▶︎ 0:00 At the end of last time, we started to talk about the algorithm that was developed over the course of the 1920s for predicting the outcomes of experiments, the outcomes of the kinds of experiments that we've been discussing here, these two paths experiments and double slit experiments, and so on and so forth. But the algorithm turns out to be astonishingly general. It gives you the kinds of results it gives you, for example, for the sorts of physical situations that classical mechanics is good at describing match up very well with the predictions of classical mechanics, and it's predicting not just in these specific experimental circumstances, but in all of the circumstances that we have any idea how to set up. It's making fantastically accurate predictions about the observed behaviors of subatomic particles, and so on.
▶︎ 1:02 We said last time that there are two attitudes
▶︎ 1:12 People thought about taking to this algorithm. Bohr's attitude was that these apparent logical contradictions that you run into, the lesson of these apparent logical contradictions that you run into is that the very aspiration to learn how to tell yourself a story about what the electrons are doing in this double slit experiment or what the electrons are doing in these two paths experiments or anything like that, the very aspiration to do that is mistaken, is misled. This is not what physics can offer us. It's supposed to be the great lesson of quantum mechanics, but this is not what physics can offer us.
▶︎ 2:11 This is not a level to which the human imagination, which, according to people who have this view, was developed for hunting and gathering and not for understanding the to-ing's and fro-ing's of subatomic particles, is just not able to get its head around situations like this. That the world, in a phrase people often used to use, is not merely stranger than we know, but stranger than we can know. And so that was one attitude typical of Bohr.
▶︎ 2:52 What you get out of this is a very militantly what's called instrumentalist attitude towards what science can do for you. What science can do for you is make predictions about how an experiment that's set up in such and such a way is going to come out. And that's it. And there may be a temptation to tell yourself stories about what's going on in between the beginning of the experiment and the end of the experiment. That temptation, that way leads to madness. That temptation is not going to pan out.
▶︎ 3:33 There was already toward the beginning, it's not clear how much these people themselves were aware of the extent to which they disagreed, but people like, say, von Neumann, were clearly thinking about it very differently. That there doesn't have to be, that the contradiction goes away if you let go of the conviction that there must always be a sensible question, there must always be an intelligible question of the form, which slit did the particle go through or which path did the particle take from the entry to the exit of the two paths apparatus?
▶︎ 4:26 You might say the lesson of this is not that we can't tell ourselves stories in a coherent way, but that the stories we're going to be forced to tell ourselves are going to be very strange and very unfamiliar, but not logically unintelligible. So for example, what you might say to yourself is that when the electron is on its way through the two paths apparatus, it's in a situation, a very definite physical situation, which people came to refer to as a superposition. It's in a very definite physical situation and such that it is a feature of that situation that asking which path it's on amounts to what philosophers have long called a category mistake.
▶︎ 5:17 That asking which path it's on is like asking about the marital status of the number five or about the weight in grams of Catholicism or about the political affiliations of this table, or something like that. The number five is not the kind of thing that has a marital status, and when the electron is passing through the two paths apparatus, it somehow becomes not the kind of thing about which it makes sense to ask what path it's on. This is a way of hanging on to anti-instrumentalist intuitions about what science can do for you. This is a way of trying to tell a story even if it turns out to be a strange story, about what's going on.
▶︎ 6:14 A part of this algorithm is a mathematical object called the wave function. Somebody like Bohr will regard the wave function as just a piece of mathematical apparatus which has a certain role in this algorithm for predicting the outcomes of future experiments given the outcomes of past experiments. Somebody like Von Neumann, on the other hand, wanted to think of this wave function as an actual description of what the particle is doing even at, in between these two experiments.
▶︎ 6:56 This wave function tells you when the particle goes into a superposition of being on this path and that, or that path, or when there is a fact of the matter about which path the particle is on, so on and so forth. Von Neumann says, "Look, the algorithm is apparently going to have to include some stipulation." For example, we saw last time, let's look at the two paths experiment again.
▶︎ 7:33 So here's the hardness box. Here's the hard path, here's the soft path, here are the mirrors. Here's the black box. We noted that if you stopped the experiment in the middle, and if you put a detector say over here that clicks if a particle passes near it, then it's the case. So without, when the detector is turned off, every white particle you feed in here comes out white there.
