Tim Maudlin, philosopher of physics at NYU, was given unlimited time and used it to build EPR from scratch: Einstein's 1905 quantization hypothesis, de Broglie's matter waves, Born's rule, and the Copenhagen doctrine that the wave function is complete. The centerpiece is history almost nobody knows: Einstein's real objection was lodged at the 1927 Solvay conference with a single particle, a pinhole and a hemispherical film, and it was about spooky action at a distance, never about determinism. Maudlin then rebuilds the 1935 EPR argument better than EPR did, showing the criterion of reality is analytic and cannot be denied, that the load bearing premise is a tacit one about causal isolation, and that momentum alone suffices so the entire position half was unnecessary. He closes by dismantling two popular escape hatches, determinism and counterfactual definiteness, and shows why Bohr's published reply was so incoherent that two of its pages sat out of order in the standard anthology for decades without anyone noticing.
Published Jul 27, 20262:58:58 video133 min readAdded Jul 29, 2026Open on YouTube →
At a glance
Tim Maudlin, professor of philosophy at New York University and one of the world's leading philosophers of physics, was told he had unlimited time. So he wrote the whole thing out in advance and read it, act by act, for nearly three hours: the real history and the real logic of EPR, from Einstein's 1905 quantization hypothesis to Bohr's incoherent 1935 reply, with zero background assumed. Curt Jaimungal interrupts only to ask the questions the audience is actually thinking.
The central claim is historical and it is a correction. Einstein's objection to quantum mechanics was never fundamentally about determinism. It was about spooky action at a distance, and he raised it in 1927 at the fifth Solvay conference using a single particle, a pinhole, and a hemispherical photographic film, eight years before EPR existed. Maudlin reads that Solvay transcript out loud, line by line, because almost nobody outside the history of physics knows it is there. The argument in it is already the whole EPR argument, minus the two particles that made it rhetorically unanswerable.
Then he rebuilds EPR itself, and rebuilds it better than EPR did. He shows the criterion of reality is analytic, true by the meanings of its words, so denying it is incoherent. He shows the paper's real load bearing premise is a tacit one nobody stated: that what Alice does in her lab does not disturb the physical state in Bob's. He shows the argument needs only momentum, never position, so the entire position half of the 1935 paper was an unforced complication. And he demolishes two escape hatches people still reach for: that determinism is a hidden premise (it is a conclusion, inferred from perfect correlations), and that counterfactual definiteness is a hidden premise (it is just determinism in unfamiliar clothes).
The bill comes due at the end. Faced with the EPR argument, Maudlin says, Bohr and company had exactly two logically available responses: embrace action at a distance as a real physical discovery, or concede the wave function is incomplete. They took neither. Bohr's published reply is, in Maudlin's phrase, an incoherent mess, and he proves it with a story: two pages of that reply were printed out of order in the standard anthology a generation of physicists learned from, and nobody noticed, because nobody was following it. Schrödinger was the one who understood, and what he wrote in response was the cat paper, where he coined the word entanglement.
This video is acts one and two. Bell's theorem is act three, and Maudlin says flatly you cannot understand Bell without first understanding EPR, because the great ironic reversal at the end is that Bell destroys Einstein's no action at a distance thesis using Einstein's own tools.
Act one: how quantum theory actually got built, 1900 to 1927
Maudlin opens with a warning about the format. This is not a normal back and forth conversation. It is a careful presentation of a century of Bell's theorem plus the problems that arise because of it, and because he wants it absolutely clear, he has essentially written everything out and will be more or less reading what is on the screen. "It's going to be a little boring because I'm going to be more or less reading what's on the screen," he says, unless he riffs on something or Curt interrupts, which is fine. Then: "So should we begin?"
It comes in historical acts. And Maudlin promises that act one contains history almost nobody listening is aware of. Historians of physics know it. It does not get talked about.
Why Planck did not start quantum theory (0:00:00)
The story starts in 1905, the year Einstein proved atoms exist, developed special relativity, proved E equals mc squared, and on top of all that really began quantum theory with his paper on the photoelectric effect.
Max Planck is usually credited as the originator, for his 1900 work on thermal radiation and black body radiation. Maudlin thinks that credit is not fair, and the reason is worth being precise about, because it is a claim about what counts as a physical hypothesis.
Planck was doing statistical calculations in an entirely normal way for a classical physicist doing statistical calculations. He knew what he was trying to get: a certain spectrum of radiation for black body radiation. He found he could get the right answer out if, instead of taking a limit going to zero, which is what you would normally do, he stopped at a certain point. So he stopped. That stopping point left little finite regions of phase space characterized by this constant h. He knew it gave him the result he wanted.
What is not clear is whether Planck thought he was quantizing anything. It is not clear he had any real physical hypothesis about what he was doing at all. He just noticed that it worked.
So when you ask who really proposed the quantization of a classical quantity, the answer is Einstein, in 1905. And Einstein was not worried about black body radiation. He was worried about a stubborn little experimental fact about metals.
The photoelectric effect, and what was actually surprising about it
The photoelectric effect was a known property of certain metals: when light fell on them, it created an electrical current. It was also known how that current related to the light, and the relationship is a very surprising one.
The bare fact that light on metal starts a current is not surprising from a classical perspective at all. The light is obviously delivering energy to the metal, and intuitively you need to deliver energy to knock electrons free and get a current going. The surprise is in how the energy translated into current.
Classically, light is an electromagnetic wave, characterized by a frequency and an amplitude. The frequency tells you essentially what color the light is. The amplitude tells you how bright it is. And classically, when you attribute energy to an electromagnetic wave, that energy depends on both. You can raise the energy by raising the frequency, and you can raise the energy by raising the amplitude, by making it brighter.
So you would expect to be able to increase the current either way: crank the frequency up, or crank the brightness up. It does not work like that.
Instead there is a critical frequency, a critical color as it were. As long as the light is below that frequency, no current flows at all, no matter how bright the light is. Make it brighter below the threshold and you do deliver more energy, and the metal will heat up. What you will not get is the electrical current. The instant you cross above that frequency you start to get current, and from there, increasing the brightness increases the current.
That is the data. And the classical model of light as an electromagnetic wave does not have any obvious way of making sense of it.
Figure 1. The shape of the data Einstein was trying to explain in 1905. A classical wave carries energy that depends on both frequency and amplitude, so the dashed line is what classical physics expects: enough brightness at any color should eventually free electrons. What actually happens is a hard threshold in frequency that brightness cannot buy its way past. Einstein's fix was to say the energy arrives in discrete packets whose individual size is set by frequency alone.
The quantum hypothesis, and what is actually quantized (0:07:20)
Einstein noticed you can make sense of the data with a genuinely quantum hypothesis, a discretization hypothesis. Say the light is delivering energy to the metal in discrete small packets, and the amount of energy in each packet is a function of the frequency. Raise the frequency and you raise the energy of each packet. Raise the brightness and you raise the number of packets.
To that extent it looks like the light is delivering energy more the way a set of particles would. And now the threshold explains itself. If the individual packets do not have enough energy to dislodge an electron, it does not matter how many of them you throw at the metal. No current. As soon as you have even one packet above threshold, you start to get current.
The link between frequency and packet energy is the famous formula:
E = hν
There is Planck's constant again. The h Planck found in his statistical calculations now shows up connecting the frequency of light to the energy of these quanta.
Then Maudlin stops to make a point that is almost always slurred over in popular accounts. Notice what is quantized here. It is not really energy.
A photon, a quantum of light, can have any energy you like. You just pick the right frequency. There is a continuum of frequencies, each frequency gives you an energy, so there is a continuum of possible photon energies. What is discrete is this: at a fixed frequency, the energy seems to be delivered in packets, each of which carries an energy determined by that frequency.
Waves on a beach, bullets on a beach
Then the analogy, and Maudlin does not rush it, because it is doing real work.
If light is a wave like a water wave hitting the beach, it carries energy and, as it hits, distributes that energy across the beach. Equally. 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 coming in where a few pebbles get shot way up, getting a whole lot of energy, and the others get nothing. The energy is not being equally distributed across the beach. It is more like people are shooting bullets at the beach. Imagine a bunch of people with guns firing at it. If a pebble gets hit, it jumps. If it does not, it does not. You do not expect the energy to be spread evenly.
And the bullet model extends cleanly to the threshold. If it takes a certain minimum energy to dislodge a pebble and your ammunition is too weak, individual bullets do not deliver it and you get no effect at all. Upgrade the ammunition, which is the equivalent of upgrading the frequency, and now they do have enough. Past the critical threshold, suddenly the rocks start to jump. And the more bullets being shot, the more rocks jump. That is the brightness.
Wave particle duality is already there in 1905 (0:12:30)
So in the 1905 paper, accounting for the photoelectric effect, Einstein introduces a kind of wave particle duality. The energy of the wave seems to be delivered more the way a particle would deliver energy than the way a classical wave would. The actual calculation is rather complicated, and there were still wave characteristics in Einstein's theory.
You need them. Light does behave like a wave. It refracts, it interferes, it does all sorts of things that settled the old classical debate: when the corpuscularians like Newton went up against the wave theorists, the wave theorists won, because light displays interference and refraction.
So the duality is there from 1905. Light is in certain respects behaving like a wave, and in other respects like a particle.
Curt pushes on the word. Is it really a duality, or is it that the quantum object has wave characteristics and particle characteristics, and duality is not quite the right term given how we use dualities elsewhere in math and physics, where a covector is dual to a vector?
Maudlin grants it immediately. It is certainly not a technical notion of duality as would be used in math, and the word is not supposed to connote that here. When people started talking this way he does not think they had a strict mathematical understanding either. All they meant was that somehow this thing is in certain ways behaving like a wave and in other ways like a particle. That is all.
Myth one: the Jekyll and Hyde picture
Curt then raises the version of duality the audience has almost certainly been taught: that the thing either behaves like a particle or behaves like a wave, never both, and it switches between the two. Is that correct?
"No, I would say nobody would take that."
Maudlin calls it the Jekyll and Hyde picture. There is one guy, sometimes he behaves like Jekyll and other times very differently like Hyde, and he switches, and it is quite dramatic when he does. Nobody thought that was going on. It would just be crazy to try to make such a theory. The claim Maudlin actually made, that you have a single thing whose behavior is in certain ways characteristic of waves and in other ways of particles, is true at all times. There is no trigger that flips it from particle mode into wave mode. You could imagine such a theory. He cannot imagine anybody taking it seriously. What would the trigger even be?
Myth two: which way information flips the switch
Curt presses because he knows the audience has seen the animations: if you have the which way information, it starts to act like a particle, and if you do not, it acts like a wave.
Maudlin's answer starts with a friendly execution. "So I'll even dunk a little 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." The five words were: don't look, wave; look, particle. That does suggest the Jekyll and Hyde picture, with being looked at as the trigger, "and that's just of course lunacy, right? Because what do you mean, looking at a particle? The whole thing makes no sense." He adds that he is sure Sean would not defend it, and that trying to reduce any theory to five words is not a great idea.
Then the actual physics. All of this business about which way information and the double slit and why the interference goes away is explained in a perfectly comprehensible manner just by looking at the Schrödinger evolution of the wave function. And the Schrödinger evolution is always wave. Schrödinger's equation is a wave equation and it governs the wave function as a wave. That is what explains why the interference goes away when you change the physical situation in certain ways.
Characterizing those changes as giving you which way information leads you in the wrong direction. You make certain physical changes to the situation, you plug Schrödinger's equation in, you see what happens. And what you notice is that the interference degrades continuously. Which is fatal to the switch picture: if it is either a particle or a wave, how can there be a continuum between the two behaviors? But there is one. There is a continuum between having sharp interference bands and having none.
The obvious solution nobody took: both
Maudlin adds that this puzzled Bell, who said he was always puzzled by it. Once they noticed there was both wavelike behavior and particle like behavior, they started worrying: is it a wave, is it a particle, is it a wavicle, whatever. And it did not occur to them, Bell says, that there was an obvious solution available. Maybe there is both a wave and a particle. 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 are both there.
That is the pilot wave picture, and it will come back later in the lecture as the escape route Einstein was sympathetic to. It is an obvious way of explaining why you have both sorts of characteristics. Not the only way, but an obvious one.
And if someone genuinely wanted to make physics out of the idea that a photon is sometimes in particle mode and sometimes in wave mode, they would have to give an account of when it does what. "And good luck with that."
De Broglie turns it around: matter waves (0:20:40)
Einstein solved the photoelectric effect by attributing particle like behavior to things that were classically waves. So it occurs to de Broglie, a very young guy: turnabout is fair play. Why not think that things we classically call particles can display wave behavior?
Take an electron. Classically it is a particle. Classically it is always somewhere, it moves around in some continuous way, it is not spread out, it does not interfere. De Broglie says: if you took classical electromagnetic waves and gave them particle like behavior, why don't I take classical particles and give them some wavelike behavior?
But you need the linkage. What kind of wave should you associate with a given particle? And de Broglie, taking Einstein as his model, made the link with Planck's constant. A wave needs a wavelength, so:
λ = h / p
A classical particle has a momentum p, so say the wavelength is h over p. Planck's constant again. Now, in a situation where classically you would say this particle has such and such a momentum, you can say you expect it to display the wave behavior associated with a wave of wavelength lambda.
A wave has both a wavelength and a frequency, so he needs the frequency too. There he used the same equation Einstein used:
E = hν
But he ran it in the other direction. Einstein was saying: I know my light has frequency nu, what is the energy of these quanta? De Broglie is saying: my particle has an energy, the classical one half m v squared, and if I want to associate a frequency with it, what will it be? Same equation, but now you put in the E and derive the nu.
So from a classical particle, which has a momentum and an energy, de Broglie gets two equations that hand him a wavelength and a frequency. Then he can think about the behavior of waves with that frequency and wavelength. And that led to people actually going out and looking for interference behavior, wavelike behavior, in electrons.
Where we actually are: 1924, before the "birth" of quantum theory
Then Maudlin stops to recap, and the recap is the historical punchline of act one's first half.
We are only in 1924. This is before what is normally called the birth of the new quantum theory, which is 1925 and 1926. And already de Broglie, plus Einstein back in 1905, have laid the foundations of the new quantum theory.
What is called Heisenberg's breakthrough, now 1925, was matrix mechanics. And what Maudlin has just given you has no matrices in it in any obvious way. It is just very different from what Heisenberg was doing. He declines to go into what Heisenberg was doing. It was clear, and it was something else. He is trying to tell a reasonably smooth story, and the story gets smooth after Heisenberg, when Schrödinger develops wave mechanics in 1926.
Then there were various proofs that at least in certain circumstances the two theories gave the same predictions, so they were generally considered different mathematical presentations of the same theory. And here comes the sociological fact that decided the next century of physics education: because people with classical training were very good at working with waves and really had not learned to work with matrices, pretty much everybody started working with Schrödinger's presentation rather than the matrix mechanics.
1900Planck stops a limit short to fit the black body spectrum, leaving finite cells of phase space characterized by h. Maudlin: it is not clear he thought he was quantizing anything.
1905Einstein proposes the genuine quantization: light delivers energy in packets of E equals h nu. This, not Planck, is where quantum theory starts. Wave particle duality arrives with it.
1915Bohr's old quantum theory. Electron orbits treated as planetary, restricted by fitting waves around them, which gives the allowed transitions and therefore the atomic spectra. No probabilities anywhere in it.
1924De Broglie runs Einstein backwards: classical particles get matter waves, with lambda equals h over p and E equals h nu. The foundations are now laid, one year before the official birth.
1925Heisenberg develops matrix mechanics, unfamiliar mathematics that almost nobody was trained for.
1926Schrödinger develops wave mechanics. Shown equivalent in predictions, and adopted almost universally because classically trained physicists could already solve wave equations.
1926Born squares the wave function and reads the result as probabilities for measurement outcomes. Maudlin: completely out of left field. Schrödinger did not like it.
1927Copenhagen and Solvay. Bohr and Heisenberg insist the wave function is complete and the indeterminism is real. Einstein raises the pinhole objection at the fifth Solvay conference. Nobody changes their mind.
1932Von Neumann writes the collapse into the mathematical foundations of the theory as a real physical change, instantaneous and global.
1935EPR. Einstein, Podolsky and Rosen recast the 1927 objection with two particles and a criterion of reality. Bohr abandons everything to reply and cannot make his own reply work. Schrödinger writes the cat paper and coins entanglement.
Figure 2. The chronology Maudlin walks, with the credit reassigned. The usual story dates quantum theory to 1925, gives Planck the origin, and gives Einstein an objection about dice. On this telling the origin is 1905, the foundations are in place by 1924, and the objection lodged in 1927 and repeated in 1935 is about action at a distance from beginning to end.
What Schrödinger thought the wave function was, before Born got to it
So by 1927 the new quantum theory is certainly in place and people are talking about it. We have Schrödinger's wave mechanics, which introduces the wave function everyone is now familiar with: a complex valued function over the configuration space of a system. That is what the wave function mathematically is. Schrödinger specified its dynamics in Schrödinger's equation, and that dynamics is a wave dynamics. So the wave function will evolve in a wavelike way. There will be interference, there will be spreading, there will be essentially refraction like behavior, all the things you associate with waves.
And nobody quite knew what to do with it until Born came along and gave it the probabilistic interpretation: take the wave function, square it, treat those numbers as probabilities for measurement outcomes. That is where probabilism enters standard quantum mechanics, and with it the failure of determinism. The theory no longer gives strict predictions about what is going to happen. It gives you different possibilities and assigns probabilities to them.
Curt asks the question a good student asks. Most students are taught the Born rule alongside the Schrödinger equation, so it is difficult to imagine what the Schrödinger equation would be doing without it. What did Schrödinger think the wave function was? And did Born only invent the rule because of single particles, because you then have to make sense of dots appearing on a screen? How could those two ever have been separated?
Maudlin calls it a very good question, and the answer is a genuinely useful piece of history.
First, Schrödinger did not particularly like Born's suggestion when he made it.
Second, follow the actual development. If you read Schrödinger's big paper, it is a four part paper, and what he does in the first three parts is entirely stationary or static situations. Nothing is changing in the environment, and you are looking for eigenstates, certain kinds of stationary solutions to the equations.
For what purpose? For the case that really got this going for Bohr: atoms. You wanted to know what energy levels are available to electrons, because the picture was that electrons in an atom can only be in certain energy states. Jump from a lower to a higher one and they have to absorb a certain amount of energy. Decay down and they emit energy as light. And that was supposed to explain the atomic spectra you could actually see. Light from the sun, light from a neon tube, is not a uniform spectrum. It has very definite bands where the light is being produced.
The old quantum theory, which preceded 1925, is where Bohr, back around 1915, was laying down rules for the orbits electrons can occupy, thinking of the orbits as planetary, as little particles going around. You restrict the orbits in certain ways that have to do with getting waves to fit around them. That gives you a set of orbits, which gives you the possible transitions, which gives you the spectra of light.
And for what they were doing, that is essentially a static situation. You are solving for stationary solutions, and what matters about the solutions is what energies you associate with them.
Then the point: you can do all of that without using Born's rule. Nothing about Born's rule, nothing about probabilities, anywhere in it. It is just, can I get the spectra right?
There is a lot you can do that way. In a static situation, nothing is changing, so what would the probabilities even be probabilities of? In the first three sections of that paper Schrödinger is dealing only with stationary solutions, and the wave function he uses is real. It is a real valued function, not a complex one.
Then he asks what happens if the situation is not stationary. What if there is an electric or magnetic field and it is varying? And here he is forced into something, and he is explicitly unhappy about it. He says: I am going to now use a complex function. The values will not be real numbers anymore, they will be complex numbers. It was the only way he could think of to handle the non stationary case.
Maudlin lands the irony. When a student learns quantum mechanics today, the first thing they are told is that a wave function is a complex function. "So we start at a position where Schrödinger just barely got to and wasn't happy about." He was hoping to replace that complex function with a real one. He just could not figure out how.
And then Born arrives and suggests squaring this complex function and treating the results as probabilities. Why square it? Maudlin's verdict: "that's kind of completely out of left field." But of course, for many purposes, it worked.
Which is exactly why the situation was so confusing. Nobody really understood what was going on. Maudlin does not know precisely what Born thought, but Bohr certainly insisted the probabilities were fundamental, that they reflected an innate indeterminism in nature itself. Schrödinger was upset about that. Pauli, Maudlin thinks, was upset about that. It did not go over well. It was a very confused situation.
The Copenhagen doctrine, stated precisely (0:26:40)
During this period Bohr and Heisenberg are working together to lay down the principles of what is usually called the Copenhagen interpretation, or the Copenhagen school. And Maudlin isolates the one principle everything in the rest of the lecture will turn on.
The main principle 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 the randomness or probability introduced by Born's rule reflects an actual failure of determinism in nature. Nature itself is not deterministic.
Bohr was very insistent that they had crossed a threshold out of classical physics that you could not go back over. You are giving up determinism. You are giving up the ability to visualize what is going on, and Bohr was very insistent on that too. And insofar as you think you need to visualize things in order to understand them, you are giving up on understanding.
But Bohr kept saying, in Maudlin's paraphrase: "We've reached the end of the road. 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."
Hold onto both halves of that. The wave function is complete, and this is the end of physics. Every objection Einstein raises for the next thirty years is an objection to those two sentences, and every reply Bohr gives will be a refusal to give up either one.
Solvay 1927: Einstein's pinhole, and the objection nobody quotes
Now we are in 1927, and at the fifth Solvay conference all the big shots get together and, as we know, have a nice photograph taken of them all together. There was a lot of discussion of quantum theory, and in that discussion Einstein first raises his objections to the theory as it is being expounded by Bohr and Heisenberg.
These objections are very important, Maudlin says, because they tell you what was on Einstein's mind from the beginning.
By 1927 people knew you could use Born's rule together with the wave function and the Schrödinger equation to make statistical predictions. You evolve the wave function with the Schrödinger equation, square it to extract probabilities, use those probabilities to make statistical predictions. And it worked. And even though the new quantum theory is credited to Heisenberg and matrix mechanics, by 1927 people were mostly working in the Schrödinger wave picture.
So Einstein focuses down on the wave function, because in the Schrödinger presentation the central object you use to describe a system is the wave function. And what he notices is this: one and the same mathematical object can be used to represent a physical system with different physical meanings. Different interpretations of what is being represented. He is very clear about it.
Sometimes, he says, when we describe something, the description is merely statistical. We are not describing an individual system. We are describing an ensemble, usually an ideal infinite ensemble of systems. And he thought that was the natural way to understand this Schrödinger wave.
He was very worried about how Bohr was trying to understand it instead. So he zeroes in on one 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? The second would be a statistical understanding.
And he raised the problem with an example that, Maudlin says, most people do not know. "But if you don't understand this example you won't see where Einstein is coming from."
The apparatus: a pinhole and a hemispherical detector (0:41:20)
At Solvay, this was not a formal presentation. It was Einstein raising objections in discussion, and we have the records.
He imagines a beam of, say, electrons being shot at a barrier with a very small hole in it. Beyond the pinhole there is a screen, and not just a screen but a hemispherical screen, centered on the hole, so the screen is the same distance away in all directions. Maudlin flags that detail as going to be kind of important.
And we know from de Broglie that the electrons have associated wave behavior. They have frequencies and wavelengths and they behave the way water waves or electromagnetic waves do. So what do they do? When you shoot a wave through a small hole, it diffracts. What comes out the other side is an expanding wave, a semicircular wave in the water case, and in another dimension a growing hemispherical wave, because the wave diffracts and comes out of the pinhole going in all directions at once.
Figure 3. Einstein's figure two from the 1927 Solvay discussion, rebuilt. The apparatus is deliberately minimal: one particle at a time, one hole, and a film held at a constant distance so that no direction is privileged. The diffracted wave reaches every point on the film. Exactly one spot ever appears. If the wave function is a complete description of that single particle, then the appearance of the spot must instantaneously annihilate the wave everywhere else on the film, or you would sometimes get two spots or three. That instantaneous global annihilation is what Einstein calls action at a distance, and it is why he says conception two contradicts the postulate of relativity.
Einstein: "Despite being conscious of the fact that I have not entered deeply enough into the essence of quantum mechanics, nevertheless I want to present here some general remarks. One can take two positions towards 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, 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 Broglie waves which impinge approximately normally on S and are diffracted at O." That is de Broglie's idea again, that even electrons exhibit wave behavior. "Behind S there are spherical waves which reach the screen P and whose intensity at P is responsible for what happens at P."
So there is the picture. Electrons coming in, the little hole O, arrows going out in all directions toward a hemispherical screen that is the same distance away everywhere.
Then Einstein says: we can characterize the two points of view as follows. And this is the crux. He is saying, look, we are agreed on the mathematics. But physically, what are we talking about? What exactly does this wave function represent?
Conception one. "The de Broglie Schrödinger waves do not correspond to a single electron, 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."
Picture it: you shoot these electrons at the pinhole, each one gets diffracted or shot off out of the pinhole in some direction. Shoot a million and follow the cloud, and the whole cloud spreads out hemispherically. That is conception one.
Conception two. "The theory claims to be a complete theory of individual processes." Maudlin stops on both words. Notice complete. Notice individual. The theory purports to tell us everything about the individual process, about an individual electron.
"Each particle directed towards the screen, so far as can be determined by its position and speed, is described by a packet of de Broglie Schrödinger 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 a state of resolution, Maudlin reads him to mean thinned out, as you would expect. You shoot the wave in, it comes out in all directions, and it thins as it goes. By the time it hits the hemispherical screen it is rather thin. And thinner still the further away the screen is.
"According to the first, purely statistical, point of view, the squared wave function 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 at the screen you square psi, and it comes out pretty uniform across the film. And you ask: Born tells me this number is a probability, but the probability of what? Einstein's answer on conception one: if you have a large collection of particles and you arbitrarily pick one, that number is the probability that that particle is somewhere near there.
"According to the second conception, the squared wave function expresses the probability that at a given instant the same particle is present at a given point, for example on the screen."
Shoot a single particle through. As the wave spreads out, it represents that single particle itself 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." Two things, then, in conception two: the wave function describes a single individual system, and it is a complete description of it. If the wave spreads out, the particle spreads out.
Why conception two buys you something real
Then Einstein concedes what conception two has going for it, and this part matters, because it is what makes the debate a real debate rather than a preference.
"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 that the theory contains the consequence that the conservation laws are valid for the elementary process. It is only from two that the theory can derive the result of the experiment of Geiger and Bothe, and can explain the fact that in the Wilson cloud chamber the droplets stemming from an alpha particle are situated very nearly on continuous lines."
Why does that follow? Because if you are explaining single continuous tracks through a cloud chamber, you are talking about a single particle and what it is doing. You are not talking about a collection. And conservation laws holding for the elementary process, not just on average across an ensemble, is the same kind of claim. Conception two gets you those. Conception one does not.
The objection: why is there never a second spot?
"But on the other hand, and this is the main point, I have objections to make to conception two."
"The scattered wave directed towards P does not show any privileged direction. If the squared wave function 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."
Here is the argument, slowly. You have this single particle. Send it through. The wave goes through the hole and spreads out uniformly in all directions toward the screen. Suppose you say this wave completely describes the single particle. Then the wave reaching all these different points on the screen is supposed to represent that it is physically possible for that single particle to interact at all of them.
But then, why can't the particle interact at more than one place? Why can't it interact over here because the wave got there, and also over there because the wave got there too? If the particle itself is thinning out and spreading in all directions, how do you avoid it acting at several points on the screen?
On a collection of particles you have no problem at all: some of them interact here, some of them interact there. But for a single particle, what could that even mean?
