▶︎ 0:00 Before the interlude about non-locality, we were talking about initial reactions on the part of people like von Neumann or Wigner or others, who were, in some sense, trying to be realistic. Who were in some sense trying to tell the kind of story that Bohr had forbidden people to try to tell about what's going on in between measurements and so on, who were trying to use pieces of the quantum mechanical algorithm, mathematical components of the quantum mechanical algorithm, like the wave function as realistic representations of what these particles are doing in between experiments. And we saw that, and this is what we were calling the measurement problem, the way von Neumann tries to formulate things, it seems like there's a necessity of positing two completely different sorts of fundamental laws of the evolution of this wave function in order to account for the kinds of behaviors we see in these two paths experiments.
▶︎ 1:33 There is a way that the wave function of a given system evolves when the system is not undergoing a measurement or an observation. That's given by von Neumann's Rule One, which refers to this differential equation called the Schrodinger equation, in accord with which the wave function is supposed to evolve. And then there is this other rule, von Neumann's Rule Two, which applies when the wave function, when the particle that the wave function describes is measured. So, for example, in the two paths experiments, if we stop the experiment in the middle and go measure which path the electron is actually taking, that forces the electron to choose one path or another in the way that the Schrodinger equation will never do. And in order to account for that, von Neumann thinks there needs to be a separate law which applies only when measurements are taking place.
▶︎ 2:45 And the obvious thing to say about this, and this is all stuff that we've already talked about, the obvious thing to say about this is that words like measurement don't belong in a proposed fundamental physical theory of the world. Measurement is a vague English term. That's not the kind of precision that we expect of a fundamental physical theory of the world.
▶︎ 3:17 This was followed by fifty or so completely wasted years of people coming up with other proposals for trying to draw the boundary between that set of physical situations in which von Neumann's Law One applies, and that set of physical situations in which von Neumann's Law Two, von Neumann's Law Two is sometimes referred to as the law of the collapse of the wave function on measurement. So those physical situations in which von Neumann's Law One applies and those physical situations in which von Neumann's Law Two applies. And instead of using words like measurement, people use an equally useless collection of terms like macroscopic or irreversible or indelible or conscious, or something like that. And it's strange and funny that it wasn't obvious to all of these people that all of those words are exactly as useless as the original word measurement in these contexts.
▶︎ 4:34 And that's where things stood. Wigner hoped that references to consciousness were going to turn out to offer us a sharper delineation between those physical circumstances in which Rule One applied and those physical circumstances in which Rule Two, the rule of the collapse of the wave function, applied. That doesn't work out either. It feels in retrospect like people should have known better.
▶︎ 5:09 Anyway, that went on for a very, very long time. That went on essentially from the early 1930s until sometime in the 1980s. Well, it's not exactly true that people were doing things vis-à-vis this business of drawing the boundary in the way I'm describing. All anybody had to say was this useless talk about macroscopicness and indelibility and measurement and recording and consciousness and so on and so forth until the 1980s.
▶︎ 5:57 In the 1980s, for the first time, a scientifically serious theory of the collapse of the wave function was proposed by three Italian physicists named Ghirardi, Romini, and Weber, and it's subsequently been known as the GRW theory. The GRW theory, first of all, gives up on the thought that what needs to be done here is to locate the boundary between that set of physical circumstances in which Von Neumann's rule one applies, and that set of physical circumstances in which Von Neumann's rule two applies. They don't take this approach of trying to draw a boundary. They very cleverly write down a single law, which involves a small stochastic modification of Von Neumann's law number one, that is a small stochastic modification of the Schrodinger equation.
▶︎ 7:16 It goes essentially like this. Let me describe how the theory works for the case of a single particle. The rule of the evolution of this wave function for a single isolated particle is going to be that the wave function of the particle evolves almost all the time in perfect accord with the Schrodinger equation, that is with Von Neumann's law number one. But every now and then, very, very rarely, for a single particle, the way GRW originally wrote their theory down, this event that I'm about to describe happens on average once in 10 to the 12th years. It happens very, very, very rarely, but every now and then, the smooth continuous deterministic Schrodinger equation, law number one evolution of the wave function, is interrupted by a stochastic event.
▶︎ 8:21 This event is genuinely stochastic. That is, it has a certain fixed probability of happening per unit time. But there's no deterministic rule that will allow you to predict when it's going to occur. Every now and then, a stochastic event occurs which transforms the wave function of this particle from whatever it was prior to this event, evolving along in accord with the Schrodinger equation, to a wave function that represents a particle, about whose location in space there is a determinant fact of the matter.
▶︎ 9:12 So for example, if one of these events were to occur while an electron is in the middle of these two paths apparatus, now the probability of it occurring to any such particle is extremely small, because it takes a short time to get through the two paths apparatus, but if it did occur, then what you would get would be precisely this stochastic event affects a choice for the particle of being either on the hard path or on the soft path. That is, it would have exactly the effect of what Von Neumann's rule number two would refer to as a measurement of the location of the particle. If the particle gets located by this stochastic event on the hard path, then it's going to act like a hard particle, and if you remember the two paths discussion, the color statistics at the end are now going to go from 100% white to 50/50, and so on. Good.
▶︎ 10:17 These events in the life of any single particle are very, very rare, as I've said. So, if you were to modify Von Neumann's rule one in the way that GRW suggest, that's not at all incompatible with our experience with two paths experiments and so on, because the probability of any one of these particles getting hit on its way through the two paths apparatus is just absolutely minuscule, to the point of being completely negligible. So, this proposal to begin with has the advantage that it doesn't seem to contradict any of what we experimentally know to be true about the strange behaviors of these subatomic particles.
▶︎ 11:11 But the theory is designed in such a way that if you have a macroscopic object, which is in a superposition of being, say, here and here, if you have a baseball or if you have a pointer on a measuring device, which is in a superposition of being here and here, then it turns out that if even so much as a single one of the constituent particles of this baseball gets hit by one of these stochastic events, one of these GRW stochastic events, and if you have something the size of a baseball, or if you have something the size of a pointer on a measuring apparatus, the probability that at least a single particle in there is gonna get hit by one of these stochastic events per minute or per second becomes very high, just because the number of particles, of subatomic particles, involved in an object like that is astronomical.
