▶︎ 0:01 These are going to be some talks that are meant to introduce the foundations of quantum mechanics. I have some friends here to help me out, who you'll meet. Let me just jump right in.
▶︎ 0:19 I want to start off by telling some stories about things that can happen to electrons. I guess it's fair to say that I think these are among the most unsettling and surprising stories to have emerged from the natural sciences since the scientific revolution of the 17th century. The experiments I'm going to describe, I'm going to describe them schematically, but they're all experiments that have actually been done.
▶︎ 0:58 I'm going to talk about what would happen if you did these experiments with electrons. But, for various technical reasons, some of these experiments are easier to do with neutrons. Some of these experiments are easier to do with photons. That's not going to affect the logical structure of the situation, which is mainly what I want to get across.
▶︎ 1:21 And I'm also going to say that these stories are going to involve measurements of various measurable physical properties of electrons. Once again, it's not going to be important to the logic of the situation exactly what physical properties those are. For people who want to look into it more deeply, the properties I'm going to be talking about measuring are different components of the intrinsic spin of electrons. But here, we'll refer to them by facetious names just to keep things simpler.
▶︎ 2:00 One of the properties whose measurements we're going to be talking about here, let's call the color of these electrons. Once again, electrons don't actually have colors. I'm talking about certain components of the intrinsic angular momenta of these electrons. To keep it simple, let's call one of these properties the color of the electron. And it happens to be a feature of electrons that when you measure this property, there appear to be only two possible numerical values that this color property could take on, say, plus one or minus one. Let's call one of them black and the other one white.
▶︎ 2:46 So it turns out to be the case that every electron whose color you measure either turns out to be a black electron or it turns out to be a white electron. You never see green electrons or purple electrons or yellow electrons, or anything like that. Another of the properties we're going to be measuring, we're going to be talking about measurements of, is we'll call the hardness of the electron. That only has two possible numerical values as well. Let's call one of those values hard and the other one soft.
▶︎ 3:21 Good. So like I said, it turns out, well, the first thing to say is these are properties that we've known how to measure in a very routine way for something on the order of 100 years now. We're very good at measuring these color and hardness properties in the laboratory. The way you measure them is by arranging a certain configuration of magnetic fields. There's a certain configuration of magnetic fields, which will deflect an incoming white electron in one direction and will deflect an incoming black electron in a different direction, and similarly for hard and soft electrons.
▶︎ 4:09 I'm going to refer to these arrangements of magnetic fields as boxes, as measuring boxes. It's routine, it's easy to construct in the laboratory, something that you might want to call a hardness box. This is a box with three apertures. You feed an electron into this box. If the electron you feed in is a hard electron, then the magnetic fields on the inside arrange things so that the electron exits the box by the hard aperture. If the electron you feed in is a soft electron, then the effect of these magnetic fields on the inside is to shoot the electron out through the soft aperture.
▶︎ 4:59 We can build, in a very similar way, color boxes. You feed an electron into the input aperture of a color box, it comes out this aperture if it's a black electron, and it comes out that aperture if it's a white electron. Good. Like I say, we've been very good for something on the order of a century now at measuring these properties, at manipulating electrons with these properties, and feeding them into the boxes we want to feed them into, so on and so forth.
▶︎ 5:43 Once you have boxes like this, one thing that might occur to you right away once you've discovered these properties, learned how to measure them. And by the way, it's going to be important to a lot of what we're going to say here that these measurements are repeatable in the way you would expect a measurement of a bonafide physical variable to be. That is, if I measure the color of an electron and I find it to be white and I immediately feed it into a second color box, 100% of the time it'll come out the white aperture of that second color box. And if it came out the black aperture of the color box, and I feed it immediately into another color box, it'll come out the black aperture of that color box.
▶︎ 6:33 There are things you can do to electrons, as we're going to see, which can affect their color values. So it's not the case that any electron that's ever come out a white aperture is going to come out the white aperture of any color box you feed it into at some later time in its life. But if you keep the environment free of things that could disrupt these color and hardness values, if you repeat two measurements in a row, you'll always get the same result. If that weren't true, we would begin to be puzzled about what we even mean by speaking of ourselves as measuring a physical variable when we carry out a measurement like that.
