▶︎ 0:01 Bohr says, "In accordance with this situation," or he's referring to something more or less like this, "There can be no question of any unambiguous interpretation of the symbols of quantum mechanics other than that embodied in the well-known rules which allow us to predict results to be obtained by a given experimental arrangement described in a totally classical way." The idea is, and we're gonna talk more about this later, what was developed was a fairly straightforward and explicit algorithm for predicting the outcomes of these experiments given the arrangement and the outcomes of these initial color measurements.
▶︎ 0:57 So you had an algorithm into which you plug whatever arrangement you've set up. You plug the outcomes of the measurements you did on these particles before you fed them into the hardness box, and you use it to predict the outcomes of these color measurements over there. And this algorithm works. The name of this algorithm is quantum mechanics, and this algorithm works very well, spectacularly well in making these predictions. Indeed, it makes predictions which are staggeringly more accurate than any previous physical theory.
▶︎ 1:42 But Bohr is adamant, because of arguments more or less along the lines of the one I've given you, that any attempt to tell yourself a story, to offer yourself a picture, to tell yourself an intelligible story about what's going on in between the time you put the electron in here and the time you measured its color out there, any attempt to do anything like that is stupid, and is going to fail, and is going to collapse into paradox and contradiction. And this is a profound moment in the history of science, in the history of the aspirations of the scientific activity.
▶︎ 2:38 Let me just mention, there's a lot one could say about this, and I don't think a good history of this has been written yet, but this is going on at the same time as various other intellectual movements are going on, the rise of modernism in literature and in painting, so on and so forth. All kinds of, there's some sense in which in the zeitgeist that was around then, the original aspirations of the scientific activity were akin to the aspirations of, say, the 19th century naturalistic novel, or something like that, that there was some possibility of just straightforwardly saying what happened, saying who did what. And these were thought to have collapsed under pressure from all kinds of angles, from the development of psychoanalysis, all kinds of, there was supposed to be a crisis of representation that was affecting things like the novel, that was affecting things like painting, so on and so forth.
▶︎ 4:03 And it seems to me that at least part of what must have been going on with Bohr was some idea like, you think you have a crisis of representation? You got trouble, you have trouble getting to the bottom of people's motivations of this. I got trouble with rocks here. It's coming up at a much more elementary level, in a much more shocking and radical way.
▶︎ 4:38 There were certainly a lot of people in literary modernism, especially people in the Bloomsbury circle, like Virginia Woolf, who were very aware of what was going on in physics and who were clearly trying to reflect it, trying to find connections between what was going on in physics and what they took to be a crisis of representation in the hopes espoused by something like the 19th century European novel. This wasn't completely independent of a larger historical zeitgeist that was around at the time. And in that context, this sounded really cool.
▶︎ 5:31 There were smart people who said, "Well, here's another attitude you could take." Once again, go back to the fact that we seem to have run out of logical possibilities here. This was much later than Bohr. This was around the 1960s. People said, "Look, another attitude you could take is, no, no, no, there's a story to tell about how the electron got from there to there, but the story violates logic." The story represents the first case in history of an empirical scientific discovery about the laws of logic.
▶︎ 6:21 There were people at the time, people like John von, the mathematician von Neumann, or Schrodinger, the discoverer of the Schrodinger equation, and so on and so forth, who were not as comfortable as Bohr apparently was with just giving up the possibility of telling a new story at all about what's going on between there and there. The way I'm about to describe this story isn't explicitly what any of them said, but how things looked after the dust settled, after a while. The idea was, wait a minute. There's a way to get out of this straightforward logical contradiction by saying something like this: maybe in the period between the initial color measurement and the final color measurement when the electron is inside the apparatus, the electron is in some kind of a situation, a situation which has never been dreamt of before for something like a material particle, but which is not obviously a logical contradiction in the way we were suggesting it might be.
▶︎ 7:54 Maybe there are modes of being available to things like electrons. Maybe there are situations that electrons can be in where for some reason a question of the form, "Is it on the soft path or is it on the hard path?" doesn't make sense. In the same way that, for example, a question of the form, "Is the number five married or single?" doesn't make sense. Or a question of the form, "Does Catholicism weigh more or less than five grams?" Or a question of the form, "Is this table a Republican or a Democrat?"