▶︎ 12:17 The way the theory is designed is that if just one of the particles in the baseball gets hit by one of these stochastic events, the baseball as a whole will, as it were, be forced to choose between being here and being here, and it'll end up either here or here, exactly in accord with the normal statistical predictions of quantum mechanics regarding how a measurement of the baseball, if it were to be performed, would come out.
▶︎ 12:53 One of the beautiful features of this theory is that it just falls out of the theory of the fundamental mathematical formulation of the theory in a very straightforward way, that if so much as a single particle in the baseball would experience one of these stochastic events, it not only forces that particle to choose between being here and here, but that happening to that particle drags the entire baseball along with it. When we actually do a measurement.
▶︎ 13:32 Say we do a measurement of which path it's on. So we set up a device which makes a beep if the particle goes by the device, or we set up a device with a pointer that swings here or there, that stays where it is if the particle doesn't go by it and swings to a different position if the particle does go by it. Good. That's not exactly analogous to the baseball, but in terms of mathematical structure, it sort of is. In quantum mechanical language, what happens when I turn such a device on is that according to Von Neumann's rule one, the whole situation is going to enter into a superposition of the particle being on this path and the device going off, and the particle being on that path and the device not going off.
▶︎ 14:32 Now, we imagine, of course, this stochastic event is very unlikely to happen to the particle itself, but we imagine that one of the particles in the measuring device, of which there are millions, say, one of the particles in the pointer, is forced to choose by one of these stochastic events whether it's over here or it's over here. It turns out to fall very naturally out of the mathematical structure of this theory that that is not only going to drag the whole pointer along with it, it's going to drag the measured particle along with it too. So the pointer getting forced to choose between this direction and that direction is going to force the particle that the pointer is measuring to choose between the hard path and the soft path.
▶︎ 15:22 This comes about because of a phenomenon of the mathematical structure of quantum mechanics called entanglement. This is exactly the feature of quantum mechanics that leads to the non-localities that we saw in connection with Bell's theorem. Here, there is something like that, something like a non-local effect. The pointer being forced to choose between this position and that position is going to force the particle that the pointer is entangled with as a result of this measurement interaction that took place between them. That's going to force the measured particle itself to choose between the hard path and the soft path, and to be correlated with the pointer in the way the measuring device was designed to produce a correlation.
▶︎ 16:17 So yeah, that's not exactly analogous to the baseball, because the particle isn't itself a part of the baseball, but the particle has a similar relation to the pointer, this relation of entanglement, the similar mathematical relation to the pointer as the constituent of the baseball has to the whole baseball. So if any part of the pointer gets forced to choose, the particle that the pointer is entangled with is going to get forced to choose as well. What about cases
▶︎ 16:50 in which different results of measurement don't get registered in different positions? Is that possible? Oh, yeah. No, that's a really good point. What these stochastic events tend to do is to localize particles in space. And to localize any other particles that those particles may be entangled with, in the way that's implied by the nature of the entanglement. But you're absolutely right. What these stochastic events tend to do is to localize material objects in space.
▶︎ 17:25 There is an assumption behind this theory, that if we can manage to ensure that macroscopic material objects more or less always have more or less determinate positions, we will have solved the measurement problem. Now, one can say, and it's very natural to say, but that doesn't seem right. There are all kinds of measuring instruments that indicate the outcomes of the measurements they did in some way other than moving something around in space. There are measuring instruments that indicate the outcome of the measurement by flashing lights of different colors, or by making different kinds of noises or something like that.
▶︎ 18:10 With the noises, it's not so hard to imagine what's going on. Noises involve moving around masses of air molecules so that if you make everything macroscopic have a definite position, you're gonna force the device to choose to make a noise or not to make a noise. With different colored lights, it's a little bit harder, and there's a general assumption in the background here that sooner or later, all measurements end up being recorded in the spatial position of something or other. Even if it's not until I write down an inscription in a laboratory notebook or I report verbally what the outcome of the measurement was or something like that, there are all kinds of cases here that are worrisome.
▶︎ 19:04 I wrote a paper with a friend of mine many years ago when this theory first came out analyzing a measurement where the outcome is recorded by allowing a subatomic particle to run into a fluorescent, an old-fashioned fluorescent television screen and making a dot of light either emanate out of the top half of the screen or out of the bottom half of the screen. And it turns out that if you analyze a situation like that, via the GRW theory, it's pretty clear that none of these stochastic events are gonna force a choice between two outcomes until the light signal starts getting processed by your retina or by your visual cortex, or something like that. So that seems uncomfortably late, and then you start worrying, what if dolphins' brains aren't like that or what if martians' brains aren't like that? So, there are worries associated with that in this theory.
▶︎ 20:14 There's a lot to say about them. There's been a lot of discussion of this. These are discussions that you can find in the various books that I mentioned at the outset. But there is a lingering worry that, exactly as you say, the way in which this theory is committed to a claim of the form that everything is going to be okay at the end of the day, as long as you can guarantee that macroscopic material objects always have more or less determinate spatial positions, there's a worry about whether that's true at the end of the day or the extent to which that's true at the end of the day.
▶︎ 21:02 I guess there's two kinds of worries there. One is just the idea that this is somehow conspiratorial.
▶︎ 21:09 Audience: I don't really like the idea that, for instance, when I'm even measuring the position of a particle, of a single subatomic particle, it's actually the wave function of the entire measuring apparatus that's deciding which outcome is going to be-
▶︎ 21:25 Say more what you mean by conspiratorial.
▶︎ 21:27 Audience: Well, because there is this intuition that it must be the position of the actual subatomic particle that I'm measuring.
▶︎ 21:34 I see. But in this case-
▶︎ 21:35 Audience: Yes.
▶︎ 21:36 This will certainly deny that.
▶︎ 21:43 Audience: But that's, you know...
▶︎ 21:45 This will certainly deny that. But the probabilities of the measurements coming out one way or another will be exactly the quantum mechanical probabilities. But you're right. It's not presenting a situation in which what's going on, how things come out when you do what's normally called measuring the position of this particle is determined by what the particle is doing before you measured it. That's true.
