▶︎ 0:00 I want to talk about a certain very deep intuition, very primordial intuition that we have about the structure of the world, a very deep conviction with which we make our way around in the world, a conviction which in modern physical discourse is referred to as the principle of locality. And very crudely, this is the conviction that what happens at a certain particular point in space and time only directly affects things that are immediately adjacent to it in space and time.
▶︎ 0:51 The fact that I used the word directly in what I just said is important. It's, of course, the case that our experience is full of instances of somebody doing something or something happening at a certain point in space and time and producing an effect at a remote point in space and time. So, if I flip a light
▶︎ 1:18 Switch on one side of a room, a light may go on at the other corner of the room, so on. But in instances where that happens, we have a very deep conviction to the effect that if we rip up the wall behind the light switch, we're gonna find wires running continuously from the light switch to the light that went on on the other side of the room, that we're gonna be able to tell some kind of story about my flipping the light switch having effects on the intensities of various electrical fields in the immediate vicinity of the light switch, setting some electrons in motion in a wire, which then knock into other electrons a little farther away and knock into other electrons a little farther away than that, and so on and so forth.
▶︎ 2:22 And essentially, that you've got this whole row of dominoes. That the way my flipping the switch over here produces a light going on over there has to do with the continuous succession that you can think of usefully as like a row of dominoes, of one thing knocking into another and knocking into another and knocking into another and knocking into another, continuously and without a break, stretching all the way from the location in space and time where I flipped the switch to the location in space and time where the light went on.
▶︎ 3:01 Or, for example, if I shout across the room to someone and say, "Raise your arm," and this shouting has the consequence that they raise their arm, even though they're a certain spatial distance from me. We're confident that we're gonna be able to tell a story of how that command got from me to them by means of a story about the propagation of sound waves through the air, going through the space between me and them. There'll be this mediating sequence again of toppling dominoes. There'll be this mediating sequence of me changing the air pressure in the immediate vicinity of my mouth. Those changes in the air pressure in the immediate vicinity of my mouth causing changes in the air pressure a little farther from my mouth, and so on and so on and so on and so on. Once again, stretching all the way without a break from my making this noise, "Please raise your arm," to somebody raising their arm on the other side of the room.
▶︎ 4:16 Suppose I signal you. I don't yell, "Raise your arm," but I hold up a sign that says, "Please raise your arm," or something like that. And as a consequence, you raise your arm. Once again, here, we expect there to be a story that starts with my raising this sign that says, "Raise your arm," has to do with light bouncing off the sign, light propagating from the sign to your eyes, entering your eyes, stimulating your retina, getting into your brain, producing you raising your arm. Once again, we think there's gonna be a story of the propagation of the signal from me to you that's completely local in this way, that goes continuously without a break, from me to you.
▶︎ 5:11 Other expectations about the world that this leads to are, for example, that my capacity to signal you in this way depends on what the physical conditions are in the region of space between me and you. So if there's some kind of obstruction between me and you, if there's an opaque screen between me and you, then my holding this sign up is not going to result in your raising your arm because the propagation of the light signal is going to be obstructed. This idea that the effects propagate continuously through the space between the initiating event and the final result of the initiating event entails that the capacity of these two events to be connected in this way is going to depend on what the physical conditions are in the region in between the initial cause and the final effect. And you can imagine conditions obtaining such that that propagation gets interrupted, and the initial cause doesn't lead to the final effect in the usual way.
▶︎ 6:30 Here's another signature of these things. We expect that there'll be some finite time interval between the initial cause and the final effect because this sequence of mediating causes and effects and causes and effects has to be something that unfolds over time. In classical physics, there's not an obvious upper speed limit, but there must be some finite time between the initial cause and the final effect because we expect to be able to explain what's going on to ourselves in terms of the temporal sequence. Once again, dominoes knocking into each other is a good image to have in one's mind here.