▶︎ 7:23 We have these. We're able to move these electrons around as we wish. We're able to build these color boxes. Something that it might immediately occur to us to do is to ask, we have two physical properties of electrons that we know how to measure, is there any relationship between these properties? Are the physical properties connected with one another in some way?
▶︎ 7:55 An easy way to find out if that's true, or at least to begin to get a handle on whether or not that's true, is to look for statistical correlations between the color value of a given electron and its hardness value. So, we can measure the color values of a whole bunch of electrons, measure their hardness values, and look or dump the results into a computer and ask the computer to look for correlations between those values. These experiments are easy to do, and it turns out when you do these experiments, there are no correlations whatsoever.
▶︎ 8:33 That is, it turns out of any large collection of electrons that are, say, known to be white, statistically speaking, exactly 50% of them turn out to be hard electrons and 50% of them turn out to be soft electrons. And similarly for all possible combinations. So there appear to be no correlations at all between the color value of a given electron and the hardness value.
▶︎ 9:08 Here's another experiment that it might occur to you to do, if you have these color boxes lying around in the lab. I don't know if it would occur naturally or not, but here's an experiment that people do. Suppose I set up a sequence of three boxes. I have a hardness box here followed by a color box. So here's the hard aperture, here's the soft exit aperture, here is the black exit aperture, here's the white exit aperture. And I follow it up with another hardness box. So here's the hard aperture, here's the soft aperture. Good.
▶︎ 10:19 Suppose I do the following. I feed a stream of electrons in here. The ones that come out the hard aperture, I throw them away. I only save the ones that come out the soft aperture, and those I feed into the color box. Half of those statistically will come out the black aperture, half will come out the white aperture. Throw away the ones that come out the black aperture, hang onto the ones that come out the white aperture, and feed those into the intake aperture of this second hardness box.
▶︎ 10:57 Well, by the time the electrons get here, they've all been measured to be soft here, and they've all been measured to be white here. And so it seems natural to suppose that what we're dealing with by the time we get here are electrons which are all soft and white. And so our expectation would be that feeding them into a second hardness box is just going to confirm what we already know about these electrons, which is that they're soft. So we'll expect them all to come out this aperture.
▶︎ 11:37 And the first minor surprise in this story is that that's not what happens when you do this experiment. If you take a bunch of electrons here, all of which have come out the soft aperture of this hardness box and all of which have come out the white aperture of this color box, when you feed them into a second hardness box, the statistical facts are that half of them come out the soft aperture and half of them come out the hard aperture. Good.
▶︎ 12:14 And this, like I say, is a little bit of a surprise. One might wonder what's going on there. Whatever is going on there, the effect of it is that the presence of this color box in between these two hardness boxes constitutes some kind of physical factor which can disturb the value of the hardnesses of electrons that pass through it. We did say, and it remains true, that if you've got nothing in between these two hardness boxes, then every electron that exits this hardness box by the soft aperture will exit that hardness box by the soft aperture. But the presence of this color box must constitute some kind of disruptive factor vis-a-vis the value of the hardnesses of electrons that pass through it.
▶︎ 13:10 And at this point, there are two questions that naturally occur to people. A way to put what's going on here is that the color box is apparently defective in some way. It's doing its job of measuring the colors, and it's doing that reliably. You take two boxes like this and put them one after another, they'll both give you the same color result 100% of the time. So this color box seems to be doing its job of measuring the color well, but in the course of measuring the color, it seems to be disrupting the hardness value.
▶︎ 14:10 And as soon as you see this, there are two questions that might naturally suggest themselves. Question one, can we build a better color box? Can we engineer things more carefully somehow so that what we've got is a box which not only does its job properly of measuring color, but does not, in the process of measuring the color, disrupt the hardness values of electrons that pass through it? Question two, in the case of this particular color box that we have, this defective color box, which is defective not as a measurer of color, but it's defective because it's disrupting the hardness values of electrons that pass through it. In the case of this box that we already have, we might become curious about what it is that determines which electrons get their hardness values flipped on the way through the color box and which don't.