▶︎ 8:27 If you turn the detector on, so that you're in a position to ascertain which path the particle took, what happens always is half the time this thing clicks and half the time it doesn't click. Whenever it clicks, then any other detector that you put farther down on the same route will click itself. That is, as of the moment it clicks, this electron starts to act as if there is a determinate fact of the matter about which path it's on. And all of its subsequent behaviors, like its color statistics out here, so on, are compatible after that with the claim that it's on the hard path.
▶︎ 9:14 On the other hand, if you don't put these detectors in, or if you don't turn them on, what you get is 100% white out here. Behavior which is not compatible with the thought that there is any fact of the matter about which path the electron takes through the apparatus.
▶︎ 9:36 So we have this algorithm which tells us, for example, that when we feed a white electron into a hardness box, it's going to emerge from that box on a superposition of being on the hard route and being on the soft route. The algorithm tells us that these are one of the circumstances in which these superpositions are going to arise. That that passage of a white electron through a hardness box, one of the effects of such passage is to leave the electron in one of those conditions for which it simply doesn't even make sense to ask which path it's on. In one of those conditions for which asking what path it's on is like asking about the marital status of the number five.
▶︎ 10:24 But it's also the case, it's also part of our experience, that you put a detector here to see where it is, that the operation of that detector apparently forces the electron to choose a path. Forces the electron back into a situation in which there is a fact of the matter about which path it's on, a situation in which asking which path it's on is no longer like asking about the marital status of the number five. In order to account for both of those behaviors, Von Neumann thought that the algorithm for predicting the behaviors of all physical systems, now including electrons, this is now, this algorithm is now, as I said, presenting itself as an absolutely general fundamental physical theory of the world. It looked to Von Neumann as if it was gonna need to contain two laws.
▶︎ 11:35 One law that applies when measurements are not being carried out. This is the law that's given by the famous Schrodinger equation, a differential equation that tells us how this wave function mathematical object evolves. And another law that he called the first one, law number one, and he called the second one law number two. Another law that tells us how these wave functions behave, how the states of these systems behave when measurements are being carried out. And the essence of that law is when you carry out a measurement, you force the measured system to choose some value of the observable you're measuring. It snaps suddenly into a state for which questions about that value makes sense and for which, moreover, the particular value that it has is the one that you measured it to have.
▶︎ 12:38 Von Neumann did more than that. Your intuition might be, it's a reasonable intuition to have, your intuition might be to say, "Well, look. Presumably, what happens when I do a measurement, what happens to the physical state of the world when I do a measurement, ought to be just a special case of the application of the laws that govern what happens to the physical state of the world generally." That is, the intuition is something like this: a measurement is just a name that we give to a particular kind of collision between two physical objects. Two particles can collide with one another, or two tables can collide with one another, or the kind of physical object that we call a measuring device can have a collision with some other system which happens to be the kind of system a certain property of which it is designed to measure.
▶︎ 13:42 And all of those presumably ought to be covered under the same set of fundamental general laws, and the very important thing that von Neumann was able to show is that that's not the case here. That this phenomenon that people started to call collapse, this business of forcing the system to pick a value, to pick a path, in this case, this is not going to emerge. If you try to derive it just from the law number one, the general law, applied to the special case of a collision between this electron and the measuring device, indeed, von Neumann was able to show that if you do that, if you apply law one to the measuring process itself, law one is going to give you a definite prediction, a deterministic prediction.
▶︎ 14:42 And the prediction is that the measuring device is going to go into a superposition of having clicked or not having clicked, and the brain of an observer who looks at the measuring device is going to go into a superposition of having heard a click and not having heard a click. So that, at the end of the day, there's not going to be a fact of the matter even about what the sentient observer took the outcome of the measurement to be. And the presumption is, we know, we know by a method which is more certain than the source of any other kind of knowledge we have, we know by direct introspection on our own phenomenal states that that's not what happens. That that's not the way these experiments end up. So, law one can't be completely general. It can't account for what happens when we do these measurements.