Einstein: "But that interpretation, according to which the squared wave function expresses the probability that this particle is found at a given point, assumes an entirely peculiar mechanism of action at a distance, which prevents the wave continuously distributed in space from producing an action in two places on the screen."
In that theory, if a spot forms here on the screen, that is one thing. But the formation of the spot also has the effect of destroying, eliminating the wave function everywhere else, at every other point of the screen where it had reached. And according to this theory it did reach there. Even for a single particle, the wave function got to the other parts of the screen. So why do they never create a second spot? Because as soon as the first spot forms, something happens that annihilates the rest of the wave function.
That is collapse. And Einstein says that is action at a distance, because the formation of the spot over here is causing the physical wave over there to go to zero, instantly and globally. If that change did not happen instantly and globally, then sometimes we would get two spots, or three, or more. Curt: "or three or four." Maudlin: "Exactly. And you never do." You only ever get one spot.
Einstein's own proposed fix, in the transcript: "In my opinion, one can remove this objection only in the following way, that one does not describe the process solely by the Schrödinger wave, but that at the same time one localizes the particle during the propagation. I think that Mr de Broglie is right to search in this direction. If one works solely with Schrödinger waves, interpretation two of the squared wave function implies to my mind a contradiction with the postulate of relativity."
And that contradiction is the spooky action at a distance. You need an instantaneous change in the wave function. The collapse is global and instantaneous, and that violates relativity.
What is actually on Einstein's mind in 1927 (0:48:00)
So Einstein, already in 1927, is worried about spooky action at a distance. He is worried about the completeness of the wave function. And he is sympathetic to de Broglie, who says the wave function is not complete: in addition to the wave there is a particle, the particle is always somewhere, it is always moving in some direction, and therefore if the particle is headed toward this part of the screen, no spot will form on the other part.
Curt catches the opening line and asks about it. Einstein said "despite the fact that I have not entered deeply into the essence of quantum mechanics." Was that just humility?
Maudlin flags it as a guess. Heisenberg's matrix mechanics was very unfamiliar mathematics. Schrödinger was less unfamiliar because people were used to solving wave equations. His guess is that Einstein simply did not feel he had mastered what Heisenberg had done. Maybe it was just humility. Either way, 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, and (b) it describes an individual system rather than a statistical ensemble. To avoid the two spot problem, such a theory has to collapse. And the collapses look like they violate relativity, because they would have to be instantaneous and global, faster than light.
Maudlin, on the historiography: "This is an episode that everybody should know, and I don't think that many people do." Historians know about it, but it does not get the play other episodes do. And it shows how quickly Einstein grasped the fundamentals of Bohr's understanding of quantum theory and had deep problems with it.
"But notice, the deep problems were about spooky action at a distance, not particularly about determinism." He does not mention that he dislikes indeterminism. What he mentions is that he does not like this instantaneous weird collapse.
Notice also that this example involves only a single particle. Not a pair. So there is nothing about entanglement in it. And yet he is already onto the idea that the wave function could not provide a complete description of the individual system, because if it did, the collapse would have to be a real physical change, instantaneous, in violation of relativity.
The signaling red herring, first pass
Then Maudlin makes a point he will return to twice more, because he considers the confusion around it genuinely damaging.
Einstein's worry about relativity here has nothing to do with superluminal signaling. There is only a single particle, and there is no suggestion that anybody could use this collapse to send signals. The collapse here is associated with a spot forming somewhere on a screen, and nobody has any control over where. The issue of signaling is simply not present.
So Einstein is not thinking of relativity as being about signaling. "Which it isn't."
Therefore, people who think they can solve all the problems with relativity by proving you cannot send superluminal signals miss the point. If Einstein thought that was the problem, he would not have thought there was a problem in 1927 with this single particle example.
And there are also people who think action at a distance has to be some very special thing, that you have to take the word action very seriously. But when Einstein talks about action at a distance here, the action is just the sudden change of the wave function itself. The fact that the spot forming here has the collateral instantaneous effect of annihilating the wave function elsewhere. That, for Einstein, is action at a distance, and it has nothing to do with superluminal signaling.
Why is it incompatible with relativity? Because in relativity you cannot even define an instantaneous change. There is no such thing as an instant of time. There is no objective simultaneity.
Why collapse cannot be mere updating if the wave function is complete (0:56:00)
Here is the move that Maudlin considers the sharpest thing in the 1927 objection, and it is the argument that most cleanly disposes of the most popular modern defense.
Look at the collapse of the wave function and take it seriously, which you would have to if you thought the wave function was complete. Immediately you say: that looks spooky, that looks non relativistic.
The normal reaction is for people to say no, no, no, the collapse of the wave function is not a physical change. It is just an updating. It is like Bayesian updating. You are not changing the physical world, you are changing your beliefs about the physical world, because you got new information about it. This has been the standard way of trying to defang collapse: interpret it as merely epistemic.
But Einstein is very clear. This is a complaint about conception two. And in conception two it cannot be updating, because you said the wave function was complete.
If the wave function is complete, there is no new information to update on. 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. Because if you know the wave function, and the wave function is complete, you know everything.
"So it is the nature of conception two that precludes thinking of collapse merely epistemically."
What is at stake
Conception one: statistical
Conception two: complete and individual
What the wave function describes
Not a single electron. A cloud of electrons extended in space, an ideal infinite ensemble.
An individual process. This electron, and everything about it that is governed by laws.
What the squared wave function means at the film
The chance that some particular particle of the cloud is near that point.
The chance that this same single particle is present at that point at that instant.
Conservation laws for individual events
not derivable Only ensemble averages.
derivable Which is why Einstein grants it goes further.
Geiger and Bothe, and cloud chamber tracks
not explained A continuous track is about one particle, not a collection.
explained
Does it need collapse?
No. Different members of the cloud land in different places, and nothing has to be annihilated.
Yes, and unavoidably, or the same elementary process would sometimes make two spots.
Can collapse be read as mere Bayesian updating?
Yes. The description was incomplete, so there is something left to learn.
no Completeness means there is nothing left to learn, so the change must be physical.
Compatible with no action at a distance?
Yes, straightforwardly.
no The change is instantaneous and global, which relativity cannot even express.
Whose position
Einstein, and de Broglie's pilot wave adds the particle that makes it work.
Bohr and Heisenberg, pushed explicitly, and written into von Neumann's foundations.
Table 1. The two conceptions Einstein laid out at Solvay, and the ledger he drew up between them. He grants that conception two genuinely buys you more: conservation laws for individual events, the Bothe and Geiger result, single continuous tracks in a cloud chamber. The bill for that purchase is collapse, and collapse that cannot be demoted to mere knowledge updating, because completeness leaves nothing to update on. Every line in the right hand column is something Bohr and Heisenberg accepted, and the last two are what Einstein spent thirty years saying they should not have.
The de Broglie escape route
Now watch what happens when you deny completeness. Maudlin walks the pilot wave version of the pinhole, and it is deflating in the best way.
Einstein knew de Broglie had been playing with a theory in which there is a wave and there is a particle. This is the point Bell later made: he did not understand why everybody was worrying wave or particle, wave or particle, when they could just have said wave and particle. Yes, there is a wave, and it follows a wave equation. And also there is a particle. And the wave guides the particle, determines where the particle goes.
Take that view and you are not in any trouble with relativity, because when the spot forms on the screen you genuinely 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 the entire time, following some trajectory, and you did not know what it was, and you could not figure it out from the wave function.
So: if you want collapses to be epistemic updating, you need new information to update on. 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 is because a little before it formed, the particle was very near that location headed toward the screen. That is not mysterious. That is particles forming spots where they actually hit.
It is because you do not know the location of the particle that you can update on it without any physical change. And the fact that the chance of a spot forming elsewhere immediately drops to zero is not a physical change either. It is you realizing that, because the particle was headed this way, it never had any chance of forming a spot over that way.
But the price is explicit: to do it, you have to deny the completeness of the wave function, and therefore you have to deny the entire Copenhagen approach, because completeness plus no hidden variables is exactly what Bohr and Heisenberg were insisting on. And if they hold that line, they are stuck with the collapses as real physical changes, which is precisely how it comes out in von Neumann'sMathematical Foundations of Quantum Mechanics. And that sudden collapse, in that book, is instantaneous and global. Any physical change that is instantaneous and global you cannot make sense of in relativity, independently of anything about signals.
What a local model of the pinhole experiment looks like
And here is the deflating part. Look at the actual experiment: you shoot electrons, spots form. There is nothing in the phenomena that suggests anything like collapse going on. Nothing in the phenomena demands any kind of spooky action at a distance. The natural assumption is that the particles are going through the hole and different ones go off in different directions.
So anybody could write down, off the top of their head, what Maudlin calls a local relativistic no action at a distance model of the whole experiment:
A particle gets shot. It travels along a definite trajectory, maybe accompanied by a wave that guides it.
It reaches the pinhole. It either goes through or it does not. Its little wave interacts with the pinhole somehow, and that interaction is local and unremarkable.
If it goes through, the interaction shoots it off in some direction, different in different runs. Maybe the fine dynamics of the pinhole interaction effectively randomizes the outgoing direction. You could add something stochastic there. It does not matter.
From the pinhole to the screen it propagates essentially classically, inertially, in a straight line.
It hits the screen, interacts with it, and forms a dot where it hits.
And the crucial structural point: where it hits is already decided as soon as it comes out of the pinhole. It is not decided at the last moment when it arrives. It leaves the pinhole headed in some direction, and it just goes that way. None of these interactions require any non locality or action at a distance. No threats are raised to relativity at all. This, Maudlin says, is the kind of thing Bell would have asked about: why didn't they all jump on that idea?
Curt asks whether positing a particle and a wave would entail a preferred foliation or a preferred time slice. At this point, no, because we are only dealing with a single particle, and a single particle wave function is just defined on regular physical space. The Schrödinger equation governing that single particle wave does not have to violate relativity, and they knew you could have relativistic versions: you had the Dirac equation. So you can do it relativistically. If you just have a particle accompanied and guided by its wave, all of that can be local. For a single particle system there is no obvious threat at all to relativity in this picture. So Einstein, thinking about the pinhole, would not have thought that adding a moving particle threatened relativity. Why would it?
Multiple particle systems are where the trouble starts. Maudlin flags it and moves on, because that is where act two goes.
Two kinds of locality, and Einstein liked both (1:05:00)
Curt asks the question that has been building: this word local and non local has come up many times. Are there different kinds of locality, such that Einstein would have been fine with non locality of one type but not another?
"I mean, there are. You can make fine distinctions between different types of locality. Einstein does so, and he likes all of them."
Then Maudlin draws the two that matter.
Ontological locality. The physical state of the world can be completely expressed by giving the physical state of each of a set of tiny, slightly overlapping regions. Take the entire universe, break it into little regions as small as you like, slightly overlapping so you can match them up around the edges, and for each region tell me what is going on there. For anyone who knows general relativity, this is like having an atlas of charts to cover a manifold.
If a theory is ontologically local, then by telling me what is going on in each little region, without mentioning anything outside that region, and covering the whole thing, I have nailed down the entire physical state. The entire physical state of the universe is nothing over and above the little physical states of the little pieces.
All of classical physics had that. Think of a Maxwellian electric field. How do you specify the state of the field? You say what it is here, and here, and here. For all the little regions you tell me how strong the field is and which direction it points. Do that everywhere and you have nailed it down. There is nothing else to say. Einstein recognized that field theory as developed by Maxwell was really ontologically local. Fields were local objects with local quantities and you could point your finger in space and ask what the value is right there.
Dynamical locality. This is the no action at a distance point. 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, from here to where the effect happens. It cannot have an instantaneous effect far away.
That is a different kind of locality, and it is the one at issue in the collapse worry. When Einstein worries about action at a distance, he is worried about dynamical non locality. Ontological locality he more or less took for granted, and Maudlin does not know that he even talks about it that much.
But there is a wonderful passage where Einstein talks explicitly about how in field theory things get more and more local, because you can take a microscope and focus into smaller and smaller regions of spacetime, and in each little region it not only has its own little physical state, but the laws themselves apply just in that region. You can check, in that region, whether the laws hold. Why? Because the laws are given by differential equations. Local differential equations. The laws of electromagnetism explain how the electric field right here is going to change purely in terms of the nearby electric and magnetic fields. Nothing else.
So you can focus down on little pieces, and not only do they have their own physical states, but in each little region you can check whether the laws of physics hold there. And there is nothing more for the laws to hold everywhere than for them to hold in all the little regions.
Why action at a distance would break the practice of science
Now suppose there were action at a distance. Then that would not be true. Maudlin's illustration: if by snapping my fingers I could make something happen far away, by law, then someone watching far away who sees that thing happen and wonders whether it happened according to the laws of physics has to say, "I don't know. I have to check far away and see if somebody snapped their fingers." You would have to check everywhere. Because the laws themselves would postulate action at a distance, so to know whether the laws are being satisfied, you would have to survey the whole universe.
That is a problem, and Einstein saw it as a problem. He did not deny that such action at a distance was logically possible. But he did think you could not do science in such a world, because there would be nothing like an isolated system you could experiment on. Or even a quasi isolated system. We can isolate little systems because they are local, and because we can shield them from outside influences, which have to come in continuously through the walls.
So Einstein believed in both kinds of locality. The one at issue here is the dynamical one.
The scorecard on the pinhole
Put it together. We have a very modest little theory that explains the phenomenon, which is that spots form all over the screen one by one, in a completely everyday way. Maybe it involves a little wave traveling with the particle. You need to explain the diffraction at the pinhole. Everything else is just the particle going this way, and then that way or that way in the next run. Nothing that would even vaguely threaten relativity.
And what about the wave traveling out in all directions? Run the experiment many times, with an ensemble rather than a single particle, and overlay all the trajectories, and what you see is a whole bunch of particles hitting the pinhole and then spreading out in a hemispherically expanding pattern. Which looks exactly like what the wave function does. Which suggests the wave function is not a description of an individual system at all, but a statistical description of a large, ideally infinite, collection.
But if you say that, then immediately the wave function is not complete. It certainly does not give a complete description of an individual particle. It is a kind of averaged out description of a whole collection.
So the moral of the pinhole: Bohr and Heisenberg have committed themselves to this weird action at a distance associated with wave collapse, and they committed to it by insisting the wave function is a complete description of an individual system. And you do not need to do any of that. They are not getting spooky action at a distance out of the phenomena. They are getting it out of a dogmatic attachment to the idea that quantum mechanics as it existed in 1927 was the end of physics, the final theory. Which, Maudlin says, Einstein thought was silly. Why would you adopt conception two and inherit this weird consequence when you do not have to?
And Maudlin's reading of what happened to Einstein afterwards: he thought in 1927 that these were powerful, powerful objections to what Bohr and Heisenberg were pushing, and they did not pay any attention. They did not stop. They did not say, oh yes, we made a mistake. They continued to insist that the wave function is complete.
The second 1927 objection: configuration space (1:14:00)
There is another worry Einstein has, and it comes in the record right after the passage Maudlin read. It involves systems with two particles, where everything so far has been one.
Einstein: "I should also like to point out briefly two arguments which seem to me to speak against the point of view two. This view is essentially tied to a multidimensional representation, configuration space, since only this mode of representation makes possible the interpretation of the squared wave function peculiar to conception two. Now, it seems to me that objections of principle can be opposed to this multidimensional representation."
Stop and unpack. With a single particle, the wave function is just defined on physical space, and it behaves rather like a water wave or an electromagnetic wave familiar from classical physics. With two particles, mathematically, the wave function is not defined on physical space anymore. It is defined on configuration space. And where physical space has three dimensions, the configuration space for two particles has six, for three particles nine, for four particles twelve.
A single point in configuration space represents the entire configuration of the set of particles. It specifies where each of the particles is. One particle, you are pointing out a point in space. Two, you need two points. Three, three points.
Figure 4. Einstein's second 1927 objection. Configuration space was not new and not suspect: classical Hamiltonian mechanics used it constantly. What is new is the direction of travel. Classically you start with laws stated in physical space, where the r in an inverse square law means an actual distance between actual things, and then recode them on a high dimensional space for convenience. Conception two starts with the high dimensional object and treats it as fundamental, and then it is not obvious you can get back down, or that what you get back will be dynamically local.
Einstein raises two objections to this. The first: "In this representation, indeed, two configurations of a system which are distinguished only by the permutation of two particles of the same species are represented by different points in configuration space, which is not in accord with the new results in statistics." Maudlin flags that as a technical issue about identical particles and Bose Einstein statistics, notes there are ways around it, and moves to the one he cares about.
"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."
What is he worried about? He has this idea of locality, that forces act only between nearby things and not immediately between distant things. But distant in what? Distant in physical space. And if you are not doing this in physical space, but in configuration space, it is harder even to specify what you mean by forces acting only at small spatial distances.
Maudlin's gloss: "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."
Why configuration space bites harder in quantum mechanics
Curt asks the exactly right follow up. What is the difference between configuration space in quantum mechanics and the classical configuration space of Hamiltonian dynamics?
"Mathematically, nothing at all."
You have a configuration space, you can write down Hamiltonian dynamics on it, and that is just a mathematical trick: instead of specifying where eight particles are in three dimensional space, you represent that configuration by a single point in a twenty four dimensional space, because you need twenty four numbers, three for each of eight particles. Configuration space is a classical notion. It was used all over classical mechanics and all over Hamiltonian mechanics. Maudlin adds the distinction that matters: it was configuration space and not phase space. A point in phase space specifies not only positions but also momenta, so it has six dimensions per particle. Configuration space has three. And it is that very configuration space, mathematically, that Schrödinger put his wave function on. The wave function was a complex function on classical configuration space.
Curt sharpens: is there something about the way configuration space is used in the quantum case that makes Einstein's objection bite harder than it would classically? Is it because the classical case can be translated back down to Newtonian dynamics on three dimensions, and the quantum one does not seem to?
Maudlin's answer is the cleanest formulation of the whole worry:
In classical physics the use of these high dimensional abstract spaces was merely a mathematical convenience. The real physics was stated in physical space. Take the Newtonian force of gravity, one over r squared. What is r? The distance between these two particles in physical space. So you have force laws stated in terms of things being near or far from each other in physical space, which is exactly dynamical locality. You can take those laws and express them on a single high dimensional space mathematically, but that is just a different mathematical presentation of the very same theory. You are going from a theory initially stated in physical space to a high dimensional abstract representation of it.
"The problem in quantum mechanics is that you're starting with a high dimensional abstract thing, but you're not sure what it's an abstract representation of."
And the question is: can I go back down and give myself a picture of things going on in physical space? The answer is that it is not obvious how you do that. And it is certainly not obvious that if you do it, you will end up with a dynamically local theory, where the only effects are between nearby things in physical space.
So Einstein had this worry too, in 1927. As soon as he goes from one particle to two, things get really screwy, because he is treating the wave function as fundamental rather than as a convenience for representing something better represented on physical space. When conception two takes the wave function seriously as fundamental and complete, the space it is defined on takes on an entirely new significance from the one it has in classical mechanics, where you understand that the real physics can all be specified in terms of things going on in physical space.
The aside Einstein did not make: Curie's principle and determinism
Before closing act one, Maudlin offers a bonus argument, explicitly flagged as an aside, and explicitly flagged as not Einstein's.
The 1927 complaint was about instantaneous action at a distance and a threat to relativity. He did not mention indeterminism. Einstein is popularly presented as if what really worried him about quantum theory was fundamental indeterminism, the God plays dice material. But if you start in 1927, you do not see him complaining about indeterminism. You see him complaining about spooky action at a distance, and doing it with this simple example.
You could, however, promote the 1927 argument into a conclusion about indeterminism, using what is called Curie's principle, after Pierre Curie. Curie said: suppose you have a system with some symmetry, and the laws respect that symmetry. Then if it has the symmetry at any time, it has the symmetry at all times. Curie's principle is for deterministic theories.
Now apply it. Assume the wave function is complete. In the pinhole situation, the entire physical situation has a symmetry around the axis through the pinhole, and the wave function has, or could have, that symmetry too. If it evolves deterministically, it always has to have that symmetry. But we know that at the end of the experiment the symmetry is broken: a spot forms here, or there, or there. So by Curie's principle, 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. Einstein does not make that argument. But you could, and it shows how these considerations lead you to see the role indeterminism plays in the standard theory. Indeterminism comes out as a consequence of completeness, not as the thing Einstein was objecting to.
"End of act one."
Act two: EPR, 1935 (1:25:00)
Eight years later. Maudlin's read on the intervening period is that Einstein's Solvay comments were very powerful and, as far as he knows, had very little effect.
Then in 1935, Einstein, Podolsky and Rosen produce a paper making basically exactly the same points Einstein was making in 1927, but in a way that appeared to them to be rhetorically sharper. And it involves a system of a pair of particles rather than a single particle, so the issue of the wave function living on configuration space does come into it.
To repeat the geometry: for a single particle, configuration space is three dimensional, because the configuration of a single particle is just where it is in space. For a pair, you indicate the configuration by saying where both particles are. Two points, six numbers, a six dimensional space.
And not only is the wave function in the EPR paper defined on that six dimensional space, it is a highly entangled wave function between the two particles. Maudlin notes carefully that Einstein does not say that, because the term entanglement had not yet been invented. Schrödinger invented it later in 1935, after reading the EPR paper. But it is a fact about that particular state, and it will matter.
What two particles buy you
One advantage is decisive. With two particles, Maudlin says, I can take one and send it to Alice over here, and take the other and send it to Bob way over there. Alice and Bob now each have a particle to play with, and their labs can be put arbitrarily far apart. Which makes the worry about spooky action at a distance very easy to understand and very hard to wave away:
Can it be that anything that happens in Alice's lab influences the state of affairs in Bob's lab, physically, or the other way around? That would be clearly spooky action at a distance in Einstein's mind.
Triage: the conceptual part, the logical part, the technical part
Before he touches the argument, Maudlin separates it into three pieces, and gives a verdict on each. This triage is the organizing device for the entire second half of the lecture.
The conceptual part. They introduce some terminology, lay out what they mean by their words, and lay out some principles. "I think all of that is exactly right."
The logical part. How does the argument unfold, what steps does it 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 make it more complicated than it needs to be."
The technical part. Because of the particular example they use, there are genuine mathematical problems. He is not going to go into them at all. They are there. Later the example gets changed in a way that removes them, so they will not bother us. The EPR argument is not affected by these technical considerations.
The title is the thesis
Start at the beginning. What is the title? "Can quantum mechanical description of physical reality be considered complete?" The very same question Einstein raised in 1927. Is the wave function complete? The quantum mechanical description he is referring to is the wave function, and the setting of the whole thing is again Schrödinger's wave mechanics.
The issue of completeness was already raised in 1927. What is new in 1935 is that they are far more careful to explain what they mean by a complete description. Maudlin's read: Einstein was frustrated because he had tried to get these points across and they would not go across, so now they are being very careful.
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 is 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." That is what we would call empirical success. Fitting experiment, fitting the data, making correct predictions.
"This experience, which alone enables us to make inferences about reality, in physics takes the form of experiment and measurement. It is the second question which we wish to consider here as applied to quantum mechanics."
Maudlin underlines it: they are not questioning the predictions of standard quantum mechanics. Not once, anywhere. The question is completeness.
The condition of 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. We shall call this the condition of completeness."
If there is something in physical reality that is not represented in your theory, then your theory is not complete. It does not describe all of physical reality. Maudlin: how could you complain about that?
He then makes the point that gives completeness its teeth, and it is a point about what it means to call a theory fundamental. Of course you can give incomplete descriptions. When we describe a glass of water by its temperature, that is not a complete description. It gives you a statistical average. There are lots of different specific microscopic ways the glass could be that result in exactly the same temperature. To get a complete description you have to go down to all the fine details.
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 are admitting that you are describing things in a coarse grained way, that maybe there are interesting things to say at that level, but it is not the end of physics, because the physics has to go down into the details.
Which is precisely the thing Bohr would not concede. Bohr's line was that this is the end of the road.
The criterion of reality, and why it is not a definition
"The second question is thus easily answered as soon as we are able to decide what are the elements of physical reality."
Now there is a new problem. To be complete, the theory has to describe every piece of physical reality. How do I know I have got a piece of physical reality? They answer with a criterion. And here Maudlin stops the lecture to make a distinction he says many people do not understand, though EPR are perfectly clear about it.
A criterion is not a definition. A definition gives necessary and sufficient conditions. A criterion gives only sufficient conditions. If something meets the criterion, you know it is of that sort. If it does not meet the criterion, you know nothing: it might still be of that sort. But meeting the criterion is enough. And enough is all the argument needs.
From the paper: "The elements of physical reality cannot be determined by a priori philosophical considerations, but must be found by an appeal to results of experiments and measurements." We cannot figure out what the world is made of just by thinking. "A comprehensive definition of reality is, however, unnecessary for our purpose." They are not going to try to define what it takes to be real. "We shall be satisfied with the following criterion, which we regard as reasonable."
And then the criterion, in italics in the original:
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.
Maudlin flags the opening clause as absolutely essential: without in any way disturbing a system.
Read it slowly. Suppose I have a system, and without disturbing it in any way I can predict the outcome of some experiment on it: I am going to weigh it, or do a momentum measurement, whatever. If, before the experiment is done, I can predict with absolute certainty and accuracy how it will come out, then there must be an element of physical reality in the system corresponding to that. There must be something in the system that is making it do that.
"That seems really hard to deny."
The paper continues: "It seems to us that this criterion, while far from exhausting all possible ways of recognizing a physical reality, at least provides us with one such way, whenever the conditions set down in 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."
Maudlin explains what they mean by the quantum mechanical half of that. Everybody says that if a system is in an eigenstate of an operator, the momentum operator, the position operator, whatever, which means you can predict with certainty what a measurement of that quantity will give you, then the system has that quantity. It has that momentum. And EPR say that is true. It is as true in quantum mechanics as anywhere else. People take the ability, from the theoretical description, to make a perfect prediction as a sign that the system itself has the corresponding property.
Maudlin's verdict on the conceptual apparatus: "I think they're perfect."
Why you cannot get out by denying the criterion (1:32:40)
People who do not like the conclusion of the EPR argument, and there are a lot of them, have to find something to complain about. So very often they pick on the criterion of physical reality and say they will escape the argument by denying it.
Maudlin's claim is that you cannot coherently deny the criterion, because in a philosopher's terminology it is analytic. It follows just from the meanings of the words in it.
Here is the derivation, and it takes about thirty seconds once you see it.
The condition is: I can accurately predict the outcome of an experiment on a system without in any way disturbing the system. What does without in any way disturbing mean? Without in any way altering its physical state. Whatever I do to make this prediction cannot change the physical state of the system.
So suppose I do this thing that does not at all disturb the system, and now I can predict what it is going to do. Then there must be an element of physical reality in the system making it do that. How can you deny that? Something is ensuring it is going to do that, and it has to be its physical state.
But now push it back one step. Suppose I do this without in any way disturbing the system. That means that before I did whatever I did, the system was already in that state. I did not change the state. So even before I was able to make the prediction, even before I did whatever it was that let me make it, the system already had that property. Why? Because I know that after I do it, it has the property, and by definition I did not 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."
Then a refinement worth keeping. Notice the criterion does not even demand that I actually make the prediction. It is enough that I be in a situation where I could make the prediction without disturbing the system. If that is even possible, then there must be some element of reality in the system, because the system's situation is independent of what I do. It is independent of my making the prediction or not making it. Maudlin adds that he thinks this is accurate, that it works in modal logic, that everything is okay with it.
"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?"