▶︎ 8:44 These are kinds of questions that philosophers are very familiar with. They're referred to as category mistakes. If somebody says, "By the way, is the number five married?" you say, "No." And the guy says, "I see. So number five is a bachelor." You say, "No. Neither of those is the case," and there's no logical contradiction there. The number five is not the kind of thing that has a marital status.
▶︎ 9:19 I'm not making a contradiction as if I were saying the number five is both married and unmarried. It's neither. The category doesn't apply to the number five. And it's not the case that if this table isn't a Democrat, it must be a Republican or an Independent. That's not the case. These questions of political affiliation just don't apply to tables.
▶︎ 9:48 Now, if we take that approach here, it's admittedly a much stranger situation, because there are circumstances, like before we feed the electron in here, where it seems to make perfect sense to ask where the electron is, and the question has an answer. The electron is right here. And when the electron comes out the other side of the apparatus, it again makes perfectly good sense to ask where the electron is. The question has an answer. The electron is here. But the suggestion here is that when this white electron passes through a hardness box, the hardness box puts it into some condition in which asking about whether it's taking the hard path or whether it's taking the soft path is like asking about the
▶︎ 10:48 Marital status of the number five. Or to put it in a more positive way, what we want to say is that the electron enters some state on passing through a hardness box, that is, a white electron does. A hard electron doesn't do this. A hard electron just comes out here, no problem at all. But a white electron fed into a hardness box apparently, or at least on this way of trying to tell the story, enters into some kind of radically unfamiliar physical condition in which there is simply no fact of the matter about where it's located in space.
▶︎ 11:32 There's no fact of the matter more particularly about whether it's moving along the soft path or moving along the hard path. And then, somehow, the effect of passing through this black box, this recombination box, is to restore there being a fact of the matter about where the electron is. This is radically unlike, say, the case of the number five. There are no circumstances in which the number five has a marital status. There's no circumstances in which this table has a political affiliation.
▶︎ 12:17 With electrons, the case, if you want to try to tell the story this way, the case seems to be different. Electrons can sometimes be in situations where it makes sense to ask about their location in space, or about which of these two paths it's on, and there seem to be other circumstances in which, if you want to tell the story this way, it fails to make sense to ask where the electron is. There is, as a fundamental matter, no fact of the matter about whether the electron is on the soft path or on the hard path. This is, of course, very, very strange.
▶︎ 13:00 By the way, and of course there's a long and venerable tradition in all areas of human speculation that if you don't understand something, at least you can make up a name for it. So people say, in circumstances like this, when they're trying to tell the story this way, that this white electron, after it emerges from the hardness box, is in a superposition of traveling along the soft path and traveling along the hard path, and what that means is the following set of things. One, if you look for it anywhere other than on the soft path or the hard path, you won't find it. But there is no fact of the matter about whether it's on the soft path or it's on the hard path. Asking about whether it's on the soft path or on the hard path is like asking about the marital status of the number five.
▶︎ 14:03 A mathematical apparatus was developed throughout the course of the 1920s, and that was more or less in finished condition by the end of the 1920s, for predicting when these sorts of circumstances are going to arise. And for predicting much more generally, making predictions, sometimes deterministic predictions, as in this case. Other times, probabilistic predictions. An apparatus, a mathematical apparatus was developed, a mathematical algorithm was developed into which, like I was saying, you plug the external circumstances, is there a total of nothing box along the soft path, what are the initial conditions? What was the result of the color measurement over here for predicting the outcomes of measurements later on?
▶︎ 15:05 Audience: Would it be fair to say when you hit a wall in the development of fundamental sciences, instead of giving up something like logic, you instead give up on things like location?
▶︎ 15:22 Well, you give up, there's a lot of things, that's always a delicate kind of balancing act, yes. I would think logic is one of the last things you want to give up on.