▶︎ 15:42 What you find in von Neumann's book is a very bizarre formulation, where he says apparently there are two fundamental laws. There's the law that governs the behaviors of physical systems when they're not being measured. That's Schrodinger's equation. That's law number one. And there's a law that governs what happens to these physical systems when they're being measured. That's this collapse postulate, this demand that the state of the system choose one or the other of the values of whatever property it is that's being measured, that it snaps either into a state where it's on the hard path or into a state where it's on the soft path. And then things go on as before in accord with the Schrodinger equation until the next time a measurement occurs.
▶︎ 16:37 So the way things get left in von Neumann's famous book is, as I said, that the fundamental laws of physics look like this. Law number one applies when measurements aren't going on. Law number two applies when measurements are going on. And that's, of course, insane. If for no other reason than the word measurement is a vague English word, that doesn't have anything like the requisite precision to be playing this kind of role in the theory that's supposed to be the fundamental and universal physical theory of the world.
▶︎ 17:28 Audience: And the reason why you said that von Neumann was an improvement from the previous attitude is because at least the guy tried to introduce two laws to consistently account,
▶︎ 17:43 Well, I, that,
▶︎ 17:43 I would say, first of all, I'm not even sure I would say improvement, although from my point of view, it certainly is. But there's the following contrast. Von Neumann is clearly not satisfied with being an instrumentalist in the way that Bohr is. Von Neumann is in the business of trying to tell a story, about what happens between this time and this time. It's a strange story. But it's not a logically unintelligible story.
▶︎ 18:14 Indeed, Bohr seems to have thought. Bohr had some, and this is just one among many, many, many very puzzling things about Bohr's attitude. But Bohr's reaction to this sort of logical contradiction, he elaborated a little further on the impossibility of telling a story. He had a shtick that he referred to as complementarity.
▶︎ 18:48 He said, "Look, here's a little more detail about why it's impossible to tell any story. If you have one of these detectors here, then you must treat the particle from the beginning as having a position which you are detecting. If you don't put one of these detectors here, you must treat the particle from the beginning as having a definite color. And those two properties are complementary here. You can't entertain them both at the same time."
▶︎ 19:37 And I don't know if anybody ever said to him, "Yeah, fine. Let's learn a new language, of superposition." It seems to have been some kind of very deep principle for him that we don't have that option. That we don't have an option to leave the classical language behind. Von Neumann is trying to do something just like that. "No, no, no. We need a new language to describe what this electron is doing. It's just wrong to talk about positions versus colors or something like that. But there's no reason why we can't learn this language. There's no reason why we can't go native here."
▶︎ 20:28 Bohr seems to have thought that that was just a crazy thing to do. I wish I had something more illuminating to say about why he thought that. I just don't quite know what to say, and subsequent developments certainly haven't borne out the claim that this isn't a language we can learn to use, and to be descriptive with and so on and so forth.
▶︎ 20:54 Anyway, von Neumann certainly differs from Bohr in this respect. No, we can have a logically coherent but very strange story about what the electron is doing, and von Neumann is unmistakably in the business of trying to tell a realistic story about what the electron is doing, but the realistic story he initially has to tell is just crazy.
▶︎ 21:26 This is just a comment, because I think in popular circles you often hear people, for example, see the interference pattern in the double-slit experiment and they say, "Oh, this shows wave-particle duality." So sometimes electrons behave like a wave and sometimes they're like particles.
▶︎ 21:41 Audience: So in this framework, would that mean when you're following law one, they're in some sense this wave across space, and then when you're following law two and measure it, they're a particle?
▶︎ 21:50 Not exactly. Does this make a bit more sense to you?
▶︎ 21:52 Audience: Not quite.
▶︎ 21:52 I wouldn't say the distinction falls along the lines of law one, law two. It's more like this. If you only do a measurement at the beginning and at the end, it depends where you do the measurements. If you only do a measurement at the beginning or at the end, you're setting up a situation where you have to think of this system as represented by a wave. A wave which can, in some sense, take both routes, although not in any familiar sense. If you're setting up a situation where you're going to put a detector by one of the routes, then you have to be modeling this thing to yourself as a particle. In order to get the right results in this case, you have to be modeling this thing to yourself as a particle.