The premise EPR never wrote down (1:40:50)
There is a place, really throughout the EPR argument, where they appeal to a principle of no spooky action at a distance. The appeal is tacit. They do not come out and say it. But it is clear that they use it. So Maudlin makes it explicit.
We have two particles. Send one to Alice, send one to Bob. They can do whatever experiments they want on their particles, and their labs can be situated as far apart as we like. "They could be a hundred billion light years away as far as we're concerned." They are also separated such that Alice's experiment is done at space like separation from Bob's, so not even light could get from one to the other in time to influence it.
The claim, then: in such a case, whatever Alice does, or whatever happens in her lab, does not disturb Bob's particle or the physical state in Bob's lab. And vice versa.
Curt raises the objection a working physicist raises. Would Heisenberg not put up his hand and say that Einstein's antecedent, the "if you don't disturb the system" part, will never obtain, because of the uncertainty principle?
Maudlin's answer is a category correction, and it is one of the most useful thirty seconds in the video. He is not sure why anyone would bring up the uncertainty principle here, because we are talking about two different particles. Alice does something to one particle and Bob does something to an entirely different particle. The uncertainty principle does not even apply. It is a claim about predictions concerning a single particle: I cannot simultaneously predict its position and its momentum accurately, and the better I can predict one the worse I can predict the other. But that is a claim about individual particles.
What is at issue here is whether goings on in one lab disturb the physical state in a very, very distant lab.
It is true that when Heisenberg and Bohr talked about this, they always talked about how, if I do an experiment with an electron microscope or whatever, then when I probe the particle I disturb the particle. Fine. "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? That would be spooky action at a distance."
This is the tacit assumption. Because Alice and Bob can be separated as far as we like, EPR are justified in saying that anything Alice does, any outcome in her lab, does not disturb Bob's physical situation, and vice versa.
And here is the exit that is available, and the exact price of taking it. 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 are saying, I am down with spooky action at a distance.
"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 notice the logical shape of the denial. If you deny causal isolation, the EPR criterion of reality does not become wrong. It just does not apply, because the criterion requires that you make the prediction without disturbing the system you are predicting about. "It's not that you're saying the criterion is wrong. You're just saying the criterion doesn't apply, by signing on to spooky action at a distance."
Curt: then you should not deny it. If that were Heisenberg's position, he should have just said, I believe in spooky action at a distance, I accept it.
Maudlin: "But that's one thing he never did, and Bohr never did. They never just said, yes, we believe in spooky action at a distance."
Signaling is a red herring, and a dangerous one (1:45:57)
Curt raises the standard modern defense: we get around Einstein's objections because you cannot signal, you cannot send information.
"Look, nothing he said has anything to do with signaling."
Even in 1927, when Einstein worried about the sudden collapse of the wave function, the issue was not signaling. He did not think, oh gosh, you could use that to signal. "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."
Einstein's objections were never of the form: I think using quantum mechanics you could signal superluminally. If he had thought that, he would have said go do this experiment and see whether you can. That was never his worry. It is a straw man. Einstein does not require the ability to signal in order to say there is action at a distance.
Then Curt asks the deeper version of the question, and Maudlin says it is an excellent one. Forget Einstein the man. What about special relativity, the theory as such? Does special relativity allow superluminal non signaling while forbidding superluminal signaling?
Maudlin's answer is that his first book, Quantum Non-Locality and Relativity, is exactly on this question. Everybody, or almost everybody, thinks relativity prevents something from going faster than light. But what?
Does it prevent particles from going faster than light?
Does it prevent energy from going faster than light?
Does it prevent causation from going faster than light?
Does it prevent signals from going faster than light?
Or does it prevent nothing from going faster than light?
He has a chapter on each of those positions, and the answer is that there is no canonical answer here.
But this much is absolutely clear: Einstein did not think the issue was signaling. Because if he had, he would not have been worried about relativity in all these cases where there is no possibility of signaling. If the wave function collapse is a real physical process, and the spot forming here on the hemispherical screen changes the physical situation everywhere else, then for Einstein that is spooky action at a distance. And you cannot use it to signal, because you have no control over anything.
Maudlin then gives the definition of signaling, and it is worth having exactly, because it is what makes the no communication theorem so much weaker than people take it to be. To signal, the sender has to have something under their free control, and the receiver has to have something they can observe that will go differently depending on what the sender does. That is just the definition. And none of that is at play in the pinhole. "But man, action at a distance is an issue here. That just proves that Einstein didn't think of it in terms of signaling. 100 percent he didn't think of it that way. And you shouldn't."
Then the consequence, stated as sharply as he states anything in three hours: "Even if you can prove you can't signal faster than light in a theory, that doesn't prove the theory is relativistic. That's the mistake people make. And all these people doing quantum field theory and appealing to the equal time commutation relations, that's all the same mistake. They're saying, oh gee, we can't signal, therefore this is relativistic. Nope. Doesn't follow. Just doesn't follow."
The EPR state, written out and taken apart (1:48:45)
Now the mathematics, and Maudlin does it in full, one factor at a time.
In EPR they write down a state for the joint system of two particles. It is a capital psi, the state of the whole joint system, and it has an x1 and an x2 in it. Two variables, each three dimensional, so six dimensions total. x1 ranges over all of three dimensional space and so does x2. The wave function assigns its values to pairs of positions, one for x1 and one for x2. To configurations. That is why the wave function is defined on configuration space.
The state itself:
Ψ(x1, x2) = ∫ from -∞ to +∞ exp[ (2πi/h) (x1 - x2 + x0) p ] dp
Maudlin makes two housekeeping remarks. First, it is an integral over dp, over all possible momenta from negative infinity to positive infinity. Second, there is an x0 in the formula, which is confusing, because x0 is not a variable. x1 and x2 are variables and x0 is just a constant. "They shouldn't have used x. That was a bad idea." The constant plays no important role and he ignores it. This is also where the genuine technical problems with the mathematics live, and they make no difference in the end.
Now the anatomy. For those who know a little calculus, integrating means adding up all these contributions, a different contribution for each value of p. So what is being added? Dropping the constant, each piece has the form:
exp[ (2πi/h) (x1 - x2) p ]
And if you remember how exponents work, that can more usefully be written as a product:
exp[ (2πi/h) x1 p ] × exp[ (2πi/h) x2 (-p) ]
One factor depends only on x1, the other only on x2. So it is what is called a product state: you can separate the x1 part from the x2 part cleanly. And each of those pieces is a momentum state. The first is what you would use to represent a particle that definitely has momentum p. The second represents a particle that definitely has momentum minus p.
So each individual piece represents a situation where particle one is in an eigenstate with momentum exactly p, and particle two is in an eigenstate with momentum exactly minus p. Which means the total momentum of the pair is zero, because p plus minus p is zero. Each piece is an eigenstate of total momentum zero.
But the EPR state is not that state. The EPR state is what you get when you integrate over all possible values of p. It is a superposition of all these different states, every one of which has total momentum zero.
So the joint state has zero total momentum, and it is built only out of states like that. The EPR state is an eigenstate of total momentum zero.
However, because of the integration, the EPR state is not an eigenstate for either particle one or particle two separately. In the EPR state, particle one has no particular momentum. No definite momentum at all. Particle two has no definite momentum at all. Neither is in an eigenstate. Nonetheless the joint system of one and two definitely has zero momentum.
Figure 5. The EPR state, taken apart the way Maudlin takes it apart. Each piece of the integral factorizes into two sharp momentum states with opposite momenta, so every piece carries total momentum zero, and therefore so does the superposition. But the superposition is not an eigenstate of either particle's own momentum. On the Copenhagen rule that a system has a quantity only when it is in the corresponding eigenstate, this means neither particle has any momentum, while the pair definitely has one, and the pair is spread across two arbitrarily distant laboratories.
Pause for reflection: what Copenhagen has to say about that state
Maudlin stops here deliberately, because he wants the strangeness on the table before the argument runs.
He has been giving the Copenhagen story. And the Copenhagen story is that systems only have physical features when they are in the appropriate eigenstates of the associated operators. In the Copenhagen view the only systems that have momenta at all are ones in eigenstates. If you are not in an eigenstate of momentum, you simply do not have a momentum. If you are not in an eigenstate of position, you simply do not have a position.
We saw that the reality criterion demands the other direction: if you are in an eigenstate, so that you can predict the outcome of a momentum measurement, then yes, there is an element of physical reality, you have a momentum. But Copenhagen goes further. It says not merely that those particles have momenta, but that only those particles do.
And therefore, according to Copenhagen, neither particle in the EPR state has a momentum.
"And that, I say, is a curious state of affairs." If you are Bohr, you have to say: particle one has no momentum, particle two has no momentum, and yet the joint system of particle one and particle two, taken together, does have a definite momentum, namely zero.
Furthermore you can verify that claim empirically. Have Alice and Bob both do momentum measurements. What you find is that even though you cannot predict what Alice will get, and you cannot 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. Add them and you get zero. That is a genuine prediction of quantum mechanics.
So here is a large system, and not just large but spatially separated, particle one way over here and particle two way over there, whose joint state is not determined, according to Copenhagen, by the individual states of its parts. That is a strange situation.
And we accept the prediction. If both Alice and Bob make momentum measurements, knowing the EPR state initially, we cannot predict what either one will get, but we can predict they will get opposite results.
Then Maudlin says the thing that reorganizes the whole 1935 paper: "What we've now noticed, and this is not controversial, is enough to reach the EPR conclusion. We've done enough." And notice, he says, that he has not mentioned position at all. He is just talking about momentum.
The logical core, streamlined (1:56:45)
Here is the argument, in the form Maudlin thinks EPR should have given it. He is explicit that it is not the way they run it, but that it follows from their own principles, and he says outright that he thinks they should have.
We create a pair of particles in the EPR state. We send them off, one to Alice, one to Bob. Both of them are going to make momentum measurements, and they are going to carry out their experiments very far apart, at space like separation, so that not even light could get from one to the other. Both of them know the particles were prepared in the EPR state. That is fine, we can tell them beforehand.
Question: can Alice, without in any way disturbing Bob's particle, accurately predict the outcome of a momentum measurement on his particle?
Assume the accuracy of quantum theory. Then certainly Alice can get herself into a position where she can accurately predict the outcome of Bob's measurement, by measuring her own particle. Whatever number she gets for momentum, she says Bob is going to get minus that, because the total momentum is zero. So she certainly can get into a position to predict his outcome.
The question is whether, in doing that, she disturbed Bob's particle. Remember, all she did was measure the momentum of her own particle.
"Now it's here where the locality assumption of EPR comes in." Tacitly, they think of course she didn't. She is way over there, he is way over there, nothing she did changed his state. What she did put her in a position to make that prediction, but it did not disturb his state. And that is the fundamental tacit locality assumption of the EPR argument: it seems so obvious to them that they do not even mention it explicitly. What Alice does in her lab cannot disturb Bob's physical situation. That would be spooky action at a distance.
If we accept that, then Alice is able to predict the outcome of Bob's experiment without disturbing his particle. So by the reality criterion there must be an element of physical reality in his particle that determines what the outcome will be.
"But now we're done."
Why? Because the EPR state does not tell you what that value is. It does not represent it. So it omits it. Therefore the EPR state is not complete. There must be more to the world than is given by that wave function.
Figure 6. The argument as Maudlin says it should have been written: three premises, four steps, momentum only, no mention of position anywhere. Premise two he argues is analytic, so it cannot be denied. Premise one nobody disputes, least of all EPR, who explicitly grant the theory's correctness. That leaves premise three as the only place to push, and pushing there is exactly the same as accepting spooky action at a distance. The fork at the bottom is exhaustive, which is what makes Bohr's refusal to take either branch so hard to interpret.
Maudlin then makes the Copenhagen picture even more vivid, because on that view something stranger still is happening. When the two particles are sent out, neither has a momentum. Alice measures and gets some momentum for her particle. She can now predict Bob's. And furthermore, because she did that, she collapsed the wave function, and Bob's particle went from having no momentum at all to having a momentum. 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: assume Alice's experiment does not disturb the physical state of Bob's particle, and you get their conclusion. The quantum description is incomplete. "Notice I never mentioned position from beginning to end. I was just working with momentum. Argument over."
Tally the ingredients: the reality criterion, the assumption of no spooky action at a distance, and the accuracy of the quantum mechanical predictions. That is all we used. Out comes the incompleteness of the quantum description.
And since the reality criterion is analytic and cannot be denied, you have exactly two options. Accept that the quantum description is incomplete, or accept that Alice's operations in her lab do disturb the physical state of Bob's particle, which is spooky action at a distance. Einstein thought that between those two it is obvious. Spooky action at a distance is crazy. Just deny that quantum mechanics is complete.
Why EPR ran it the long way, with position too (2:04:40)
That is not what EPR do. What they do is exactly that, and then they repeat the whole thing for position.
If Alice, instead of measuring 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. And the very same argument that proves Bob's particle already had a momentum can be used to prove it already had a position. Therefore, in reality, Bob's particle has both a momentum and a position.
And that makes it much worse for Copenhagen. Because there is no quantum state that ascribes a definite position and a definite momentum at the same time to a particle. No such wave function exists. No wave function is simultaneously an eigenstate of the position operator and an eigenstate of the momentum operator. That is mathematically impossible. So if you think the wave function is complete, and you think the condition for having a property is being in an eigenstate, you cannot accept that there are particles with positions and momenta at the same time.
Maudlin then admits a genuine gap and fills it with an honest hand wave. The momentum correlation is easy to see: total momentum is zero. Why the EPR state should also give perfectly correlated position measurements, so that each party can predict the other's position result, is not obvious at all from looking at the state. It is true, but it is not obvious. And it is technically awkward, because there are no genuine position eigenstates. They are really delta functions, which are not functions but distributions, and things get complicated. He is not going into any of that. It does not really matter.
But here is an intuitive argument, and he flags that he does not know how accurate it even is. Suppose the particles were shot out toward Alice and Bob at some pre established moment from a central source, and Alice and Bob are equally far away. If they measured their positions at the same time and found very different distances from the source, they would infer that they had different momenta, and therefore that the total momentum was not zero. Why? Because the way you actually measure momentum is by measuring position at a time, knowing when the particle was released, taking distance over time to get a velocity, and multiplying by mass. So if the position measurements were completely uncorrelated, you would also have to say the momenta cannot be as correlated as we claim they are. On that reasoning it is maybe not so surprising that there is a perfect correlation between simultaneous position measurements.
The paper's own conclusion, and the objection it pre empts
Here is how EPR close.
"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 what they think they have now shown is that even though the momentum and position operators do not commute, momentum and position do have 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 simultaneous reality. 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."
And again, tacitly, they are using the no action at a distance principle to say that what one experimenter does does not disturb the other.
Then EPR anticipate the objection, and reject it. "One could object to this conclusion on the grounds that our criterion of reality is not sufficiently restrictive. Indeed, one would not arrive at our conclusion if one insisted that two or more physical quantities can be regarded as simultaneous elements of reality only when they can be simultaneously measured or predicted. On this point of view, since either one or the other, but not both simultaneously, of the quantities P and Q can be predicted, they are not simultaneously real. This makes the reality of P and Q depend upon the process of measurement carried out on the first system, which does not disturb the second system in any way. No reasonable definition of reality could be expected to permit this."
Maudlin reads out the structure of that rejection. Their point is that what is real in Bob's lab would depend on what Alice does, while granting that what Alice does does not disturb the second system in any way. So they reject that move outright. It is not the right way to think about things. It is not a matter of prediction, not a matter of what you can predict. It is a matter of what is 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, that's no spooky action at a distance."
Maudlin's own verdict on the position half: "As I say, you could get there quicker and easier just focusing on momentum. But okay, they did it their way."
Determinism is inferred, not assumed (2:14:00)
Now the correction that Maudlin says is the hardest one to get across, and the one he flags in advance as mattering for what comes later.
Two complaints are usually attributed to Einstein: no spooky action at a distance, and God does not play dice. We have seen exactly where the no action at a distance demand enters the EPR argument, and it is central. By appealing to no action at a distance you argue there is no disturbance, and by arguing there is no disturbance you argue there is an element of reality.
What about determinism? Is it tacitly assumed somewhere in the argument?
"The answer is no. And it's really important that the answer is no."
"It is important to note that to the limited degree to which determinism plays a role in the EPR argument, it is not assumed but inferred. What is held sacred is the principle of local causality, no action at a distance. Of course, mere correlation between distant events does not imply action at a distance, but only correlation between the signals reaching the two places. The signals must be sufficient to determine whether the particles go up or down, for any residual undeterminism could only spoil the perfect correlation."
Then the part Maudlin calls the important point, still Bell: "It is remarkably difficult to get this point across, that determinism is not a presupposition of the analysis. There is a widespread and erroneous conviction that for Einstein determinism was always a sacred principle. The quotability of his famous God does not play dice has not helped in this respect."
And then Bell on the historical casualty: among those who had great difficulty seeing Einstein's position was Bohr. Pauli tried to help him out, in a letter of 1954. Maudlin reads Pauli's letter, and it is the funniest and most damning document in the lecture:
"I was unable to recognize Einstein whenever you talked about him, either in your letter or your manuscript. It seemed to me as if you had erected some dummy Einstein for yourself, which you then knocked down with great pomp. 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 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."
Maudlin: "And you can imagine he was annoyed, and he probably was annoyed." Einstein has been trying for years to say what his objection is, and people keep attributing to him positions he does not hold.
Curt checks his understanding: Einstein does not start with determinism, he ends with it as a conclusion, not as an ingredient in the input. Maudlin corrects the framing slightly, which is worth having exactly right. In the EPR argument as given, determinism is not among the premises. 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. You do not go into the game assuming determinism.
Bell's summing up of Born's confusion is next, and it is where Maudlin points to what he calls a classic line. Born, long afterwards, editing the Einstein Born correspondence, wrote: "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 at B cannot teach us anything about the state of affairs at A."
Bell's response: "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 at the other."
Why the correlations have to be perfect, and why that is a detail
The EPR argument runs logically on the existence of perfect correlations between the outcome in Alice's lab and the outcome in Bob's, and Maudlin proposes to call such perfect correlations EPR correlations, since they are the correlations that show up in that paper.
Given the definitions in the paper, they have to be perfect for two reasons.
First, the criterion of reality requires Alice to be able to "predict with certainty, that is with probability equal to unity" the outcome of Bob's experiment, together with the condition that she in no way disturbed the physical state in his lab. So the criterion, narrow as it is, requires perfect predictability, and perfect predictability requires perfect correlation. Given the outcome in Alice's lab there is exactly one outcome that could occur in Bob's. Which is true here, because of the total momentum being zero.
Second, and this is the one that produces determinism: because the correlations are perfect, a local theory must be deterministic. The state of the particles entering the labs must absolutely determine what the outcomes will be. Because if it did not, how could you be sure the two outcomes always come out opposite?
But the logic of the argument does not actually need perfection, and Maudlin will spend the next stretch showing that. Loosen perfect correlations to almost perfect, or merely strong, correlations, and the basic logic does not change. Einstein would still say: something is wrong here, if you think the wave function is complete.
Trivial correlations: the torn dollar bill and Bertlmann's socks (2:16:54)
Before the loosening, the point that must be nailed down: when you have these perfect correlations, there is nothing weird about the correlations. Nothing at all. They are everyday. They happen all the time. This is exactly why, when Born said Einstein could not accept that finding out something in one location tells you something about another location, the answer is that of course Einstein accepts that.
Everybody uses the same two examples. Maudlin uses both.
Take a dollar bill and tear it in half. Shuffle the halves behind your back, put them in two envelopes, send one envelope to Alice and one to Bob. That is the preparation procedure, and Alice and Bob both know it. They obviously have no idea which half is in their envelope. But when Alice opens hers and sees the right half, she immediately knows Bob will see the left half when he opens his. She can now perfectly predict what he is going to see. And in doing so she does not disturb the state of Bob's envelope at all.
Bell's version is Reinhold Bertlmann, and this is true: Bertlmann always wore socks of mismatching colors. You could never predict on a given day what color sock he would have on any foot. But as soon as you saw that his right sock was pink, you could immediately infer, by standard Bayesian conditionalization, that the other sock is not pink. Another trivial example of a perfect anticorrelation. And obviously seeing one sock does not affect the other.
Curt asks a good small question: why did Bell need Bertlmann's socks rather than regular socks? Was it to get an anticorrelation? No. Maudlin thinks it is because Bertlmann was a funny guy and a friend of his. You could make the same point by saying every day Bertlmann puts on differently colored socks and you are never sure whether they will both be red or both be green. It would make the same point. He thinks the conference may even have been a tribute to Bertlmann, and notes that Bell drew a beautiful little sketch of Bertlmann in the paper, in his own hand. "I think he was just being friendly."
So what do these trivial examples show? Nothing much of interest. They certainly show that perfect correlations between distant systems are unremarkable, contrary to what Born said Einstein could not accept. There is nothing wrong with them. They do not suggest in any way that there is spooky action at a distance. Just that there are correlations between distant systems.
It is also trivial that the criterion of reality works in these cases. See one sock, predict the other. See one half of the dollar bill, predict the other. Without in any way disturbing it. And what follows is that there is an element of reality that determines the outcome: which half was actually in Bob's envelope all along, or which color Bertlmann's sock had all along. If you thought you had a complete physical description of the world and it did not mention the colors of Bertlmann's socks, you are just saying it is not a complete description. You left something out.
Maudlin then draws the structural moral, and it is the hinge of the whole treatment. In these trivial examples the preparation procedure is describable but incomplete. When you put the halves of the dollar bill in the envelopes, one half goes in one and one goes in the other, and the preparation procedure does not tell you which. When Bertlmann gets up, all you said is that he puts on differently colored socks, not which color goes on which foot. Those are incomplete descriptions. And it is precisely because they are incomplete that you can update on new information, because you started without complete information.
If you thought the wave function was complete, then knowing the wave function means having complete information, and you cannot update on anything, because there is nothing to update on. In the trivial cases, the correlations are already fixed at the source in an everyday way.
What does paradox mean? Usually a paradox is an argument whose conclusion is contrary to common opinion, in Greek the doxa, the opinions of everyday folk. Or at least contrary to reasonable expectation. It is only paradoxical if the conclusion is surprising.
But the existence of these correlations, between what Alice sees and what Bob sees, is not paradoxical. And the actual conclusion of the paper is that the wave function is incomplete. Which does not violate any widely held opinion or any common sense. Most people have no views on it. It is not as if everybody was walking around thinking quantum mechanics was complete and had their world shattered. So calling it a paradox is very strange.
"What it actually rejects is Bohr's Copenhagen school dogma. The dogma that the wave function is complete, that that's the end of physics, that there's nothing more to say. So it helps to call it a paradox, because it sort of suggests that there's something paradoxical about it. What's paradoxical is actually the Copenhagen view."
And then he reads the passage from Bertlmann's Socks that he plainly loves, and calls just beautiful:
"It is in the context of discussions like these that one must envision the discussions of the Einstein Podolsky Rosen correlations. Then it is a little less unintelligible that the EPR paper caused such a fuss, and that the dust is not settled even now. It is as if we had come to deny the reality of Bertlmann's socks, or at least of their colors, when not looked at. And as if a child had asked: how come they always choose different colors when they are looked at? How does the second sock know what the first has done?"
Maudlin's gloss: there is nothing paradoxical about Bertlmann wearing differently colored socks. There is something really paradoxical about saying that before you looked at them the socks did not have any colors, and that your looking at them brought the colors into existence. That is weird in itself. But it is weirder still if 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 has done?
Bell: "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. For them these correlations simply showed that the quantum theorists had been hasty in dismissing the reality of the microscopic world. In particular Jordan had been wrong in supposing that nothing was real or fixed in that world before observation. For after observing only one particle the result of subsequently observing the other, possibly at a very remote place, is immediately predictable. Could it be that the first observation somehow fixes what was unfixed, or makes real what was unreal, not only for the near particle but also for the remote one?"
That is the spooky action at a distance sitting inside the view that observation creates reality, which, Maudlin notes, is what you hear about quantum theory all the time.
Bell's finish: "For EPR that would be an unthinkable spooky action at a distance. To avoid such action at a distance they have to attribute, to the space time regions in question, real properties in advance of observation, correlated properties which predetermine the outcomes of these particular observations. Since these real properties, fixed in advance of observation, are not contained in quantum formalism, that formalism for EPR is incomplete. 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 notice where determinism enters. It enters because if the correlations are to be perfect, then the previous states of the objects have to determine the outcomes. If there were any chanciness there, the two distant objects could not track each other in what they do.
The conservation law gambit (2:26:30)
Now a comment Maudlin says people often make, and which he names in order to kill.
The gambit: look, we have this correlation between the momentum measurements Alice and Bob make, and there is an easy explanation. Conservation of momentum. 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 gets the opposite. What is so puzzling about that?
"And that just misses the point." Here is why, and it is exact.
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 the local momenta, and what the global momentum is at all times is just the sum of all the local momenta of the particles.
But here, if the wave function is complete, neither particle has a momentum. So you cannot think the total momentum is the sum of theirs. They do not have momenta. That does not happen in classical physics.
And if they do not have pre measurement momenta, then you have two puzzles rather than none. First, how does any outcome arise on either side at all? It somehow has to be brought into existence. It is not discovered, it is brought into being. Second, and worse, the exactly opposite momentum has to suddenly be brought into existence on the other side, a hundred million miles away.
"That's spooky action at a distance."
So invoking conservation of momentum does not dissolve the problem. It renames it. Conservation of a global quantity that is not the sum of local quantities is precisely the thing that needs explaining.
Relaxing perfection: the Shannon information version (2:32:30)
The arguments so far run on perfect EPR correlations. Maudlin now shows they do not have to, and the reformulation is arguably the most valuable thing he adds to EPR, because it is what makes the argument robust against the obvious experimental complaint.
You could demand, instead of perfect prediction, prediction with say ninety five percent accuracy, and make an equally plausible argument. The perfection of the correlations is not the logical backbone. Perfection is assumed in exactly two places: where you say you have to be able to predict with certainty, and where you conclude that a local theory must be deterministic, since otherwise you could not guarantee opposite results every time.
Someone will say the perfect case is very idealized and in real life you never get perfect correlations. Fine. Reduce it to imperfect correlations in a simple way and draw exactly the same conclusion. Because what is really going on is this 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? Can I say with more accuracy what it might do?
If I can, and I have not disturbed the system, then I did not know something initially about the system, and I have learned something that must have already been there.
You relax the reality criterion a bit and the argument goes through. The key to the criterion is that whatever you do to improve your predictions must not disturb the system you are predicting about, and the assumption is that because Alice and Bob are so separated, nothing either does disturbs the other's physical state. It is the distance and the timing, because the experiments can be done at space like separation, so not even light could carry a signal from one lab to the other about what was being done and what came out. That is Einstein's worry about relativity.
So restate it in terms that did not exist at the time, in terms of Shannon information. The real question becomes: does what Alice does and sees give her Shannon information about Bob's system? Which is really just asking whether it lets her improve her predictions about Bob's system. If she can do that without disturbing his system, then her initial representation of his system must have been incomplete. It could be improved.
She has learned something about his system. If she learned something about his system, then there was stuff about his system she did not know. But she knew its wave function. She knew its quantum state. So the quantum state has to be incomplete.
And notice the bonus, which Maudlin flags carefully. Because we do not require perfect prediction here, we also do not infer determinism. This was exactly Bell's point that EPR do not assume determinism, they infer it, and for that inference they needed perfect correlations. Weaken to imperfect correlations and you still get the incompleteness of the wave function, but you are no longer able to infer that the underlying dynamics has to be deterministic. Determinism was only ever there to recover perfect correlations.
