroy said. Well, no, not something DeBrois said. Okay, so he praises, right, we saw that Einstein knows that DeBroi 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 DeBroyd 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 you're not in any issue about relativity because essentially 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 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 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. And then the fact that 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've 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 DeBroy'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 we're 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. And that sudden collapse, which is in that book, is instantaneous and global. And so you see why Einstein would think it violates relativity, and 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. 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 suggests anything like that going on. There's nothing in the phenomena that demand any kind of spooky action in 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, 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 of spots forming in all these different places. And this is the kind of thing that Bell would have said, 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. 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? 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 Schrodinger 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 knew you could have relativistic versions of the Schroden's equation, right?

You had the Dirac equation. So you can do that relativistically. And if you just have this particle that's, as it were, 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 a 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. Got it. For the single particle, and again, you start with this 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.

I would it be. Okay? So anyway, 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 pinhole. It's following a definite trajectory. When it reaches the pinhole, it either goes through or doesn't, and 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 pinnacle, hole to the screen, it pretty much propagates classically, inertially, straight-line trajectory to the screen.

Why think anything else? Right? 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 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 in a distance, anything like that right? It would give

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 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. 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? Right. I mean, there are, you can make fine distinctions between different types of locality. Einstein does so, and he likes all of them. Okay, I mean, okay, 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, 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 theory is ontologically 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 regions, I then nail down the entire physical state. Okay? So the whole, the entire physical state of the universe is as were nothing in over and above the little physical states of the little pieces. So we can call that ontological locality.

All of classical physics had that. I mean, you think of 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 ontologically 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, some speed from here to where it's going to have its effect. 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 ontological locality for granted. I don't know that he even talks about it that much. But there's a wonderful 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 space time. 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, local differential equations, right? The laws of 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 just focus down on little pieces, and not only do they have their own physical states, 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 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 law. themselves would postulate the spooky action at a distance. So to know if the laws are being satisfied, I'd have to check everywhere. That's a problem.

Einstein saw that as a problem. 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 a 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 phenomena, which is that these spots form all over the screen one by one, in a very everyday way. Maybe it involves a little wave that goes along with the particle. We need to explain the diffraction that happens at the pinhole. But everything else is just the particle going this way and then it shoots out that way or that way or that way. 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. 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 expanding way. And so that would kind of look like what the wave function does. So that would say, suggest that the wave function is not really 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. But if you say that, then immediately you're going to say the wave function's not complete, right? It certainly doesn't give you a complete description of an individual particle. It's just a kind of averaged out description of, 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, that you don't need to do anything like that. That commitment of 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 existed at that time, was the end of physics, was the final theory. right and of course he thinks you know that's silly right he's going to why would you do that why would you adopt convention too 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 can 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 stop them. They didn't say, oh yeah, we made a mistake. They continued to insist that the wave function is complete. They continue insist, you know.

Now, there's another worry that Einstein has about this, which comes in the record right after what I rent. 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 me to speak against the point of view too. This view is essentially tied to a multi-dimensional representation, for emphasis configuration space, since only this mode of representation

makes possible the interpretation of size squared peculiar to conception too. Now, it seems to me that objections of principle opposed to this multidimensional representation. So again, let's stop for a minute. He says once you move, 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 is not defined on physical space anymore. It's defined on configuration space. And whereas 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. 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 system. So he says, it seems to me that objections of principle can be opposed to this multidimensional 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. 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.

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 and quantum mechanics versus a classical configuration space of Hamiltonian dynamics or what have? Mathematically, nothing at all. Nothing. You have a configuration space. You can write down Hamiltonian dynamics and 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 particles. Configuration space is a classical notion. It 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 was in phase space, I should mention that. In phase space, a point in phase space specifies not only the positions, but also the momentum of all the particles. So it has six dimensions for every particle, but configuration space has only three. But it is that very configuration space mathematically that Schrodinger put

his wave function on. 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 to be able to... Let me just say this. Look, 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 Newtonian force of gravity, one over R squared. 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 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 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 screwing. 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 written in terms of functions on configuration space, on phase space, really. But it was just considered to be a mathematical convenience.