▶︎ 22:54 The wave-particle duality is easier to understand in the context of the double-slit experiment. So maybe that's very helpful. Here's the situation in the double-slit experiment. Here's the electron gun, here is the screen with two slits, and there's the fluorescent screen.
▶︎ 23:17 The idea is this. There are different situations with which people were very familiar. You have water waves, you have something going up and down in a tub of water, and waves start coming out, and you have obstructions like this, and you see what the wave pattern is over here. These interference patterns are very familiar from things like water waves or sound waves or light waves or something like that.
▶︎ 23:53 So the thought was, when both slits are open, and there's no detector to tell you which slit the thing is going through, that's when you're going to get this interference pattern. That's when you have to think of the electrons, now we're thinking of these as electrons, not water waves. That's when you have to think that in order to make sense of this interference pattern, you have to think of the electrons as a wave, whatever exactly that's supposed to mean. If you have a detector here that's turned on, that's going to change the landing pattern to that. You have to think of the electrons as particles.
▶︎ 24:40 You want to ask a question like, but how do I think of the electron simpliciter? This is supposed to show that that's an insane question. That that's a question that can't be asked. You have to think in a new, complementary way. And as I said last time, Bohr had this very late 19th century European philosophical education. This is all about Hegel. This is all about thesis and antithesis and so on and so forth.
▶︎ 25:17 This is a very elaborate way of saying, "You want a story? There's no such thing. There's no such thing." Once again, I'm conscious of not making the kind of sense of Bohr that it feels like a teacher is obliged to make, but I just don't know what the hell the guy was talking about. I really don't.
▶︎ 25:44 We're on the train with von Neumann now. Von Neumann's trying to tell a realistic story, but he's got a terrible story. On the other hand, von Neumann has shown it doesn't feel like there's an option of the form, well, just throw out the collapse postulate, because you can't get it from law number one. And you can't throw out law number one either, because law number one is absolutely crucial to making the right predictions about how experiments come out.
▶︎ 26:17 So you're apparently stuck with these two laws, and it looks like what you need to do is come up with a way of locating the boundary between that set of physical situations in which law one applies, and that set of physical situations in which law two applies. And von Neumann's suggestion was the location of that boundary is the location indicated by the word measurement. That's not a good way to locate the boundary.
▶︎ 26:56 Astoundingly, for about 40 or 50 years after this, people wasted their time coming up with equally ridiculous ideas about where the boundary lay. So instead of using words like measurement, people used words like macroscopic. At the level of the macroscopic, the boundary is such that, once you get into macroscopic superpositions, law number two kicks in. Well, what does macroscopic mean? Or thermodynamically irreversible. Once you get to the level of thermodynamically irreversible processes, law number two kicks in. What the hell does that mean?
▶︎ 27:52 Or once recordings of the outcome of the experiment have become indelible, then law number two kicks in. You mean it matters what kinda ink you use? It's really crazy, this history of speculation. It's really undignified, this history of speculation. It was clearly getting you nowhere. Let me just discuss in a little bit more detail the maybe the most interesting and most extreme episode in this particular history of speculations about where to draw the boundary.
▶︎ 28:46 Eugene Wigner, who was a very distinguished physicist, Nobel Prize winner, made enormous contributions to the development of quantum mechanics, was interested in this problem, and thought that a principled place to draw the line might be at the level of consciousness. That consciousness might have something important to do with this. The proposal would be something like this. Law one applies under all circumstances unless and until the evolution that's proceeding in accord with law one produces a situation where a certain sentient, embodied sentient being enters into a superposition of two states that correspond to two different occurrent conscious mental states. The mental state of hearing the click on the detector and the mental state of not hearing the click on the detector.
▶︎ 30:05 And the thought was that it's that that nature abhors. Law one is there to forbid just those kinds of superpositions of consciously different states. So the idea is nature evolves along in accord with law one until law one lands us in a situation of the kind that von Neumann had proved many years before it will land us in. Lands us in a situation where what we're dealing with is a superposition of one state in which I heard the device click and another state in which I didn't hear the device click. That is, the state in which asking whether or not I heard the device click is like asking about the marital status of the number five. A state in which there is no fact of the matter about whether I even think I heard the device click or not.