▶︎ 15:19 Apparently what's happening here is that half of these soft electrons are making their way through the color box with their original hardness value, namely soft, intact, and the other half are getting their hardness values flipped from soft to hard. So, like I said, there are two questions. Can we engineer this box better so that it doesn't disrupt any of the color values? And second question, in the case of this defective box that we have, can we develop some kind of an understanding, can we develop some kind of an account of what it is that determines whether a given electron on its way through the color box ends up getting its hardness value flipped or its hardness value is left alone?
▶︎ 16:17 First question, can we build a better color box? There's not going to be any rigorous proofs one way or the other about this, but what we can do is try to engineer these color boxes as carefully as we can, try to spend a lot more money on them, think of different ways of measuring the color, think of different arrangements of magnetic fields that would all do the trick in one way or another. So you experiment around a lot with lots of different designs for this color box with more and more careful engineering of the color box, so on and so forth.
▶︎ 17:08 And the impressive result here is that it's not merely the case that you don't succeed in building a color box which leaves the hardness values intact. It's much more than that. You find that no matter what you do, as long as what you end up with is a box that does its job of measuring colors, as long as that's what you end up with, you seem to be stuck with a box that flips the hardnesses of, statistically speaking, exactly 50% of the electrons that pass through it. No amount of engineering, insofar as we can tell, no amount of redesign of this color box, as long as it remains a device that succeeds in measuring the color, nothing we can do seems to move those 50/50 statistics a thousandth of a percent off of exactly 50/50.
▶︎ 18:13 Like I said, there's certainly no proof that it's in principle impossible. But the fact that all of these redesigns, all of this more careful engineering, doesn't move the statistics one-thousandth of a percent off of 50/50 suggests that there's some kind of principle operating here. Yes, that is, suggests. It can't do anything more than suggest that. This is just a bunch of experiments.
▶︎ 18:45 But, yes, what people took it to suggest is that there is something deeper going on here which this experience is reflecting. That the fact that we're just not getting anywhere with all these redesigns, with all this more careful machining, so on and so forth, the fact that it's getting us nowhere. The fact that as long as what we've still got is a box that can measure color, every such box we're able to construct flips the hardnesses of exactly 50% of the electrons that pass through it. That suggests that there is some kind of principle operating behind the scenes here. It's not just that we can't get ourselves to a perfect box. It's that we're not getting anywhere. We keep walking and we're exactly in the same place as we were. We're exactly as far from this perfection as we were when we started out. Now we're addressing the second question.
▶︎ 19:49 The fact is that for the colored boxes we have, these colored boxes seem to flip the hardnesses of half of the electrons that pass through them and leave the other half untouched. How does it get decided which half, which electrons get their colors fli-, which, excuse me, which electrons get their hardnesses flipped on the way through the color box and which don't? Well, here's a way to try to address that. Once again, we're just going to be doing the best we can here. We're not going to be giving logical proofs of anything.
▶︎ 20:33 Run this a bunch of times. Try to hold all of the physical situation, except for the motions of the electrons, as constant as we can between the runs. And maybe over here, when electrons are first on their way in, measure everything you can think of about them. Their velocities, the exact angles at which they're coming in, how hungry they are, I don't know. Anything you can think of. Measure anything you can think of over here. Keep track of the outcomes of these measurements and match them up with the question of whether or not the hardness got flipped on the way through the color box. Dump it all into a computer. Look for correlations.
▶︎ 21:31 It turns out, once again, I'm describing just a body of empirical experience. None of this logically proves anything. But it turns out that we can discover no correlations whatsoever between the properties of the electrons coming in and this question of whether or not their hardnesses get flipped on the way through the color box. Another thing to say, narrow down the incoming, the range of incoming, of properties of these incoming electrons. Make sure they all have exactly the same velocity. Make sure they're all exactly as hungry as one another. So on and so forth. See if that has any effect on these statistics. It has none.
▶︎ 22:23 And once again, the impressive thing is not just that we're unable to find really reliable predictors over here of whether or not the hardness is going to get flipped. No matter how we filter things over here, it has no effect whatsoever. It doesn't move the statistics of flipping a thousandth of one percent off of 50/50.