▶︎ 22:15 But the worry with the example you took at the end, that's a straightforward worry about GRW making inconsistent predictions.
▶︎ 22:23 Audience: I don't know what you mean by inconsistent. Empirically incon-... Like, or whether it's going to...
▶︎ 22:32 Suppose it's the case. And this is what actually happened, when this friend of mine and I wrote this paper about the TV screens. GRW responded sort of in the following way. They said, "Well, yeah, it's true. That's kind of embarrassing. The case you've described is kind of embarrassing. It would have been nice to get the thing decided before it gets into your brain." Indeed, you can imagine situations in the GRW theory where you have a superposition of these two luminous dots. Or where, more impressively, what you have on a TV screen is a quantum mechanical superposition, not a superimposition, but a quantum mechanical superposition of the TV screen holding an image of Lucy's face and the TV screen holding an image of Desi's face, for people who are familiar with the Lucy show.
▶︎ 23:44 And until somebody walks into the room, according to this theory, and looks at it, there wasn't a fact of the matter about whether it was Lucy's face or Desi's face, and the only thing that forced it to choose was stuff that was going on in your visual cortex after you looked at it.
▶︎ 24:04 So there were two stages to GRW's response. In our original paper, we said, "Look, it looks like nothing's going to happen before it hits an observer's eyes," and we left it at that. And GRW ran around and found some neuroscientists and came back with a claim that that's true, nothing's going to happen before it hits the retina, but if you analyze the behavior of the retina and the behavior of deeper parts of the brain, the optic nerve and the visual cortex and so on and so forth, it turns out that the way human brain anatomy works is that the number of ions that get squirted across synapses in processing visual information is large enough to allow these GRW stochastic events to kick in quickly.
▶︎ 25:00 So they said, "So it is likely that by the time the brain gets involved, everything's going to be okay." And after all, what evidence do you have that stuff was okay before you walked into the room?
▶︎ 25:13 Audience: Good.
▶︎ 25:17 That leaves lots of worries hanging. Number one, that's later than I expected it to be. I thought that what this theory was going to do for us was to get the macroscopic world looking like we think it looks like. Second of all, even if we do wait till then, what if we improve our brains surgically so that they can store information in smaller numbers of ions? Or what if dolphin brains don't work that way, or Martian brains don't work that way? Or something like that.
▶︎ 25:50 So I think the right thing to say about this theory is that there is a worry of this form. The question is, can we do better with other theories? Blah, blah, blah. There is a worry of this form. This theory le- let me,
▶︎ 26:09 There's a glass half empty and a glass half full way of looking at it. If you compare it to the earlier history of speculations about collapse, where people are talking about consciousness and macroscopicness and measurement and so on and so forth, this is such a vast improvement, such a sudden improvement, so much more recognizably a theory in the scientific tradition than any of those were, that people were enormously thankful for it. On the other hand, you settle down, you get over your initial excitement, you subject this theory to careful scrutiny, there are certainly things to worry about, of exactly the kind you've brought up.
▶︎ 26:57 Audience: Can I ask a question about the realism project? Because that's your project.
▶︎ 27:02 Right.
▶︎ 27:02 Audience: GRW says, if I understand, collapsed, little collapsed, delta or little hill-
▶︎ 27:08 Right.
▶︎ 27:08 Audience: is the particle. And then before the collapse, it's a smeared particle? Like it has two.
▶︎ 27:15 That's a different, that's a slightly different story, but here's what you could say sticking very close to the standard way of talking about things. Here's what the story says. Particles can be in situations where there is no fact of the matter about their positions. That's not anti-realism. If I say there's no fact of the matter about the marital status of the number five, that doesn't mean I'm an anti-Platonist. That doesn't mean that I don't believe in the existence of the number five. It just means that I think the number five is not the sort of object that has a marital status. That inquiring into the marital status of the number five represents some kind of category mistake.
▶︎ 28:04 The sort of flat-footed realist approach here would be to say here's the true story of what happens to electrons when you put them through a two-pans apparatus. They go into a state, a genuine condition of being that we can describe with our equations in which there fails to be a fact of the matter about where they're located in space. That doesn't mean that we're unrealistic about what's going on. That just means that we've made a discovery, a surprising discovery. That particles like electrons can, under certain circumstances, be in situations which we didn't previously think they could be in. That electrons have, as it were, modes of being or modes of moving available to them in which, under certain circumstances, there's no fact of the matter about where they are. There are plenty of other facts of the matter about them. They're in precisely this superposition of being here and here. There's lots that we can say about them.
▶︎ 29:13 So this is supposed to be a perfectly realistic view of what's going on. There are other speculations later down the road, which maybe we'll get to, but just as a flat-footed beginning, no, we say about this electron, it's in a superposition when it's moving through the two pans.
▶︎ 29:30 Audience: So the wave equation is the electron? Describes the electron?
▶︎ 29:34 Describes correctly and completely, describes the electron. Yes, yes, yes.
▶︎ 29:39 Audience: So in other words, a new physical state particles can be in that we didn't know of that we call a...
▶︎ 29:51 Superposition.
▶︎ 29:52 Audience: That's the understanding, right?
▶︎ 29:54 That's the understanding. Sure.
▶︎ 29:55 Audience: Not that it's not real.
▶︎ 29:56 No, no, no.
▶︎ 29:56 Audience: Not that it's not physical.
▶︎ 29:58 It's not at all the case
▶︎ 30:00 Audience: It's just we didn't know about it before.
▶︎ 30:00 that we are abstaining from talking about what this particle is doing when it's on its way through the apparatus. We can talk about it. We have a language for talking about it, the wave function. We have a colorful language about the wave function. We talk about superpositions and so on and so forth. This is all supposed to be part of a realistic description of what's going on. This is not a case of obeying the Bohrian edict that we should not attempt to say anything about what's going on. This strange new thing is going on. We can say exactly when it goes on, when it ceases to go on. Blah, blah, blah. Yes, this is supposed to be a realistic description of what's going on.