The key to the whole argument, then, is that the spatial separation between Alice's lab and Bob's lab effects a causal isolation between what happens in those two labs during their experiments. Deny that, and you are signing on to spooky action at a distance in Einstein's sense. And none of it suggests that you can signal from one lab to the other, or requires that any signaling protocol exist. It is just the fact that you can improve your state of knowledge without disturbing the system. If you want to deny that, you are saying you are disturbing the system, and that is spooky action at a distance, whether or not the disturbance lets you signal.
Local and indeterministic: a theory that is both (2:35:24)
To prove that locality is not secretly determinism, Maudlin sketches what a local indeterministic theory looks like.
When Alice does her experiment there is some chance, say ninety percent, that it turns out this way and ten percent that it turns out the other way, and those are fundamental chances. Same for Bob. But they are local, because which way Alice's turns out has no influence on Bob's and does not let you predict better what will happen to Bob's. And which way Bob's turns out does not improve your predictions about Alice's. That means the statistical spreads between the two systems are statistically independent of each other. Neither gives information about the other.
That is a local indeterministic theory, and it exists as a coherent option. Which proves that the locality assumption is not per se an assumption of determinism. It only lets you infer determinism if you have perfect correlations.
To sum the section: the EPR argument, from no action at a distance and perfect correlations to the incompleteness of the quantum mechanical description, is valid. It is sound and it is simple. And the same argumentative structure works given no action at a distance and less than perfect correlations: if Alice's predictions for Bob can merely be improved by her observations, and the physics is local, then the initial description she had must have been incomplete. That version yields the conclusion EPR wanted without entailing determinism, which only follows with perfect correlations.
Counterfactual definiteness is just determinism in costume (2:37:40)
One thing that comes up a lot in discussions of Bell's theorem and EPR is a condition called counterfactual definiteness, sometimes CFD. People claim it is a fundamental assumption of EPR, or a fundamental assumption of Bell.
What does it mean? A theory supports counterfactual definiteness if the theory lets you 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. Counterfactual is short for contrary to fact conditional. A conditional is an if then, and it is contrary to fact if the if part is not what actually happened, but what could have happened. If I had dropped the bowl, it would have broken.
Curt supplies an alternative example, "if you did not step on the computer it wouldn't have broken," flags it as an inside joke, and Maudlin, deadpan: "Yeah, that one's true too."
We use counterfactual conditionals all the time in everyday life and we take them to have definite truth values. When you say you could have saved that person if only you had gotten up and thrown them the rope, that is a counterfactual conditional. It is saying that if reality had been different in this way, it would have been different in that way. Very common things.
And it is sometimes asserted that there is a tacit assumption in the EPR argument, or in Bell's argument, 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 they can get out of these arguments by denying counterfactual definiteness. Neither argument assumes it.
Because, in fact, counterfactual definiteness is just the same as determinism.
I can tell you what would have happened had things been different if I use a deterministic theory, because then, if I fill in the details enough, the theory tells me what would have happened. If the theory is not deterministic, if it is merely probabilistic, the theory will not tell me what would have happened. It will only tell me what might have happened.
Curt catches the distinction and says it is super interesting: what could have happened is different from what might have happened. Maudlin corrects him gently to the right pair: what would have happened is different from what might have happened.
The demonstration is clean. Suppose I have a deterministic theory and I ask what would have happened if I had dropped the bowl. According to the theory it would have fallen to the ground and broken. Yes, that would have happened. Now suppose I have an indeterministic theory, coins with irreducible chances, ninety percent heads and ten percent tails. I do not flip the coin. What would have happened if I had? The right thing to say is that I cannot tell you exactly what would have happened. It might have come up tails and it might have come up heads. There is no definite fact, if the fundamental dynamics is indeterministic, about what would have happened had things been different. Usually there is a range of ways it might have played out, because the indeterminism allows for different outcomes.
So the assumption of counterfactual definiteness is the assumption of determinism. And what Maudlin has argued, and what Bell argued over and over, is that EPR do not assume determinism. They infer it. So they do not assume counterfactual definiteness either. 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 denying determinism. Because it never runs on determinism. It runs on no action at a distance. It runs on no spooky action at a distance."
Curt notices the verbiage and asks a good pedantic question: you said no action at a distance, then you said no spooky action at a distance. To Einstein, isn't all action at a distance spooky?
"The spooky is just rhetorical. It's not as if Einstein would have said, oh, there's good action at a distance and there's spooky action at a distance, and I'm okay with good action. No, spooky is just his way of saying he thinks action at a distance is not something he's willing to accept in a physical theory."
Maudlin's closing verdict on the terminology: when people bring up counterfactual definiteness, they are using unfamiliar terminology to talk about determinism in a roundabout way. And what they say, that the arguments presume counterfactual definiteness, is a roundabout way of saying they presume determinism. And it is false. Neither argument presumes determinism. "It's just a distraction."
Bohr's reply, and the two pages nobody noticed (2:44:00)
Now the reckoning. The EPR argument runs from causal locality to the incompleteness of the quantum mechanical description, and that argument is valid.
In response, Maudlin says, Bohr and company had only two logically pertinent responses. There were only two things they could do.
Embrace the action at a distance as a real, novel, unexpected physical discovery.
Concede that the quantum mechanical formalism they use does not supply a complete physical description of a system.
"Those are the only options. And for sure they didn't embrace that there was action at a distance. And they also didn't say that the quantum mechanical description is incomplete. So of the two logically possible responses, they took neither."
Which is why, Maudlin says, it is very hard to understand what it is they were claiming. And in particular, Bohr writes a response immediately after the EPR paper comes out in 1935, published in the same journal, Physical Review. "And it's an incoherent mess. Nobody understands that paper."
Then, prefaced with "I've wasted so much time, but I'll tell you a little story," comes the anecdote that lands harder than any argument.
When Maudlin learned this material, everybody of his age got a big red book called Quantum Theory and Measurement, edited by Wheeler and Zurek. It contained reproductions of all the foundational papers, not retypeset, just copied and thrown into this big fat book. It contained the EPR paper, and of course it contained Bohr's response, and everybody read that.
Many years later, after Maudlin had read it and worked with it, he was talking to Sheldon Goldstein, and Shelly said: by the way, did you ever notice that in that book two pages of Bohr's response have been switched? They are out of order.
Maudlin had not noticed. He talked to other people. Nobody had noticed.
"And if you try to read it, you turn the page and the sentence isn't even grammatical."
Why did nobody 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. It's just Bohr producing words that you can't follow."
He adds that Bell himself talks about not being able to understand Bohr, in appendix one to Bertlmann's Socks, where Bell tries to parse what Bohr is saying and gives up. He says he cannot make any sense out of it. And Bohr himself said he was never satisfied with his own response, and was still working on it when Einstein died.
What Bohr actually said, and why it misses
Maudlin also documents the reception, because the reception is evidence about the argument's force.
Einstein had been complaining since 1927 about these very same things. You might think 1935 would land the same way, that people would say there is Einstein again with the same old complaints. That is not at all what happened. Switching from the single particle case to the two particle case, where you can send one to Alice and one to Bob, completely changed the rhetorical force of the argument.
Léon Rosenfeld, Bohr's associate, later reported: "This onslaught came upon us as a bolt from the blue. Its 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, Bohr immediately started dictating to me the outline of such a reply. Very soon, however, he became hesitant. No, this 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."
Maudlin's reading of that passage: whatever Bohr thought he had as an answer, when he himself tried to articulate it, he could not.
Bohr later wrote: "Due to the lucidity and apparently incontestable character of the argument, the paper of Einstein, Podolsky 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."
Maudlin flags the last phrase. Bohr loved the word visualization, Anschaulichkeit in German, probably because it is a word Kant used a lot, and Kant was very worried about it, and about space as the form of outer intuition.
But the EPR argument has absolutely nothing to do with visualization. "They don't ask you to visualize anything. All they ask you to accept is that what Alice does in her lab doesn't disturb Bob's particle, and what Bob does in his lab doesn't disturb Alice's particle. You don't have to visualize a thing."
So the appeal to visualization is Bohr falling back on a set of ideas that had been bouncing around in his head forever, and not responding to the argument.
Worse, the published reply recycles material about single particles and measuring position and momentum on single particles, which is not to the point, because you have two particles. "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 Bohr writes in that paper is not to the point.
Schrödinger's confession, and the birth of entanglement (2:52:00)
Schrödinger's response, on the other hand, Maudlin calls really interesting.
In 1935 Schrödinger writes a paper, The Present Situation in Quantum Mechanics, which everybody knows as the cat paper. That paper is written because of EPR. In footnote seven he cites Einstein, Podolsky and Rosen and says: "The appearance of this work motivated the present, shall I say, lecture or general confession."
Maudlin savors it. Schrödinger is responding to EPR and he is not saying I am going to lecture you. He is saying I am going to confess something. He appreciated the argument, and he appreciated the role that entanglement plays in the argument, which Maudlin thinks even Einstein did not really appreciate.
And in that paper Schrödinger introduces the term Verschränkung, which we translate as entanglement.
"So everything to do with entanglement starts with EPR. The importance of it, the physical significance of it, all of that comes out of that paper."
"Okay, so we got to the end of act two."
Where act three goes: the ironic reversal
The lecture closes on what it was supposedly always about, which has not happened yet. Maudlin: "You can't understand Bell. You cannot understand Bell without understanding EPR."
Curt sets up the handoff deliberately, telling the audience that since acts one and two are their own video, they should write their questions in the comments and Tim can pick them up in act three.
Then Maudlin states the destination. Bell's paper is called On the Einstein Podolsky Rosen Paradox. His starting point is that you have read and understood the EPR paper. Unfortunately most people have not read it, and many who have read it have not understood it. So if you want to understand Bell you have to start by understanding EPR.
And where it ends up is seeing how Bell begins where Einstein left off, and then ironically runs an argument to the conclusion that Einstein was wrong about spooky action at a distance. That you cannot get away from it. That you need it. That no local theory, in Einstein's sense, can work, can make the right predictions.
"So 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."
Which is exactly why the groundwork matters. If you want to reject Bell's conclusion, you have to reject something. And people unfortunately think they can get out of Bell's conclusion by saying they just do not believe in determinism, or something like that. "But that's no good, because it was never an assumption."
Key takeaways
Einstein started quantum theory, not Planck. Planck stopped a limit short because it gave him the black body answer he wanted. It is not clear he thought he was quantizing anything or had any physical hypothesis at all. Einstein's 1905 photoelectric paper proposed the quantization of a classical quantity, with E equals h nu.
What is quantized is not energy. A photon can have any energy you like, you just pick the frequency. What is discrete is that at a fixed frequency the energy arrives in packets whose size that frequency fixes.
The Jekyll and Hyde version of wave particle duality is not anybody's view. Nothing switches from wave mode to particle mode. The interference degrades continuously as you change the physical situation, which by itself kills the switch picture. Schrödinger evolution is always wave evolution.
Einstein's real objection was lodged in 1927, not 1935, and it used one particle. A pinhole, a hemispherical film, and the question of why a single spreading wave never produces two spots. Suppressing the rest of the wave the instant one spot forms is a global instantaneous physical change, and that is what he called action at a distance.
Determinism was never his complaint. In the 1927 record he does not object to indeterminism. He objects to instantaneous collapse. Pauli had to write to Bohr in 1954 to tell him he had erected a dummy Einstein and knocked it down with great pomp.
Collapse cannot be demoted to Bayesian updating while completeness is maintained. Updating requires something you did not know. Completeness means there is nothing you do not know. Pick one.
Locality comes in two flavors and Einstein wanted both. Ontological locality: the whole state is nothing over and above the states of small overlapping regions. Dynamical locality: no instantaneous influence at a distance. Classical field theory has both, and local differential equations mean you can check whether the laws hold by looking only at a small region.
Configuration space was never the problem. The direction of travel is. Classical mechanics recodes physical space laws onto a high dimensional space for convenience. Conception two starts with the high dimensional object and cannot say what it represents, and there is no guarantee of getting back down to something dynamically local.
The criterion of reality is analytic. If you can predict an outcome with certainty without disturbing a system, then it had the property before you predicted, because not disturbing it means not changing it. You cannot escape EPR by denying the criterion.
The EPR argument only needs momentum. Maudlin runs it in four steps with no mention of position. The position half of the 1935 paper adds rhetorical force against Copenhagen, since no wave function is simultaneously an eigenstate of position and momentum, but it is not needed for the conclusion.
The load bearing premise is the one EPR never wrote down: that spatial and space like separation gives you causal isolation, so nothing Alice does disturbs Bob's physical state. Denying it does not refute the criterion of reality, it just makes the criterion inapplicable, at the price of endorsing spooky action at a distance.
Signaling is a red herring, and a dangerous one. Proving no superluminal signaling does not prove a theory is relativistic. Einstein's 1927 objection involved no possibility of signaling whatsoever, since nobody controls where a spot forms.
Conservation of momentum does not explain the correlation. In classical physics global momentum is the sum of local momenta. If the wave function is complete, neither particle has a momentum, so the global conservation law does not follow from a local one, and both outcomes have to be brought into existence rather than discovered.
Perfection is a convenience, not the backbone. Recast the criterion in terms of Shannon information: if Alice can merely improve her predictions about Bob without disturbing him, her description was incomplete. That gets incompleteness without perfect correlations, and without inferring determinism.
Counterfactual definiteness is determinism in unfamiliar clothing, so denying it defeats neither EPR nor Bell. What would have happened is a deterministic notion. What might have happened is what an indeterministic theory gives you.
Bohr had exactly two available replies and took neither. His published response is, on Maudlin's reading, incoherent, and the proof is that two of its pages were printed out of order in the standard anthology and a generation of physicists did not notice. Bohr said he was never satisfied with it and was still working on it when Einstein died.
Schrödinger is the one who understood. The cat paper was written because of EPR, calls itself a general confession, and coins the word entanglement. Everything about entanglement starts there.
Chapters
0:00:00 Einstein's Quantization Hypothesis
0:07:20 Photoelectric Effect Implications
0:12:30 Wave-Particle Duality Myths
0:20:40 De Broglie's Matter Waves
0:26:40 Copenhagen's Completeness Doctrine
0:34:10 Solvay 1927: Two Conceptions
0:41:20 Pinhole Diffraction Problem
0:48:00 Collapse and Relativity Violations
0:56:00 Epistemic vs. Ontic Collapse
1:05:00 Ontological vs. Dynamical Locality
1:14:00 Configuration Space Objections
1:25:00 EPR's Criterion of Reality
1:32:40 Analyzing the Reality Criterion
1:40:50 Causal Isolation and Locality
1:48:45 Entangled Momentum Eigenstates
1:56:45 Logical Core of EPR
2:04:40 Position-Momentum Simultaneous Reality
2:14:00 Inferring Determinism from Locality
2:26:30 Conservation Laws and Information
2:37:40 Counterfactual Definiteness Debunked
2:44:00 Bohr's Incoherent Response
2:52:00 Schrödinger's Entanglement Confession
Notable quotes
"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."
Tim Maudlin, 0:02:13, on why the lecture exists
"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."
Tim Maudlin on Planck in 1900, 0:04:39
"So I'll even dunk a little 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."
Tim Maudlin, 0:15:34
"It didn't occur to them, he says, the obvious solution. Maybe there's both a wave and a particle."
Tim Maudlin on Bell's puzzlement at the whole duality debate, 0:19:20
"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."
Tim Maudlin's paraphrase of Bohr, 0:27:00
"That peculiar mechanism of action at a distance is what we call collapse of the wave function."
Tim Maudlin, reading Einstein's 1927 Solvay objection, 0:45:36
"But notice, the deep problems were about spooky action at a distance, not particularly about determinism."
Tim Maudlin on Einstein in 1927, 0:50:10
"It is the nature of conception two that precludes thinking of collapse merely epistemically."
Tim Maudlin, 0:54:50
"The problem in quantum mechanics is that you're starting with a high dimensional abstract thing, but you're not sure what it's an abstract representation of."
Tim Maudlin on configuration space, 1:19:23
"Every element of the physical reality must have a counterpart in the physical theory. We shall call this the condition of completeness."
Einstein, Podolsky and Rosen, 1935, read at 1:30:01
"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."
The criterion of reality, read at 1:32:09
"If it didn't have the property before, but it did have the property after, then I disturbed it. This is just analytic. So I just don't see how one can question this criterion."
Tim Maudlin, 1:37:46
"We're not talking about whether Alice's actions disturb Alice's particle. It's: do Alice's actions disturb Bob's particle way over there? That would be spooky action at a distance."
Tim Maudlin, 1:42:18
"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."
Tim Maudlin, 1:45:57
"Even if you can prove you can't signal faster than light in a theory, that doesn't prove the theory is relativistic. That's the mistake people make."
Tim Maudlin, 1:48:30
"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."
Tim Maudlin on the Copenhagen reading of Alice's measurement, 2:01:39
"Notice I never mentioned position from beginning to end. I was just working with momentum. Argument over."
Tim Maudlin, 2:02:00
"No reasonable definition of reality could be expected to permit this."
Einstein, Podolsky and Rosen rejecting the measurement dependent alternative, 2:09:19
"It seemed to me as if you had erected some dummy Einstein for yourself, which you then knocked down with great pomp. He was not at all annoyed with you, but only said you were a person who will not listen."
Wolfgang Pauli, writing to Bohr about Einstein in 1954, read at 2:12:26
"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 at the other."
John Bell on Born's account of the dispute, read at 2:14:24
"It is as if we had come to deny the reality of Bertlmann's socks, or at least of their colors, when not looked at. And as if a child had asked: how come they always choose different colors when they are looked at? How does the second sock know what the first has done?"
John Bell, Bertlmann's Socks and the Nature of Reality, read at 2:23:36
"Paradox indeed, but for the others, not for EPR."
John Bell, read at 2:24:50
"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."
Tim Maudlin, 2:48:10
"It's an incoherent mess. Nobody understands that paper."
Tim Maudlin on Bohr's 1935 reply, 2:44:57
"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 just is words."
Tim Maudlin on the two switched pages in Bohr's reply, 2:46:04
"This onslaught came upon us as a bolt from the blue. Its effect on Bohr was remarkable. As soon as he had heard my report of Einstein's argument, everything else was abandoned."
Léon Rosenfeld on Bohr receiving EPR, read at 2:49:12
"The appearance of this work motivated the present, shall I say, lecture or general confession."
Erwin Schrödinger, footnote seven of the cat paper, read at 2:52:22
"You can't understand Bell. You cannot understand Bell without understanding EPR."
Tim Maudlin, 2:53:32
"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."
Tim Maudlin, 2:55:18
The reconstruction above is history and logic, and on both counts Maudlin is on firm ground: the Solvay record says what he says it says, the criterion of reality argument is his own and it is tight, and Bohr's 1935 reply really is a document that specialists have struggled with for ninety years. But it is worth being clear about which parts of this lecture are settled and which are Maudlin taking a side in a live dispute.
Settled, or nearly so. That Einstein's objection was about locality rather than determinism is now the standard scholarly view, and Bell, Pauli and the historical record all support it. That the EPR argument is valid given its premises is not seriously contested. That entanglement enters physics through Schrödinger's 1935 response is straightforwardly true. That the position half of the EPR paper is dispensable is a technical observation others have made too.
Contested. The claim that the criterion of reality is analytic, true by the meanings of its words alone, is Maudlin's argument, and philosophers who take an operationalist or QBist line will resist it precisely where he says resistance is incoherent, by declining to treat "element of physical reality" as a notion the criterion can pick out at all. The verdict that Bohr's reply is simply incoherent is widely shared but not universal: there is a literature that tries to reconstruct Bohr as making a defensible point about the contextual definition of physical quantities, and Maudlin's answer, that this is not to the point because the two particle case is not about disturbing your own particle, is a position rather than a consensus. And his insistence that no superluminal signaling does not amount to relativistic respectability is a genuine minority stance among working physicists, most of whom treat microcausality in quantum field theory as settling the matter. Maudlin knows this, which is why he wrote a book with a chapter on each candidate reading of what relativity forbids.
Absent, by design. Bell's theorem is not in this video. Everything here is the setup, and the setup ends with Einstein's tools in good order and his conclusion apparently secure. What act three does with those tools reverses the conclusion. Until then, the honest summary of the state of play in 1935 is the one Maudlin gives: the argument was valid, the two available replies were both refusals Copenhagen would not make, and the one person who fully understood what had been proved responded by writing a confession.
Full transcript
========================================
But notice the deep problems were about
spooky action at a distance, not
particularly about determinism. I'm
really going to try to do this once
[music] properly from beginning to end.
What's going on with EPR? What's going
on with Bell? This is Tim Mlin,
professor of philosophy at New York
University and one of the world's
leading philosophers of physics. Today,
I'm thrilled to bring you a lecture with
the breathing room. It requires to
explain quantum physics and what Bell
did with zero background knowledge.
[music]
>> I've been told I have an unlimited
amount of time. On this channel, I,
Kircha Mungle, interview researchers
regarding their theories of reality with
rigor and technical depth.
>> Unfortunately, most people haven't
understood the EPR paper. This is to set
the record straight once and for all on
what the great ironic reversal at the
end is that Bell undermines Einstein's
fundamental thesis that there's no
[music] action at a distance but he
undermines it using Einstein's own
tools.
Professor, welcome. I'm super excited.
Thank you for coming.
>> Um I'm very glad to be here. So, this
title, okay, as far as I can see, EPR
Bell, the completeness of the wave
function, spooky action at a distance
and all that. That's the title of this.
Take it away. The title of the YouTube
video may be something that can fit into
the character
>> count of the YouTube video and I went to
all that trouble.
>> Uh, okay. So, let me explain to anybody
watching this what this is.
>> It's not a kind of normal back and forth
conversation designed that way. It it
was supposed to be a real careful
presentation
uh a century of Bell's theorem and then
a little bit on the problems that arise
because of Bell's theorem. And in
preparing for this I thought all right I
have a kind of I've been told I have an
unlimited amount of time which is unlike
what I normally have. Usually you have
to squeeze it down. And I thought, all
right, if I really do have a lot of
time, I'm really going to try to do this
once properly from beginning to end.
on with Bell? What Einstein was
thinking? What Bell was thinking? Other
things that happened in the meantime,
the logic of Bell's argument, and the
conclusions of it. So that's what this
is all about. I should say that because
I want this to be ab absolutely clear.
Uh I've essentially written everything
out.
>> Perfect.
>> And it's going to be a little boring
because I'm going to be more or less
reading what's on the screen. Uh unless
I I riff on something or Kurt has some
something he wants to interrupt me about
and ask me about which is fine. Uh but
don't be surprised that that's what's
going on. Okay. So should we begin
please? Okay. So this comes in various
acts, historical acts. I think there'll
be some history here that almost nobody
listening to this is aware of.
Historians of physics are aware of it,
but it's not usually talked about. So
we're going to start in 1905.
The honest moralists when Einstein
develop proved that there were atoms and
developed the special theory of
relativity and proved equals MC² and on
top of that really began quantum theory
with his paper on the photoelectric
effect. So let's just begin there. So
although plank is usually credited with
being the originator of quantum theory
because of work he did on uh thermal
radiation in black body radiation in
1900.
I think it's really not fair to say that
began what became what we now think of
as as quantum theory. Why? He was doing
some statistical calculations in a
normal way for a classical physicist
doing statistical calculations. He knew
what he was trying to get. He was trying
to get a certain spectrum of radiation
for black body radiation. He found that
he could get the right answer out if
instead of taking a limit going to zero,
which is what you'd normally do, he
stopped at a certain point. And so he
stopped. And that point had little
finite regions of phase space which were
characterized by this plank constant h.
He knew that gave him the result he
wanted. It's not clear that he thought
that what he was doing was quantizing
anything. It's not clear that he had any
real physical hypothesis about what he
was doing. He just noticed that it
worked. So when you really ask who
really proposed quantization of a
classical quantity, it's Einstein in
1905. Now what was Einstein worried
about? He wasn't worried about black
body radiation. He was worried about the
photoelectric effect. And the
photoelectric effect was a known
property of certain metals that when
light fell on it, it created a current,
an electrical current. And it was known
how that current was related to the
light. And it's a very surprising way
that it's related to the light. I mean,
it's not surprising from a classical
perspective that light on a metal might
start a current. It's obviously
delivering energy to the metal. And you
need to deliver energy to the metal
intuitively to knock electrons free and
get a current going. But the way that
that depend that that that energy
translated into current was very
surprising. So let's go through the
surprise. Classically you think of light
as an electromagnetic wave and it's
characterized by a frequency and an
amplitude. The frequency tells you
essentially what the color of the light
is and the amplitude tells you what the
brightness of the light is. And
classically when you attribute energy to
an electromagnetic wave, it depends on
both the frequency and on the amplitude.
So you can increase the energy by
increasing the frequency and you can
increase the energy by increasing the
amplitude by making it brighter. So you
would think that if light falling on a
metal is creating a current, you could
increase the current either by changing
the frequency and making it higher or by
changing the amplitude and making it
brighter. But it actually turns out it
doesn't work like that. Um the
dependency of the current doesn't go
like that. Instead, what happens? Well,
there's a critical frequency of light.
Uh a critical color as it were. And as
long as the light is below that
frequency, no current flows at all, no
matter how bright the light is. And as
soon as it goes above that frequency,
you start to get current.
Uh so the current isn't just a function
of the delivered energy, right? If you
make it brighter, if it's below the
frequency and you make it bright
brighter, you do deliver more energy and
the and the metal will heat up. But what
you won't get is this electrical
current. Once you get above that
frequency, as you increase the
brightness, you increase the current. So
the classical model of light as an
electromagnetic wave doesn't have any
obvious way of making sense of that kind
of data. So Einstein noticed that you
can make sense of it if you have a kind
of really quantum hypothesis or
discretetization hypothesis. You say it
looks like the light is delivering
energy to the metal in discrete small
packets and the amount of energy in each
one of those packets is a function of
the frequency. As you increase the
frequency, you increase the energy of
each packet. And as you increase the
brightness, you increase the number of
packets. So to that extent it looks like
the light is delivering energy more like
particles would more like a set of
particles. If the particles don't
individually don't have enough energy if
none of them has enough energy to
dislodge an electron as it were then it
doesn't matter how many of them you
throw at it. It's not going to get a
current. And as soon as you have even
one that's above that threshold then you
will start to get a current. Uh so this
picture of energy being delivered in
quanta or packets in discrete
units is suggested by the way the
photoelectric effect works and the
hypothesis of how the frequency of the
light is connected to this energy of
these quanta is given by the famous
formula E= H new. So there we have
plank's constant again. plank. The one
plank discovered in his calculations is
now showing up and connecting together
the frequency of the light to the energy
of these quanta, right? quant of energy
and then you would say that would
explain
why below a critical new you just don't
get any current at all because because
the quanta are not delivering each each
individual quantum is not delivering
enough energy to dislodge an electron
and that is that is the quantum
hypothesis as it appears here. Now
notice
what's quantized here isn't really
energy. A photon or a quantum of light
can have any energy you like. You just
have to pick the right new. Right?
There's a continuum of different
frequencies and each frequency gives you
an energy that gives you a continuum of
en possible energies of photons.
It's rather that at a fixed frequency
the energy is seems to be delivered in
these discrete packets each of which has
an energy that's determined by the
frequency. Okay. So what's this kind of
like? Um this would was a tremendous
surprise for people who thought of light
as a wave because if you think if
light's like a wave like a water wave
hitting the beach that of course carries
energy and as it hits the beach it
distributes that energy but it
distributes the energy equally across
the beach. If the beach is made of
pebbles and a ra wave crashes on it, all
the pebbles get jostled a little bit.