When conception two takes the wave function seriously is 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? Einstein is frustrated clearly with Borne Heisenberg, with Conception 2. He thought he'd given very powerful arguments against conception 2, but Copenhagen didn't change their minds, right? 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. The 1927 argument involves only a single particle, but already Einstein's worried about multi-particle systems. Now, this is a very quick thing. Notice his complaint against conception two was about spooky action,

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. He talks about spooky action at distance, but then also fundamental indeterminism is 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 at a distance. And he does that just with the simple example. Now, you could promote the argument in 27 into a conclusion of indeterminism. 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 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 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 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, forms there. And that breaks the symmetry. So then by Curie's principle, you could say if you want to maintain

that the wave function is complete, you have to be committed to indeterminism. 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 1. Okay. Act 2, eight years later, EPR argument. Again, 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, Podolski, 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. 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, at least 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, 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 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. Einstein doesn't say that because the term entanglement had not yet been invented. It was invented by Schrodinger later in 1935 after he reads the EPR paper.

But 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 there 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, 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.

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? That's the focus of the paper. The quantum mechanical description referring to there is the wave function. The setting of this whole thing again is in Schrodinger's wave mechanics. The issue of completeness was already raised in 27, and now there are 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.

Think of the mathematical theory or whatever. We shall call this the condition of completeness. If there's something in physical reality that's not represented in your theory, then your theory's not complete, right? Your theory doesn't describe all of physical reality. He said, 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 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 It's enough, right? Meeting the criteria 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. 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 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 weigh it or I'm going to, you know, 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 condition 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 they go on and 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 the system's in an eigenstate of an operator, like the momentum operator, the position operator, whatever. If the wave function is in an eigenstate,

which means you can predict with certainty what a measurement of that will give you, then the system has that quantity, right? It has that momentum. And he says that's true, that's as true in quantum mechanics as anywhere else. People take the ability 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've left something out, and then it's not complete. So I think that, again, how could you complain about that? Of course, you can give incomplete descriptions.

When we describe 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 nailed down everything that's there. a fundamental theory purports to give a complete description. 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-grained way, that maybe they're interesting things to say about it

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 you 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. But I think if you think about it, you can't coherently deny the criterion. It is in a philosopher's terminology, analytic.

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. 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 this. that, right? How can you deny that? I mean, look, you know it's something's assuring that's going to do that. It has to be its physical state. 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? Why? Because I know after I do it, it has the property, and by definition, I didn't disturb it.

So by definition, it had the property before I did it. 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. Because you're saying that the system, what its situation is independent of what I do. It's independent of by 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. 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're going to get out of this by denying the criterion of reality. And that's what I'm saying here. 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. what grounds could one possibly have for denying this criterion, right, that they give? Now, there is a place really throughout the EPR argument where they appeal to 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 a thing. 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 100 billion light years away as far as we're concerned, right? They're just, they are separated.

They're also separated in a way that Alice. This 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. Car shopping this civic holiday weekend. Most car dealerships are closed and all you'll find are crickets. Not Performance Auto Group. They're open this Saturday and Holiday Monday for their annual Civic Holiday Sales event. Celebrate this long weekend with rates from zero percent. They might be closed. Performance Auto Group is open to serve you. Join Performance Auto Group this Saturday or Civic Holiday Monday 9 to 5 for the best time to shop this summer. 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 physical state in Bob's lab and vice versa. 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. All right? Okay, now this is important because the listener may think, well, wouldn't Heisenberg listening to the previous slide, raise his hand and say, well, Einstein, you're 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 space-time points. Yeah, I'm not, I mean, I mean, I'm not sure why he would bring up the uncertainty principle here, because we're just talking about two different particles. We're talking about Alice doing something to one particle, and Bob doing something to an entirely different particle.