▶︎ 22:57 Audience: Are you sure they all have exactly the same properties?
▶︎ 22:59 No.
▶︎ 22:59 Audience: Only those that you can measure?
▶︎ 23:02 No, well, I didn't understand. We can keep track of all the ones that c-, oh, you mean all the properties that we can. No, of course not. We just have to think of all the properties we can. And take advantage of all the properties that we know how to measure, and see if that's having any. Once again, the thing to keep in mind is, we're not asking for the moon here. We're not asking to find some set of properties which will tell us for sure whether the hardness is going to get flipped on the way through the color box or not. All we want is to find some way of filtering things here that are going to move the flipping statistics one millionth of one percent off of exactly 50/50, and we find nothing. Nothing.
▶︎ 23:59 We have a suggestion that there is nothing about the initial conditions here that determines in advance which electrons get their hardnesses flipped on the way through the color box and which don't. That is what this kind of experience seems to suggest. And this is the first time that this happened in the history of physics. What these kinds of experiments seem to suggest is that even on a microscopic level, there seems to be an element of chance in how systems like this evolve from here to here. Because nothing that we're able to measure about this seems to shed any light at all on the question of whether these electrons are going to get their hardnesses flipped by passing through a color box or not.
▶︎ 24:58 Audience: Can you just say a little bit about what you mean by chance? Because a lot of people might associate it with something like magic. There's room for a magical fairy to go in the box that we cannot measure with physical stuff, that's doing its work.
▶︎ 25:18 No. We're looking for regularities in nature. And it looks like all we can come up with to say about this is that whatever kinds of electrons I have going in, I feed in a large ensemble, half of them are gonna come out the soft aperture there, and half of them are gonna come out the hard aperture, statistically speaking. So we're gonna be relying in this discussion on an idea that most of us have some rough and ready sense of what we mean by probabilistic claims. We think of flipping a coin, we think of rolling a die, something like that. Of course, you're absolutely right that the business of being fully clear and explicit about what we mean by probability claims is a highly non-trivial business, philosophically.
▶︎ 26:21 Audience: Well, maybe that was not the question that Claire wanted to ask, but it is true that people usually associate chance with unpredictability.
▶︎ 26:30 Right.
▶︎ 26:30 Audience: And that's why I think it was important for you to emphasize the fact that what's really surprising here is not so much the fact that measuring color messes with the hardness measurements.
▶︎ 26:43 Right.
▶︎ 26:44 Audience: But the fact that however you control, even if you vary all the properties of electrons you put in the hardness box, there is no way for you to change the statistics.
▶︎ 26:55 Good, good. And that's the fact. Good.
▶︎ 26:56 Audience: That suggests the fact.
▶︎ 26:56 That's right.
▶︎ 26:57 Audience: That the law, it's like a law.
▶︎ 26:59 That's very helpful.
▶︎ 26:59 Audience: A probabilistic law.
▶︎ 27:01 Good, good.
▶︎ 27:02 Audience: But there is predictability. Not predictability on any individual outcome.
▶︎ 27:07 Yes, there's statistical predictability.
▶︎ 27:09 Audience: But there is. And that's what differs this from magic. Or from just chaos, or something like that.
▶︎ 27:17 Right, good. Thank you. Good.
▶︎ 27:25 Let's just pause for a minute and note a corollary of this. Suppose, so, first big discovery, there's a suggestion here, and this is the first time, as I say, there was all kinds of talk about probability and chance during earlier periods of physics, but those occasions were always associated with situations in which we don't know what the exact micro state of the world is. And the chance had to do with ignorance of present circumstances. The reasons that we couldn't make definite predictions toward the future had to do with ignorance of present circumstances. What's suggested by these experiments is that this is not like that. The business of evolving through time at a certain moment involves events, involves transitions from one state to another, which are genuinely irreducibly chances.
▶︎ 28:44 Another side remark. Suppose that we wanted to somehow put ourselves in a position, that is suppose we wanted to build what you might call a super box. This will be a box with not three apertures, but I guess five apertures. So I have a box like this. I'm fantasizing about a box like this. I feed electrons in here, they come out here if they're hard and black. They come out here if they're hard and white. They come out here if they're soft and black. They come out here if they're soft and white.