▶︎ 15:38 Indeed, I'm not even sure I know what it would mean to give up on logic. According to this algorithm, being in a state like an electron which is in a hard state is in a superposition of being black and being white. A while ago, we were talking about the fact that we couldn't put ourselves in a position to say about a given electron at any time, "Oh, this electron is both black and soft." And that got stuck with the name uncertainty relation. The word uncertainty makes it sound like this is a question of knowledge, this is a question of our not knowing something.
▶︎ 16:27 In light of these experiments, you reason like this. We know it's a property of a hard electron that you put it into the box, it comes out this way. We know it's a property of a soft electron that you put it into a box, it comes out that way. What we're learning here is that if you put a white electron into this box, it comes out in a superposition of this way and that way. If you put a white electron into this hardness box, there is no fact of the matter about which aperture it came out of. If this is a good hardness box, what that suggests is that a white electron is itself already an electron for which there is no fact of the matter about whether it's hard or soft.
▶︎ 17:16 So, when we said earlier on, which is true, there's no way we can put ourselves in a position to point at a given electron at a given moment and say this electron is now both soft and black. That's not a limitation of ours. What these experiments suggest is that what's going on there is that when an electron is known to be white, it's not the case that we don't know what its hardness is. It's the case that asking about its hardness is like asking about the marital status of the number five.
▶︎ 17:59 The situation here is that the character of what we're missing here is metaphysical rather than epistemic, if you adopt this way of telling the story. If you go with Bohr, you don't try to tell a story.
▶︎ 18:18 You just forget about it. You adopt a sort of instrumentalist picture of science. What science is for is to predict the outcomes of later measurements from the outcomes of earlier measurements. Once upon a time, people were naive and silly, and what they thought they were gonna get from science was a picture of what's going on in the world. Now, we've grown up. Growing up is always painful, but this is what happened here.
▶︎ 18:49 That's what's going on according to Bohr, in a way that I think most people now who look at foundations of quantum mechanics think was very harmful. He set himself up as a sort of prophet or a guru, who made these declarations that there must be no speculation about what's going on in between the beginning of the experiment and the end of the experiment and ran around spouting little aphorisms like, "Clarity tends to crowd out depth," which you say, "Wow, that's really disappointing." That's true. And aphorisms like, "A trivial truth is a truth whose negation is false. A deep truth is a truth whose negation is also true," and you say, "Wow, I used to look up to you. I used to look up to scientists."
▶︎ 19:56 Anyway, what happens over the course of the 1920s, early 1930s, is that this algorithm, at least a version of this algorithm which leaves out technical questions about what to do with the special theory of relativity and so on and so forth. A version of this algorithm is developed over the course of the 1920s and is more or less in place by the end of the 1930s,
▶︎ 20:30 And this algorithm is absolutely general. You plug into this algorithm any experimental setup you like, and any initial outcomes of any physical experiments, and the algorithm spits out for you predictions about how future physical measurements are going to come out. So for example, people were able to show that if what you plug into this algorithm are the kinds of questions that we're used to Newtonian physics being able to answer, like where the planets are going to be two weeks from now, or where a certain cannonball is going to land if it's shot at a certain angle at a certain velocity. Arguments were developed to show that this algorithm, in cases where classical physics made the correct predictions, this algorithm made very similar predictions to the predictions of classical physics.
▶︎ 21:30 So this algorithm was proposed as a new complete fundamental physical science. It wasn't the kind of fundamental physical science that we had previously thought we wanted. It wasn't the kind of fundamental physical science, unless you went in for this superposition kind of talk, but according to Bohr, it wasn't the kind of algorithm that we had hoped physical science was going to give us, and if you wanted that, if you wanted the original aspirations of physical science, what you needed to do was grow up.
▶︎ 22:12 Good, but there were other people involved in developing this algorithm who were thinking about it more realistically, but as, for sure, implying very, very strange things about how material particles like electrons or photons or neutrons can behave, and part of the way the algorithm worked, and this is going to be something that's later on going to arise as a very deep problem for us which we're going to want to talk about a lot, a peculiarity about this algorithm.