But this is like a wave comes in and a
few pebbles get shot way up, get a whole
lot of energy, and the other one's
nothing. Like the energy is not being
equally distributed across the beach.
And it's more like people are shooting
bullets to the beach, right? So imagine
a bunch of people with guns firing
bullets at the beach. then if a pebble
gets hit it will jump up and if it
doesn't it won't and you don't expect
the energy be distributed evenly. Um so
you get this kind of particulate model
that seems to be connected with this
behavior and uh as I say the the model
is like this bullet model and you can go
further you can say well if you're
shooting bullets and it takes a certain
amount of energy minimum amount of
energy to dislodge a pebble then if your
ammunition is too weak and individual
bullets don't deliver that you'll get no
effect. But as soon as you upgrade the
ammunition, which would be the
equivalent of upgrading the frequency,
now they do have enough. Once you get
beyond the critical threshold, suddenly
the rocks will start to jump. Um, and
the more bullets that are being shot,
the more rocks will jump. That's like
the brightness.
So what happens is in this in this 1905
paper when Einstein tries to account for
the photoelectric effect he introduces a
kind of wave particle duality. Right? It
certainly he says that the energy of the
wave seems to be delivered more the way
energy would be delivered by a particle
than it would be by a classical a
classical wave. Um now there are still
wave characteristics and there were wave
characteristics in Einstein's theory.
The actual calculation is rather
complicated but part of it was these
particle like this particle-like
behavior of the light. Um you still of
course need some wave characteristics of
light because light does behave like a
wave. It refracts, it interferes. It
does all sorts of things that when there
was the original debate between the
corpuscularians like Newton and the wave
theorists, the wave theorists won that
debate, classical debate because light
does display wavelike characteristics of
interference and refraction and so on.
Uh so then you have this idea of wave
particle duality already is there in
1905. Light is in a certain respect
behaving like a wave and in some other
respect behaving like a particle. All
right. I'm sorry. Would you say that
it's a wave particle duality or would
you say that it's more like the quantum
object has wave characteristics and
particle characteristics, but that
duality isn't quite the correct term in
the way that we use dualities in math
and physics otherwise. Like a co- vector
is dual to a vector or something. Yeah,
it's yeah, it's certainly not a
technical notion of duality as would be
used in math. So yeah, that's the the
the word isn't supposed to
conote that when I when I'm using it
here. And I think when people started
talking about it, I don't think they had
a a strict mathematical understanding.
Um, all they meant was somehow this
thing is in certain ways behaving like a
wave and in other ways behaving like a
particle. That's all. One of the ways
that it could be saved is if this is
true that it either is going to behave
like a particle or it's going to behave
like a wave. It never behaves like both.
That whenever it's behaving like a
particle then it's behaving like a
particle but not a wave. So I've heard
some people say that. And I'm sure the
audience have heard other lecturers say
that or popularizers of science. Is that
correct?
>> No, I would say I I would say nobody
takes would would take that. That's a
kind of Jackal and Hyde picture, right?
I mean, there's one guy and sometimes he
behaves like Jackal and other times he
pa behaves very differently like Hyde.
Um
and and he switches between the two,
right? It's really quite dramatic when
he switches between Jackal and Hyde. I
don't think anybody thought that was
going on, that it sometimes is just a
particle and at other times is just a
wave and it somehow switches between the
two. It would just be crazy to try to
make such a theory. Um the the the the
claim that I made which is that in
certain ways you have a single thing and
in certain ways its behavior is
characteristic of waves and in other
ways of particles. that is going to be
true at all times. It's not like there's
a trigger that switches it from particle
mode to wave mode, right? I mean, you
could imagine such a theor I can't
imagine anybody taking it seriously. I
mean, that's just kind of crazy, right?
What would the trigger be? Some people
heard that from the double slit. I'm
just trying to cuz I know the audience
may be thinking but but I've seen other
popularizations or other animations of
this and that that if you look if you
have the which way information then it
starts to act like a particle and if you
don't then it starts to act like
>> okay so I'll I'll even dunk a little bit
on my friend
>> I want to preempt what the audience may
be thinking just so that you can dispel
any incorrect notions from
popularization
>> no no this is fine this is good look I
can dunk a bit on my friend Sean Carol
who tried to do something which you
shouldn't try to do which is reduce
quantum theory to five words [laughter]
and his five words were don't look wave
look article and that sort of suggests
this jackal and hyde thing but the
trigger is being looked at and that's
just of course lunacy right because what
do you mean looking at a you know
looking at what do you mean by looking
at a particle I mean the the whole thing
makes no sense and I'm sure Sean would
not defend it he you know trying to
reduce any theory to five words is not a
great idea. Um the the this this thing
about which way information and so on
and double slit and why the interference
goes away. All of that is explained in a
perfectly comprehensible manner
just by looking at Schroinger evolution
of the wave function and the Schroinger
evolution is always wave. Schroinger's
equation is a wave equation and it
governs the wave function as a wave.
and it explains why the interference
goes away when you change the physical
situation in certain ways. I subscribe
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They even covered how dark energy may be
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for 35% off. People characterize those
ways as giving me which way information
or whatever. That's just it that that
just leads you in the wrong direction.
You make certain physical changes to the
situation. You plug Schroinger's
equation in. You see what happens and
you notice that in a in in fact in a
continuous way the interference slowly
degrades which if you thought either
it's a particle or it's a wave. Well,
how can there be this kind of continuum
between the two behaviors? Right?
There's a continuum between the behavior
where you have sharp interference bands
and you have don't have interference
bands. Um, so no, that that jackal and
hyde kind of picture is clearly
incorrect and I don't think anybody
would defend it who was serious about
it. Um, I should say it puzzled Belle
and he said he was always puzzled about
once they noticed that there was both
this wavelike behavior and this
particle-like behavior and then they
started worrying well is it a wave or is
it a particle or is it a wavele or
whatever that it didn't occur to them he
says the obvious solution maybe there's
both a wave and a particle right it the
thing behaves somewhat like a wave
because there is a wave and it behaves
somewhat like a particle because there
is a particle and they're both there. Um
that's the pilot wave picture that we're
going to talk about later and it's an
obvious way of explaining why you have
both of these sorts of characteristics.
Um not the only way but that's an
obvious way to do it.
>> Great. But as I say, if someone were to
try to really make physics out of the
idea that that a photon at sometimes is
in particle mode and at other times is
in wave mode. and they then would have
to give you an account of when it does
what and good luck with that. I mean,
that's really that's not going to be a
serious theory. Anyway, you you had both
of these characteristics and and and
Einstein solves the problem of the
photoelectric effect by attributing
particle-like behavior to things that
were classically waves. So, it occurs to
De Bruyne, very young guy. Well,
turnabouts, fair play. Um, why don't we
think maybe things we think of
classically as particles can display
wave behavior, right? Just and that then
he started talking about matter waves.
Um, so again, you have an electron
classically it's a particle.
Classically, it's always somewhere. It
moves around in some continuous way.
It's not like a wave. It's not spread
out. It doesn't interfere or anything
like that. And De Bruyne says, "Well, if
you took classical
electromagnetic waves and gave them
particle-like behavior, why don't I take
classical particles and give them some
wavelike behavior?" Uh, and he then made
some you you then need a way again to
link what will the wave behavior be?
What kind of wave should I associate
with these particles? And de Bruy as
we'll see taking Einstein as his model
said all right I can make that linkage
using plank's constant. So one of them
is this lambda equals h over p lambda if
if something's going to be a wave it has
to have a wavelength lambda
and de bruy said okay a classical
particle has a momentum p so let me just
say that lambda equals h over p. There's
planks constant again. Right now I can
say if class if in a classical situation
I would say this particle has such and
such a momentum. I can say well then I
expect it to to display wave behavior
that would be associated with a wave of
wavelength lambda. And what about but a
wave has both a wavelength and a
frequency. I needed new. So there he
used the same one that Einstein used. E
equals H new of course um Einstein was
going the other direction. Einstein was
saying well I know my light has
frequency new what is the energy of
these quant and de is saying well my
particle has energy like 12 mv^2
classical energy
>> mhm
>> if I want to associate a frequency with
it what will it be I'll use the same
equation right but now I'm putting in
the e and deriving the new so he he says
if I take a classical particle which
would have a momentum and an energy I
have two equations that will give me a
frequency and and a wavelength and then
I can think about the the behavior of
waves with that frequency and
wavelength, right? Um and that then led
to people actually looking for
interference behavior, wavelike behavior
of electrons.
And you sort of see how de got there. So
let's just recap where we are, right?
We're only in 1924. This is actually
before what's normally called the birth
of the new quantum theory which is 2526.
And already de Bruy and Einstein back in
1905 have laid the foundations of the
new quantum theory. What's called the
breakthrough of Heisenberg which is now
1925 was the matrix mechanics. And what
I've given you has no matrices in it in
any obvious way. And it's just very
different from what Heisenberg was
doing. And I don't want to go into what
Heisenberg was doing. I mean, it was
clear and it was something else. Uh, but
I'm telling trying to tell a reasonably
smooth story. And the story gets smooth
when after Heisenberg
develops the matrix mechanics,
Schrodener develops what's called wave
mechanics 1926.
And then there were various proofs that
at least in certain circumstances, the
two theories gave the same predictions.
So they were generally considered to be
just different mathematical
presentations of the same theory. And
furthermore, because people with
classical training were very good at
working with waves and really hadn't
learned to work with matrices, pretty
much everybody started working with
Schrodener's presentation in terms of
wave mechanics um rather than with the
matrix mechanics. So we're now in 1927.
The new quantum theory is certainly in
place and people are talking about it.
We have Schroinger's
wave mechanics which which involves the
introduction of the wave function that
we're all familiar with which is a
complex valued function which he didn't
like using complex values. He was a
little upset that he had to do it but he
was forced into it. a complex valued
function over the configuration space of
a system. So that's what the
mathematically what the wave function is
and Schrodener specified its dynamics in
what we call Schrodener's equation and
that dynamics is a wave dynamics. So the
wave function governed by Schroinger's
equation is going to evolve in a
wavelike way. There'll be interference.
There'll be spreading
uh there'll be refraction essentially
refraction-like behavior. All the things
you would associate with wave behavior.
Nobody quite knew what to do with this
wave function until Bourne came along
and gave it this probabilistic
interpretation where he said, well, what
we're going to do with the wave function
is square it and then treat those
numbers as probabilities for measurement
outcomes. Mhm. Um that's where the
probabilism comes into standard quantum
mechanics. The failure of determinism.
You say the theory no longer gives
strict predictions about what's going to
happen. It merely gives you different
possibilities and assigns probabilities
to them. And during this period, Bore
and Heisenberg are working together to
lay down principles of what's usually
called the Copenhagen interpretation or
the Copenhagen school.
And the main principle of that school we
want to focus on is the insistence that
the quantum mechanical description the
wave function of a system is complete.
It tells you everything there is
physically about the system and that
this randomness
or probability that's introduced by
Bourne's rule reflects an actual failure
of determinism in nature. Nature itself
is not deterministic.
And
Boore was very insistent that they had
passed a threshold from classical
physics that you couldn't go back over.
You're giving up determinism.
You're giving up uh
the ability to visualize what's going
on. What Bore was very insistent on
that. And in so far as you think you
need to visualize things to understand
them, you're giving up on understanding.
But Bour kept saying, "But we've reached
the end of the road. I mean, this theory
is the final theory, and the reason you
don't have a good time understanding it
is your problem, not nature's problem."
>> For Schroinger, he proposes this wave
function equation.
>> Most students when they're taught
quantum mechanics, they're taught the
Borne rule along with the Schroinger
equation. So it's difficult to think
what what would the Schroinger equation
be doing without the Borne rule like
what did Schroinger think the wave
function was and then did Borne only
invent that because of single particles
cuz then you have to make sense of dots
that are appearing on the screen or like
how could those two ever be separated?
>> I mean that's a that's a very good
question. Schrodener I believe didn't
particularly like Bourne's suggestion
when he made it. Um
I if you if you're if you're tracking
the development
and you follow the development I gave
you where
De Bruy makes this suggestion that we
ought to start treating matter particles
using these wave characteristics and
then we have wave equations for them. Um
what what really happened is that if you
if you read Schroinger's big paper, it's
a four-part paper when he introduced the
m the uh wave mechanics and what he does
in the first three parts is all
stationary or static situations.
Okay, so they're the kinds of situations
where
nothing is changing in the environment
and you're looking for what we call
iigen
states or certain kind of stationary
solutions
to these equations. For what purpose?
Well, in the case of, for example, the
one that that really got this going for
bore, in the case of atoms,
you wanted to know what are the energy
levels of the different that are
available to electrons
because the picture was that electrons
in an atom can only be in certain energy
states. And if they jump up from a lower
one to a higher one, they have to absorb
a certain amount of energy. And if they
decay down, they emit energy in terms of
light. And that was supposed to explain
the atomic spectra that you could see,
right? You just see that the light
coming from the sun or the light coming
from, you know, a neon tube or whatever
um is not a uniform spectrum. It has
very definite bands where the light is
being produced.
and the old quantum theory which is what
preceded
1925 and so on. This is 1915. Bore is
laying down these rules for the orbits
that electrons can be in thinking of the
orbits as planets as really little
little particles in planetary orbits.
and you restrict the orbits in certain
ways that have to do with wave getting
waves to fit around these orbits. That
gives you a set of orbits and that gives
you these transitions what these
transitions are possible and that gives
you the spectra of light. Okay, that's
essentially for what they're doing a
static situation.
You're just solving for stationary
solutions to your equations. And then
what's important about the equations is
what energies you associate them with.
Right? [snorts] Now you can do all that
without using Borne's rule. Nothing
about Bourne's rule, nothing about
probabilities there at all. It's just
can I get the spectra right?
So that's a kind of example of what you
could do
uh in a you know in a static situation
what are their probabilities of anyway
as it were in a static situation
nothing's changing.
Um right right so there is a lot that
you could do now in fact what what
Schroinger does in that paper is the
first three sections he's just dealing
with these stationary solutions and the
wave function he uses is real it's not
complex it's a real valued function
and then he says well what happens if
the situation isn't stationary what
happens if there's something that's
being changed if I've got some electric
field or something magnetic field and
it's it's it's varying.
Then he said, I'm he's forced into it
more or less. He's unhappy about it.
He's explicitly unhappy about it. He
says, well, I'm going to now use a
complex function. I'm going to the
values of the function are not going to
be real numbers anymore. They're going
to be complex numbers. It was the only
way he could think of to deal with this
this non-stationary situation.
Um,
when we learn quantum mechanics, as you
say, when a student learns it, the first
thing they're told is a wave function is
a complex function.
>> So, we start at a position where
Schrodener just barely got to and wasn't
happy about. He was hoping to replace
that complex function with a real
function. Uh, he says so, he just
couldn't figure out how to do it.
So you know the the Bourne's
coming into this and suggesting squaring
this complex function first of all why
why square it squaring the complex
function and then treating that those
numbers as probabilities that's kind of
completely out of left field. Um but of
course for many purposes it worked. So
that's why the situation was so
confusing.
Nobody really understood what was going
on. And and and
when I don't know what Borne exactly
thought, but when when when certainly
Bore insisted that these probabilities
when you got them were fundamental that
they reflected indeterminacy, innate
indeterminism in nature itself
and Schroinger was upset about that. I
think Powi was upset about that. This
that did not go over well.
>> [sighs and gasps]
>> Um so it it was a very confused
situation. Okay. So there we are in
1927. This stuff has come out and at the
fifth SV conference all the big shots as
we know get together and have a nice
photograph taken of them all together.
And there was a lot of discussion of the
quantum theory. And in that discussion,
Einstein
first raises objections
to the quantum theory as it's being
exposited
by Boore and Heisenberg. And these
objections are very important. They tell
you what was on Einstein's mind from the
beginning. So we're 1927. People knew
you could use Bourne's rule together
with the wave function together with the
Schroinger equation and make some
statistical predictions, right? You use
the Schroinger equation to evolve the
wave function. You squared the wave
function to extract some probabilities.
You use those probabilities to make
statistical predictions. And it worked.
and even though the new quantum theory
again is attributed to Heisenberg in the
matrix mechanics
really even by 1927 I think people were
mostly working with this Schroinger wave
mechanics picture and so Einstein is
focused down on the wave function
because this is now if you use the
Schroinger presentation
the central object you're using to
describe your system is a wave function.
So he's very focused down on the wave
function and
he notices that one in the same
mathematical object can be used to
represent a physical system with
different physical meanings, right? With
different physical interpretations or
understandings of what's being
represented. And he's very clear about
it. And he says sometimes
when we describe something the
description is a merely statistical one.
That is we're not describing an
individual system. We're describing an
ensemble usually a kind of ideal
infinite ensemble of systems. And he
thought that that's the natural way to
understand this Schroinger wave.
and he was worried but he was very
worried about about how bore was trying
to understand it. Um and so he was he
really is focused down on this very
simple question. When I write down a
wave function, is that supposed to
describe a single particle or only a
collection of particles? A large
collection of particles, right? So the
second would be a statistical
understanding.
And he raised some problems about this
with an example which in which I think
most people don't know but if you don't
understand this example you won't see
where Einstein is coming from that
involved a pinhole and a hemispherical
detector. Okay. So at the SV conference
and we have records of the discussions
at the conference. So this was not you
know Einstein giving a formal
presentation. It's just him him raising
objections. And so he imagines this
situation where you have a a a beam of
say electrons and they're being shot at
a barrier with a pinhole in it with a
very small hole in it and beyond the
pinhole there's a screen and not just a
screen but a hemispherical screen. So
the picture is you've got this screen
with a hole in it and then around
centered around that hole is a large
hemispherical screen where the screen is
the same distance in all directions.
Okay, that's going to be kind of
important. And we all know that that the
idea was from De Bruy that gee the
particles the electrons have associated
wave behavior. They have frequencies and
they have wavelengths and they'll behave
the way water waves or you know
electromagnetic waves do. Well, what do
they do? Um when you shoot a a wave
through a small hole, it defracts. What
comes out the other end is a wave like a
semic-ircular wave or an expanding wave
in water. A semic-ircular wave in
another dimension you get a a growing
hemispherical wave because the wave
defracts and as it were comes out of the
pinhole going in all the different
directions. So here's a transcript of
that discussion. This is a transcript in
a recent book by Anthony Valentini and
uh Guido Baktia about the SV conference.
And I'm just going to read this right if
I can. So Einstein, despite being
conscious of the fact that I've not
entered deeply enough into the essence
of quantum mechanics, nevertheless, I
want to present here some general
remarks. One can take two positions
toward the theory with respect to its uh
postulated domain of validity, which I
wish to characterize with the aid of a
simple example. Let S be a screen
provided with a small opening. O figure
two, we'll see figure two in a minute.
And P, a hemispherical photographic film
of large radius. Electrons impinge on S
in the direction of the arrows. Some of
these go through O. And because of the
smallness of O and the speed of the
particles are dispersed uniformly over
the directions of the hemisphere and act
on the film. Both ways of conceiving the
theory now have the following in common.
There are de boy waves which impinge
approximately normally on s and are
defracted at o. So this is again de br
introduces this idea that even electrons
will exhibit wave behavior. Behind s
there's a sphere there are spherical
waves which reach the screen p and whose
intensity at p is responsible for what
happens at p.
So there's the picture. There's figure
two. You see the electrons coming in.
You see the little hole o. You see the
arrows going out in all directions
toward the hemispherical screen which is
equal distance away. Right? We can
characterize the two points of view as
follows. So Einstein says look what
we're agreed as it were mathematically
that part of the description. But
physically what what are we talking
about here? What what exactly does this
wave function represent?
And he gives you two conceptions.
Conception one, the De Bruyne Schroinger
waves do not correspond to a single
electron. Right? The Deceer waves is
what we would call the wave function,
but to a cloud of electrons extended in
space. The theory gives no information
about individual processes, but only
about the ensemble of an infinity of
elementary processes. So you imagine,
you know, you're shooting these
electrons at this pinhole and imagine
that it they just each one gets somehow
defracted or shot off out of the pinhole
in different directions. But if I shoot
a million of them and I just follow that
cloud of electrons as it were, then the
whole cloud will then spread out
hemispherically. Right? That's
conception one. Conception two, the
theory claims to be a complete theory of
individual processes. Notice the word
complete there.
>> Mhm.
>> Right. Of and notice the word
individual, right? That the theory
purports to tell us everything about the
individual processes about an individual
electron. Each particle directed toward
the screen so far as can be determined
by its position and speed is described
by a packet of the de Schroinger waves
of short wavelength and small angular
width.
This wave packet is defracted and after
defraction partly reaches the film T in
a state of resolution
by which I think he means by a state of
resolution that it's been thinned out as
you would imagine. You you shoot this
wave in it comes out in all directions
and it thins out as it as it goes out
and by the time it hits this
hemispherical screen it's rather thin,
right? and it'll get thinner and thinner
the further the screen is. Okay.
According to the first purely
statistical point of view, size squared
expresses the probability that there
exists at the point considered a
particular particle of the cloud. For
example, at a given point of the screen.
So again, you now have s squared at the
screen. You can you you square sigh.
It's actually going to be pretty uniform
across the screen. And you say, but what
is that number? You know, Bourne tells
me it's a probability. The probability
of what? And Einstein says, well, if I
have this large collection of particles
and you just as it were arbitrarily pick
a particle, you can think of that as the
probability that that particle is
somewhere there near the screen.
Right? According to the second
conception two s^ squ expresses the
probability that at a given instant the
same particle is present at a given
point for example on the screen right so
he's saying you just shoot a single
particle through in the second
conception as this spreads out it
represents the particle itself that
single particle in some sense spreading
out and the probability is the
probability of some kind of action of
that particle on the screen. Here the
theory refers to an individual process
and claims to describe everything that
is governed by laws. So again the two
points in conception two the wave
function describes a single individual
system and furthermore is a complete
description of it. It describes
everything about it. So if the wave
spreads out then the particle spreads
out. The second conception goes further
than the first in the sense that all the
information resulting from one results
also from the theory by virtue of two
that the converse is not true. It is
only by virtue of two by the second
conception right that the wave function
describes individual systems and is
complete. It's only by virtue of two
that the theory contains the consequence
that the conservation laws are valid for
the elementary process. It's only from
two that the theory can derive the
result of the experiment of Geigger and
Boa and can explain the fact that in the
Wilson cloud chamber the droplets
stemming from a alpha particle are
situated on very nearly on continuous
lines. Why? Because you're you're trying
to explain single continuous lines
through a cloud chamber then you're
talking about a single particle and what
it's doing. You're not talking about a
collection. You're talking about what a
single particle is doing. Mhm.
>> But on the other hand, and this is the
main point, on the other hand, I have
objections to make to conception 2. The
scattered wave directed toward P does
not show any privilege direction. If
size squared were simply regarded as the
probability that at a certain point a
given particle is found at a given time,
it could happen that the same elementary
process produces an action in two 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 I say
this this wave completely describes a
single particle.
The wave goes through the hole and
spreads out uniformly in all directions
toward the screen. And that's supposed
to represent that it is physically
possible for that single particle to
interact with all these different points
on the screen where where the wave is
reaching. Right? But then he says, "But
then why can't the particle interact at
more than one place? Why can't it
interact over here because the wave got
there and interact over here because the
wave got there?" Right?
How could you avoid if if the particle
itself is, as it were, thinning out and
spreading out in all different
directions, how can you avoid it acting
at different points on the screen? And
again, if you're talking about a
collection of particles, then you have
no problem because you say, well, some
of them can interact over here and some
of them can interact over here. But for
a single particle, what could that mean?
>> Right? He says but that interpretation
according to which s^ squ expresses the
probability that this particle notice
that this we're talking about a single
particle is found at a given point
assumes an entirely peculiar mechanism
of action at a distance which prevents
the wave continuously distributed in
space from producing an action in two
places on the screen. That peculiar
mechanism of action in a distance is
what we call collapse of the wave
function.
That is in that theory
you say all right if a spot forms here
on the screen that's one thing but that
formation of the spot also has an effect
of destroying eliminating the wave
function everywhere else at every other
point of the screen where it had reached
right and according to this theory it
did reach there right even for a single
particle the wave function got to the
other parts of the screen. Why don't
they ever create a second spot? Because
as soon as the first spot forms,
something happens that annihilates
the rest of the wave function. That's
collapse of the wave function. And he
says that's action at a distance, right?
Because the formation of the spot over
here is causing the physical wave over
here to go to zero
instantly
and globally.
Because if that change didn't happen
instantly and globally, then sometimes
we'd get two spots or three or more etc.
>> or three or four. Exactly. And you never
do.
>> Yeah.
>> Right. You only ever get one spot. In my
opinion, one can uh remove this
objection only in the following way. One
does not describe the process solely by
the Schroinger wave but at the same time
one localized the particle
uh
sorry during the during the propagation
I think that Mr. De Bruyne is right to
search in this direction. If one works
solely with the Schroinger waves,
interpretation two of SI squared implies
to my mind a contradiction with the
postulate of relativity. And that's
because of the spooky action at a
distance, right? Because you need this
instantaneous change in the wave
function. The collapse is global and
instantaneous and that violates
relativity.
So Einstein already in 1927
is worried about spooky action in a
distance. He's worried about the
completeness of the wave function
and he's sympathetic
to De Bruy
who says the wave function isn't
complete. The wave function doesn't tell
you everything. In addition to the wave
function, there's this particle and the
particle is always somewhere and it's
always moving in some direction and
therefore if the particle is headed in
this direction to the screen, no spot
will form on the other part of the
screen.
>> So this demonstrates an understanding of
quantum mechanics. But the first
sentence he said, if I could read it
correctly, had said something like
despite the fact that I haven't ventured
deeply into the essence of quantum
mechanics, like what did Einstein mean?
Was he just being humble or what? But I
I couldn't say I think my this is a
guess. My guess is you know Heisenberg
especially the matrix mechanics this was
very unfamiliar mathematics.
You know Schroinger was less unfamiliar
because they were used to dealing with
wave equations and solving them. My
guess is that you know he just hadn't
felt like he had mastered what Eisenberg
had done and so on.
>> I see. Uh but you know whatever you
maybe it was just being humble but you
can see his worry is already there in
1927.
>> And the worry is against a conception
in which a the wave function is
complete. It tells you everything about
B an individual system. It's not a
statistical description description of
an individual system and it's complete.
And in order to avoid problems, it has
to collapse,
right? In order for this thing to work,
it has to collapse. And the collapses
look like they violate relativity and
they're uh because they would have to be
instantaneous and global, faster than
light.
At least that's what I assume he means
by that. So again, this this is an
episode that everybody should know,
and I don't think that many people do. I
mean, historians know about it,
but it doesn't get the play that other
episodes do. And it just shows how
quickly Einstein
grasped the fundamentals of Bour's
understanding of quantum theory and had
deep problems about it. But notice the
deep problems were about
spooky action at a distance.
Not particularly about determinism. I
mean, he doesn't mention that he doesn't
like indeterminism. What he mentions is
he doesn't like this instantaneous weird
collapse of the wave function.
>> Mhm. Okay. Notice this example involves
only a single particle, not a pair of
particles or anything. And so there's
nothing about entanglement and so on,
but he's already on to this idea that
that that this wave function could not
provide a complete description of the
individual system. Uh if it did, as I
say, the collapse of the wave function
would then have to be a real physical
change. It would have to be
instantaneous and it would have to
violate relativity. So we have again
spooky action at a distance. already
1927. He's worried about that. Now, all
of these worries about
action at a distance, violations of
relativity, and so on are connected to
conception two, not to conception one.