So the uncertainty principle doesn't even apply. That really applies to predictions about a single particle. I can't simultaneously predict accurately its position and its momentum, for example. And the better I can predict the one, the worst I can predict. 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 would even the uncertainty principle come up here? Right? I mean, it's true the uncertainty principle was when people, 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 way over there.

Right. right. That would be spooky action at a distance, right? 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 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. It seems crazy to them. 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, ensure causal isolation of the experiments from each other, right? Nothing going on in Alice's lab influences or changes in physical state and Bob.

nothing going on in Bob's Bob, influences or changes the physical state analysis. 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. If you say that, then the EPR criterion of reality just doesn't apply. It's not that the criterion's 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. If you deny that, then again, it's not that you're saying the criterion is wrong, we're just saying the criterion doesn't apply by signing on to spooky action at a distance. Okay? Then you shouldn't deny it.

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. 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. I know you cover 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. not able to send information. So you're saying, no, Einstein still had objections even without that. Look, nothing he said has anything to do with signaling. And as I say, when he worried 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 superlumnal signaling? Look, this is a good, excellent question. 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 fast than light? Does it prevent energy from going fast 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, 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've no control over anything. To signal you have to control something. 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 man, action at a distance is an issue here. It 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's relativistic. Okay? That's the mistake people make and all these people doing quantum field theory and appealing to the equal time commutation relations.

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 the EPR, they write down a state for this joint system of two particles. Because it's of two particles, you notice, big psi, that's the entire state of the joint system, has an X-1 and an X-2. Those are two variables, each three-dimensional, right? So it would be six-dimensional. X-1 ranges over all three-dimensional space. X-2 ranges over, all of three-dimensional space.

The wave function is assigned, its values are assigned, to pairs of positions, one for X-1 and the other for X-2, 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 blah, blah, blah. I'll talk for a minute about this thing. You'll notice it's an integral of 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 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 he shouldn't have used X, right? They shouldn't have used X. That was a bad idea. 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 they don't make any difference in the end. Okay, but X1 is a spatial variable pertaining to particle 1, 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.

So you can think of that as adding a bunch of little pieces, one piece for each different possible value of p. So what is being added here? Well, if we just forget about the constant, I just don't want to deal with that x-0. 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 goes, can more usefully be written just as a product. E to the 2 pi i over h x1 times p, e to the 2 pi i over h x2 times negative p, right? one times p, one times 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 eigenstates.

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 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. 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 two. So in the EPR state, we would say, particle one has no particular momentum, no definite momentum at all. Article 2 has no definite momentum at all.

It's not in an eigenstate. Nonetheless, the joint system of 1 and 2 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, because in the Copenhagen view, the only systems that have momentum 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 we saw the reality criteria and 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. And if you could make that prediction without disturbing the system, you actually have a momentum. But according to Copenhagen, it's not merely that those particles have momentum, but that only those particles have momentum. The only particles that have momentum 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 bore, 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 a prediction of quantum mechanics. So that's a strange situation, right? That's a very weird situation of a large system. And 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 by, according to Copenhagen, by the individual state. of its parts. That's a strange situation. Now, we accept that. So we accept this prediction. If both

Alice and Bob 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 we've now noticed, and this is not controversial, is enough to reach the EPR conclusion. 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.

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. Once we know that the total momentum is going to always come out to be zero, why didn't they run it this way? okay, anyway, 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, it's face-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 zero. So in fact, 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 is of the EPR argument comes in. And it's so, it 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 is. humble bit, right? And 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 would just argue 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. 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 discovers, or anyway, gets an outcome of some momentum for her particle.

She can now predict Bob's. 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, though. Yes. Notice I never mentioned position from beginning to end. I was just working with momentum here. Just working with momentum. Argument over. Now, they don't do it that. So, you know, you've got, what?

it 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 derive the incompleteness of the quantum description. Since the reality criterion is analytic, you can't deny that. You have only two options, except 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, except spooky action at a distance. Those are your two options. Either you admit it's into complete or you accept spooky action at a distance. Einstein thought between those two, it's obvious.