▶︎ 22:59 Let me back up a little bit. The algorithm uses a particular kind of mathematical object. There are several ways to represent this object, but one common way to represent this object is with a mathematical object called a wave function. Quantum mechanics uses these wave functions to say what there is to be said about the physical situation of an elementary particle or of a collection of elementary particles that form a table or a computer or a university or anything else. This is supposed to be a completely universal physical theory. It uses these wave functions to represent whatever it is one can represent about these physical objects.
▶︎ 23:50 If you're somebody like Bohr, all these wave functions do for you is serve as part of a prescription for calculating the results of future experiments or calculating the probabilities of results of future experiments. If you're someone like von Neumann, this wave function is something from which you can read off, even at intermediate times here, what there are facts about, what there aren't facts about, so on and so forth, so that the wave function of a particle that's in the middle of passing through this apparatus is a mathematical object from which you'll be able to read off the information that, as it's passing through, there's no fact about, there's no fact of the matter about its hardness, there's no fact of the matter about whether it's on the hard path or the soft path, but it's also the case that the algorithm predicts that after it passes through the black box, there is going to be a fact of the matter about its position and there's going to be a fact of the matter about its color.
▶︎ 24:54 Good. The name of this algorithm, as I said, is quantum mechanics, and what is important to know about this algorithm is that notwithstanding how puzzling this is or how discouraging, how puzzling it is conceptually if you're trying to be a realist about it, or how disappointing it is if you're giving up on the realist project. Notwithstanding all that, this algorithm was the most powerful, accurate, successful recipe for calculating the probabilities of the outcomes of experiments ever developed in the history of physics.
▶︎ 25:45 It was astounding. More or less overnight, the entire separate science of chemistry became a homework problem in quantum mechanics. And you could, at least for simple atoms where you could really solve the equations of motion, you could show why hydrogen atoms behave exactly the way they do, and why they combine with the other atoms they combine with, and fail to combine with atoms that they don't combine with, and so on and so forth.
▶︎ 26:20 The success of this was beyond belief, and indeed, 20 years later, at the height of World War II and then of the Cold War, this algorithm made theoretical physicists the masters of the universe. They were determining the fate of human history. They were the people to whom everyone looked for advice and for guidance. I want to point out something curious about this algorithm.
▶︎ 26:55 So what the algorithm does for you is tell you how this wave function, from which you can read off either future predictions if you're Bohr, or you can read off all the facts that there are facts about, and all the things that there are facts about, and which things there aren't facts about, and so on and so forth, about a particle passing through this device. What the algorithm does for you is give you equations of motion like the Schrodinger equation, which determine how these wave functions evolve in time. Just as Newton's equations of motion told us how the positions of material particles evolve as time goes on. Now, this quantity position of the particle in Newtonian mechanics, or position of the set of particles, is being replaced by another mathematical quantity, the wave function. And what you want from physics in either case is to tell you how these things change with time.
▶︎ 28:03 And there is an algorithm to tell you how this wave function changes with time. Bohr is cautioning you all the time, "Do not under any circumstances think of the wave function as some kind of description of what the system is doing. The business of describing what the system is doing is hopeless." Other people, like von Neumann, like Schrodinger, with more scientific realist sympathies, wanted to try to think of the wave function as indeed a description of what the system you're talking about is doing, but it's describing the system doing very, very weird things. It's describing the system being in circumstances in which even asking about its location in space is like asking about the marital status of the number five.
▶︎ 28:59 Good. That having been said, there's something weird about the algorithm itself. And this is a second problem, and this is a second reason why Bohr thought that the whole project of scientific realism had collapsed. Had not just collapsed, but more dramatically, had committed suicide. It wasn't killed by philosophical critique, it was killed by itself.
▶︎ 29:38 Among the things that this algorithm had better explain is why it is that when I insert a particle detector here. So let's consider a certain setup. I have this two paths apparatus. Maybe I've got a total of nothing box here, but it's turned off for the moment. So when the total of nothing box is turned off, every white electron I feed in here comes out white there. The algorithm predicts that. It also predicts that when I switch the total of nothing box on, every white electron that I feed in here comes out black there.