So, he again he's saying, I've got a
mathematical formalism here, sure, but
that doesn't tell me how to understand
it as a physical theory.
And bore 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 super lumininal signaling.
you only have a single particle and in
this situation there's no suggestion
that somehow anybody could use this
collapse of the wave function to send
signals. I mean in this case the
collapse would be associated with just a
spot forming somewhere on the screen.
That's it. And nobody has any control
over where that's going to form. So the
issue of signaling isn't there.
And so Einstein isn't thinking of
relativity as about signaling.
which it isn't.
So people who think, "Oh, I can solve
all the problems of relativity by just
proving that you can't send super
luminal signals miss the point.
If Einstein thought that was the
problem, he wouldn't thought thought
there was a problem in 1927 with this
single particle example." Right? And
there are also people who somehow think
oh action at a distance has to be some
very special thing and you have to take
action very seriously and so on. But
this when Einstein really talks about
action at a distance here and again the
action is just the sudden change of the
wave function itself. That's the you
know that the fact that the spot forming
here has the collateral instantaneous
effect of annihilating the wave function
elsewhere. that for Einstein is action
at a distance and nothing to do with
superumal signaling
but he says it looks like it's
incompatible with relativity which you
see why because in relativity you can't
even define an instantaneous change
because there's no such thing as as an
instant of time
>> in relativity there's no objective
simultaneity
when people worry so when you just look
at the collapse of the wave function and
you say well let me take that collapse
seriously which you would have to if you
thought the wave function was complete.
Immediately you're going to say, "Gee,
that looks spooky. That looks that looks
non-relativistic."
The the normal reaction to that is
people say, "No, no, no, no. The
collapse of the wave function isn't the
physical change. It's just an updating.
It's like Beijian updating. It's
changing not the physical world,
changing your beliefs about the physical
world because you got new information
about it, right? And this has been a
standard thing of of people trying to
defang the collapse by interpreting as
merely epistemic as updating.
But Einstein's very clear here. This is
a complaint about conception 2. And in
conception two, it can't be updating
because you said the wave function was
complete.
And if the wave function is complete,
there's no new information to update on
what's you know what saying the wave
function is compi 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 is
conception too. Now, here's something De
Bruyne said. Well, no, not something De
Bruyne said. Okay, so he praises, right?
We saw that Einstein knows that De
Bruyne has been playing with a theory,
the pilot wave theory, where there is a
wave and there is a particle. And that
was Bell says at one point he doesn't
understand why everybody was worried
about wave or particle, wave or
particle, and why they just didn't think
wave and particle, which is what De
Bruyne thought. Yes, there is a wave and
it
follows a wave equation and also there's
a particle and the wave guides the
particle. The wave determines where the
particle goes. Right? That's the basic
idea of the pilot wave theory. If you
take that view then rel you're not in
any issue about relativity
because
it's essentially when the when the spot
forms on the screen you do get new
information. You get information about
where the particle was. The particle was
going in some direction from the pinhole
to the screen all the time. It's going
the the entire time it's following some
trajectory and you don't know what it
is. And you can't figure out just from
the wave function what it is.
So if you want collapses
to just be epistemic updating,
then you need new information you can
update on.
And if you have both a wave and a
particle, then even if you know the
wave, you can update on the position of
the particle.
And and none of that requires spooky
action at a distance or anything
mysterious.
When a spot forms somewhere on the
screen, it's because a little bit before
it formed, the particle was very near
that location headed in the direction of
the screen. That's not mysterious. And
that doesn't involve spooky action at a
distance. It just involves particles
forming spots where they actually hit
the screen. It's because you don't know
that location of the particle that you
can update on it without that being a
physical change. Right? And then the
fact that the the chance of a spot
forming elsewhere immediately is reduced
to zero. Again, that's not a physical
change. It's just you realizing that in
fact because the particle was headed
this way, it had no chance of forming a
spot over that way. There you can make
the collapses merely epistemic or merely
updating or beijan. But the point is if
you want to do that with collapses, you
got to have something to update on. And
if the wave function is complete, you
don't have anything to update on because
you already know everything. So you can
take de Bruyy'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 Copenhogen approach because
that's what Bore and Heisenberg were
insisting that the wave function was
complete and that the theory could not
be improved upon by adding any more
physical structure what were called
hidden variables.
Right? And if they do that, then they're
stuck with the collapses as real
physical changes, which is the way it
comes out in vonoman's mathematical
principles of quantum mechanics.
Um, and that sudden collapse which is in
that book
is instantaneous and global.
And so you see why Einstein would think
it violates relativity in independently
of anything about sending signals or
anything else. Any physical change
that's instantaneous and global, you
can't make sense of in relativity.
Well, of course, what Einstein saw was
that if you think of that actual
experiment where you're just shooting
these electrons and these spots are
forming, there's nothing in the
phenomena that suggest anything like
that going on. There's nothing in the
phenomena that demand any kind of spooky
action at a distance. The natural
assumption is just the particles are
going through the hole and different
ones are going off in different
directions. And so we could give and
anybody could do this off the top of
their head. What we would call a local
relativistic no action at a distance
model of the experiment um which is that
yes, a particle gets shot. It's
traveling along a definite trajectory.
Maybe it's accompanied by a wave that's
guiding it. Fine. When it gets to the
pinhole, some of the particles go
through and their waves interact with
the pinhole somehow. And the result of
that is to shoot the particle off in
different directions in different
experiments. And then the distribution
over many experiments is a spots forming
in all these different places.
Uh and this is the kind of thing that
Bell would have said, why didn't they
why didn't they all jump on that idea?
You don't have to decide between
particle and wave. You just postulate
there's both particle and wave.
>> Mhm. Kurt here. Note that if you'd
rather listen to toe, we're on Spotify,
iTunes, everywhere with a podcast
catcher, you can just search my name or
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remember to hit subscribe.
>> At this point, would positing a particle
and a wave also entail a preferred
foliation or a time slice that's
preferred? it at this point it wouldn't
because we're only dealing with a single
particle
and a single particle wave function is
just defined on regular physical space
and the Schroinger equation which would
govern the dynamics of that wave that
single particle wave that doesn't have
to violate or you can use the durac
equation I mean they they they knew you
could have relativistic versions of the
Schroden equation, right? You had the
DAR equation.
So you can do that relativistically.
And if if you just have this particle
that's as it were accompanying the wave
that's accompanying the particle and
sort of guiding the particle, all of
that can be local and you don't need any
spooky action at distance to do that. So
for a single particle system,
there's no obvious threat at all to
relativity in this picture.
Now we're going to get to multiple
particle systems soon. Then there is
going to be you know but for the single
particle and again you start with the
single particle example of the pinhole.
>> So Einstein thinking about that wouldn't
have thought gosh if I put in a particle
that's moving that's going to be a
threat to relativity. Why would it be?
Okay. Um so anyway I'm I'm not going to
read I mean I have this all written out
but now I'll just people can go read it.
You know the steps are you shoot the
particle at the spin it's at the
pinhole. It's following a definite
trajectory. When it reaches the pinhole,
it either goes through or doesn't. And
the the little wave with it maybe
interacts, but that can all be local and
nice. And then it comes out the other
end. If it goes through, it comes out
the other end and can be refracted or
shot off in different directions. Then
from the pinhole to the screen, it
pretty much propagates classically
inertially straight line trajectory to
the screen. Why think anything else,
right? Um, and then when it gets to the
screen, okay, the particle hits the
screen, interacts with the screen, and
forms a dot where it hits it. But where
it hits it is already decided as soon as
it comes out of the pinhole, right?
Where it where it hits is not decided at
the last moment when it gets there.
Where it hits is decided when it leaves
the pinhole, it's headed in some
direction. It just goes that way. And
that kind of theory would account for
all the phenomena without any spooky
action at a distance anything like that
right. Um it would give the the pinhole
would essentially randomize the
direction of the outgoing particle
probably because of the fine dynamics of
the interaction with the pinhole. Maybe
you could add something stochastic
there. It doesn't matter. Then it just
travels off along the hem along to the
screen and then it forms dots where it
hits. And so none of these interactions
would require any non-locality action at
a distance. No threats are raised to
relativity. All right? So that's just
what we were talking about. This word
local and non-local has come up many
times. Are there different kinds of
locality such that Einstein would have
been okay with non-locality of a type B
but not of a type A or what have you or
does local always refer to the same
thing?
>> I mean there are you can make fine
distinctions between different types of
locality
Einstein does so u and he likes all of
them. [laughter]
Okay. I mean, uh, okay. Um, and and he
says, so, so let me just make two two
distinctions.
One, we might call onlogical locality,
which means the physical state of the
world can be completely expressed if you
just give me the physical state of each
of take the entire universe and break it
down into tiny little regions that
slightly overlap.
Okay? But tiny regions as small as you
like. And for each little region, tell
me what's going on there. So you tell me
what's going on here, what's going on
here, what's going on here. And they
slightly overlap so you can match them
up around the edges. For those people
who know general relativity, this is
like having a chart, an atlas of charts
to cover it.
If a if a theory is onlogically local
then by telling me what's going on in
each individual little region without
mentioning anything else outside that
region but by covering the entire thing
with these little [clears throat]
regions I then nail down the entire
physical state. Okay. So that the whole
the entire physical state of the
universe is as it were nothing and over
and above the little physical states of
the little pieces. So we can call that
ontological locality.
All of classical physics had that right?
I mean you think of a a a Maxwellian
electric field. How do I specify the
state of the field? I tell you what it
is here. I tell you what it is here. I
tell you what it is here. Right? For all
the little regions I just tell you how
strong is the electric field and in what
direction is it pointing. And if I tell
you that for all the little regions I've
nailed it down. That's it. There's
nothing else to say.
Okay. So, Einstein
recognized that the field theory
as developed by Maxwell and so on was a
really onlogically local theory. These
fields were local objects that had local
quantities and you could ask you could
point your finger in space and say what
is the value of it here? What is the
value of it here? Okay. And that's all
there was to it.
Einstein certainly believed that he also
believed in what we can call dynamical
locality. This is the no action at a
distance point which is that if
something happens in this little region,
the only way it can have an influence
elsewhere is for something to propagate
at some speed less than the speed of
light in relativity. something to
propagate with some speed from here to
where it's going to have its effect,
>> right? It can't have an instantaneous
effect far away. That's the no action at
a distance. That's a different kind of
non-locality. That's dynamical
non-locality. That's the one I'm talking
about here. When he worries about action
at a distance, he's worried about
dynamical non-locality. He sort of took
on locality for granted. He I don't know
that he even talks about it that much,
but there's a a wonderful
um place where Einstein is talking very
explicitly about how in the field theory
things get more and more local because
you can as it were take a microscope and
focus into smaller and smaller regions
of spaceime 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
the the laws of of uh electromagnetism
explain how the electric field right
here is going to change merely in terms
of the nearby electric and magnetic
fields. Nothing else.
So you can you can just focus down on
little pieces. And not only do they have
their own physical states, but but in
that little region, you can check, do
the laws of physics hold there? And
there's nothing for the laws of physics
to hold everywhere except for it to hold
in all the little regions.
Now, if there were action at a distance,
that wouldn't be true. Right? If I if by
snapping my fingers, I could make
something happen far away by law. Then
if I'm watching far away and suddenly
that thing happens and I say, "Gee, I
wonder if if that happened by the laws
of physics," I'd say, "I don't know. I
have to check far away and see if
somebody snapped their fingers." Right.
I have to check everywhere.
>> Right. Right. Right.
>> Because the laws themselves would
postulate this spooky action at a
distance. So to know if the laws are
being satisfied, I'd have to check
everywhere.
That That's a problem. And Einstein saw
that as a problem. He didn't he didn't
deny that that kind of action in a
distance was logically possible. But he
did think that you couldn't do science
in such a world because there would be
nothing like 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 phenomenon which is that these spots
form all over the screen one by one. uh
in in a very everyday way. Maybe we
involves a little wave that goes along
with the particle. We we need to explain
the defraction that happens at the at
the pinhole, but everything else is just
the particle going this way and then and
then it shoots out that way or that way
or that way. And uh and and certainly
there's nothing that would even vaguely
threaten relativity and all that. So
what about this wave that's traveling
out in all directions, right? That's not
the whole story. That's not complete.
on. If if we do this over and over again
many many times and we have an ensemble
of particles and not a single particle
then if we were to watch that ensemble
as it were all of their trajectories
overlaid on each other exactly what we
would see is a whole bunch of particles
going in hitting the pinhole and then
spreading out in a hemispherically
uh uh expanding way, right? And so that
would kind of look like what the wave
function does. So that would suggest
that the wave function is not really uh
a description of an individual system
but it's some kind of statistical
description of a large collection
ideally infinite collection infinite
collection of systems. Um but
if you say that then immediately you're
going to say the wave function's not
complete right it's certainly not
doesn't give you a complete description
of an individual particle it's just a
kind of averaged out description of a
whole collection of particles
and so in the case of the pinhole
we get this moral which is that even
though it seems to Einstein that bore
and Heisenberg have committed themselves
to this weird action at a distance
associated with wave collapse and
they've committed themselves to that by
insisting the wave function is a
complete description of an individual
system. Uh
that you don't need to do anything like
that, right? That that that commitment
of that that that they're getting spooky
action at a distance not out of the
phenomena at all. They're getting it out
of this
dogmatic
attachment to the idea that quantum
mechanics as it as it existed at that
time was the end of physics was the
final theory right and of course he he
thinks you know that's silly
right he's you know why would you do
that why would you adopt convention two
and get this weird consequence when you
don't have to do that um and I I Think
what if you want to understand Einstein
what happened to Einstein afterwards was
that he just couldn't con I think he
thought in 1927 these are powerful
powerful objections to what Boore and
Heisenberg were pushing and they didn't
pay any attention they didn't they
didn't stop them they didn't say oh yeah
we made a mistake they continued to
insist that the wave function is
complete they continue to insist you
know um
Now
there's another
worry that Einstein has about this which
comes in the record right after what I
read. So this is the next thing he says
and I just want to note it here. It
involves systems that have not a single
particle which everything we've done up
until now is a single particle but
systems with two particles. So he says I
should also like to point out briefly
two arguments which seem to be to speak
against the point of view too. This view
is essentially tied to a
multi-dimensional representation
parenthesis configuration space since
only this mode of representation makes
possible the interpretation of size
squared peculiar to conception too.
Now it seems to me that objections of
principle opposed to this
multi-dimensional representation.
So again let's stop for a minute. He
says once you move I I said before if
you have only a single particle the wave
function is just defined on physical
space and it kind of behaves like a
water wave or an electromagnetic wave
familiar from classical physics. When
you have two particles, mathematically
the wave function sigh is not defined on
physical space anymore. It's defined on
configuration space.
And whereas phys if physical space has
three dimensions, the configuration
space for two particles has six
dimensions and for three particles has
nine dimensions and for four particles
has 12 dimensions. Mhm.
>> A single point in configuration space
represents the entire configuration of
that set of particles. A single point in
configuration space specifies where each
of the particles is. And so if you only
have one particle, okay, you're just
pointing out a point in space. If you
have two, you need two points. If you
have three, you need three points and so
on.
Now, conception 2 wants the wave
function to be complete. and that that's
really giving you the deep physical
picture of the of the system. So he says
it seems to me that objections of
principle can be opposed to this
multi-dimensional representation. In
this representation indeed, two
configurations of a system that are
distinguished only by the permutation of
two particles of the same species are
represented by different points in
configuration space. Okay, that's a
that's a technical issue we could go
into and there are ways around that but
it's the second one I want to point out
which is not accord with the new results
in statistics. I mean this has to do
with Bose Einstein statistics but let's
not worry about that. The furthermore
part is interesting. Furthermore, the
feature of forces acting only at small
spatial distances
finds a less natural expression in
configuration space than in the space of
three or four dimensions. So again,
what's he worried about there? He's
again has this idea of locality that
forces only act between nearby things,
right? Forces don't act immediately
between distant things. But distant
what? distant in physical space.
>> Uhhuh.
>> But he says if you're not doing this in
physical space, but you're doing it in
configuration space,
it's harder to even specify what you
mean by forces acting only at a small
spatial distance.
It's as if spooky action at a distance
in physical space is almost going to be
hard to avoid if you're theory is stated
in configuration space.
Einstein seems to see that
and that's going to be the key to what's
going to happen. And briefly speaking,
what's the difference between a
configuration space in quantum mechanics
versus a classical configuration space
of Hamiltonian dynamics? mathematically
nothing at all
>> nothing you have a configuration space
you can write down Hamiltonian dynamics
in configuration space that's just a
mathematical trick that is instead of
specifying say where eight particles are
in three-dimensional space you represent
that configuration by a single point in
a 24dimensional space why because I need
24 numbers I need three numbers for each
of my eight eight particles
configuration space is a classical
notion. was used all over classical
mechanics. It was used all over
Hamiltonian mechanics and the
configuration space. Well, the
mathematical thing they used in quantum
mechanics was the classical
It wasn't phase space. I should mention
that in phase space, a point in phase
space specifies not only the positions
but also the momenta of all the
particles. So, it has six dimensions for
every particle. But configuration space
has only three. But it it is that very
configuration space mathematically that
Schroinger put his wave function on.
Right? The wave function was a complex
function on classical configuration
space.
What I mean to say is is there something
in particular about the way that
configuration space is being used in the
quantum case where Einstein's objections
bite more so than in the classical case?
Is it because the classical case can
then be translated back to Newtonian
dynamics on 3D whereas the quantum one
doesn't seem I mean let me just say this
look in in classical physics the use of
these highdimensional abstract spaces
was merely a mathematical convenience
the real physics was stated in physical
space the Newtonian force laws I mean
take take Newtonian force of gravity 1 /
r 2 what's r the distance between these
two particles in physical space,
right? In physical space.
So, of course, you have these force laws
and they're stated in terms of things
being near or far from each other in
physical space. That's this kind of
locality, dynamical locality.
You can take those laws and then express
them on a single highdimensional 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
highdimensional abstract representation.
The problem in quantum mechanics is that
you're starting with a highdimensional
abstract thing, but you're not sure
what's an abstract representation of.
>> Got it?
>> Right. And the question is, can I go
back down
and and give myself a picture of things
going on in physical space?
>> And the answer is it's not obvious how
you do that. And it's certainly not
obvious given what they're doing that if
you do that you're going to end up with
a dynamically local theory where where
the only effects are by nearby things in
physical space. So Einstein was worried
about that too. Einstein had this worry
in 1927. He saw as soon as I go from one
particle to two, things get really
screwy here because I'm treating the
wave function as fundamental and not
just as a convenience to represent
something that's better represented on
physical space. Okay, I'm now saying
what I just said. Of course, you know,
these configuration spaces as abstract
objects were used all the time in
classical mechanics. People knew all
about them and they were used to using
them. Hamiltonian mechanics was stated
was was written in terms of functions on
configuration space on phase space
really but that it was just considered
to be a mathematical convenience when
conception 2 takes the wave function
seriously as fundamental and complete
right then that's a new situation the
space it's defined on would seem to take
on an entirely new
significance
than it does in classical mechanics
where you understand that the real
physics is all can be specified just in
terms of things going on in physical
space. Okay. So after the solve
conference where are we? Um Einstein is
frustrated clearly with Warren
Heisenberg with conception too. He
thought he'd given very powerful
arguments against conception too but
Copenhagen didn't change their minds.
Right. Um, he of course never claimed to
show that the Copenhogen interpretation
was inconsistent or made the wrong
predictions or anything. What he showed
in 1927 was that it was unnecessarily
committed to spooky action at a
distance, right? Instantaneous changes
in the state of a particle because you
had instantaneous changes in the wave
function and the wave function was
supposed to be a complete representation
of the state of the particle. Um, the
1927 argument involves only a single
particle, but already Einstein's worried
about multiparticle systems. Um, now
this is a very quick thing. Notice his
complaint against conception 2 was about
spooky action at instantaneous action at
distance, threat to relativity. Uh, he
didn't mention indeterminism there.
Einstein popularly is presented as if
what really worried him about quantum
theory was indeterminism
was really you know I mean he talks
about spooky action at distance but then
also fundamental indeterminism this god
plays dice stuff but notice if you start
in 27 you don't really see him
complaining about indeterminism you see
him complaining about spooky action in a
distance and he does that just with this
simple example
um now you could promote the argument in
27 into a conclusion of indeterminism
and this is just an aside by using
what's called Curi's principle Pierre
Cury and Curi said look suppose I have a
system that has some symmetry and the
laws respect the symmetry that if it has
a symmetry at any time it has a symmetry
at all times and here we're assuming if
we assume the wave function is complete
in the pinhole situation the entire
situation the physical situation has a
symmetry around on this axis that goes
through the pinhole and the wave
function would also have that symmetry
or could have that symmetry and that
would tell you that it if it evolves
deterministically
it always has to have that symmetry I
mean curious principles for
deterministic theories but we know that
at the end of the experiment we break
the symmetry that is a spot forms here
or forms there or forms there and that
breaks the symmetry so then by cur's
principle you could say if you want to
maintain that the wave wave function is
complete, you have to be committed to
indeterminism.
Um, and then God would have to play
dice. Now, Einstein doesn't make that
argument. You could make that argument
and you can see how some of these
considerations might lead you to see the
role of indeterminism in the standard
theory. End of act one. Okay. Act two,
eight years later, EPR argument. Again
the Einstein I think if you read
Einstein's comments they're very
powerful as far as I know they didn't
have a lot of effect then what happens
in 1935
Einstein 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.
um and it involves now a system of a
pair of particles rather than a single
particle. So this issue of the wave
function being on configuration space
sort of does come into it. Um at least
you know this is something that's going
to be used to make this more powerful.
So now I'm just repeating what we said
for a single system the configuration
for a single particle configuration
space is three-dimensional because the
configuration of a single particle is
just indicating where it is in space. So
you just point to a point in space. If
space is three-dimensional that's what
you got. If you have a pair of particles
then you indicate the configuration by
telling me where both particles are. So
now I have to give you two points. I
have to give you six numbers as it were.
You have a sixdimensional space.
Not only is the wave function in the EPR
paper defined on this sixdimensional
space, it is a highly entangled wave
function. What we would call an highly
entangled wave function between the two
particles. Um Einstein doesn't say that
because the term entanglement had not
yet been invented. It was invented by
Schrodener later in 1935 after he reads
the EPR paper. But but [clears throat]
that is a fact about that particular
thing and we'll talk about that.
>> What's the advantage of having two
particles? Well, one advantage is that I
can take one particle and send it to
Alice over here and another particle and
send it to Bob way over there. And
because Alice and Bob now each have a
particle to play with and they can be
put in their labs arbitrarily far apart,
this worry about spooky action at a
distance is very easy to understand.
Can it be that anything that happens in
Alice's lab influences the state of
affairs in Bob's physically or the other
way around? Right? That would be clearly
spooky action at a distance in
Einstein's mind. Now, there are three
parts of the EPR argument. I want to
triage this and keep them separate.
There's the conceptual part where they
introduce some terminology and they lay
out what they mean by words and they lay
out some principles. Right? I think all
of that is exactly right. There's then a
logical aspect. How does the argument
unfold? What steps do they go through? I
think the argument was unnecessarily
complicated. I think you can give a
simpler, more direct argument to the
conclusion they come to. and I will do
that and I'll mention how they I think
make it more complicated than it needs
to be.
I think it can be improved in that
respect.
>> Then there are some technical aspects
because of the particular example they
use that are mathematical problems.
I'm not going to go into those at all.
Um but they're there. I'm just
mentioning it later. We're going to
change the example in a way that gets
rid of those technical problems so they
won't bother us. that the the the
experiment the the EPR argument is not
affected by these technical
considerations.
Okay, let's start at the beginning. We
want to understand EPR again. What's the
title? Can quantum mechanical
description of physical reality be
considered complete? The very same
question Einstein raised in 1927 still
on that. Is the wave function complete?
Right? That's the focus of the paper.
The quantum mechanical description he
referring to there is the wave function.
The setting of this whole thing again is
in Schrodener's wave mechanics.
The issue of completeness was already
raised in 27. And now they're even more
careful to explain what they mean by a
complete description. This is part of
the conceptual being conceptually clear.
I think Einstein was just frustrated
because he tried to get these points
across and they wouldn't go across. So
they're trying to be very careful.
So here's the quote now. Some quotes
from the paper. In attempting to judge
the success of a physical theory, we may
ask ourselves two questions. One, is the
theory correct?
And two, is the description given by the
theory complete? It's only in the case
in which positive answers may be given
to both of these questions that the
concepts of the theory may be said to be
satisfactory.
The correctness of the theory is judged
by the degree of agreement between the
conclusions of the theory and human
experience. So that's what we would call
empirical success, right? Fitting
experiment, fitting the data, getting
the data right, making correct
predictions, that's correctness.
This experience,
empirical experience, which alone
enables us to make inferences about
reality in physics, in physics takes the
form of experiment and measurement. It
is the second question, not the one
about correctness. Right? So they're not
questioning the predictions of standard
quantum mechanics. It is the second
question which we wish to consider here
as applied to quantum mechanics. Is it
complete? Then they have to define what
they mean by completeness. Whatever the
meaning assigned to the term complete,
the following requirement for a complete
theory seems to be a necessary one.
Every element of the physical reality
must have a counterpart in the physical
theory. Right? Think of the mathematical
theory or whatever. We shall call this
the condition of completeness. Right? If
there's an if there's something in
physical reality that's not represented
in your theory, then your theory is not
complete. Right? You haven't [laughter]
you haven't your theory doesn't describe
all of physical reality. They said you
that has to be right. The second
question is this easily answered as soon
as we're able to decide what are the
elements of physical reality. Now you
see you have another problem right to be
complete the theory has to describe
every piece of physical reality. How do
I know I've got a piece of physical
reality? So they're going to answer that
question by providing a criterion
of physical reality. And again many
people I think do not understand what a
criterion is although they're perfectly
clear about this. Okay, so let's just
again go slowly. A criterion is not a
definition,
right? A definition is supposed to give
you necessary and sufficient conditions
for something. A criterion just gives
you sufficient conditions. Not ne not
necessary conditions. It's just if
something meets the criterion, you know
it's of that sort. But if it doesn't
meet the criterion, you don't know it
isn't of that sort, right?
But it's enough, right? Meeting the
criterion is enough. Again, from the
paper, the elements of physical reality
cannot be determined by op priori
philosophical considerations, right? We
can't figure out what the world is made
of just by thinking, but must be found
by an appeal to the results of
experiments and measurements. A
comprehensive definition of reality is
however unnecessary for our purpose. So
they're not going to try and define what
it takes to be real.
We shall be satisfied with the following
criterion
which we regard as being reasonable.
Here's the criterion and in in italics.
If without in any way disturbing a
system, notice that that's absolutely
essential. If without in any way
disturbing a system, we can predict with
certainty, that is with probability
equal to unity the value of a physical
quantity. then there exists an element
of physical reality corresponding to
this physical quantity. So suppose I
have a system
and I can without any way disturbing the
system I can somehow predict say the
outcome of an experiment. I'm going to
I'm going to weigh it or I'm going to
you know uh do do a momentum measurement
or whatever. If I'm able before that
experiment is done to predict with
absolute certainty and accuracy how
that's going to come out,
then there must be an element of
physical reality in the system that
corresponds to that, right? There must
be something in the system that's
resulting in it doing that.