▶︎ 7:19 So those are two signatures of a world that's local, that in cases where something causes something else which is remote, either in space or in time or in both from the initial cause, the capacity of this kind of causal chain to function is going to depend on what's going on in the region of space and time in between the cause and effect. It should take a finite amount of time. It should be possible for us by looking carefully, by placing enough measuring instruments or something like that in the region between the initial cause and the final effect, to see a physical process of propagation unfolding. In the case of my yelling to you, we ought to be able to measure sound waves propagating in the region between us. In the case of my signaling to you by waving my arms, we ought to be able to measure the propagation of light waves in the region between the two of us. In the case of a chain of dominoes, we expect to be able to see the dominoes.
▶︎ 8:35 These are supposed to be physical effects in every sense of the word. We can see them. We can measure them. We can tell a story about how they're unfolding in accord with the familiar laws of physics, and so on.
▶︎ 8:49 Another signature. So we've so far got, I guess, three. One, it should be possible to tell a story about this propagation. This propagation should have physical measurable effects that we can intervene with. This propagation should be the kind of thing whose existence depends on what the physical conditions are in the region of space and time through which the propagation is taking place, and we ought to be able to see it, and one more thing.
▶︎ 9:33 This is a little less strict, but our natural expectation would be that in cases where something over here affects something over there, the strength of the effect we would roughly expect decreases as the distance between the first cause and the final effect gets larger and larger. We tend to think of this first cause as shooting off effects in all directions, and they thin out as you go farther away. The principle is that the direct effects, the unmediated effects, are always local in the sense that the unmediated effects are always on conditions immediately adjacent to the initial cause, both spatially and temporally. That's the way direct effects work in the world.
▶︎ 10:34 This is not a prejudice of modern physics or anything like that. This is a very deep conviction, something much, much older than modern science, something much, much older than the scientific revolution of the 17th century. This is something that we've suspected about the world forever. Indeed, this is something presumably hardwired into us by natural selection. This is something that predates human existence in the world.
▶︎ 11:10 There's a clear sense in which dogs believe in locality and in which mice believe in locality in the sense that the lion isn't gonna kill them unless the lion is where they are, both spatially and temporally. Fish believe in this. I don't know how far back it goes. But it's very deep in the way the world seems to present itself. It's an intuition which probably predates the existence of human beings in some vague sense.
▶︎ 11:48 Violations of this kind of intuition are, in many cases, the hallmark of magic. I stick a pin into a voodoo doll and a guy gets a stomachache across town. And in that case, we're not thinking of this role of dominoes. But somehow, my sticking this pin into the voodoo doll directly and in an unmediated way causes something else to happen at a remote point in space. That's the signature of magic. And that it is the signature of magic is a symptom of how deeply convinced we are that the natural world works in what I'm calling a local way.
▶︎ 12:43 I wanna say something about the fate of this intuition, about the relationship of this intuition to the development of modern physics from the scientific revolution to the present day, because there's a really, really interesting story there.
▶︎ 13:08 This story gets going the minute that the modern scientific project gets going in earnest with Newton. Newton writes down his laws of motion and his universal theory of gravitation, and it's part and parcel of Newton's universal theory of gravitation that if you have two material bodies at a certain distance from one another in space, these two bodies exert a force on one another. They exert a gravitational force on one another. And the way Newton originally writes this law down, it's a blatant violation of this intuition of locality. These two bodies, there's no account, there's no attempt to give an account of anything, of these two bodies exerting a force on one another by means of some kind of effect on the space in between them, which propagates from one body to another.
▶︎ 14:19 It's a consequence of Newton's Law of Gravitation, if you take it seriously, that if I were to move one of these bodies, then the force on the other body would immediately change, without any other physical effect going on in the space between those two bodies. Newton writes down this Universal Law of Gravitation. This law, combined with Newton's Laws of Motion, F equals ma, are a fantastic success. They suddenly, in one swoop, show that the explanation of the motions of the planets is exactly the same thing as the explanation of why rocks fall in the vicinity of the Earth and why projectiles in the vicinity of the Earth carve out the trajectories they do in space and so on and so forth.