▶︎ 30:24 But there's a third thing that happens. Suppose the total of nothing box is on. It's not going to matter to this if it's on or off. Suppose the total nothing box is on. A further piece of our experience in the laboratory is that if I put a detector here, then two things happen. One, if the detector goes off, then all future events to look for the particle will find it with certainty on the hard route. And moreover, the color statistics out here will be 50-50.
▶︎ 31:08 So, the mere act of placing a detector, the mere act of looking, of asking where the particle is. So remember the situation. We take ourselves to have very compelling reasons to believe, these reasons, that when the detector isn't there, there is simply no fact of the matter about whether the electron is on the hard route or on the soft route. But it's also true that when we do put the detector there and turn it on, the electron immediately starts to behave like a familiar hard electron that's on the hard route or like a familiar soft electron that's on the soft route.
▶︎ 31:58 So there is something about looking for where. So, you take an electron, which when you first approach it, is in one of these superpositions, is in one of these states for which there is no fact of the matter about whether it's on the hard route or on the soft route. You look for it on the hard route. Apparently, the act of looking for it here does something very violent. It first forces the electron, as it were, to choose. It first forces the electron from this state it was in, in which there was no fact of the matter about whether it was on the hard route or it was on the soft route, and forces it into one of the conditions, either being on the hard route or being on the soft route where there is a fact of the matter about what route it's on. There was a fantasy that was very much at the heart of the physical project up until quantum mechanics of what you
▶︎ 33:12 Might call passive observation. Everybody knew, of course, that in order to observe anything, in order to get any information about any physical system, you had to interact with it physically in one way or another. After all, the embodied information needs to get from whatever you're looking at into your head. So you have to bounce light off it, or smack into it, or something like that. But the thought was that if you were careful enough, you could, in principle, reduce the degree to which you disturbed a physical system by observing it as low as you wanted. It's just a matter of doing the engineering more carefully. It's just a matter of spending enough money. It's just a matter of trying as hard as you can.
▶︎ 34:06 Audience: So, by looking for it, you, passing the electron through the detector, not a human looking at the result.
▶︎ 34:13 I don't know what I mean. I don't know what I mean. Here's what people observed in the laboratory. You do something as a result of which you can know which path the electron took, and it obeys. It snaps onto one route or another somehow. And then it keeps going on its way as if it were always on that route. And the outcomes of future experiments are exactly as if it was always on that route.
▶︎ 34:48 Audience: I ask that question because at this point, many people assume when you say, "Looking for it," what's meant is a person looking at the results, right?
▶︎ 34:58 And the fact is that people didn't know whether they meant that or not. Let me tell you what von Neumann for-. If you look at von Neumann's formulation of this algorithm, which sort of became standard after that. Von Neumann wrote a very famous book, I think, before the end of the 1920s. Do you remember when? I think it was '29. '29 or something like, called Mathematical Foundations of Quantum Mechanics, where he says, "Here's the algorithm. The rules about how these wave functions evolve have two different components. There's one rule that applies when you're not looking at the system or measuring the system." What did he mean by that? I don't know. He didn't know. So you're right that it's being left open to that interpretation.
▶︎ 36:03 Here's what he wrote down. And he wrote this down in order to account for all these experiments. "Look, in order to get all the predictions right," so said von Neumann, "it seems like there are gonna need to be two rules about how these wave functions change with time, one of which applies under certain circumstances and the other of which applies under other circumstances." He called them Rule One and Rule Two. He said Rule One is given by these differential equations, the Schrodinger equation, which tells you smoothly how this wave function that describes the system evolves with time. That's what's gonna tell you that if you don't have a detector here, and you feed a white particle, it's definitely gonna come out white here, so on and so forth.
▶︎ 36:58 Then he says, "But look, we gotta account for what happens when we put these detectors in." Apparently when you look, I believe the word he uses in the book is when a measurement is performed. When a measurement is performed, the usual Schrodinger rule gets suspended. And it's replaced by a rule of the form, well, when you look, depending on what you're looking for, say if you're looking for the position of the particle, the Rule Two is the particle gets forced to choose a position. And then goes on from there. Or the particle gets forced to choose a value of whatever it is you measured and then goes on from there, and this is coupled with a rule about the probability that the particle will end up choosing this or that.