Spooky action at distance is crazy, just denied that quantum mechanics is complete. Now, that's not what I just did is 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 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. 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 describes 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 problem,

property is that you're in an eigenstate, you can't accept that there are particles that have positions in momentum 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, So 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 technically, it's even a little hard to get your hands around because you have to use, because there are no really position eigenstates, there are really delta functions, which aren't functions, their distributions, and things get common. complicated, okay? 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-established moment, right? They were sent out from a

central source, and Alice and Bobber equally far away, then 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 momentum, 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. Anyway, 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. 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 do is they've proven that

even though momentum operator and position operator don't commute, the momentum and position do of simultaneous reality. 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 experimenter 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. Ban. 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 criteria 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 of, either one or the other, but not both simultaneously, the quantities P and Q can be predicted, they are not simultaneously real, right? This makes the reality of P&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 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 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, Bertelman's Sox in the Nature of Reality. it's 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 and the idealized example of bone, 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 the sacred principle. The quotability of his famous God does not play dice has not helped in this respect. Among those who had great difficulty seeing Einstein's position was born, Pauley tried to help him out in a letter of 1954. So here's quote from Pauley'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 directed some dubbing 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. And this is one. The EPR argument nowhere assumes determinism.

It infers it. So it's 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 in the argument, okay, EPR given argument, it has certain premises. among those premises is not that the theory must be deterministic. 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, again, the end of the quote from Bell. Bourne had particular difficulty with the Einstein-Pidowski rose an argument.

Here's the summing up long afterwards when he edited the Einstein-Bore correspondent. So this is now a quote from Bourne. 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 he thought Einstein held that, that if two events happened 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. 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, 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? And that's true because of the total momentum thing. 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 allow these correlations to go from perfect correlations to almost perfect correlations or just strong correlations, the basic logic of the argument isn't going to change.

Okay? That you would still, Einstein would still say, look, something's wrong here if you think the way 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 every day. They're obvious. They happen all the time. That's why when Born says Einstein couldn't accept that by finding out something in one location, you can determine something about a different location. He says, then 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 went off to Bob. 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. That's a trivial example. Bell talks about the example

Berylman's socks. So Reinhardt Berylman apparently, and this is true, he always wore socks of dispatching colors, different colors. You could never predict on a given day what color sock you 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 Bertelman socks and not just regular socks? Was it because he wanted to show an anti-correlation? No, well, I think because Burtleman was a funny guy and he was a friend of his.

I don't think there's any deep reason. Of course, you could make the same point by saying every day Burtleman 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. I think it's just Burtleman was a funny guy, right? And he was a friend of it. I see. I think, you know, he was, there was a, this was actually, it may have been,

the conference was a tribute to Burtleman. I'm not sure. Anyway, he even draws a beautiful little, a beautiful little drawing of Bertelman in the paper. I mean, his own hand sketched Bertelman. I think he was just a friendly thing. What are these trivial examples? They show nothing much of interest, right?

Certainly they show that these kinds of perfect correlations between distant systems, unlike what Bourne said, they don't show anything, right? It's nothing wrong with them. They don't suggest in any way that there's spooky action at a distance, just that they're correlates. just that there are correlations between different systems. Also trivial in these cases that the criterion of reality works here, right?

Once you see one sock, you can predict about the other one. Once you see 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 Burtleman'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 Burtleman'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 Burtleman gets up, all you said is that 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 a point we'll see that Bell makes. people talk about the EPR paradox. Even Bell's papers 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 are the 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 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. So to say that it isn't, that's not paradoxical. It's just

observation. Calling it a paradox is a very strange, right? What the conclusion violates is not common sense and not widely held opinion and not something that seems obvious. The only thing it actually rejects is born 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 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 Burdleman-Sox. Bell says, it's in the context of discussions like these, that one must envision the discussions of the Einstein-Pedolsky-Roson 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 Bertelman's socks, or at least of their colors, would not look 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? I mean, this is just beautiful. There's nothing paradoxical about Bertelman wearing different colored socks. There's something really paradoxical about saying, before you looked at them, the socks did. And it's not a lot of have any colors. And you're looking at them, brought the colors into existence. 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 predicted. could it be that the first observation somehow fixes what was unfixed or makes real what was