That seems
really hard to deny.
It seems to us that this criterion,
while far from exhausting all the
possible ways of recognizing a physical
reality, at least provides us with one
such way whenever the conditions set
down and it occur regarded not as a
necessary but merely as a sufficient
condition of reality. This criterion is
in agreement with classical as well as
quantum mechanical ideas of reality.
I'll say a word because he they go on to
explain the second part when they say
this is accepted even in quantum
mechanics. What do they have in mind?
They have in mind this everybody says if
a systems in an igen state of an
operator like the momentum operator, the
position operator, whatever. If the wave
function is in an igen state, which
means you can predict with certainty
what a a measurement of that will give
you, then the system has that quantity,
right? It has that momentum.
Mhm.
And he says that's true. That's as true
in quantum mechanics as anywhere else.
people take the ability from the from
the theoretical description to make a
perfect prediction to be a sign that the
system itself has the corresponding
property. So let's just look at these.
These are the pieces of the conceptual
apparatus. And I think they're perfect,
right? I mean, how could you deny when
they say for whatever you mean by a
complete physical theory, it better be
that every aspect of physical reality is
res represented in the theory, right? If
you've left something out, you left
something out and then it's not
complete. So I I think that again, how
could you complain about that? Of
course, you can give in incomplete
descriptions. When when we describe a a
glass of water just by its temperature,
that's not a complete description. It
just gives you a statistical average,
right? There are lots of different
specific ways the glass of water could
be at micro level that result in exactly
the same temperature. So, that's an
incomplete description. To get to a
complete description, you have to go
down to all the fine details and get all
nail down everything that's there.
Right? A fundamental theory purports to
give a complete description. If you're
if you admit that your theory is not
complete, you're admitting it's not
fundamental. You're admitting that
somehow you're only describing this in a
coarse grain way that maybe there are
interesting things to say about it in
this at this level of description, but
it's not the end of physics because the
physics has to go down into the details.
people who don't like the conclusion of
the EPR argument, and there are a lot of
them, they have to find something to
complain about, right? So often they
pick on the criterion of physical
reality. They say, "Oh, I'm going to get
out of their argument by just denying
the criterion."
Um, but I think if you think about it,
you can't coherently deny the criterion.
It is in in a philosopher's terminology
analytic.
Um, it follows just from the meanings of
the words in it. So let's see why the
condition is if I can accurately predict
the outcome of an experiment on a system
without in any way disturbing the
system.
What does that mean? Without in any way
altering its physical state that's the
criterion I whatever I do to make this
prediction it cannot change the physical
state of the system.
So suppose I do this thing that doesn't
at all disturb the system and now I can
predict what it's going to do. Then you
say all right there must be an element
of physical reality in the system that's
making it do that right
how can you deny that I mean you know
it's it's something's assuring it's
going to do that it has to be its
physical state. Um but if I now suppose
I do this without in any way disturbing
the system that that means that before I
did whatever I did the system was
already in that state I didn't change
the state even before I was able to make
the prediction even before I did
whatever it was that allowed me to make
the prediction the system already had
that property. Why? Because I know after
I do it has the property and by
definition I didn't disturb it. So by
definition it had the property before I
did it. Right? If it didn't have the
property before, but it did have the
property after then I disturbed it.
>> Right? This is just analytic. So I just
don't see how one can question this
criterion. Now notice the criterion
doesn't even demand that I actually make
the prediction. It's just that I be in a
situation where I could make the
prediction without disturbing it. If
that's even possible,
then there must be some element of
reality in the system, right? Because
you're saying that the system what its
situation is independent of what I do.
It's independent of my making the
prediction or not making the prediction
or whatever. If it's just possible for
me to do this, then there must be an
element of reality in the system. Um, I
think that's correct. I think that's
accurate. I think it works in modal
logic. I think everything's okay with
it. I don't think you can you're going
to get out of this by denying the
criterion of reality. And that's what
I'm saying here. If it's if it's really
an analytic criterion, you can't say I'm
going to avoid the conclusion of this
argument by denying the criterion.
That's just incoherent. Um what grounds
could one possibly have for denying this
criterion,
right? That that heat they give.
Now, there is a place really throughout
the EPR argument
where they appeal to a a principle of no
action at a distance, no spooky action
at a distance.
The appeal is tacit. They don't come out
and say it, but it's clear that they use
it. And so, I want to be explicit about
it. So, again, we now have two
particles.
>> Sure.
>> Send one to Alice. Send one to Bob.
Alice and Bob can do whatever
experiments they want on their
particles, right? And their labs can be
situated as far apart as I like. They
could be a 100red billion light years
away as far as we're concerned, right?
They're just they they they are
separated. They're also separated in a
way that uh Alice's experiment can be
done at what we call space-like
separation from Bob. So that even light
couldn't get from one to the other in
time to influence it. Okay. So that's
the situation claim in such a case
whatever Alice does or whatever happens
in her lab does not disturb Bob's
particle or the state of the sit
physical state in Bob's lab and vice
versa right if we separate these
particles we put them in the separate
labs we take them very far apart Alice
can do whatever she wants Bob can do
whatever he wants neither will disturb
the other's physical state right okay
now this is important cuz the listener
may think well wouldn't Heisenberg
listening to the previous slide raise
his hand and say well Einstein your
antecedent namely that if you don't
disturb the system then so and so that
will never obtain because of my
uncertainty principle. Well that's not
true if you're at different spaceime
points.
>> Yeah, I'm not I mean the
I mean I'm not sure why he would bring
up the uncertainty principle here
because we're just talking about two
different particles,
right? We're talking about Alice doing
something to one particle and Bob doing
something to an entirely different
particle. So the the the uncertainty
principle doesn't even apply. That
really applies to
predictions about a single particle,
right? I can't simultaneously predict
accurately its position and its
momentum, for example. And the better I
can predict the one, the worse I can
predict the other. But that's just a
claim about individual particles. This
is a claim about
the goings on in one lab not disturbing
the physical state in a very very very
distant lab. So why why why would even
the uncertainty principle come up here
right? Um I mean it's true the
uncertainty principle was when people
when when when Heisenberg and Boore
talked about this they always talked
about oh if I do an experiment like an
electron microscope or whatever then
when I probe the particle I disturb the
particle or something like that right I
disturb the target but we're not talking
about whether Alice's actions disturb
Alice's particle
sure maybe they do or Bob's actions
disturb Bob's particle. Probably they
do. It's Do Alice's actions disturb
Bob's particle [laughter]
way over there.
>> Right. Right.
>> That would be spooky action at a
distance.
>> Right. This is the this is the tacid
assumption they're making that because
they can separate Alice and Bob away
from each other as far as they like,
they are justified in saying that
anything Alice does, any outcome in her
lab, whatever, does not disturb Bob's
physical situation,
anything Bob does, any outcome in his
lab does not disturb Alice's physical
situation. Now, you could blankly deny
that,
but then you would just have to say,
"No, I do think what Alice does disturbs
Bob's physical situation, and that is
spooky action at a distance." Then
you're just saying, "No, I'm I'm I'm
down with spooky action at a distance."
Right? You could do that. EPR don't even
imagine anybody would do that. It never
occurs to them that anybody would do
that. [laughter]
It seems crazy to them. And and you
know, Einstein, I think, never it never
occurred to him that any of his
opponents would simply blankly say,
"Yes, we believe in spooky action at a
distance." If you do, notice what
happens. Let me finish it here. So what
EPR assume in their argument is that
what we call space-like separation or
anyway separating Alice and Bob very far
from each other ensure causal isolation
of the experiments from each other.
Right? Nothing going on in Alice's lab
influences or changes the physical state
in Bob's. Nothing going on in Bob's lab
in Alice's. You could just deny that,
right, and sign on to it and say, "No,
what Alice does messes up Bob, or what
Bob does messes up Alice." Um, if you
say that, then the EPR criterion of
reality just doesn't apply. It's not
that the criterion is wrong, it just
doesn't apply because the criterion
requires that you make the prediction
without disturbing the system you're
predicting about. What EPR assume is
that anything Alice does will not
disturb Bob's particle and anything Bob
does will not disturb Alice's particle.
Uh if you deny that then again it's not
that you're saying the criterion is
wrong. You're just saying the criterion
doesn't apply by signing on to spooky
action at a distance.
>> Okay. Then you shouldn't deny it. Right?
In other words, if that were
Heisenberg's position, if Heisenberg
said, "But wait, Einstein, I already
believe that something Alice does here
can influence Bob's thing way over
there." Then he should just say, "No, I
believe in spooky action at a distance,
right?
I accept it."
>> But that's one thing he never did and
Boore never did. They never just said,
"Yes, we believe in spooky action at
Disney." I know you covered this
earlier, but just to hammer the point
home, many people think that, well, we
get around Einstein's objections because
you're not able to signal. You're not
able to send information. So, you're
saying no, Einstein still had objections
even without
>> Look, nothing he said has anything to do
with signaling. And as I say, when he
worried about about this sudden change
in the collapse of the wave function,
even in 1927, the issue wasn't
signaling. He didn't think, oh gosh, you
could use that to signal.
It has nothing to do with signaling.
Signaling is a red herring and it's a
dangerous red herring because people
think that oh if you can't signal then
no problem.
But Einstein's objections were never of
the form I think using quantum mechanics
you could superwomanally 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 super
lumininal 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 super luminal
non-signaling but disallow superal
signaling? Look, this is a good
excellent question. Um, the first book I
wrote, quantum non-locality and
relativity is exactly on this question.
Namely, everybody thinks relativity
prevents something from going faster
than light or almost everybody.
But what what does it prevent from going
faster than light? Does it prevent
particles from going faster than light?
Does it prevent energy from going faster
than light? Does it prevent causation
from going faster than light? Does it
prevent signals from going faster than
light or does it prevent nothing from
going faster than light? I mean I in my
book I have a chapter on each of these
positions
>> and the answer is there's no canonical
answer here. But certainly it is
absolutely clear Einstein didn't think
the issue was signaling
cuz if he thought the issue was
signaling he wouldn't be worried about
relativity in all these cases where
there's no possibility of signaling.
I mean if the wave function collapse is
a real physical process and by the spot
forming here on the hemispherical screen
the physical situation everywhere else
changes for Einstein that's spooky
action at a distance but you can't use
that to signal because you have no
control over anything right to signal
you have to control something
you have to the the sender of the signal
has to have something under their free
control and the receiver of the signal
has to have something they can observe
that will go differently depending on
what the sender does. That's just the
definition of signaling.
And none of that is at play here.
There's no suggestion that's an issue
here. But but man, action at a distance
is an issue here. That just proves that
Einstein didn't think of it in terms of
signaling.
100% he didn't think of it that way. And
you shouldn't. Got it. Okay? And
therefore, even if you can prove you
can't signal faster than light in a
theory, that doesn't prove the theory is
relativistic.
Okay, that that's what people that's the
mistake people make. And all these
people doing quantum field theory and
appealing to the equal time commutation
relations. I I mean I don't want to go
into all that. That's all that same
mistake. It's all that mistake. It's
that mistake that they're saying, "Oh,
gee, we can't signal therefore this is
relativistic." Nope. Doesn't follow.
Just doesn't follow. Anyway, in EPR,
they write down a state for this joint
system of two particles because it's of
two particles. You notice big sigh,
that's the entire state of the joint
system has an x1 and an x2. Those are
two variables.
Each three-dimensional, right? So, it
would be six-dimensional. X1 ranges over
all of three-dimensional space. X2
ranges over all of three-dimensional
space. The wave function is assigned,
its values are assigned to pairs of
positions, one for x1 and the other for
x2 to configurations. That's why the
wave function is defined on
configuration space. So they write down
this wave function. It's there in front
of you. It's the integral from minus
infinity to infinity to blah blah blah.
I'll talk for a minute about this thing.
You'll notice it's an integral dp. It's
an integral over all possible momentum.
all momentum from negative infinity to
positive infinity.
You'll also notice that it has in the in
the formula there's x1 x2 and then
there's an x0. That's a little confusing
because x0 isn't a variable, right? x1
and x2 are variables and x0 is just a
constant. So they he shouldn't have used
x, right? They shouldn't have used x.
That was a bad idea. Um the constant is
not going to play any important role
here and I won't talk about it. This is
where there are technical details about
the mathematics of this that we could go
into but that they don't make any
difference in the end. Okay. Uh but x1
is a spatial variable pertaining to
particle one. X2 is a spatial variable
pertaining to particle 2 and x0 is just
a constant. So we'll ignore it. So let's
just I mean look at this state for those
of you who know a little calculus can
integrate that sigma calculus thing is
saying add up all of these contributions
different contributions for different
values of p because you'll notice p is
sitting there it's e to the 2 pi i over
h x1 - x2 + x0 that whole thing times p
and you're integrating that over all
possible values of p. Mhm.
>> Okay. So, you can think of that as
adding a bunch of little pieces, one
piece for each different possible value
of p.
So, uh what is being added here? Well,
if we just forget about the constant, I
just don't want to deal with that x0.
You're adding up a bunch of pieces that
have this form that I have here. E 2 pi
i over h
x1 - x2
that whole thing times p.
And that if you remember how exponents
goes can more usefully be written just
as a product. E 2 pi I over HX1 * P E
the 2 pi I over HX2 * negative P right
1* P 1 * negative P and that state that
I just wrote there that single state is
what's called a product state because
you'll notice it's just taking a part of
it that's merely a function of X1 and
multiplying it by another part that's
merely a function of X2 and that's it.
So you can separate as it were the X1
part from the X2 part. And each of those
pieces are what we call momentum states.
So each piece is what you'd use to
represent a particle that definitely has
the momentum P in terms of X1 and
definitely has the momentum minus P in
terms of X2. Okay. So that state
represents a situation where particle
one quantum mechanically is in an igen
state. 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
igen state of total momentum zero. So I
hope anybody who knows quantum mechanics
can see that's that what that state is.
But remember the EPR state isn't that
state. The EPR state is what you get
when you integrate I'll go back when you
integrate over all the possible values
of P
states that look like that.
So it's what we call a superposition.
The EPR state is a superposition of all
these different states each of which has
zero total momentum. Okay.
So we see that this joint state has zero
total momentum and the EPR state is
built out only of states like that. So
only out of states that have zero
momentum. So the EPR state has zero is
is an igen state 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 igen state for
either particle one or particle 2. So in
in the EPR state, we would say particle
one has no particular momentum, no
definite momentum at all. Particle 2 has
no definite momentum at all. It's not in
an igen state. Nonetheless, the joint
system of one and two definitely has
zero momentum.
Okay, that's the standard way we would
talk about that state. Now, pause for
reflection.
I'm giving you the Copenhogen story
here, right? The Copenhogen story is
systems only have physical features when
they're in the appropriate igen states
of the associated operators.
That's a weird situation that I just
described, right? because you say look
uh because in the Copenhogen view the
only systems that have momenta at all
are in ien states. If you're not in an
ien state you just don't have that
property. If you're not in an igen state
of position, you just don't have a
position. Right?
And the we saw the reality criterion
demands that if you are in an igen
state, so you can predict the outcome of
a momentum measurement, then yes, you
have a momentum, right? There's a
element of physical reality. Um, and if
you could make that prediction without
deter disturbing the system, you have,
you know, you actually have a momentum.
But according to co Copenhogen, it's not
merely that those particles have
momenta, but that only those particles
have momenta. The only particles that
have momenta are ones that are in igen
states. If you're not in an igen state,
you just don't have a momentum. And
therefore, according to Copenhogen,
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 2 taken
together does have a definite momentum,
namely zero. Furthermore, you could say,
well, we can verify that claim, verify,
empirically verify total momentum zero.
How have Alice and Bob both do momentum
measurements?
And what you'll find is that even though
you can't predict what Alice will get
and you can't predict what Bob will get,
you can predict that Alice will get
exactly the opposite of what Bob gets.
If Alice gets P, Bob gets minus P,
whatever P is. And when we add them up,
we'll get zero, right? And that's true.
That's that's that's a prediction of
quantum mechanics. So that's a strange
situation, right? That's a very weird
situation of a large system and in not
just large but remember this system
consisting of particle one and particle
two is spatially separated. Particle
one's way over here and particle 2 is
way over there. That the state of that
joint system is not determined by
according to Copenhogen by the
individual states of its parts.
That's a strange situation. Now we
accept that. So we accept this
prediction. If both Alice and Bob make
position, make momentum measurements
initially knowing the EPR state, we
can't predict what either one will get,
but we can predict they'll get opposite
results.
I say what what we've now noticed and
this is not controversial is enough to
reach the EPR conclusion. Right? We
we've done enough. When I say we've done
enough, notice I haven't mentioned
position at all here. I'm just talking
about momentum. Why have we done enough?
>> Okay, so the logical situation is this.
Um, and again, this is not the way they
run the argument, but from their
principles, you can run the argument
this way, and I think they should have
uh once we know that the total momentum
is going to always come out to be zero,
right? Why didn't they run it this way?
Okay, wait, make I could make guesses,
but let me not. Here's the argument. We
create a pair of particles in the EPR
state. We send them off. One to Alice,
one to Bob. Alice and Bob are both going
to make momentum measurements.
Now, what we know, and they're going to
carry out their experiments very far
apart at space-ike separation. Even
light couldn't get from one to the
other, and so on. They both know, Alice
and Bob both know that the particles
were prepared in the EPR state, right?
They're aware of that. That's fine. We
can tell them beforehand. Question.
>> Okay. Can Alice predict
without in any way disturbing Bob's
particle what the outcome of a momentum
measurement on his particle will be? Can
Alice without disturbing Bob's particle
accurately predict the outcome of his
momentum measurement?
Well, we're assuming the accuracy of
quantum theory and certainly we know
that Alice can get herself in a position
where she can accurately predict the
outcome of Bob's measurement by
measuring her own particle. Right?
Whatever number she gets from momentum,
she's going to say, "Well, Bob's going
to get minus that because we know the
total momentum is zero."
So, in fact, she c 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
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
disturb his state,
>> right?
>> But if that's true, then
right here's where the fundamental tacet
locality assumption of the EPR argument
comes in. And it's so it's so seems so
obvious to to them, they don't even
mention it explicitly, right? That what
Alice does in her lab can't disturb
Bob's physical situation.
That would be spooky action at a
distance. If we accept that then we say
Alice is able to predict the outcome of
Bob's experiment without disturbing his
particle. So there must be an element of
physical reality in his particle that
determines what the outcome will be.
Right? Then we just apply the reality
criterion and we say there must be
something in Bob's particle that
determines the momentum that's going to
come out. Right? But now we're done.
Why? because the EPR state doesn't tell
me what that value is. It doesn't
represent that. You know, I just argued
there must be an element of reality
which is the momentum of Bob's particle,
but the EPR state doesn't tell me what
that is. So, it omits that. Right?
Therefore, the EPR state isn't complete.
There must be more to the world than is
given by that wave function.
Right?
It
In fact, I mean the Copenhogen view says
something even weirder in a way. The
Copenhogen view says when we send these
two particles out, one goes to Alice,
one goes to Bob, neither has a momentum.
>> Now Alice makes her measurement and and
and discovers or anyway gets an an
outcome of some momentum for her
particle. She can now predict Bob's.
>> 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,
>> Because of what she did. That's spooky
action at a distance in spades, man.
I mean, that's as spooky as you can get
as far as Einstein goes. He thinks
that's crazy. So, if you just assume
that Alice's experiment doesn't disturb
the physical state of Bob's particle,
then we get their conclusion. The
quantum description is incomplete. QED.
>> Yes. Notice I never mentioned position
from beginning to end. I was just
working with momentum here. Just working
with momentum. Argument over.
>> Now they don't do it that. So you know
the the you you've got what went into
this? The reality criterion, the
assumption of no spooky action at a
distance and the accuracy of the quantum
mechanical predictions. That's all we
used. We derived the incompleteness of
the quantum description.
Since the reality criterion is analytic,
you can't deny that. You have only two
options. Accept that quantum description
is incomplete or accept that Alice's
operations in her lab do disturb the
physical state of Bob's particle. That
is, accept spooky action at a distance.
Those are your two options. Either you
admit it's incomplete or you accept
spooky action at a distance. Um,
Einstein thought between those two, it's
obvious spooky action at distance is
crazy. Just deny 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 part, the momentum
of her particle, decides to measure its
position,
then she can accurately predict the
outcome of a position measurement that
Bob will make." uh that the very same
argument that proves that Bob's particle
already had a momentum can be used to
prove it already has a position. Right?
And therefore
in reality Bob's particle has both a
momentum and a position.
Right? That makes it even worse for
Copenhogen
because there is no quantum state that
ascribes a definite position and a
definite momentum at the same time to a
particle. No such wave function exists.
No wave function is simultaneously an
igen state of the position operator and
an igen state of the momentum operator.
That's impossible. That's mathematically
impossible. So if you think the wave
function is complete and you think that
the condition for having a property is
that you're in an igen state, you can't
accept that there are particles that
have positions and momenta at the same
time. Now you might wonder I just I gave
you an argument for the correlation
moment came because the total momentum
is zero, right? The technical thing is
it's not obvious at all looking at the
EPR state why it would have this feature
that also if if Alice measures position
at a moment and Bob measures position of
his particle at a moment that they'll be
perfectly correlated that each one from
their result can accurately predict the
other's result. That's true, but it's
not obvious. And it's a little
technically it's even a little hard to
get your hands around because you have
to use cuz there are no really position
states. They're really delta functions
which aren't functions. They're
distributions and things get
complicated. Okay? Uh and I'm not going
to go into any of that. It doesn't
really matter. I'll give you a quick
intuitive argument. I don't know if this
is really how accurate it even is, but
it's a way of thinking about it. Why
would you expect that if Alice and Bob
make position measurements at exactly
the same time that each can predict the
position of the other's particle? Well,
suppose these particles were shot out at
Alice and Bob at some pre
pre-established moment, right? They were
sent out from a central source and Alice
and Bob are equally far away.
Then if if they as it were got very
different distances from the source
measuring their positions at the same
time they would infer that they had
different momenta right that their
momentum total momentum wasn't zero.
Why? Because you normally actually the
way you measure momentum is by measuring
the position at a time knowing when the
particle was released taking distance
over time and getting a velocity and
then multiplying by the multiplying by
the mass and getting a momentum.
>> So if the position measurements were
like completely uncorrelated then they
would also say the momentums can't be as
correlated as we claim they are. Right?
So anyway, I think it's maybe not that
surprising that somehow you would have
this perfect correlation between
position measurements taken at the same
time. Um anyway, what what EPR do is
they prove it for momentum and then they
prove it for position and then they say
look Bob's particle has to have both
there must be an element of reality of
Bob's particle for its momentum and an
element of reality for its position. And
that's even impossible to represent
quantum mechanically. Um so here's what
they say at the end of the paper.
Previously we proved that either one the
quantum mechanical description of
reality given by the wave function is
not complete or two when the operators
corresponding to two physical quantities
do not commute the two quantities cannot
have simultaneous reality. And now what
they think they've do is they've proven
that even though momentum operator and
position operator don't commute, the
momentum and position do have
simultaneous reality. Right? Starting
then with the assumption that the wave
function does give a complete
description of the physical reality, we
arrived at the conclusion that the two
physical quantities with non-commuting
operators can have physical reality. And
again, tacitly they're using the no
action at a distance principle to say
that what one experimental does does not
disturb the other. Thus, the negation of
one leads to the negation of the only
other alternative two. We are thus
forced to conclude that the quantum
mechanical description of physical
reality given by wave functions is not
complete. Bad QED, right? Quantum state
is not complete. As I say, you could get
there quicker and easier just focusing
on momentum, but okay, they did it their
way.
One could object to this conclusion on
the grounds that our criterion of
reality is not sufficiently restrictive.
Indeed, one would not arrive at our
conclusion if one insisted that two or
more physical quantities can be regarded
as simultaneous elements of reality only
when they can be simultaneously measured
or predicted. Right? That you have to be
able if you want to say they
simultaneously exist, then you have to
be able to simultaneously predict or
measure them. on this point of view
since either one of either one or the
other but not both simultaneously of the
quantities P and Q can be predicted they
are not simultaneously real right this
makes the reality of P and Q depend on
the process of measurement carried out
in the first system which does not
disturb the second system in any way
notice again their point is what's real
according to this criterion in Bob's lab
depends on what Alice does but they say
what Alice does does not disturb the
second system in any way. No reasonable
definition of reality could be expected
to permit this. So they just reject
that. That's not the right way to think
about things. It's not a matter of
prediction. It's not a matter of what
you can predict. It's a matter of what's
there. And you can get a handle on
what's there by figuring out what you
can predict without disturbing.
And if you 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 a distance and God
does not play dice, right? And we've
seen exactly where the no action at a
distance demand comes in centrally in
the EPR argument, right? It's by
appealing to no action at a distance
that you argue there's no disturbance
and by arguing there's no disturbance
you argue there's an element of reality.
So that's there. What about determinism?
Somehow do they tacitly assume
determinism somewhere in this argument?
The answer is no. And it's really
important that the answer is no. So
here's a quote from John Bell in this
wonderful paper Bleman socks 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 in the
idealiz 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 a
sacred principle. The quotability of his
famous God does not play dice has not
helped in this respect. Among those who
had great difficulty seeing Einstein's
position was bore. Powi tried to help
him out in a letter of 1954. So here's
the quote from Powie's letter. I was
unable to recognize Einstein whenever
you talked about him either in your
letter or your manuscript. It seemed to
me you'd erected some dummy Einstein for
yourself which you then knocked down
with great paw. In particular, Einstein
does not consider the concept of
determinism to be as fundamental as it
is frequently held to be as he hold 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
for years what his objection is and
people keep attributing him positions he
does not hold. Um and this is one
the EPR argument nowhere assumes
determinism.
It infers it.
>> So is what you mean to say that look
Einstein doesn't start with determinism.
He ends with it as a conclusion not as
an ingredient in the input. It's
deduced. Well, no that that no that in
the argument okay EPR given argument it
has certain premises
among those premises is not that the
theory must be deterministic
okay but at the end of the argument you
reach the conclusion
that if the theory is to be local it
must be deterministic from the
assumption of locality you infer the
necessity of determinism
but you don't go into the game assuming
determinism
Okay. I mean, we'll get to that in a
minute. Here's the end of this quote.
So, so again, there the the end of the
quote from Bell. Bourne had particular
difficulty with the Einstein Pedoski
Rosen 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 that's he thought
Einstein held that that if if two events
happen in different places then seeing
the one gives you no information about
the other.
And Bell says, this is a classic line,
misunderstanding could hardly be more
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
Now, the EPR argument runs logically on
the existence of perfect correlations
between the outcome of the experiment in
Alice's lab and the outcome of the
experiment in Bob's lab. And I will just
call such perfect correlations EPR
correlations because they're the
correlations that show up in that paper.
Given the definitions in the paper, they
have to be perfect for two reasons,
right? The first reason is that the
criterion of reality requires Alice to
be able to quote predict with certainty
that is with probability equal to unity
the outcome of Bob's experiment
and then with the condition the writer
that she in no way disturbed the
physical state in Bob's lab. So the
criterion of reality and again it's not
a definition just a criterion very very
narrow criterion requires perfect
predictability and perfect
predictability requires perfect
correlation it means that given the
outcome in Alice's lab there is only one
outcome that could occur in Bob's lab
right um and that's true because of the
total momentum thing
uh but if you think about the logic of
the argument it's pretty clear that that
perfect predictability,
you could run the argument with a weaker
condition. Right? If you just if you
just allow these correlations to go from
perfect correlations to almost perfect
correlations or to strong correlations,
the basic logic of the argument isn't
going to change. Okay? Um that that that
you you would still Einstein would still
say, look, something's wrong here. if
you think the wave function is complete.