▶︎ 30:46 What we want out of this realistic description is that it had better not spread to baseballs and tables and inscriptions and results of experiments. There are certain features of the world which we are committed by our longstanding everyday experience to thinking there must be facts of the matter about. There may fail to be facts of the matter frequently about, say, the position in space of a single electron. There had presumably better not fail to be facts of the matter, at least not frequently, about the positions of tables and chairs and baseballs and stuff like that.
▶︎ 31:35 You got to design your theory in such a way that these random stochastic events accomplish at least the following two things. When they have almost no effect on individual microscopic systems, isolated microscopic systems, which we know from experience behave according to rule one. The fact that all the particles in the two paths experiment come out white at the end indicate that they're behaving according to rule one all the time. They're never experiencing any collapses. So you want that, and you also want it to be the case that when you do do a measurement, the likelihood of one of these spontaneous events dragging the whole assemblage one way or the other becomes very high.
▶︎ 32:28 Their theory does both of those things, and it does it without using any of these bad words to locate a boundary or to pick out a trigger or something like that. If we needed to supplement these stochastic events happening on the microscopic level with also special claims about what measuring instruments do or something like that, then the theory would not be nearly as attractive as it is. We don't need to do the second thing. The stochastic events on the micro level are what take care of everything. We're not making any special assumptions here about what it is to be a measuring device. Measuring devices are just modeled as ordinary physical devices in exactly the way they're modeled in classical mechanics or something like that.
▶︎ 33:21 It's the microscopic stochastic modifications that are doing 100% of the work here. Good. That, as I said, as I warned, very, very crudely, is the situation with the GRW theory. And the GRW theory is probably the best of the theories we have in a general tradition that now includes a number of proposals that fall under the description of being scientifically respectable versions of something like a collapse theory. There's another completely
▶︎ 34:04 Different tradition of trying to come to grips with this measurement problem. Once again, what the problem is, is that if we let everything always evolve in accord with von Neumann's rule number one, if we let everything always evolve in accord with the Schrodinger equation, then the deterministic and unambiguous prediction is going to be that when we carry out a measurement of, say, which path the electron is on in the two paths apparatus, the world is going to go into a superposition of the electron being on the hard path and the measurement having recorded that the electron is on the hard path, and the observer who looked at the measuring device being in a brain state which is connected with believing that the electron is on the hard path, superimposed with the electron being on the soft path and the measuring device indicating that the electron is on the soft path, and the observer's brain state being in the state that corresponds to believing that the electron is on the soft path.
▶︎ 35:18 And the problem is supposed to be, again, that this doesn't happen, because if we read superpositions in the standard way that we're taught to read them, that's going to mean that at the end of this measurement, there's no fact of the matter about where the pointer is pointing, and there's no fact of the matter about where I, who looked at the pointer, take the pointer to be pointing, and so on. And the thought is that we just know in a more direct, empirical way than we know anything else that that's not the case. That there does end up to be a fact of the matter about where the pointer is pointing, that there does end up being a fact of the matter about where I take the pointer to be pointing, and so on. That's why we need von Neumann's rule number two.
▶︎ 36:10 There is a tradition going back to the thesis of a physicist named Hugh Everett, that he did at Princeton in the 1950s, of hoping that, as a matter of fact, if you examine things more closely, there is no need for von Neumann's rule number two at all. That this wave function that we normally take to be representing a superposition of these two states is really how measurements end up. Let's put it this way. What is it that led us to think, in the case of the two paths apparatus, that we couldn't tell a story about what was going on in that two paths apparatus that involved the electron having taken one of the paths or the other?
▶︎ 37:18 What stood in the way of telling a story like this was the fact that they all came out white at the end, the fact that you have at the end these interference phenomena, which both the state corresponding to the electron taking the hard path and the state corresponding to the electron taking the soft path have to, as it were, contribute to, in order to get this white result at the end. So the thing that stood in the way of our telling ourselves a story according to which the electron either took the soft path or took the hard path is this so-called interference effect that we can measure at the end, this 100% white output that we can measure at the end.
▶︎ 38:08 Here's a fact which the Schrodinger equation predicts. Imagine shooting not an electron through this two paths apparatus, but a slightly larger object, like a silver atom. It turns out we can do these two paths experiments with silver atoms too, and they work in the same way. You have to take a little more care than in the neutron case, anyway, to isolate it from air, to evacuate the chamber, isolate it from air molecules, and so on. But it still works. You can even do it nowadays with relatively small molecules, multi-atomic molecules.
▶︎ 39:01 But as the thing that you're sending through the two paths apparatus gets larger, these interference effects, for various reasons, also having to do with entanglement, these interference effects get, as a practical matter, more and more difficult to measure. By the time you get to a large molecule, you don't have to get anywhere close to a baseball. By the time you get to a large molecule, these entanglement effects make it basically impossible to measure these interference effects at the end.
▶︎ 39:41 This doesn't change the fact that the mathematics looks exactly the same, that you have what in the mathematics corresponds to a superposition of the molecule or the baseball going this way and the molecule or the baseball going that way. But it is true that the business of empirically confirming this phenomenon, which is what seems to stand in the way of saying that you have this or this or this and this or something like that, that gets harder and harder to measure. So there is some idea that this suggests that we ought to think, or that there's an excuse for thinking about a state in which a baseball is in a superposition of being here and here very differently than the way we think about a state in which there's a single neutron in a superposition of being here and here.
▶︎ 40:46 In the case of a neutron, there are things that we can easily measure, which ought to persuade us that talking about that neutron as if it's either here or here or in both places or anything like that is just unworkable. When things get large enough so that for all practical purposes those measurements become impossible, you might say to yourself that when things get like that, it becomes sensible to regard these two branches of the superposition as two genuine self-contained worlds, in one of which the particle is on the hard path, and there's a measuring device that indicates that it's on the hard path, and there's an observer who believes it's on the hard path. And in the other of those worlds, there's an electron which is on the soft path, and a measuring device which indicates that it's on the soft path, and an observer who believes it to be on the soft path.
▶︎ 42:00 The idea is that when things get sufficiently macroscopic, this is, of course, vague, but it's not, at least according to its proponents, it's not vague in the damaging way that talk of measurement was vague or something like that. You want to know the exact fundamental description of the world, it's this wave function. And this wave function branches in this way, and that's the whole story of the world. But there is talk which they will now regard as vague and emergent talk, which becomes more and more a viable way to talk when the superimposed states become more and more macroscopically different from one another. And so it becomes harder and harder to measure these interference terms between them.