▶︎ 37:58 For example, in a case like this, this rule, it's called the Born rule, will tell you that the particle has a 50% chance of choosing the hard route and a 50% chance of choosing the soft route, and whichever one it chooses, you'll go on from there. Here are the facts on the ground. These two rules taken together, coupled with some idea like everybody knows when you're making a measurement and when you're not. That's a dangerous thing to say. I don't know if that's true, but you apply it in the laboratory, you know when you're making a measurement, you know when you're not making a measurement. We know when to apply Rule One and when to apply Rule Two. This combination of Rules One and Two turns out to be the most spectacularly successful algorithm for predicting the outcomes of experiments in the history of the world.
▶︎ 39:00 This, as it stands, is clearly madness. Even if you're Bohr, even if all you're looking for is something which is completely agnostic about what the story is of how the electron gets from here to here. If you want an algorithm that is going to predict in detail and correctly the probabilities of outcomes of any measurement at all, you have to know exactly under which circumstances you're supposed to apply rule one and exactly under which circumstances you're supposed to apply rule two. And different claims about when you should apply rule one and when you should apply rule two are going to lead to different predictions about how later experiments are going to come out.
▶︎ 39:55 It turns out that relatively reasonable differences are going to lead to differences in predictions which are very hard to detect with currently available technologies, but this can't be the way a fundamental theory of physics looks, even if you're only after an instrumentalist theory.
▶︎ 40:19 Audience: In this algorithm, given some arbitrary wave function, is it the case that there's nothing I can... there may be cases where there's nothing I can measure about it with certainty without changing it and having to apply rule two?
▶︎ 40:31 No.
▶︎ 40:31 Audience: Or is there always going to be something I can measure...
▶︎ 40:33 No.
▶︎ 40:33 Audience: ...and try to confirm...
▶︎ 40:34 Yeah. It turns out there's always something you can measure whose outcome the Schrödinger equation by itself will predict with certainty. That is, it's always going to be the case that there's something you can measure and get the correct prediction about it without having to apply rule two. That's a technical point that I'm not sure how to justify quickly or off the cuff, but that's a very good question, and the answer is yes.
▶︎ 41:10 There are two big further topics I want to discuss in these sessions, in these videos. One of them is a problem with this algorithm has now been put on the table. As it stands, the distinction between the situations in which we're supposed to apply von Neumann's rule one and the situations in which we're supposed to apply von Neumann's rule two are supposed to be distinguished from one another by whether or not there's a measurement going on. And it's just as clear as it can be that the English word measurement doesn't have anything like the requisite precision to play a fundamental role in what's supposed to be our most fundamental physical theory.
▶︎ 42:09 We're going to need a new theory which in some way or other takes care of these measurement situations and takes care of the non-measurement situations in some more precise, unified way, and there are several really interesting, really profoundly different proposals on the table that have evolved over the course of the last 50 years or so, for trying to come to grips with this problem, for trying to imagine what an algorithm would look like, or a description involving these superpositions of what particles are doing would look like that handles these distinctions in something that looks more like the way we expect the fundamental physical theory to handle them.
▶︎ 43:13 We're going to be a little bit more precise in future lectures about exactly what the problem is. We've alluded to it here. We need to sharpen it up a little bit. And once we've sharpened it up, we'll be in a position to talk about attempts to come to grips with it.
▶︎ 43:33 The one other topic I want to discuss here is the other great shock that came out of the foundations of quantum mechanics, which has to do with the intuition that physical events can only affect other physical events that are immediately contiguous to them, both in space and time. That things only directly affect other things that are right next to them. That if something I do here affects something I do there, it must be that there's a row of dominoes in between them. Maybe they're hard to see, where one is knocking the next one over, and one is knocking the next one over.
▶︎ 44:21 And another thing that quantum mechanics turns out to pose a radical challenge to, is a challenge that's almost as radical as the challenge to realism itself, which we talked about today, is the challenge to this intuition that the way the world must work at a fundamental level, is in a so-called local way. Those are the two large topics that I'm thinking about discussing in future lectures.