▶︎ 29:47 So a box like this would, if we had a box like this, by means of a box like this, we could put ourselves in a position to say after we've put an electron in and observed which aperture it exited by, we'd be in a position to say, "Good, that electron is now hard and black," or, "That electron is white and hard." That is, it would put us in a position to announce simultaneously both the color value and the hardness value of this electron. Good.
▶︎ 30:28 But if you think about how you would build such a box, you immediately run into the following problem. Look, presumably what you would do, the way you would build such a box is make an arrangement where you say, "First pass the electron through a color box and then pass it through a hardness box." And based on the outcomes of those two, you decide where to shoot it out. But of course, what we've just learned is that that's not going to work. Because once we pass it through the hardness box, the outcome of the color measurement is no longer reliable. The color may have been scrambled.
▶︎ 31:11 And similarly, if you pass it through the hardness box first, or if you pass, I forget which one I said, you pass it through the color box first. And you could do something like smooshing the two boxes together, by which I guess you would mean use a configuration of magnetic fields inside the box, which is a direct sum of the magnetic fields inside those two boxes. It turns out that's not going to work either.
▶︎ 31:44 It seems to be the case that because of the way color measurements disturb hardness values and because of the way hardness measurements disturb color values, it seems to be beyond our capacities in what is suggested, what these experiments suggest is a fundamental principled way, it seems to be beyond our capacities to, by hook or by crook, ever put ourselves in a position to be able to say about a certain electron, its hardness value now is such and such and its color value now is such and such. We can measure the color of any electron as accurately as we like and we can measure the hardness of any electron as accurately as we like. But what appears to be the case is that color measurements mess up hardness values and hardness measurements mess up color values and that seems to make it impossible ever to put ourselves in a position where we can say about both the color and the hardness of some given electron at some given time, I know what they are. It's black and it's soft, for example. Good. Good.
▶︎ 33:09 This is an example, a very simple example, of what's referred to in the quantum mechanical literature as the uncertainty principle. You'll usually find this described in the literature in a situation where the two variables under consideration aren't color and hardness, but say the position of an electron and its momentum. But this is an example of exactly the same thing.
▶︎ 33:40 We call observable properties like color and hardness incompatible with one another because our experience is that there is no procedure by means of which we can put ourselves in a position to simultaneously know both of those values. Like I say, these variables like this, color and hardness, position and momentum are referred to as quantum mechanically incompatible with one another, or we say that there is an uncertainty principle relating color and hardness. If we're sure about what the color value is, we're totally at sea about what the hardness value is and vice versa.
▶︎ 34:28 Audience: So does this suggest that it's about our uncertainty and we just can't know that it's both hard and black? Or that it can't be both hard and black?
▶︎ 34:38 The way it looks at this point in the story is the first. That is, it looks like it's an epistemic issue. You're anticipating completely correctly that it's gonna turn out to be something deeper than an epistemic issue. We're gonna run into that as we continue the story a little further, but that's a very good sort of question to keep in the back of one's mind.
▶︎ 35:05 It's called the uncertainty principle. The suggestion is that this has to do with limitations on what we can know, not with limitations on what there can simultaneously be facts about. That judgment is gonna evolve. Let's elaborate the story a little further.
▶︎ 35:27 Consider the following contraption. More complicated contraption. Down here I've got a hardness box. Here is the hard exit aperture, here is the soft exit aperture. Here's the route that an electron emerging from the hard aperture would follow, and here's the route that an electron exiting the box by the soft aperture would follow. And here I placed something I'll discuss. Call it an electron mirror.
▶︎ 36:15 What this mirror does, and this claim about what it does is something that can be independently verified by taking the mirror out of the apparatus and doing the appropriate experiments on it. This mirror doesn't alter any of the properties of this electron. It doesn't alter its hardness value, it doesn't alter its color value. All it changes is the direction in which the electron is moving. The electron bounces off the mirror in the way that light bounces off an optical mirror.