▶︎ 42:58 When things start to get large enough, when the various branches start to get sufficiently macroscopically different from one another, I don't know what the right word is to use here, because this is a view that I'm, at bottom, very confused by. But it becomes more and more permissible or not improper or something like that to start talking about these superpositions as cases where what happens is that the world splits into a multiplicity of different universes. In each of these universes, there's an observer who's unaware of the other one.
▶︎ 43:44 The structure of the equations that govern the evolution of the wave function are going to explain why. That is, the fantasy about this theory, a metaphor that Everett often used to describe it is somebody says, "If there are all these other worlds, why don't we see them?" Everett says, "That's exactly like people asking during the scientific revolution, 'If Newton is right that the Earth is in motion, why don't we fall off?'" The answer in the Newtonian case is exactly the same theory, that is F equals MA plus the law of gravitation, which entails that the Earth is in motion, is in very rapid motion around the sun, also entails that if it were, we wouldn't feel it, that if it were, we wouldn't fall off. The claim about the Schrödinger equation is exactly the same feature of the Schrödinger equation that produces this branching also guarantees that an observer who is on one branch won't be aware of the existence of any of the other branches.
▶︎ 45:08 Now, this very talk of an observer being on one branch is a little weird, is a little hard to make sense of. I'm not sure what to say about it. But there is this idea that when the various branches become sufficiently macroscopically distinct from one another, it begins to make sense, although this is an approximate way of talking, this is a vague way of talking, it begins to make sense to talk about this quantum state depicting a multiplicity of independent universes that evolve from thereon in a way that's more or less independent of one another, and in which they won't become aware of one another's existence.
▶︎ 46:02 So, our impression that the measurement of, say, which path a particle is on in the two-paths device had a single determinate outcome is just false. Like our impression that the Earth is stationary in Newtonian mechanics is just false. It's an illusion produced by the dynamics in just the way that our impression that the Earth is stationary is an illusion produced by the selfsame dynamical laws as demand that the Earth is in motion in the first place.
▶︎ 46:37 If this can be made to work, then all of the hysteria about how to impose a collapse, about when to impose a collapse, about where to impose a collapse, about what causes the collapse, it was all a complete waste of time. We don't need it. You take Sidney Coleman, who was a very famous physicist at Harvard up until ten or so years ago, used to call this way of talking "quantum mechanics in your face." Just because it is just von Neumann's rule number one. There's a way of resisting the temptation to mutilate this rule with any kind of a collapse postulate, either a collapse postulate triggered by things like measurement or consciousness, or even the small stochastic modification of the Schrodinger equation that we encounter in something like the GRW theory.
▶︎ 47:47 If you just calm down, if you look at what the Schrodinger equation all by itself is telling you, you're going to find that it's giving you a picture of the world which fully explains your empirical experience of it. This is, in my judgment, for a whole host of reasons, a very difficult theory to make clean sense of. But the part of it that's received the most attention, not because it's the hardest to make sense of, but because it's at least a place where a question can be posed in a clear and crisp way, is this.
▶︎ 48:37 If somebody asks what our reasons for believing in anything like quantum mechanics is, those reasons have to do with its probabilistic predictions about how experiments come out. We note that the frequencies of certain outcomes of certain experiments are exactly the type that one would take to be confirmatory of a fundamental probabilistic law. So our evidence for quantum mechanics consists entirely of evidence for the claims that its probabilistic predictions are correct, that its chance predictions are correct.
▶︎ 49:19 And there's just prima facie a puzzle about a theory like this. If the world is just deterministically splitting all the time and there is for sure, at the end of the experiment, going to be a you that sees the electron on the hard path and a you that sees the electron on the soft path, it's just not clear what kind of sense one could make of this probability talk. One might be tempted just to drop all the probability talk. But if you drop the probability talk, you're dropping all the stories you know how to tell about what our empirical evidence for quantum mechanics is in the first place. So it doesn't seem like there's an option to drop the probability talk. And if there's no option to drop the probability talk, it's not clear what it refers to or what it's about.
▶︎ 50:15 This is, after all, a completely deterministic theory. If one, by analogy, if one says to you, you stroll over and you have a chat with an amoeba that's about to divide, and you say to this amoeba, "Tell me, what do you think the chances are that you'll end up as the one on the right as opposed to the one on the left?" That's a strange question. And the amoeba would rightly react to it by saying, "That's a strange question. I just don't understand the question." Who's the me, first of all, that we're talking about?
▶︎ 50:53 There seem to be a bunch of ways I could talk about what things are going to be like after I split. I might say that the me that exists now just doesn't survive this splitting process, or I might say that I am, in some sense, in both the left and the right. But to say something other than that, like the probability is two-thirds that I'm going to be on the left and one-third that I'm going to be on the right, it's just not clear what kind of sense that could make. It's not clear what kind of room you have to make clear what this probability talk is about in the context of something like the many-worlds interpretation of quantum mechanics.
▶︎ 51:38 One should say, what I've said so far is just the beginning of this story. It is universally acknowledged by proponents of the many-worlds interpretation that what I've just said does amount to an important challenge for their picture. Something that they have to have some kind of answer to. There's been a tremendous amount of ingenuity poured into the project of trying to make sense of probabilities in the many-worlds interpretation.
▶︎ 52:17 Let me just recommend two books to look at at this point. There's a very helpful conference that was held at Oxford about 10 or 15 years ago. And the papers from that conference were collected in a book called Many Worlds?, which will give readers a very useful survey of various attempts, mostly to make sense out of this probability talk in the context of the many-worlds interpretation. Also, there's a book by David Wallace called The Emergent Multiverse, which is what most people now would identify as reporting on the state of the art in terms of attempts to make sense out of the many-worlds interpretation, and in particular, attempts to make sense out of ordinary probability talk in quantum mechanics in the context of the many-worlds interpretation.