unreal, not only for the near particle, but also for the remote one? 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 tribute 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 objects have to determine the outcomes. If there was any chanceyness there, then the two distant objects couldn't track each other in what they do. Now, there's a comment that people often make,

here. I'll call it the conservation law gambit. And they say, look, we've got this correlation between the momentum measurements made by Alice and Bob. And there's an easy explanation for that. It's conservation momentum, right? 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 constant. of momentum. Why is that a big deal? I've heard people say this, right? What's so puzzling about that? And that just misses the point, right? Because 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 momentum. And what the

global momentum is at all times is just the sum of all the local momentum 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 momentum, right? That doesn't happen in classical physics. So if they don't have pre-measurement momentum, 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. these arguments are running on perfect EPR correlations. 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 know, if you can go, what is the logical backbone of the argument?

The perfect correlations, as 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 disturbing the system you make perfect predictions, you just, oh, anyway, this is, the bell just makes this point here. Again, I'll repeat it, about why you infer determinism, not assume it.

Of course, mere correlation between distant events does not imply action at distance, but only correlation between the signals reaching the two. In the ideal examples of bone, the signals must be sufficient to determine 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 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 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 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 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 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 was being done in the lab and what the outcome was. That's the worry that Einstein has about relativity. So we can reformulate this in terms of what we would, in modern information theory, which didn't exist at the time, in terms of Shannon

information. 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. you'll notice, 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. There must be, 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 it's quantum state, so that the quantum state has to be incomplete. Right, right. So 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 deterrent, So this was part of Bell's point that EPR don't assume determinism, they inferred 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 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 Einstein's sense,

and to repeat something we said a minute ago, none of that suggests that you can signal from one lab to the other. It doesn't require that any kind of signaling protocol exists. 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 mechanical description, is valid, good argument, it's sound, And it's simple, right? Not very complicated. The same argumentative structure can be 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 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 without entailing determinism. That only follows if we have perfect correlations. One thing that comes up a lot in discussions of Bell's theorem in EPR is a condition that's called counterfactual definiteness or CFD sometimes. people claim that it is a fundamental assumption of EPR or a fundamental assumption of Bell at the beginning that things are counterfactually definiteness. What definite?

What does that mean? A theory supports counterfactual definiteness 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 you 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 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 one's true, too. That's an inside joke for those who are. Yeah, that one's true too. We use these counterfactual conditionals all the time in everyday life. We take 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 thrown them the rope, that's a counterfactual conditional. It's saying 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 sometimes asserted that there's a tacit assumption in the EPR argument or in Bell's argument that there's counterfactual definiteness, 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 definiteness. It's not true. Neither argument assumes counterfactual definiteness. In fact, counterfactual definiteness is, just the same as determinism, right? 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 counterfactual definiteness is just a fancy way of saying they assume determinism. If you want a $3,000 a month payday for life, what would you feel free to do? Maybe take a long weekend, every weekend, or try a bunch of new hobbies. Would you feel free to upgrade and listen ad-free? Don't worry, we get it. Every $20 ticket could win you $3,000 a month for life and supports life-saving cancer

research at the Princess Margaret. Feel free to buy your payday for life ticket today. Raffle number 155-214. responsibly. You said something super interesting. What could have happened is different than what might have happened? Sure, because 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 asked, 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, right? I have

coins 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'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 determinateness 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 definiteness. Insofar 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 definiteness 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. I noticed verbiage. You just, you said it runs on no action at a distance.