▶︎ 36:50 We can build devices like this. These are, again, simple arrangements of magnetic fields. We can build devices like this, and like I say, we can take them out of the apparatus and confirm that every hard electron that comes in here exits as a hard electron there, every soft electron that comes in here exits as a soft electron there, every black electron exits as a black electron, every white electron exits as a white electron. Good. Got another mirror down here with the same degree of innocence.
▶︎ 37:29 Here we have something I'll call a black box. This box is also innocent in a similar way. So these two paths, the mirrors are arranged in such a way that these two paths converge at the black box. Here are the properties of this black box. If you send a soft electron in here, it emerges here as a soft electron. If you send a hard electron in here, it emerges there as a hard electron. So at least within this setup, this black box is hardness-innocent as well. Good.
▶︎ 38:14 And now, so you set up an apparatus like this. This is usually an experiment that's done with neutrons, and you'll be able to find detailed, explicitly physical descriptions of experiments like this if you Google neutron interferometry. I'm gonna pretend that we're doing this experiment with electrons, just to keep everything consistent. In principle, it could be done with electrons. The fact of the matter is that the fact that electrons are electrically charged make these kinds of experiments technically more difficult to do with electrons than they are with neutrons, which are electrically neutral. Anyway, this is our schematic neutron interferometry experiment. Let's do several experiments with this contraption.
▶︎ 39:11 Put in white electrons here, measure their hardnesses here. You'll get 50/50. Why will you get 50/50? Well, half of them will go this way, half of them will go that way. The half that go this way are hard here, hard here, hard here. You get a hard result. The half that go this way are soft here, soft here, soft here. You get a soft result. Good.
▶︎ 39:44 Put in hard electrons here and measure color at the end. Well, then everything is innocent. These all go this way, they're hard here, hard here, hard here. Color should be 50/50. They are. That's exactly what you get if you feed in a bunch of soft electrons here and measure the color at the end. It'll be soft here, soft here, soft here, random colors. Good.
▶︎ 40:15 Now, suppose you put a bunch of white electrons in here and measure color at the end. What should we expect? Well, we should expect that half of them will take the hard route and half of them will take the soft route. Consider the ones that take the hard route. They'll be hard here, they'll be hard here, they'll be hard here. The color statistics should be 50/50. Consider the ones that take the soft route. They'll be soft here, they'll be soft here, they'll be soft here. The color statistics should be 50/50. Since half of white electrons will take the hard route and half will take the soft route, the overall color statistics at the end ought to be 50/50.
▶︎ 41:06 And the surprise is that this is not what happens. What happens when you do this experiment, you feed in a bunch of white electrons here, you measure their colors at the end, the colors at the end are 100% white.
▶︎ 41:26 Once again, just to emphasize the degree to which this is surprising, we've taken white electrons and passed them through a hardness box, and everything else is innocent. We know that passing through a hardness box randomizes color values. For some reason that has to do with the fact that we're putting these two routes back together before we make the color measurement, that's not happening here. These electrons, once they get out here, remember their original color. They're 100% white.
▶︎ 42:10 In this case, like I said, for some reason that apparently has to do with the fact that we put the two routes back together before we measured the color, passing through this hardness box causes no disruption of the color. For every white electron we feed in here, if we do the experiment properly, if we do it carefully, we get a white electron out there.
▶︎ 42:36 Let me say one or two other things about this. You might think that the reason the merging of the two routes makes a difference is that some of the electrons that go this way are bumping into some of the electrons that go that way, and having some kind of effect on one another. That's easy to eliminate. We have very good control over these experiments. We can easily arrange things so that the electrons are being fed in here so slowly, one at a time, that there's never more than a single one of them anywhere in the apparatus at any moment.
▶︎ 43:18 For a typical such apparatus, it takes a small fraction of a second for the electron to pass through it and come out the other side. We can arrange it so that we only feed in one electron per minute or one electron per hour or one electron per week. It doesn't decrease this effect at all. Electron by electron, even with only one electron in the apparatus at any given time, 100% of the ones that go in here white come out there white.
▶︎ 43:52 This is very odd. If you ask yourself a question like, focus on the fifth electron that you sent through. How did it get from there to there? You don't want to say it took this route because you know that it's a feature of electrons that take this route that their color statistics are 50/50, and this one isn't. You know it's a feature of electrons that took the hard route that their color statistics are 50/50. In this case, it isn't.