▶︎ 53:27 For whatever it's worth, my own sense of things is that these attempts haven't yet succeeded, and I'm not optimistic that they can succeed, but this is by no means a settled question. This is a hotly debated question nowadays. Anyway, that's a second tradition of attempts to. I got a question. Good.
▶︎ 53:57 Audience: So we're trying to understand probability in the context of many worlds. A very naive thing to say is when people are talking about probabilities or chances, they say something like, "Oh, there's a world where I do and a world where I don't." Is there anything connecting that to this story? Another way of putting it is, the story of probability in GRW as you told it is that there's these fundamental stochastic chance laws, which is an unanalyzed base thing about what probability is and how it starts. Could one not also just say that's incomprehensible, and so here's another way of looking at it. All that probability is is there's a measure on possible worlds. Something like that.
▶︎ 54:43 So it was at least in the beginning, although I think people have gotten much more sophisticated than this, a kind of double standard response. People would say, "Nobody knows what probability is. How come it's not this? There's no satisfactory philosophical analysis of what probability is. What makes you think it's not this?" There's a serious question there. It is the case that there isn't a widely agreed upon, a satisfactory philosophical analysis of probability.
▶︎ 55:20 It does seem fair to at least point this out. In every case in physics or elsewhere prior to Everett, where we're tempted to say something like, "The probability that such and such will occur five minutes from now is .7." It's been a feature of all of those cases, even if we don't know what probability is, you might say we know this much about it, it's a feature of all those cases that there's something about the future of the universe that we don't know for sure at the moment when we say that. It would be nonsensical to say that if there was nothing that we didn't know for sure about the future evolution of the universe.
▶︎ 56:11 There may be various different reasons why we don't know. We might not know because although the laws of evolution are perfectly deterministic, we have only incomplete information about the present conditions. That's the kind of thing that goes on in classical statistical mechanics. Or it might be that the reason we don't know what's going to happen in the future is that even if we had all the information about initial conditions, we would be confronted by the fact that the fundamental dynamical laws are themselves stochastic, that's what's going on in say the GRW theory.
▶︎ 56:52 In this case, it seems like neither of those is going on. That is, nothing would be sharpened up by a more precise microscopic description of the situation before I do the measurement of which path the particle is on. That's not the problem here. And of course, it's not that the, so, what's going on here is that, let's put it this way. The challenge for a many-worldser is to make it plausible that it makes sense for me to say something like, "The probability," and I don't even know what the words are, "The probability that the outcome of this experiment that I am going to witness will be soft path is .7." To say that at the same time as I have no ignorance whatsoever about the future physical evolution of the world.
▶︎ 57:56 Now, there's an immediate temptation to say, "No, of course it's not the case that there's anything third personal that I don't know about the future evolution of the world. What I don't know and what these chances are about is where I'm gonna end up." But then the referent of this "I" becomes very mysterious. That's what we were talking about in the case of the amoeba. There's a lot more to say about this, but if people just say, "Well, shit, nobody knows what probability means, I can make it mean anything I want," that seems a little unfair.
▶︎ 58:38 It does seem to be a feature of every previous kind of sensible discourse that includes a statement like, "The probability that this is gonna happen is .7," that there's something about the future of the world that I'm not presently certain of, and that's what seems absent here, and that's what seems very puzzling. Like I say, that having been said, if you look at Deutsche's book that I mentioned, or if you look at this book, Many Worlds?, you will find a variety of spectacularly ingenious proposals for trying to make sense out of this talk in the presence of this complete lack of uncertainty about what's physically gonna happen in the future. Those are really interesting. I'm expecting you to come up with a new one in due time, which I'll be very interested in seeing.
▶︎ 59:44 But for reasons that I don't have a chance to go into here, although here again I can recommend a book. First of all, there's an essay of mine in this collection, Many Worlds?. There's also an essay that forms the last chapter of a book I published a few years ago called After Physics which goes through various of these strategies for trying to make sense out of these probabilities and explains why I'm skeptical about them. But once again, it would be misrepresenting the situation to say that there's anything like consensus about this at the moment.
▶︎ 1:00:33 Audience: Stupid cartoon question. So if I set up a contraption that measures an electron passing through a measurement device, and in the case if it come out black, the contraption will shoot me in the head, if it comes out white, it wouldn't. So, in those instances, I do the measurement, and it turns out it shoots me in the head, and as I bleed to my death, I know for sure in another universe that person lived. So, it seems like I do know a lot if the chances are 50/50.
▶︎ 1:01:16 No, but that was exactly the point. You know everything. You know everything. So, what sense can talk about probabilities make? There's a nice story in this vein, which maybe I'll take a second to tell. David Lewis, toward the end of his life, got interested in the many-worlds interpretation of quantum mechanics, and was interested in cases exactly like the one you're describing.
▶︎ 1:01:48 And what's poignant about this story is that this happened, David Lewis wrote this paper just by coincidence. When he first delivered this paper at a conference, I was asked to comment on it. I was asked to provide a little commentary afterwards. David Lewis wrote this paper at a time when he knew he was about to die of diabetes. His diabetes was getting much, much worse.
▶︎ 1:02:17 And his thought was that suppose you do a measurement where, if it's on the soft path, you immediately get killed, and if it's on the hard path, you see it as on the hard path. His thought was, this is a thought which I never really understood, and this is what my comment was about, that in that case, the probability you should assign to seeing it on the hard path is one. You'll definitely see it on the hard path because you go entirely into whichever branch of you survives. And what he quickly realized was that this is gonna result in an ultimate fate of human beings that is worse than any nightmare that anybody has ever constructed.
▶︎ 1:03:15 So suppose you go stand in front of a train. And the train runs you over, there's gonna be a very small but non-zero quantum mechanical probability of your surviving, but you're gonna be surviving in a kind of agony that no human being has ever experienced. And that's definitely what's gonna happen to you, that's what probability one what's gonna happen to you if you do this. So you have this man who's about to die and who is inventing stories about how, if many worlds is true, there are things much, much, much worse than death.