▶︎ 31:06 Audience: That would mean that even if you place the particle detector in the two-path apparatus,
▶︎ 31:11 Right.
▶︎ 31:11 Audience: before I look,
▶︎ 31:12 Correct.
▶︎ 31:12 Audience: which one is not white.
▶︎ 31:14 Correct, correct, correct. Before I look, there's no fact of the matter about whether it clicked or not. When I look and I become conscious of whether it clicked or not, that's when law number two kicks in. That's when we have a collapse.
▶︎ 31:34 Here's why Wigner thought this was cool.
▶︎ 31:38 Audience: Just to paraphrase that, what I'm hearing is basically somebody telling me that we make the world how it is?
▶︎ 31:55 No. But our conscious states, I was just about to elaborate on this. It is true that what goes on in our consciousness has an effect, a very profound effect on the physical world. Here's what Wigner thought about this. Wigner wrote an essay which became very famous and widely read in the 1960s and '70s, and which subsequently gave rise to a huge new age industry where it still flourishes. Wigner wrote a famous essay called On the Mind-Body Problem, in which the thought was the following.
▶︎ 32:38 First of all, on this view, yes, conscious entities behave physically differently than entities that are not conscious. Conscious entities, it's only in the evolutions of conscious entities that law number two ever applies. Physical, inanimate, unconscious entities never evolve by themselves in accord with law number two. They always obey law number one. Wigner thought, "Wow, this is the coolest thing in the world." Here's why.
▶︎ 33:20 There's long been a worry, there's long been an anxiety, to the effect that the mechanical conception of the world that we get from Newtonian mechanics, that we get from Maxwellian electrodynamics, so on and so forth, it has no space in it for anything like a mind. We're just collections of billiard balls, these anxieties centered around worries about freedom of will versus determinism and so on and so forth. There was this longstanding vague anxiety that there was a tension between the picture of the world that's being presented to us by post-Renaissance physics, and the way we're used to thinking of ourselves as agents and as sentient.
▶︎ 34:24 Wigner says, "Look at the irony of this. If I'm right about this, it's not merely the case that physics is not hostile to there being mental entities that are utterly distinct from mere collections of billiard balls. It's not merely the case that physics isn't hostile to that. Physics needs that. That's what produces collapses. The existence of consciousness." So Wigner thought that he had turned the traditional mind-body problem on its head, or that the advent of quantum mechanics had turned the traditional mind-body problem on its head.
▶︎ 35:07 It's not merely that our conception of ourselves as physical objects and our conception of ourselves as something else aren't hostile to one another. It's not merely that there's no tension between them. They need each other. The only thing in the world that can produce these collapses, and we need these collapses in order to explain these experimental results, the only thing that can produce these collapses is mentality.
▶︎ 35:35 Indeed, hold on just one second. Indeed, Wigner said, "You wanna know what the difference between mental objects and material objects is? We have the answer here. What you mean by a purely material object is an object that always obeys law one. What you mean by an embodied mentality, by an embodied consciousness, is a system that sometimes obeys law two. That's the difference between minds and bodies. That's why minds and bodies, that's why the physical account of the world and a sort of dualistic, mentalistic account need each other."
▶︎ 36:19 Not only are they not hostile, they depend on each other.
▶︎ 36:23 Sorry, I cut you off.
▶︎ 36:24 Audience: The fun thing about listening to your lectures more than once is I'm just as lost the second time as the first time. Now, it sounds to me, to hear that, there may be at times no facts of the matter about the world.
▶︎ 36:52 Wait, wait, wait. No, no, no, no, no. No, no, up until there is a. There isn't a fact of the matter about the position of the electron. When I say there's no fact of the matter about the marital status of the number five, that doesn't mean anything like there are no facts of the matter about the world. There are facts of the matter about the sum of five and three, so on and so. It just doesn't happen to be a fact of the matter about the marital status of the number five.