Now when you have these perfect
correlations, so one thing to say is
when you have these perfect
correlations, there is nothing weird
about the correlations. They're every
day. They're obvious. They happen all
the time. That's why when Bourne says
Einstein couldn't accept that by finding
out something in one location, you can
you can determine something about a
different location. He says that of
course Einstein accepts that. So we have
these trivial examples. Everybody uses
these. Take a dollar bill, tear it in
half, shuffle them between your back,
put them in two envelopes, send one
envelope off to Alice, one off to Bob.
Right? That's the preparation procedure.
Alice and Bob both know the preparation
procedure.
They obviously have no idea when they
get the envelopes which half is in their
envelope. But of course, when Alice
opens her envelope and sees the right
half, she immediately knows that Bob is
going to see the left half when he opens
his envelope. Right? He she can now
perfectly predict what he's going to
see. And in doing so, she doesn't
disturb the state of Bob's envelope at
all. Right? That's a trivial example. Um
Belle talks about the example of
Berlman's socks. So Reinhardt Berlman
apparently, and this is true, he always
wore socks of mismatching colors,
different colors. You could never
predict on a given day what color sock
he would have on any foot. But as soon
as you could see that his right sock was
pink, you could immediately, this is by
standard Beijian 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
Beijian 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 Belle
have to go to Bleman socks and not just
regular socks? Was it because he wanted
to show an anti-correlation?
>> No. Well, I think because Bleman was a
funny guy and he was a friend of his.
>> [laughter]
>> I I don't think there's any deep reason.
Of course, you could you you could make
the same point by saying every day
Burleman puts on different colored
socks, but you're never sure whether
they'll both be red or both be green,
right? It would make the same point. Uh
I think it's just Bleman was a funny
guy, right? And he was a friend of
>> I see I think you know he there was a
this was actually it may have been the
conference was a tribute to Berlman. I'm
not sure. Anyway, he even draws a little
a beautiful little drawing of Bertleman
in the paper. I mean his own hand
sketched Burleman. I think he was just
just a friendly thing.
>> Um what do these trivial examples show?
They show nothing much of interest,
right? Certainly they show that these
kinds of perfect correlations between
distant systems uh unlike what Bourne
said. They don't show anything, right?
[laughter] It's nothing wrong with them.
Um they don't suggest in any way that
there's spooky action at a distance just
that there are correlations between
different system between distant
systems. also trivial in these cases
that the criterion of reality
uh you works here right once you see one
sock you can predict about the other one
once you one half of the dollar bill you
can predict about the other one without
in any way disturbing it
>> what follows it 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 Bleman'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
Burleman'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 Burleman
gets up, all you said is he puts on
different colored socks, but you didn't
say which colored sock goes on which
foot. So those are incomplete
descriptions. And that's why because
they're incomplete that you can update
on new information because you start out
without complete information. If you
thought the wave function was complete,
then if you knew the wave function, you
have complete information
and you can't update on anything because
there's nothing to update on. So in the
trivial cases, these correlations are
already fixed at the source in an
everyday way. So is this a paradox? And
again, this is uh uh a point we'll see
that Bell makes. People talk about the
EPR paradox. Even Bell's papers on the
Einstein on the paradox of Einstein,
Podsolski and Rosen. Is it a paradox?
What does paradox mean? Usually a
paradox is an argument whose conclusion
is contrary to common opinions. In
Greek, the doxa or opinions of everyday
folk
>> or at least against some kind of
reasonable expectation, right? It's only
paradoxical if the conclusion is
surprising. But you know that there are
these correlations is not paradoxical
between what Bob sees in Alice sees and
the momentum that's not paradoxical.
And the actual conclusion of the paper
is that the quantum mechanical
description is is incomplete. That the
wave function is incomplete. That
doesn't violate any widely held opinions
or any common sense right. I mean most
people have no views on that. It's not
like they say oh my god we thought
quantum mechanics was complete. Um, so
to say that it isn't, that's not
paradoxical. It's just an observation,
right? [laughter]
Calling it a paradox is a very strange,
right? It it what it what what the
conclusion violates is not common sense
and not widely held opinion and not
something that seems obvious. What it
the the only thing it actually rejects
is boring Copenhogen school dogma. The
dogma that the wave function is
complete. that that's the end of physics
that there's nothing more to say. So it
helps to call it a paradox because it
sort of suggests that there's something
paradoxical about it. What's paradoxical
is actually the Copenhogen view that's
paradoxical.
So here's again from Bleman Sox Bell
says it is in the context of discussions
like these that one must envision the
discussions of the Einstein Pedolski
rose and 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
Breleman's socks or at least of their
colors when not looked at and as if a
child had asked how come the socks
always choose different colors when they
are looked at. How does the second sock
know what the first sock has done?
Right? Right? I mean, this is just
beautiful.
There's nothing paradoxical about
Burleman wearing different colored
socks. There's something really
paradoxical about saying before you
looked at them, the socks didn't have
any colors.
>> And you're [clears throat] looking at
them brought the colors into existence.
Right? That's weird in itself. But it's
even weirder if the two socks looked at
by two different people in two different
places always choose different colors.
How do they know? How does one sock know
what the other sock has done? Paradox
indeed, but for the others, not for EPR.
EPR did not use
the word paradox. They were with the man
in the street in this business. Right?
These correlations simply showed that
the quantum theorists were hasty, too
hasty in dismissing the reality of the
microscopic world,
>> which is of course what they like to do.
In particular, Jordan had been wrong in
supposing that nothing was real or fixed
in the world before observation. For
after observing only one particle, the
result of subsequently observing the
other possibly very remote place is
immediately predictable. Could it be
that the first observation somehow fixes
what was unfixed or makes real what was
unreal? not only for the the the near
particle but also for the remote one,
right? You see the spooky action at a
distance in that view that observation
creates reality which is what you hear
about quantum theory all the time.
Here's the end of this quote. For EPR,
that would have been an unthinkable
spooky action at a distance. To avoid
such action at a distance, they have to
attribute to the space-time regions in
question real properties in advance of
observation, correlated properties that
predetermine the outcomes of these
particular observations.
Right? Since these real properties fixed
in advance of observation are not
contained in the quantum formalism, that
formalism for EPR is incomplete. And it
may be correct as far as it goes, but
the usual quantum formalism cannot be
the whole story. That's the argument and
it's absolutely right. And you'll notice
where the determinism comes in. The
determinism comes in because if the
correlations are to be perfect,
then the previous states of the of the
objects have to determine the outcomes.
If there was any chanciness there, then
the two distant objects couldn't track
each other in what they do. Okay.
Now, there's a comment that people often
make here. I'll call it the conservation
law gambit. And they say, look, um,
we've got this correlation between the
momentum measurements made by Allison
Bob, uh, and that's there's an easy
explanation for that. It's conservation
momentum, right? [clears throat] M
because we know the total momentum of
the system is zero and we know momentum
is conserved. So obviously the system
always has zero momentum. So obviously
whatever momentum Alice gets Bob will
get the opposite. Right? And the
explanation as it were is the
conservation of momentum. Why is that a
big deal? People I've heard people say
this, right? What's so puzzling about
that? And that just misses the point,
right? because
the the the global conservation law in
this case does not follow from a local
conservation law. In classical physics,
global momentum is just the sum of local
momenta. And what the global momentum is
at all times is just the sum of all the
local momenta of the particles.
But here if the wave function is
complete neither particle has a
So you can't think that the total
momentum is the sum of theirs. They
don't have momenta right that doesn't
happen in classical physics.
So if they don't have mo pre-measurement
momenta then we have this puzzle both of
how you get any outcome on either side.
It somehow has to be brought into
existence. It's not discovered. It's
brought into existence. Right? But then
in addition, the opposite momentum has
to suddenly be brought into existence on
the other side 100 million miles away.
>> That's spooky action at a distance. Now,
as I say, these arguments, I'll go over
this quickly. This is uh these arguments
are running on perfect EPR correlations.
Uh you could relax them. We could demand
not that you'd be able to perfectly
predict but I don't know say predict
with 95% accuracy something like that
and you could make equally plausible
arguments and it's not as if the
perfection of the correlations is the
logical backbone you you know if you can
go what what's what is the logical
backbone of the argument um the perfect
correlations I say are assumed in two
places one is where you say I have to be
able to predict with certainty
what happens
And the other is where we just said
because the correlations are perfect. If
you have a local theory, it must be
deterministic. It must be that the state
of the particles entering the labs
absolutely determines what the outcomes
will be.
And the reason for that is that if they
didn't, then how could you be sure that
the two outcomes will always give you
opposite results? Suppose I have a
stochastic theory, an indeterministic
theory. Then you can kind of run the
same argument. You don't require that by
not obser not disturbing the system you
make perfect predictions. You just uh oh
anyway this is Belle just makes this
point here again. I'll repeat it about
why you infer determinism not assume it.
Sure. Of course, mere correlation
action at distance, but only correlation
between the signals reaching the two.
Uh, in the ideal examples of bone, they
must be the signals must be sufficient
to determine the particles go up or down
for any residual undeterminism
could uh only spoil the perfect
correlation. You just wouldn't get the
perfect correlation in a local theory if
it wasn't deterministic. So, you do the
inference to determinism only goes
through in the case of perfect
correlations. The original EPR argument
is formulated
by appeal to perfect correlations
between the outcomes that Alice gets and
the outcomes that Bob gets both for
momentum and for position although as I
said really momentum would would do the
job. Um one might think that yeah but
that's very idealized in a real life
situation. You'll never get perfect
correlations. But if you think about the
logic of the argument, you can see that
you can reduce reduce it to imperfect
correlations in a pretty simple way and
draw exactly the same conclusions.
Because what's really going on is the
question,
can the wave function be complete
if by doing something that in no way
disturbs another system, I can at least
make better predictions about it? Maybe
not perfect predictions, but can I
improve my predictions about it?
Can I can I say with more accuracy what
it might do? If I can,
then again, if I haven't disturbed the
system, then I didn't know something
initially about the system. I've learned
something that must have already been
there about the system. So let's just
walk through quickly this case of high
but imperfect correlations. You need to
relax the reality criterion a bit and
and you can make the argument go
through. As I say, the key to the
reality criterion is that whatever you
do to improve your predictions has to
not disturb the system you're predicting
about. And the assumption is because
Alice and Bob are so separated, nothing
any either one does disturbs the
physical state of the other. It's that
distance between them and the timing of
the experiments because they can do them
at space-like separation so that not
even light could send a signal from one
to the other about what what was being
done in the lab and what the outcome
was. That's the worry that Einstein has
about about relativity. So we can
reformulate this in terms of what we
would in in modern information theory
which didn't exist at the time in terms
of Shannon information.
Right? The real question is what Alice
does and what she sees. Does that give
her Shannon information about Bob's
system? Which is really just a matter of
saying does that allow her to improve
her predictions about Bob's system. If
she can do that without disturbing his
system, then her initial
representation of the system must have
been incomplete. It could be improved.
And you'll notice that if I put this in
terms of Shannon information and just
making better predictions, more accurate
predictions, more precise predictions,
even if they're not perfect predictions,
then we don't have to worry about having
these perfect EPR correlations.
Um, there must be I if she doesn't
disturb his system in whatever she does,
then she's learned something about his
system. And if she's learned something
about his system, then there must be
stuff about his system she didn't know.
But she knew its wave function, right?
She knew its quantum state. So that the
quantum state has to be incomplete.
>> Right. Right. So in in in that case
we again get the same conclusion of the
incompleteness of the wave function
without this very strong requirement of
perfect prediction. Notice that what
happens is because we don't require
perfect prediction here, we also do not
infer determinism.
So this was part of Bell's point that
EPR don't assume determinism, they infer
it. And for that inference to go
through, they needed perfect
correlations.
If you weaken it to less than perfect
correlations, you still get the
incompleteness of the wave function, but
you do not you you are not able to infer
that the underlying dynamics has to be
deterministic. That's just to recover
perfect correlations. Okay. So again,
the key to the whole argument is that
the spatial separation between Alice's
lab and Bob's lab affects a causal
isolation between what's happening in
those two labs during the courses of
their experiments.
Deny that. You can deny it, but if you
deny it, you're just signing on to
spooky action at a distance in in
Einstein sense. And to repeat something
we said a minute ago, none of that
suggests that you can signal from one
lab to the other. Doesn't require that
any kind of signaling protocol exist.
It's rather just the fact that you can
improve the situation of your knowledge
without disturbing the system. If you
want to deny that, then you say, "I am
disturbing the system." And if you're
disturbing the system, that's spooky
action at a distance. whether or not
that disturbance allows you to signal.
So you have what we would call local and
deterministic theories. They still obey
no spooky action at a distance. They're
still local, but they're not
deterministic. So assuming locality,
assuming determinism are different
things. What would happen in a local
indeterministic theory? For example, you
might say, well, when Alice does her
experiment, there's some chance, 90%
chance it turns out this way, 10% chance
it turns out another fundamental chance.
Same thing for Bob,
but they're local because which way
Alice's turns out has no influence or
doesn't allow you to predict better what
will happen to Bob's. Which way Bob's
turns out does not allow you to improve
your predictions about Alice. That would
mean that these statistical spreads
between the two systems are
statistically independent of each other.
Neither gives information about the
other. That would be a local
indeterministic theory. And that proves
that the locality assumption is not per
se an assumption of determinism. It only
allows you to infer determinism if you
have perfect correlations. So in sum
finally although the EPR argument from
no action at a distance and perfect
correlations to the incompleteness of
quantum mechanic goal description
uh is valid good argument. It's sound
and it's simple right not very
complicated.
The same argumentative structure
can be uh worked given no action at a
distance and less than perfect
correlations. If Alice's predictions for
Bob can just be improved by her
observations
and if so then and the physics is local
then the initial description she had
must have been incomplete.
That argument yields the conclusion that
we want or that EPR wanted of the
incompleteness of the quantum
description from no action in a distance
uh uh without entailing determinism that
only follows if we have perfect
One thing that comes up a lot in
discussions of Bell's theorem and EPR is
a condition that's called counterfactual
definitess or CFD. sometimes.
>> People claim that that it is a
fundamental assumption of EPR or a
fundamental assumption of Bell at the
beginning
>> that things are counterfactually
definitess.
What definite? What does that mean? A
theory supports counterfactual
definitess if the theory allows you to
assert with perfect confidence
a counterfactual claim about what would
have happened in a particular
experimental situation had it been
different from what it actually was. So
counterfactual for those who don't know
is short for contrary to fact
conditional. A conditional is an if then
and it's contrary to fact if the if part
isn't what actually happened but what
could have happened right if I had
dropped the the the bowl it would have
broken that's a counterfactual claim
>> if you did not step on the computer it
wouldn't have broken yep
>> exactly that
>> that's an inside joke for those who are
>> Yeah that one's true too uh we use these
counterfactual conditionals all the time
in everyday life we hate them to have
definite truth values. When you say,
"Gee, you could have saved that person
if you, you know, if only you'd gotten
up and and thrown them the rope." That's
a that's a counterfactual conditional.
It's saying if the if reality had been
different in this way, it would have
been different in that way. So, these
are just kind of very common things. And
it's it's sometimes asserted that
there's a tacid assumption in the EPR
argument or in Bell's argument that
there's counterfactual definitess that
all of these counterfactuals have
definite truth conditions. Now what I
want to point out here is that's not
true. That's just not true. And then
people say, "Oh, I can get out of these
arguments by denying counterfactual
definitess." It's not true. Neither
argument assumes counterfactual
definitess. In fact, counterfactual
definitess is just the same as
determinism, right? I can I can tell you
what would have happened had things been
different if I use a theory that's
deterministic
because then I say if I fill in the
details enough, the theory will tell me
what would have happened.
>> But if the theory isn't deterministic,
if it's just probabilistic, the theory
won't tell me what would have happened.
It'll just tell me what might have
happened.
So the assumption of of counterfactual
definitess is just a fancy way of saying
they assume determinism. You said
something super interesting. What could
have happened is different than what
might have happened.
>> Sure. Because in I in well not what
could have happened what would have
happened is different from what might
have happened.
Okay. So suppose I have a deterministic
theory and I ask well what would have
happened if I had dropped the bowl and
someone says well according to the
theory it would have fallen to the
ground and broken. Yeah that would have
happened. Now suppose I have an
indeterministic theory like I have coins
that that have irreducible chances. 90%
chance it comes heads and 10% chance it
comes tails. I say well but I don't flip
the coin right. I say but what would
have happened if I had flipped the coin?
>> Yes. Yes. Then the right thing to say is
well I can't tell you exactly what would
have happened. I said it might have come
tails and it might have come heads
right there's no definite fact if the
fundamental dynamics is indeterministic
about what would have happened had
things been different. Usually there
there's a range of ways it might have
played out if things had been different
because the indeterminism in the theory
allows for different outcomes.
So the assumption of counterfactual
determinatess is the assumption of
But what I've argued and what Bell
argued over and over is that EPR do not
assume determinism.
They infer it. So they don't assume
counterfactual definitess in so far as
they get it. They infer it from the
perfect correlations.
And so you can't defeat the argument by
saying,"Well, I just don't believe in
counterfactual definitess the way you
can't defeat the argument by
determinism." Because it never runs on
determinism. It runs on no action at a
distance. It runs on no spooky action at
a distance.
>> Yes. Yeah. We just I noticed verbiage.
You just you said it runs on no action
at a distance. And then you said dot
dot. It runs on no spooky action at a
distance. But to Einstein, isn't all
action at a distance a spooky action?
Spooky. The spooky is Yeah. The spooky
is just a rhetorical.
>> Okay.
>> The spooky is just rhetorical. It's not
as if Einstein would have said, "Oh,
there's good action at a distance and
there's spooky action at a distance."
[laughter] And I'm okay with good
action. No, no, it's a spooky spooky
just his way of saying he thinks action
at a distance is physically, you know,
is not something he's willing to accept
in a physical theory.
>> Got it. People bring up this
counterfactual definitess and when
they're doing it they're it's just a
roundabout way using unfamiliar
terminology to talk about determinism.
And what they say is that the arguments
assume presume counterfactual definitess
which is just a roundabout way of saying
they presume determinism and it's false.
Neither argument the EP argument does
not presume determinism. Bell's argument
does not presume determinism
because of the perfect correlations. EPR
are able to infer determinism in a local
theory. So that's just to keep people
from being confused about this
terminology that shows up in the
literature a lot. It's just a
distraction
in some and I think we are almost there.
So the EPR argument from uh runs from
causal locality again no action at
distance to the incompleteness of the
quantum mechanical description. That
argument is valid good logical argument
in response to it. Uh sorry Boore and
company had only two logically pertinent
responses. There were only two things
they could do. Either they embrace the
action at a distance as real novel
unexpected physical discovery. They
could do that or they could concede that
the quantum mechanical formalism they
use does not supply a complete physical
description of a system. Those are the
only options
and for sure they didn't embrace that
there was action at a distance.
Actually they all and they also didn't
say that the quantum mechanical
description is incomplete. Right? So of
the two logically possible responses
they took neither. And it's very hard to
understand what it is they were
claiming. And particularly Bor writes a
response
immediately after the EPR paper comes
out in 1935. He writes a response and
it's an incoherent mess, right? Nobody
understands that paper. I mean, there's
a little story about I I've wasted so
much time, but I'll tell you a little
story. When I learned this stuff,
everybody my my of my age, we got a big
red book called quantum theor quantum
theory and measurement that was edited
by Wheeler and Zurich and it contained
reproductions of all these foundational
papers. They weren't retypet or
anything. They were just copied and
thrown into this big fat book.
>> Interesting.
>> And uh it contained the EPR paper, of
course, it contained Boore's response
and everybody read that. uh many years
later after I had read it and so on, I
was talking to Shelley Goldstein and
Shel said, "By the way, did you ever
notice that in that book two pages in
Boore's response have been switched?
They're out of order." And I said, "No,
I didn't notice that." And I talked to
other people and nobody noticed that.
>> And if you try to read it, you turn the
page and the sentence isn't even
grammatical. [snorts] Um why didn't we
notice? Because nobody's following it.
Nobody. It's It doesn't have a logical
flow. It doesn't have a clear through
line. It just is words, right? It's just
bore producing words that you can't
follow. Um Bel Bell himself talks about
not being able to understand bore in an
appendix appendix one to to this paper
um Erdleman socks. So what we have is
what does the EPR argument do? It
assumes local causality, no action in a
distance. It then argues that the that
if you assume that the quantum
mechanical description of a system
cannot be complete, there's more actual
physics that needs to be done. How did
Boore and company respond to this? Well,
one thing they could have done is just
accept the spooky action at a distance.
They could have said, "No, we think that
Alice doing something in her lab does
disturb the physical state of Bob in his
lab." that would certainly answer the
argument. Um, but they don't do that and
the only other logically possible option
for them is to admit that the quantum
description of the system is incomplete
and they don't do that either. The
problem is they don't really do anything
coherent. uh Boore in particular
immediately tries to reply to the EPR
argument and write something that gets
published in the same journal that the
EPR paper was nobody can understand it.
The conclusion of the argument
is that if you have a causally local
theory and it predicts these kinds of
distant perfect EPR correlations
then inferred not assumed from the
beginning it must be a deterministic
theory and so if you want to maintain
causal locality which is what Einstein
wanted you better go for determinism
it's the only thing that's going to work
to return these perfect correlations,
right? But if you say, "Look, I just
don't believe they're perfect
correlations. I don't think any of the
correlations you see in the lab are
perfect,
even though quantum mechanics predicts
perfect correlations here." That
wouldn't even solve the problem because
it's not that you need the perfect
correlations to make trouble for the
completeness of quantum theory. It's
really enough that Alice can do
something that improves her predictions
for Bob. Uh it's it's not that you can
it's certainly not that you can answer
EPR by saying I believe in indeterminism
because it was never an assumption of
determinism in the thing. Now how does
the EPR paper get received?
>> Um he's been Einstein has been
complaining since 1927 about these very
same things. quantum theory is not
complete and so on. You might think it
wouldn't have any effect. It's just
people would say there's Einstein again
making the same old complaints.
But in fact, that's that that's not at
all true. Switching from the single
particle case that we saw in 1927 to the
two particle cases where I can send one
to Alice and one to Bob completely
changed the rhetorical force of the
argument. Um, Rosenfeld, who's Boore's
associate, later reports the following.
This is the quote. This onslaught came
upon us as a bolt from the blue. Right?
They weren't expecting anything like
this. The effect on Boore was
remarkable. As soon as he had heard my
report of Einstein's argument,
everything else was abandoned. We have
to clear up such a misunderstanding at
once. we should reply by taking up the
same example and showing the right way
to speak about it. In great excitement,
Boore immediately started dictating to
me the outline of such a reply. Very
soon, however, he became hesitant. No,
that won't do. We must try over again.
We must make it quite clear." And so it
went on for a while with growing wonder
at the unexpected subtlety of the
argument. Whatever Boore thought he had
as an answer to this, when he himself
tried to articulate it, he couldn't.
Uh-huh.
>> Bore later himself wrote, "Due to the
lucidity and apparently incontestable
character of the argument, the paper of
Einstein pods and Rosen created a stir
among physicists and has played a large
role in general philosophical
discussion. Certainly, the issues are of
a very subtle character and suited to
emphasize how far in quantum theory we
are beyond the reach of pictorial
visualization." Notice that pictorial
visualization.
Um, Boore loved that word visualization
on shallow kite in German and probably
because it's a a word that Kant used a
lot. Kant was very worried about
analikite and visualizing things and
space is the form of outer intuition if
you know your Kant. Um, but I think what
should be clear is that the EP argu
argument has absolutely nothing to do
with visualization. Right? They don't
ask you to visualize anything. All they
ask you to is is accept that what Alice
does in her lab doesn't disturb Bob's
particle. What Bob does in his lab
doesn't disturb Alice's particle. You
don't have to visualize a thing.
>> So this appeal to visualization again is
Boore just falling back on a bunch of
ideas that has been bouncing around in
his head forever and not responding to
the argument. Um so Bore writes this
response. It's it's it's published in
Physical Review where the EPR one was
published. He recycles in that paper
some standard stuff that he'd said
before about single particles and
measuring position and momentum on
single particles, which isn't to the
point because you have two particles.
And the issue isn't whether Alice
measuring the position of her particle
disturbs the momentum of her particle.
It's whether Alice measuring the
momentum of her particle disturbs the
momentum of Bob's particle. That's a
very different, you know, issue. A lot
of what Boore writes in that paper is
not to the point. Bell himself just
tries to parse what Boore is saying at
in appendix one to Bertman's socks and
he gives up. He says I can't make any
sense out of this. Boore himself says he
was never satisfied with his own
response and he was still working on it
when Einstein died. Schroinger's
response is really interesting
>> in 1935. Schroinger writes a paper the
present situation in quantum mechanics
which everybody knows as the cat paper.
That paper is written because of EPR in
in footnote 7. Uh he writes Einstein
Podilski Rosen he cites the paper and he
says the appearance of this work
motivated the present shall I say
lecture or general confession. Very
interesting response right? I mean,
Schroer is responding to EPR and he's
not saying, "I'm going to lecture you.
I'm going to confess something."
He appreciated the argument and he
appreciated the role that entanglement
plays in the argument, which I think
even didn't really appreciate.
In that paper, Schroinger introduces the
term fer shrank, which we translate
entanglement.
So, everything to do with entanglement
starts with EPR. the importance of it,
the physical significance of it and so
on come out of that paper. There we go.
Okay, so we got to the end of act two.
We'll now have a break and then we'll
come back for a short interlude.
>> Uh and then we'll get on to Belle's
theorem, which is actually supposed to
be the subject of this entire thing. But
you can't understand Belle. You cannot
understand Belle without understanding
EPR.
This is a great place to have an
intermission. The audience will absorb
all of this. I want you to say, let's
imagine you were able to do also act
three. So, this was all one long movie.
>> This is to set the record straight once
and for all on what I'm getting you to
say this so that the audience as they
watch act one and two since it's going
to be its own video that they're
watching right now that they can think,
okay, given that that's where this is
going, I also have a couple questions.
let me write them in the comments and
maybe
>> Tim would hopefully be able to answer
that in act three as well. So our our
main point what we're trying to get to
is the significance of Bell's theorem
but Bell's paper is called on the
paradox of Einstein Pedulski and Rosen
right so he starts his starting point is
that you've read and understood the EPR
paper unfortunately most people haven't
read and many people who have read
haven't understood the EPR paper so if
you want to understand Bell you have to
start by understanding EPR are. And you
know where we're going to end up is
seeing how Bell begins where Einstein
left off and then ironically runs an
argument to the conclusion that Einstein
was wrong about spooky action at a
distance that you can't get away from it
that you need it that no local theory in
Einstein sense can work can make the
right predictions.
So, you know, the the great ironic
reversal at the end is that Bell
undermines Einstein's fundamental thesis
that there's no action at a distance,
but he undermines it using Einstein's
own tools out of EPR. And so you have to
understand what they did and what their
argument was based on because if you
want to reject Bell's conclusion, you
got to reject something. And people
unfortunately think they can get out of
Bell's conclusion by saying, "Well, I
just don't believe in determinism or
something like that." But that's no good
because it was never an assumption.
So that's where we're going with all
this. Perfect. Thank you so much. I
appreciate you spending so much time
with me. I understand it's extremely
late where you are. We'll finish up on
another date. Thank you.
>> Hi there, Kurt here. If you'd like more
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