distance. And then you said, dot, da, dot. It runs on no spooky action at a distance. But to Einstein, isn't all action at a distance of spooky action? Yes, the spooky. The spooky is, yeah, the spooky is just rhetorical. Okay. 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. 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 definiteness, and when they are doing it, it's just a roundabout way using unfamiliar terminology to talk about determinism. And what they say is that the arguments assume, presume counterfactual definiteness,

which is 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, I think we are almost there. So the EPR argument runs from causal locality, again, no action to distance, to the incompleteness of the quantum mechanical description. That argument is valid. good logical argument in response to it uh sorry bore and company had only two logically pertinent responses there are only two things they could do either they embrace the action in 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 actionated distance. Actually, 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, Boer writes a response immediately after the EPR paper comes out in 1935, he writes a response, and it's an incoherent. mess. Nobody understands that paper. I mean, there's a little story about, I have wasted so much time, but I'll tell you a little story. When I learned this stuff, everybody of my age,

we got a big red book called Quantum Theory and Measurement that was edited by Wheeler and Zurich. And it contained reproductions of all these foundational papers. They weren't re-type set or anything. They were just copied and thrown into this big, fat book. Interesting. And it contained the EPR paper, of course, it contained Boer's response, and everybody read that. Many years later, after I had read it and so on, I was talking to Shelly Goldstein and Shelly said, by the way, did you ever notice that in that book, two pages in Boar'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. Why didn't we notice? because nobody's following it. Nobody, 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. Bell, Bell himself talks about not being able to understand bore in an appendix, appendix one to this paper, Erdlman Sox. So what we have is, what does the EPR argument do? It assumes local causality, no action. action in a distance. It then argues that if you assume that the quantum mechanical description of the system cannot be complete, there's more actual physics that needs to be done. How do Gore 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, 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. Boer, 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 there are 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. It's certainly 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? Mm-hmm. He's been, Einstein has been complaining since 1926. 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 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. Rosenfeld, who's born, associate later reports the following. This is a quote. This onslaught came upon us as a bolt from the blue, right? They weren't expecting anything like this. The effect on Bohr 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, Boer immediately started dictating to

me the outline of such a reply. Very soon, however, he became hesitant. No, that's 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 Boer thought he had as an answer to this, when he himself tried to articulate it, he couldn't. Boer later himself wrote, due to the lucidity and apparently incontestable character of the argument, the paper Weinstein-Padolski 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.

Boer loved that work, visualization. enchallichkait in German. And probably because it's a word that Kant used a lot. Kant was very worried about enchallichkite and visualizing things. And space is the form of outer intuition, if you know your Kant. But I think what should be clear is that the E.P. Our argument has absolutely nothing to do with visualization, right?

They don't ask you to visualize anything. All they ask you to 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 Boer just falling back on a bunch of ideas that has been bouncing around in his head forever and not responding to the argument. So Boer writes this response. 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 issue. A lot of what Boar writes in that paper is not to the point. Bell himself just tries to parse what. And he's a what Bohr is saying in Appendix 1 to Bertelman's socks, and he gives up. He says, I can't make any sense out of this. Boar himself says he was never satisfied with his own response, and he was still working on it when Einstein died. Schrodinger's response is really interesting in 1935. Schrodinger writes a paper, the present situation in quantum mechanics, which everybody knows is the cat paper. That paper is written because of EPR.

In footnote, seven, he writes, Einstein, Podolsky, 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, Schroeder 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

EPR didn't really appreciate in that paper Schrodinger introduces the term for Schrenkung 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 2. We'll now have a break, and then we'll come back for a short interlude. And then we'll get on to Bell's theorem, which is actually supposed to be the subject of this entire thing. But you can't understand Bell. You cannot understand Bell 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 action. Act 3. 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 1 and 2, 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 3 as well. So our main point, what we're trying to get to is the significance of Bell's theory. But Bell's paper is called on the paradox of Einstein, Podolsky, 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. And, you know, where we're going to end up is seeing how Bell begins where I 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's sense can work, can make the right predictions.

So, you know, 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've 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. that that's no good because it was never an assumption.

So that's where we're going with all these. 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 day. Thank you. Okay. Hi there. Kurt here. If you'd like more content from theories of everything

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