▶︎ 37:19 Here, there are certain circumstances, not in which there are no facts of the matter about the world, there is a perfectly definite fact of the matter according to somebody like Von Neumann about the situation of the world when the electron is passing through this device. You wanna know what that fact is? It's given by its wave function, which tells us that it's in a superposition of being on this path and being on that path. That's a perfectly definite fact. It's just that there are things that we always imagined there would always be facts about vis-a-vis particles, like their positions, and sometimes there aren't facts about that.
▶︎ 37:59 So, number one, so is Wigner's position a dualist position? Absolutely. Not only is it a dualist position, it's the wackiest kind of dualist position. It's not an epiphenomenalist position, it's not a parallelist position. It's what's called an interactive dualist position. It's the kind of dualist position that Descartes had. And that not that many people since Descartes have espoused. It's not only that minds and bodies are metaphysically distinct things, but it's also not only that, that the physical state of the world can affect its mental state, which everybody agrees with, but the mental state can affect the physical state.
▶︎ 38:51 Audience: Wherever it is that you're coming from, when you come to physics, you would think that one of the motivations is to eliminate, precisely, to put dualism aside.
▶︎ 39:01 Yeah, I don't know what to tell you.
▶︎ 39:03 Audience: How do you go from Wigner's view, physical state.
▶︎ 39:05 Look, first of all, we got trouble here. We got serious trouble here. And, you know, desperate times call for desperate measures. This is, in a way, a desperate measure. But Wigner also thought the flip side of it is, no, this clears up an old problem. On Wigner's view, this is the only way he can see to make sense of this. He thought that the distinction between there being consciousness and there not being consciousness is sharper than the distinction between measurement or non-measurement, or macroscopic and microscopic, or indelible and not indelible, or something like that. Of course, the minute you think about it, there's no reason to say something like that.
▶︎ 39:55 I myself, when I was a graduate student, in one of the more depressing moments of my life, heard Wigner talking about this theory, and expressing the opinion that he thought dogs could probably cause collapses but mice probably couldn't. And you say to yourself, as you were just implying, "This is not the right way to do physics." This just seems really, really bad. And you have this guy standing there, he doesn't like mice. I don't know what the deal is.
▶︎ 40:35 He said, "Look, we're in trouble here. We got these two laws. We gotta find some demarcation. We gotta find some boundary. Some way of fixing the boundary between those situations in which law one applies, and those situations in which law two applies," because Von Neumann mathematically proved that one is not a consequence of the other, that they are real contradictory claims about how the wave function evolves.
▶︎ 41:08 So, we're stuck here. We're in a bad situation. He's trying to solve it. This is an example of how it could imaginably be the case. I think he's wrong. But he's not an idiot, and it's not as if you can't even imagine the reasons somebody might have had to be led to these conclusions. Somebody in a very scientific tradition might have had for being led to these conclusions, indeed a very distinguished physicist of the 20th century had for being led to these conclusions.
▶︎ 41:46 You do have to pause and say, and this is related to the conversation I was having with you at the end of the last session, you step back and you say, "These guys are just trying to figure out how rocks work. Trying to figure out how inanimate material objects work." And in a way that isn't crazy, in a way that's understandable to see how they got there, they're suddenly getting involved with speculations about dualism, about the difference between mind and body, and so on.
▶︎ 42:32 It's amazing that physics got worked in. Here's a way to put it. In two ways already, the physical project, the scientific project, as it was traditionally understood, was brought into a profound kind of crisis. The first is with Bohr, where you just say, "I'm sorry. The whole business of trying to make up these stories about what's going on in between one observation or another is hopeless." People don't accept that. People try to press ahead. Like Von Neumann, with the business of telling a realistic story, even if it's a strange story, so they press ahead without fear to hang on to this kind of project, and they go through a couple of ridiculous speculations about where law number two kicks in, and the next thing you know, they're involved with all these notions about the mind/body problem and so on.
▶︎ 43:45 It's a tough, deep challenge that's presented to us by the behaviors of these subatomic particles, by the very stability of matter. And there is something astonishing, something that's indicative of how much is at stake here, that you're not looking for trouble like this. You're just measuring rocks and feeding them through machines and trying to see what happens. And you get dragged into very weird places.