▶︎ 15:13 This is a fantastically successful hypothesis, this Universal Law of Gravitation, but even more or less immediately after it was written down, it was noticed by everyone that this violated what we're calling this intuition of locality, and people were puzzled and disturbed by this violation. In those days, the way people described this was they said that Newton's Law of Gravitation described action at a distance. And what they meant by action at a distance was precisely this violation of locality, that the presence of this mass here is somehow directly, and in an unmediated way, affecting this other mass here, producing an acceleration of this other mass by exerting a force on it, without any accompanying account of, as it were, how in a local way that happened, what's going on in the space between them that makes it the case that the presence of this mass here could produce an acceleration in that mass there.
▶︎ 16:27 There's no such account. Indeed, the way Newton writes the law down, the very idea of such an account is ruled out. It stipulated that this is a direct effect of one of these masses on the other, even though they're separated from one another in space.
▶︎ 16:43 This is absolutely unlike the case of the two billiard balls colliding with one another. As I say, it was widely noticed that this constituted a case of what people in the 17th century referred to as action at a distance, by which they just meant a violation of what we're calling locality here, and people were puzzled by that and disturbed by that, and no one was more puzzled and disturbed by it than Newton himself. Newton saw this. Newton was perplexed by it. The law had a lot to recommend it in terms of its empirical success, but Newton himself was convinced that the non-locality of the law he had written down meant that presumably this couldn't be the final form of the Law of Gravitation, that surely if the scientific project was going to succeed in the way Newton hoped it would succeed, it was eventually going to be replaced by a local account of how this worked.
▶︎ 17:59 And indeed, it's worth taking a minute to talk about the fact that Newton himself engaged in some speculation about what a local version of a gravitational law might look like. Here's a story that Newton entertained for about 10 minutes and quickly dismissed, because he saw, for reasons that we'll describe, that it wasn't going to work. But this just shows how compelling Newton himself thought this intuition of locality was.
▶︎ 18:38 So Newton speculated in the following way. Newton said, "You know what, what if the space, say between the earth and the moon or the earth and the sun, that we're normally thinking of as empty space, is actually swarming with tiny, invisible material particles that are running around in every direction?" So suppose you have some large material body floating in this soup of tiny particles. The particles have random velocities. Some are going this way, some are going that way, some are going this way, so on and so forth. The thought is, if you have an isolated material body floating in this soup, the impacts of these tiny particles are essentially going to sum to zero.
▶︎ 19:32 You're going to have some particles smacking into it from this direction, you're going to have some particles smacking into it from that direction. As a statistical matter, they'll cancel each other's effects out. And the net effect of floating around in this soup on the motion of this large material body will be zero. But then Newton reasoned, what if you have two material bodies at a certain distance from one another, but not terribly far away? Then the thought would be, as it were, this body is going to cast a shadow on this body, and this body is going to cast a shadow on this body. That is, the presence of this body will shield this body from some of the particles coming that way, and the presence of this body will shield this body from some of the particles coming that way.
▶︎ 20:32 So if you look at this body, there are going to be more impacting it from this side than from this side. If you look at this body, there are going to be more of these little particles impacting it from this side than from this side. The net effect of that is that this body is going to get pushed by the impact of these particles in this direction, this body is going to get pushed by the impact of these particles in this direction. It will be as if they're attracting one another non-locally, but in fact, no such thing is going on. You're going to have a complete explanation of these material bodies acting as if they're attracting one another, which is really just a case of these perfectly local billiard ball-type collisions that we were talking about a few minutes ago.
▶︎ 21:28 That would be an example, were it to succeed, of a local account of this gravitational phenomenon. It wouldn't be, if you looked at it this way, really a case of this doing anything directly to this. They'll be behaving as if they're attracting one another. That's not really what's going on. What's really going on is that they're casting these shadows on one another, that they're shielding one another from the impacts of these little particles on one side, but not on the other side.
▶︎ 22:03 There are a bunch of reasons why this can't work, and Newton quickly realized why it can't work. We can just mention a few. If this were the correct account, then the gravitational force between these two bodies wouldn't just depend on their masses, it would depend on their shapes. Different shapes will shield more or less of these particles than other shapes. Also, even if you assume they were both spherical, you can do a quick calculation of how quickly the apparent attractive force would get weaker as the bodies got farther apart.