▶︎ 1:03:57 And Lewis had this, there was a nice line somewhere in the talk where Lewis says, "You know, you wouldn't be able to report it to anyone else, but if you'd like to find out whether this theory is true, you can do so this very day. Just go out and dance in traffic, and you're gonna find out if this theory is true." Anyway, that's a little anecdote about that, but very poignant given that he knew. So what do I wanna do when I know myself to be dying? I don't want to invent comforting stories about what it's gonna be like. I don't want to invent stories about how it could be much, much, much worse than that. Anyway, that's, if there aren't other questions, that's sort of what I have to say about the many-worlds tradition.
▶︎ 1:04:58 There's a third live tradition of attempts to solve the measurement problem, which, unlike GRW, involves no modification of the Schrodinger equation, but, unlike Many Worlds, denies that the wave function is a complete description of physical reality. There's a nice quote by Bell, who was a wonderful writer, where he says, "Look, the lesson of the measurement problem, succinctly, is that either the Schrodinger equation is not right or it's not everything." The option that the Schrodinger equation is not right is the collapse theory option, the GRW option. The Schrodinger equation by itself can't be the right story of what's going on. It needs to be either supplemented by von Neumann's rule number two or by these kinds of stochastic modifications that you get in the GRW theory.
▶︎ 1:06:03 There's a third tradition, a so-called hidden variable tradition or extra variable tradition. The most successful such theory we have was first formulated by David Bohm in the 1950s. It was completely ignored at the time. Part of what facilitated ignoring it was the Un-American Activities Committee that hounded Bohm out of the country. Anyway, long story. Another book I recommend, that just tells this historical story nicely, is a book by Adam Becker called What Is Real, which tells this story about Bohm and tells lots of interesting stories about the histories, the history of these discussions over the course of the 20th century.
▶︎ 1:06:54 What's going on in Bohm is essentially this. What we have in Bohm, compared to the other two theories we've been talking about, is, you might say from a metaphysical standpoint, radically and thrillingly conservative. According to Bohm's theory, there are two kinds of concrete physical objects in the world. Say, in a world that's the kind of world that we would normally describe as consisting of a single particle. There are two kinds of concrete fundamental physical objects in that world. There's a particle, which is the kind of thing that always has a perfectly determinate spatial position, and all we want to know about this particle is how it moves around, is how its spatial position changes with time, and there is this wave function field.
▶︎ 1:07:56 And this wave function field pushes the particle around. Not exactly like a force field, but a better analogy is, you think of this wave function field as a sort of fluid, like a river. And you think of the particle as an infinitely light quark floating in the river. There are various currents in the river, and the quark just gets dragged along with these currents.
▶︎ 1:08:25 Think, for example, of the two paths experiment. In the two paths experiment, when you feed the particle into the hardness box at the beginning, you're feeding both the particle and its accompanying wave function fluid into the hardness box. The particle comes out one aperture or the other. There's a perfectly definite fact of the matter about the location of this particle in space at all times. It either takes the hard route or it takes the soft route. But the fluid splits up and goes in both directions, like a river might.
▶︎ 1:09:03 The fluid splits up and goes in both directions. At the other end of the two paths device, when the two paths get reunited, the two branches of this river get reunited with one another, and both of them can then affect the motion of the particle going forwards. So if you want to know, look, how could the particle have gone this way and yet have its later behavior affected by whether or not a wall was inserted over here? It can be affected by that, because in that case, that part of the fluid won't get all the way to the black box and have a chance to affect the future behavior of the particle.
▶︎ 1:09:47 This is a thrillingly simple and metaphysically conservative picture of what's going on. There are no superpositions here. Particle talk is fundamental talk. Particles always have definite positions, and what physics is about, just as what classical physics was about, is how the positions of particles change with time. That's it.
▶︎ 1:10:20 Couple of drawbacks about this theory. Your reaction to this theory should have been, "Why wasn't I told about this in the first place? Why did we spend all this time talking about metaphysically baroque ideas about superposition?" Blah, blah, blah. In some sense, I think that continues to be the right reaction, but it's not as simple as that.
▶︎ 1:10:47 First of all, in the case of multiple particle systems, the space that this wave function goop is floating around in is no longer three-dimensional space, but a so-called configuration space whose dimensionality in the case of, say, an n-particle system, is 3 times n. The wave function of the universe is floating around in some high-dimensional space whose dimensionality is three times the number of elementary particles in the universe. That's very different from how things look to us in our ordinary everyday experience.
▶︎ 1:11:30 A bunch of questions are of course immediately raised. One of the things we're gonna need from this theory is some kind of a mechanical account of why it looks to us as if we're making our way through a three-dimensional space when we're actually making our way through this fantastically high-dimensional space. It's not implausible that the theory can give you a good mechanical account of that.
▶︎ 1:11:56 It's also the case, as we know it must be from Bell's work, that the theory is wildly non-local. The things you do over here can, in a very mechanical way, affect stuff that's going on over there. The theory is completely deterministic. The chanciness of quantum mechanics on a theory like this has to be the kind of chanciness that you encounter in classical statistical mechanics. It has to do with uncertainty about what the initial conditions are, 'cause the theory is completely deterministic.
▶︎ 1:12:34 But unlike in classical statistical mechanics, you can imagine steady technological improvements which will give you more and more and more detailed information about what the exact initial conditions are, and in that way enable you to predict with more and more and more certainty how the universe is going to evolve into the future. In a way that has no principled upper limit, if you're willing to spend the money, if you get sufficient technological improvement.
▶︎ 1:13:11 Bohm's theory is gonna have to give us an account, and it does give us an account of why, even though your ignorance of how certain future experiments are gonna come out is just a matter of ignorance of present initial conditions, because this is a deterministic theory, there is a principled limit on how much you can learn, which is completely invulnerable to any kind of technological advancement or anything like that. There's a fundamental limit on how much you can learn about the initial conditions of the system. Although it's a completely deterministic theory, unlike in classical statistical mechanics, there are principled limits, limits that are represented by the uncertainty relations that we talked about a long time ago, on the accuracy with which you'll be able to predict the outcomes of certain sequences of future experiments.
▶︎ 1:14:11 Let me back up a little bit, in the course of this review. I forgot to mention the most attractive, what's widely considered to be the most attractive feature of the Everett interpretation, of the Many Worlds Interpretation. Unlike Bohm and unlike GRW, if one could make sense of the Many Worlds Interpretation, you would have a local account of our empirical experience.