▶︎ 44:28 Let me add to that. Suppose you modify the experiment in the following way. You stop the experiment in the middle. Or you don't stop the experiment in the middle, I'm sorry. All you do is put a little measuring device somewhere along the hard route that clicks if the electron takes the hard route, and it does nothing if the electron takes the soft route. So you insert something that's going to tell you which route the electron took.
▶︎ 45:01 The minute you insert that, or let's be a little more dramatic, insert it, but leave it off. You still get 100% white out here. Turn it on, you get 50/50 white/black out here. What always happens is that half the time this clicks, half the time it doesn't click.
▶︎ 45:24 More and more puzzling. What difference does this device make? This device doesn't change the hardness values of electrons that pass near it. It doesn't change the color values of electrons that pass near it. We can confirm that by taking it out of the apparatus and checking. But when I put it in here and I turn it on, the 100% white goes away and switches immediately to half white, half black.
▶︎ 45:53 Is that a question? Not yet. It's just a threat. It's like 80% there. So here's a way to make this more acute. And if people want to look this up, what I'm about to describe is an effect called the Aharonov-Bohm effect.
▶︎ 46:18 Very famous effect in quantum mechanics. I'm going to give you a schematic version of the Aharonov-Bohm effect, but the logic is exactly the same. I'm going to introduce a new piece of terminology. Consider a box with two apertures. Just an input aperture and an exit aperture. I'm going to call a box like that a total of nothing box.
▶︎ 46:50 If the following is the case, that all measurable properties, other than, of course, position in space, because it has to pass through the box, but all measurable properties, velocity, momentum, mass, color, hardness, everything you can think of, how hungry the electrons are. A total of nothing box is a box that leaves all measurable properties undisturbed on their passage through the box. They come out here with exactly the same set of measurable properties that they went in with, except, of course, for their position in space. All of its measurable properties are the same. And moreover, to make it even more stringent, we require that the time required to pass through the box is exactly the same time as would be required to pass through that expansive empty space. So the box does nothing.
▶︎ 47:55 Now, there's an infinite number of different ways you could build a total of nothing box. One way to build it is just to build an empty box. But another way to build it is to have a box that does all kinds of crazy things to the electron while it's inside the box, but then undoes them before it shoots it back out, and manages to do all of that in exactly the time it would take for the electron to pass through that amount of empty space. Any box that satisfies those conditions, we're going to call a total of nothing box.
▶︎ 48:38 What Aharonov and Bohm were able to show is that there are boxes that satisfy all the conditions for being a total of nothing box. This is not an empty box. This is a box with specific kinds of fields inside. But it satisfies all the requirements that I just listed of being a total of nothing box. All of the incoming properties are identical to the outgoing properties except for position and space, and the time it takes to get through the box is the same time that it would have taken an electron entering with that velocity to get through that much empty space.
▶︎ 49:26 So this is a total of nothing box. What Aharonov and Bohm discovered is that there are boxes that are total of nothing boxes. Call the specific kind of box we're talking about an AB, an Aharonov-Bohm total of nothing box. There is an Aharonov-Bohm total of nothing box. They tell you exactly how to design it.
▶︎ 49:59 And these experiments were since done and came out in the predicted ways, such that if you insert it, say, in the soft path here and feed in white electrons, they come out 100% black here, 100% black. Every single white electron that you feed in here comes out black here. We can also insert it and turn it on and off, like with the detector. When the total of nothing box is switched off, every white electron you feed in here comes out white there. When it's turned on, every single white electron you feed in here comes out black there.
▶︎ 50:45 This is very odd. Let's step back and investigate the possibility of telling ourselves a story about what happens in between this moment and this moment, what the electron does. Let's go through the logical possibilities. You ask about a given electron, could it have taken the soft path? No, because total of nothing boxes have no effects on the properties of electrons that pass through them. And the presence of this box changed this electron from white to black. So it couldn't have taken the soft route. So the soft route seems to be out.