▶︎ 22:43 In order to explain the motions of the planets, the way that force has to get weaker is, the strength of the force has to be proportional to one over the square of the distance between these two material bodies. If you do a quick calculation of how you would expect this apparent force to fall off, if a theory like this were true, it wouldn't fall off as one over R squared. It would fall off with distance in a different way. So there are a bunch of reasons why this can't be the right theory of gravitation, but it's interesting to see the degree to which Newton himself was acting in such a way as to make it clear that even in his own theory, this violation of what we're calling locality, this existence of action at a distance, was enough to convince him that this couldn't be the final theory of gravitation.
▶︎ 23:51 This intuition that when you get right down to it, when you take things apart, when you rip up the wall behind the light switch, when you analyze in detail how, when I talk to you across the room the information actually gets into your head, or when I signal you by waving my hand or by holding up a sign across the room the information actually gets from me to you into your head, there is this very deep conviction that it's going to have to be possible to look in more detail to see these physical phenomena of propagation going on. And if we can't see them, this must not be the right account of the world. Good.
▶︎ 24:41 Things got left there for 300 years or so. For 300 years you had this flagrantly non-local law sitting right in the middle of physics. And everybody... It's a good historical question to which I don't know the answer, in the intervening 300 years, how much were people bothered by this? And I don't know the answer to that question.
▶︎ 25:19 Certainly Newton and his contemporaries were bothered by it. Certainly Newton thought that meant this couldn't be the final theory of gravitation and were waiting for the final theory of gravitation. Nothing very interesting that I know of happened in these developments until 300 years later in the 19th century. Excuse me, 200 years later in the 19th century.
▶︎ 25:52 In the 19th century, people started to investigate electric and magnetic forces in a systematic way, and a similar issue arose. There is this so-called electrostatic force, the Coulomb force. This force is repulsive, this is a force that operates between charged particles. Unlike gravitation, this force can be either attractive or repulsive. It's repulsive if you have two positive charges or two negative charges. It's attractive if the charges are of opposite sign.
▶︎ 26:35 But the mathematics of this, of the way this force works is very similar to gravitation. First of all, the force is proportional to the charges, not to the masses, and its dependence on distance is that as they get farther apart, it falls off as one over the square of the distance between the two charged particles. But once again, in its original form, the so-called electrostatic law of Coulomb, you have this exact same non-locality. You have a law to the effect that if I have two charged particles, they produce forces on one another across a distance. They produce, that is accelerations in one another as a result of this force, and there's no suggestion of that in any way being dependent on any process of propagation, on any local process by means of which this charge lets that charge know that it's here, or anything like that. This seems to be a direct effect that two charges at a finite distance from one another are supposed to have on one another, according to Coulomb's law.
▶︎ 28:00 Another interesting thing happens in the 19th century in connection with these investigations of electrical forces and magnetic forces. Initially, this is a purely notational development. It's not an interesting conceptual development, or it's not treated as an interesting conceptual development. As a purely notational development, people start talking about something that they call electric fields. People describe the forces between two charged particles in the following way. They speak of one charged particle as producing an electric field around itself that goes out to infinity. Producing is maybe the wrong word, because there's no account of how it produces it, but they say a charged particle is surrounded by an electric field.
▶︎ 29:04 A charged particle, the existence of a charged particle at a certain location in space is always associated with an electric field. This electric field extends outward to infinity. It gets weaker and weaker as you go farther and farther out. Its strength decreases as one over R squared as you go farther and farther out from the electric charge. And if you adopt this kind of notation, if you adopt this kind of terminology, then you can speak of the other charged particle, not as reacting to this one that's at a distance from it, but as reacting to the electric field of this other particle. Reacting to the electric field at the point where that second charged particle happens to be located.