▶︎ 1:14:47 It happens that in the proof of Bell's Theorem that we went through, there was an unmentioned assumption, an assumption which isn't mentioned because it seems so innocent that there doesn't seem to be much of a point in mentioning it. But when we went through the proof of Bell's Theorem, we didn't mention that the proof of the theorem takes it for granted that once the measurements on these two electrons that are involved in Bell's Theorem are done, there is a fact of the matter about how this measurement came out and how that measurement came out. There is a unique fact of the matter about how this measurement came out and how that measurement came out, so that we can talk about correlations between those two outcomes and the probability that the outcome of this measurement was the opposite of the outcome of that measurement and so on and so forth.
▶︎ 1:15:44 Like I say, this seems like such an innocent assumption that it's not even worth mentioning, but it surely is an assumption on which Bell's argument depends, and it's an assumption which it should be easy to see is precisely what's denied by the Many Worlds Interpretation. There is no unique determinate fact of the matter about how any of these experiments came out. They all came out in all of the possible ways, for sure. And if you ask, "What's the degree of correlation between the outcome here and the outcome there?" It's a nonsensical question. And it's those correlations that Bell shows are impossible to explain, are impossible to explain by any local means.
▶︎ 1:16:31 It's a big attraction of the Everettian tradition that if that can be made to work, we've got a local account of our experience of the world. This is something that's very attractive to working physicists about it. The other thing that's attractive to working physicists about it is this idea that it doesn't mutilate the beautiful mathematics of the Schrodinger equation either by stochastically modifying it as they do in GRW or by adding to it as Bohm's theory does. You have this pristine mathematical structure, which is all the mathematical structure there is to Everett.
▶︎ 1:17:15 Also, you have a theory. There are people who object to this claim. I don't think they're right. But you'll find it in these books that I mentioned, you have a theory which is local, in which gets through an almost completely unnoticed loophole in Bell's argument.
▶︎ 1:17:42 A nice thing about GRW, it's fairly conservative metaphysically on the macroscopic level, modulo the worries that you brought up and that we were talking about, and all there is to the world on GRW is the wave function. The advantages of Everett, we already mentioned. The advantages of Bohm are this kind of radical metaphysical conservatism, not only on the macroscopic level but on the microscopic level as well, but it has these tremendous disadvantages about the dimensionality, so on and so forth.
▶︎ 1:18:21 Other things to mention, all of the solutions to the measurement problem that we've been talking about, the proposed solutions to the measurement problem that we've been talking about, are worked out in the context of the version of quantum mechanics that applies to non-relativistic physical systems. In the case of relativistic physical systems, the equations of motion change from the Schrodinger equation to the Dirac equation, what's called the Dirac equation or something like that. It's another conspicuous advantage of Everett that the changes involved in going from non-relativistic versions of quantum mechanics to relativistic versions of quantum mechanics are just trivial in the Everett case. Whatever version of quantum mechanics you're dealing with, you deal with just that, von Neumann's rule number one, that's it.
▶︎ 1:19:23 It's true of both Bohm and GRW that the business, part of this is because both of them are non-local, part of it is because both of them are committed to a fundamental ontology of particles and so on and so forth, there are a bunch of non-trivial questions about how you write these theories down in the case of relativistic quantum theories or relativistic quantum field theories or relativistic quantum string theories, or something like that. There's a lot of technical work to do in order to reformulate those theories in such a way that you can apply them to the language of, say, string theories or relativistic quantum field theories, or something like that. I would say nobody knows any reason yet to doubt that that can be done, but it's not easy, and it's completely trivial in the case of Everettian theories.
▶︎ 1:20:24 There were these announcements, as I say, by Bohr, that the old-fashioned, flat-footed, realistic scientific project had killed itself. And there's a quip somewhere of Mark Twain, where he says, "The recent reports of my death have been hugely exaggerated." Something like that was going on here. At least for the non-relativistic case, these announcements that any attempt to tell this story, that any attempt to tell an old-fashioned, flat-footed, literal, realistic story about what's going on behind the curtain, as it were, that produces these experimental outcomes, the claim that any attempt to do that was going to collapse into paradox and self-contradiction has just been proven multiple times wrong by explicit construction.
▶︎ 1:21:31 We have these stories. We have Bohm's theory. We have the GRW theory. Maybe we have Everett. This is just not the case. And what one can certainly say is that these proclamations of Bohr and his circle, these things that were advertised as deep philosophical arguments are just a certain kind of particularly energetic and adamant lack of imagination. We can tell these stories.
▶︎ 1:22:09 What's also true is that all of these stories are weird. All of these stories are seriously strange. One wants to make a distinction in these kinds of conversations, a very sharp distinction, between a story being strange and a story being unintelligible. Bohr's claim is that it was impossible to tell an intelligible story about what's going on. That's clearly wrong.
▶︎ 1:22:42 But somebody might want to say, and these are what people like, say, cubists, modern inheritors of Bohr, they're called cubists in the lingo, say, "Fine. Maybe the stories are intelligible. They're not believable. They're too weird. The more intellectually mature way to proceed is in a more Bohrian way, is in a more instrumentalist way." The price we're paying for insisting on telling these realistic stories is its own kind of radical departure from the scientific tradition. It's getting so weird that there's a question about whether it's worth the cost.
▶︎ 1:23:32 Once again, let me mention this further reading that I mentioned before, and I'm happy to entertain more questions about this. So there's the book by Tim Maudlin, called Philosophy of Physics: Quantum Mechanics. There's a book by Geoff Barrett, called Conceptual Foundations of Quantum Mechanics. There's a book by Travis Norsen called Foundations of Quantum Mechanics: An Explanation of the Physical Meaning of Quantum Theory. There's also this very helpful historical book called What Is Real by Adam Becker.
▶︎ 1:24:23 What I hope, as I said at the outset, to have done here is persuaded the listener that there's something puzzling here, that there's more at stake here than what the particular correct physical description of the world turns out to be. What's at stake here, and this is what has always interested me about this story, what's at stake here is whether the scientific project as traditionally understood is still up and running at all. And I guess I can leave it there. Good. Well done. Well done.