▶︎ 51:48 Could it have taken the hard route? No, for the same reason. These total of nothing boxes are known or explicitly confirmed to have no effects on the properties of electrons that pass outside of them. But once again, its presence changed this electron from white to black. So it couldn't have taken the hard route either.
▶︎ 52:18 Could it, in some sense, have taken both routes? Not in any familiar sense, for sure. If you stop the experiment in the middle and look for a particle, you'll either find an electron in the soft path and nothing on the hard path, or you'll find an electron on the hard path and nothing on the soft path. You'll never find half an electron on one path and half an electron on the other path, or anything like that. So this seems excluded, and when you put in one of these detectors, sometimes it goes off, sometimes it doesn't go off. Doesn't go off all the time. Goes off statistically half the time.
▶︎ 53:07 What about neither route? That seems pretty easy to eliminate too. If you simply block up both of these routes, nothing gets through. Or you block them up even at the end, nothing gets through. So it's not like it's going some other way or anything like that, and you can fill this whole region in between with lead so dense that even Superman can't see through it, and so on and so forth. Not gonna affect this at all. So the neither option seems ruled out, and those are the four logically available options, or so it would seem. So we've got something enormously puzzling going on here.
▶︎ 54:16 Bohr, the father of quantum mechanics, or the universally acknowledged guiding spirit of the development of quantum mechanics, thought that the lesson of examples like this is that any attempt to tell an intelligible story, any attempt to develop a mental picture of what's going on between the time I measured the color here and the time I measured the color there, is going to collapse into paradox, as it apparently just did. It apparently collapsed into a flat-out logical contradiction. Any attempt to tell yourself a story about what's going on between this measurement at the beginning and the other color measurement at the end, you're going to be reduced to babbling gibberish immediately.
▶︎ 55:28 And this was among the reasons. Bohr had several reasons for saying what I'm about to say, and we'll get to others later on. But you can already begin to see it here pretty vividly. Bohr thought that in the light of examples like this, and other examples which we're going to discuss later on, the traditional aspiration of scientific inquiry, to give us an understandable picture of what's going on, to give us an understandable picture of why things happen in the way they do had collapsed. A certain idea of what was called scientific realism, as an attitude toward the scientific activity and toward the aspirations of the scientific activity was collapsing here right before your eyes.
▶︎ 56:30 There isn't any story to tell about what happened in between this color measurement and that color measurement. Any attempt to tell such a story is going to collapse into gibberish or paradox or self-contradiction the minute you try to tell it. And this begins to offer a taste of why there's something profoundly philosophically interesting going on in quantum mechanics. This begins to offer a taste of what's at stake in the business of trying to make sense of quantum mechanics. It's not just that the world contains surprises, we're constantly astonished by new discoveries we make, or something like that. It's that, in a certain sense, the founding aspiration of the scientific activity has, according to Bohr, hit a wall here, a wall that it's not going to be able to go through, and our attitude toward the entire scientific activity is going to have to be different from here on.
▶︎ 57:52 And maybe it's worth pausing here and rubbing this in a little more. There is, of course, a long history, a 3,000-year history in Western thought, of philosophical critiques of what you might think of as a naive scientific realism. There's all kinds of skepticism. There's transcendental idealism. There's all kinds of philosophical critiques of this, what you might call naive scientific realism as somehow naive. None of those is like what's going on here.
▶︎ 58:39 This is the first occasion when the obstacle to scientific realism doesn't come from the outside, from some kind of external philosophical critique. It's as if the scientific activity itself is committing suicide. This is the moment in the horror movie when the operator tells you the call is coming from inside the house. This doesn't have any precedent in the long tradition in Western philosophy of various kinds of worries about realism. Something utterly different is happening here.
▶︎ 59:23 When realism isn't being exposed as resting on this or that assumption, or as involving this or that kind of internal tension, or something like that, the claim here is that certain experiments came out in certain ways, this pointer ended up here on this measuring device, that pointer ended up there on that measuring device, there is a certain set of outcomes of straightforward physical experiments which made it logically impossible to tell a story about what was going on in between them. This is what's at stake here. Not this or that surprising discovery about the way the world is, but a surprise about the very possibility of our being able to tell ourselves the kind of story which science had seemed to promise to us about the way the world is.