▶︎ 30:01 So you can speak of the second charged particle as experiencing a force as a result of the electric field associated with particle number one at the point in space where it happens to be. Now, as I say, this was initially regarded as a mere notational, terminological, mathematical convenience, to talk about these fields. This wasn't the kind of talk that people took ontologically seriously.
▶︎ 30:39 And nobody regarded this as some kind of solution to the puzzle about the non-locality of these forces. Like I say, there's a purely formal sense, there's a purely mathematical sense here, in which you can describe the force on particle number two as if it's arising just from the field associated with particle number one at the point in space where particle number two happens to be located. But as I said, this was regarded, at least in the early stages, as just a mathematical way of describing what force particle two would experience if it was located in any particular point, in any particular spatial relation to particle number one.
▶︎ 31:29 Throughout the course of the 19th century, and as far as I know, a very important figure in this development was Faraday, who was one of the important 19th century investigators of electricity and magnetism. Slowly, people, and like I say, I think Faraday was an especially important figure in this intellectual evolution, slowly, reasons began to accumulate, why these fields should be taken more ontologically seriously than they had been when they were originally introduced as these purely notational devices.
▶︎ 32:27 This achieves its final form, in Maxwell's equations, of the electromagnetic field, which were published toward the end of the 19th century. Faraday had anticipated a lot of the features of these equations, but they take a final, clear, pristine mathematical form in Maxwell, and when you look at Maxwell's equations, there are at least three distinct kinds of reasons to think that these fields aren't mere notational devices. That they are part of the fundamental physical furniture of the universe, no less than the particles are. By the time you get to Maxwell's equations, it's no exaggeration to say that all of a sudden, over the course of the 19th century, the fundamental ontology of the physical world has doubled.
▶︎ 33:33 As of Newton, the physical furniture of the universe is supposed to consist entirely of material particles. By the end of the 19th century, there's a pretty wide consensus among theoretical physicists that the fundamental physical furniture of the world consists of two different kinds of physical things, material particles and fields, and these two things are ontologically on a par with one another. Let me tell you why people reached a conclusion like this. I think there are three compelling reasons.
▶︎ 34:09 Reason one, it turns out, people like Faraday noticed this and so on, if you have charged particles moving around and interacting with one another electrically and magnetically and so on, if you have charged particles moving around, if you look at the total energies of a collection of charged particles and the total momentum of a collection of charged particles, they won't be conserved. There will be situations where you have charged particles coming near one another and then moving away from one another, and you add up the total energy of the particles before these interactions began, and you add them up again once the interactions are done and the particles are far apart from one another, and the energies are not the same. And the total momenta of the charged particles are not the same.
▶︎ 35:12 The idea that things like energy and momentum are conserved had, this is nowhere near the depth of the intuition about locality, but as a result of the study of Newtonian mechanics over the previous 200 years, people had developed enormous confidence in very basic physical principles to the effect that things like energy and momentum were conserved. And it was very perplexing that if you add up the energies of all the particles, in certain kinds of electrical interactions, they look as if they turn out not to be conserved and the momenta of the particles turn out not to be conserved.
▶︎ 36:02 And moreover, it was noticed by a mathematician named Poynting that there was a simple way, there was a simple formula whereby you could associate energies and momenta with configurations of electromagnetic fields, such that if you adopted this simple formula. So you have some formula, you have some algorithm. You plug in a configuration of electric and magnetic fields and this algorithm spits out a total energy. Or you plug in a configuration of electric and magnetic fields, and this second algorithm spits out a total momentum.
▶︎ 36:49 What was important about this algorithm is that it was quite simple and quite universal. And it was found that if you adopted such an idea, if you used this algorithm to associate things like energies and momenta with various configurations of electromagnetic fields, then you could prove from Maxwell's equations that the total energy and momentum of the world, including the standardly calculated energy and momenta of the moving particles and this new suggestion about how to associate energies and momenta with configurations of electromagnetic fields, if you added those two together, you got a strict conservation theory.
▶︎ 37:39 And people said. So you had a combination of several factors here. One, that people had this deep faith in some kind of principle like conservation of energy and momentum. Second, that the algorithm for associating energies and momenta with configurations of electromagnetic fields turned out to be very simple. And if you adopted this simple formula, you would get Maxwell's equations entailing the conservation of total energy and momenta, including particle energy and momenta and field energy and momenta.
▶︎ 38:21 This began to convince people. This is only one of the three reasons that I'm in the course of mentioning. This is the first one. This suggested to people, wow, there's good reason then to think that these electromagnetic fields really can be carriers of energy and momentum. And that in Maxwell's equations, what we're seeing is just as when we see two billiard balls collide, we see exchanges of energy and momentum between the two billiard balls, we can see in Maxwell's equations processes where charged particles are exchanging energy and momenta with the fields.
▶︎ 39:08 And the fields are in turn exchanging energy and momenta with the particles. And this all hangs together very nicely, and it suggests that this business of associating energy and momenta with field configurations is not idle or purely mathematical. At least, maybe it's not. Maybe this is reason to take seriously that these things can actually carry energy and momentum. Maybe this is reason to take seriously the thought that these are real, concrete physical objects, no less than material particles are. That's reason number one.
▶︎ 39:54 Reason number two, Maxwell's equations, in order to avoid certain mathematical contradictions, once again this is something that Faraday anticipated a lot of, by his own reasoning. Maxwell noticed that if you want to avoid certain kinds of contradictions, you can't stick to the claim with which, say, the Coulomb theory started out, that electric and magnetic fields are entirely determined by the positions and motions of the charged particles in the world. Indeed, one of the famous consequences of Maxwell's equations is that there could be electric and magnetic fields doing all kinds of complicated things, even in a universe in which there were zero charged particles.
▶︎ 40:56 A famous solution of Maxwell's equations is that he noticed that if you had an electric field that was oscillating like this, that would give rise to a magnetic field that was oscillating like this, which would in turn give rise to an electric field that was oscillating like this, which would in turn give rise to a magnetic field that was oscillating like that, going forwards and forwards and forwards. Maxwell was able to calculate the speed with which this disturbance propagated through empty space. So the fields have an internal dynamics of their own. It's not merely that they're determined by what the charged particles are doing. They can push and pull on each other on their own. They have this rich internal dynamical life of their own as a result of Maxwell's equations.
▶︎ 41:51 And one of the great triumphant surprises in the history of physics is that Maxwell does this calculation of the speed with which these electromagnetic disturbances propagate through space, and he gets a number which is astonishingly close to the recently measured velocity of light. Before this moment, no one in physics had the slightest suspicion that light had anything to do with electromagnetic fields or anything like that. The phenomenon of light was thought to be something completely disconnected from what physics had so far investigated, something to be investigated in the far future of physics. All of a sudden, with these developments due to Maxwell and Faraday, as you say, we suddenly knew what this thing was.
▶︎ 42:50 It was only recently that people had good measurements of the velocity of light. Light travels very fast. It had long been, people had long been interested in measuring its velocity. Galileo apparently made attempts to measure the velocity of light, which were adorably naive. He made some arrangement with somebody. "I'm gonna go on this mountain. You go on that mountain. We have our hourglasses or something like that. You open the lantern at exactly this time by your hourglass, and I'll see by my hourglass when I see it."
▶︎ 43:34 This is obviously laughable in terms of what we now know about the velocity of light. They weren't gonna get anywhere close to measuring the velocity of light. Galileo couldn't begin to tell whether the light arrived at him before it was released or not. So he had no clue. But in the late 19th century, people had much more sophisticated, much more clever ways of trying to measure the velocity of light. There were some measurements that were beginning to get accurate, and it was clear that the number that Maxwell calculated was exactly the number that, within experimental error, that these people were seeing.
▶︎ 44:23 So you've also got reason to believe that this is the second kind of reason for believing that these electromagnetic fields are not mere notational devices, but part of the concrete physical furniture, fundamental physical furniture of the universe. Why? Well, at least two reasons come out of this episode. These fields are not just things that we associate with the existence of charged particles, or we imagine charged particles producing or carrying along with them, or anything like that. They have a life of their own. They have a dynamical life of their own. They can be doing complicated things. They can be waving around in all kinds of interesting ways, even in hypothetical universes which include no charged particles at all, or no particles of any kind.
▶︎ 45:28 So these things have a dynamics of their own. Moreover, there is this phenomenon that everybody considered to be some part of the physical furniture of the universe, namely light, although they didn't know what it was. This obviously turns out to be just oscillating electric and magnetic fields. So this is a second category of reasons.
▶︎ 45:53 Finally, there's a third reason that also comes out of Maxwell's equations to take these fields ontologically seriously as parts of the furniture of the universe. It's this. In Newtonian mechanics, and this follows from the previous two considerations, in Newtonian mechanics, it's the case that if you're given the positions and the velocities of all the particles in the world at any one time, and given their masses and charges and so on and so forth, then you can predict, using the laws of Newtonian mechanics, their positions and velocities at any future time. In Maxwellian electrodynamics, that's not the case.
▶︎ 46:45 Suppose that you just want to take an interest in the particles. You don't care about the fields. It turns out that being given the initial positions and the velocities of the particles is not enough information to determine just the positions and the velocities of the particles at later times. It turns out, as we've been talking about, that what the fields are doing is not completely determined by what the particles are doing at any time, and moreover, what the fields are doing can influence what the particles are going to do later on. Light rays can run into the charged particles and start jiggling them around and so on and so forth. So particulate initial conditions are not sufficient initial conditions even to predict the future behaviors of the particles.
▶︎ 47:45 Suppose you're adamant that particles are the only things you take ontologically seriously. You're not going to be able to write down a good theory of them. In order to know just what the particles are going to be doing later on, you need initial conditions that refer not only to the particles, but to the electromagnetic fields as well. So this produces the strong impression that part of the description, the correct description of the situation that the world is in, initially, is the situation that the fields are in.
▶︎ 48:26 If you just give a complete description of the situation that the particles are initially in, that's not going to be enough to predict even the future motions of the particles. Whereas, if you include the fields in the description of the situation that the world is initially in, suddenly everything snaps into place. You have a completely deterministic theory, not only of the motions of the particles, but of the motions of the fields as well. So it looks like once you add the fields into this mix, you've got what you need. You've got what you need in order to have in front of you a complete description of what the world is doing at this initial time.
▶︎ 49:10 For all these reasons, and for others as well, which are more peripheral, there was this interesting evolution over the course of the 19th century from an attitude towards these fields as metaphysically uninteresting notational devices to a slow realization that there wasn't any very viable scientific alternative to acknowledging to oneself that these fields are really part of the fundamental furniture of the universe, completely on a metaphysical par with things like material particles.
▶︎ 49:56 Let's say how this impacts on the story of the question of locality that we've been following here. It turns out that if you look at Maxwell's equations, you have two charged particles, one here, one here. The fields are more or less quiet, except for the Coulomb fields of these charged particles initially. So this particle now experiences a force associated with the existence of this particle, which you can calculate from the Coulomb field associated with this particle.
▶︎ 50:49 But now we can ask a question in Maxwell's theory. What would happen if I were to suddenly move this particle here to another point? We know that eventually this particle would feel a different force. It would feel an attractive force pulling it in this direction rather than in that direction.
▶︎ 51:13 In Maxwell's equations, in Maxwell's theory, you can follow in detail how this happens. So you suddenly move the particle from here to here. Maxwell's equations tell you exactly what's gonna happen to the fields. Initially, the fields only change in the immediate vicinity of this particle, and outside of a certain radius from here, the field hasn't changed yet at all.
▶︎ 51:47 Those changes in the fields, we've seen how changes in electric and magnetic fields can themselves produce further changes in electric and magnetic fields. Those changes in the fields produce changes in the fields a little farther out. Those, in turn, produce changes in the fields a little farther out. You've got this outgoing wave of field changes. This wave is an electromagnetic wave similar to light. It's something whose presence you can detect.
▶︎ 52:24 It moves outward at a finite velocity, and the finite velocity with which it moves out turns out to be exactly the velocity of light once again, and it takes a finite time for this particle to feel a change in the electric force on it as a result of the motion of this one. And we now have a complete and thoroughly local story of how that change eventually propagates to this particle, how this particle eventually learns from the force on it of the fact that this particle has been moved.
▶︎ 53:07 So, at least in the electromagnetic case, we've got now what we wanted. Initially, the Coulomb force looked to be non-local in exactly the way Newton's gravitational force looked to be non-local. You sit on the problem, you work hard on the problem, you look into it in detail, it turns out that that's not what's going on. It turns out that there is a thoroughly local explanation of exactly the kind we were hoping for, that tells us what's going on there.
▶︎ 53:46 This satisfies all of the desiderata we want. The ability of the possibility of this happening depends on what the physical conditions are in the region between these two particles. It takes a finite amount of time. The process of propagation is itself a detectable physical process, which we can see unfolding, if we put measuring devices in the region between these two. We've got everything we want here. We've got a thoroughly local explanation of what's going on here. Einstein was very impressed
▶︎ 54:34 By these developments. This is what people were excited about when Einstein was in college and so on and so forth, he was a young man when or shortly after these developments had been going on. And this was one of his inspirations for the development of his theory of gravitation, the general theory of relativity. Now, the general theory of relativity is revolutionary in all sorts of ways, in a lot of ways which aren't directly relevant to our story here.
▶︎ 55:17 As people have probably heard, the general theory of relativity is a complete reinterpretation of the phenomenon of gravitation, thinking of it not as a force, but as a phenomenon in which the presence of material bodies distorts the laws of geometry, in their vicinities, distorts the structure of space and time in their vicinities in such a way as to make projectiles move around in the way they do. This is the really profound revolution of general relativity. That's not the aspect of it I want to focus on here. Another thing that general relativity does, it turns out, is do something very similar to what Maxwell does vis-à-vis the question of locality.
▶︎ 56:12 It turns out that if you move one material body, like this, the gravitational influence on nearby bodies doesn't change instantaneously according to Einstein's theory of gravitation in the way that Newton's theory demanded that it does. It changes by means of a continuous, you move one material body, it creates gravitational disturbances right near it. It creates variations in the geometry of space-time right near it. Those variations in the geometry of space-time then propagate, cause one another, to go further and further out. So you get exactly the same kind of structure.
▶︎ 57:06 This also, interestingly, propagates at the speed of light. This thing doesn't immediately feel a different gravitational force when this one gets moved. It takes a while for this to be propagated outward and it's a prediction of general relativity that if you look very, very carefully, and in the case of general relativity, you have to look very, very carefully, you'll be able to see, you'll be able to detect these disturbances. They're called gravitational waves, an analogy to electromagnetic waves. You'll be able to see these disturbances propagating outwards.
▶︎ 57:50 And, indeed, two or three years ago, a bunch of people won the Nobel Prize for a sort of spectacularly beautiful and sensitive experiment where, for the first time, they actually detected these gravitational waves that are predicted by general relativity. And with this, physics literally needed to hold its breath for 300 years, in order for this problem of non-locality in Newton's gravitational theory to be resolved along exactly the lines that Newton hoped it would be. It's replaced by a thoroughly local account, and this deep conviction that people had before the rise of modern science that dogs have, that slime has, is vindicated after 300 years by the development of theoretical physics. This is an amazing, amazing story.
▶︎ 59:07 So there's this feeling that since Newton's postulation of his universal law of gravitation, there's something terribly wrong in the heart of theoretical physics, and physics had to literally hold its breath for 300 years until, through the development of electromagnetism, through the development of a new theory of gravitation due to Einstein, inspired by these developments of electromagnetism, and finally, after going through all that, you wait 300 years and your confidence, your conviction that the world must ultimately be local is vindicated by these developments. What's interesting about this
▶︎ 1:00:01 The story, what's poignant about this story, is that the whole thing blows up 10 years later. Einstein proposes his theory of gravitation in more or less final form around 1915, 1918, something like that. A couple of years later, you see the beginning of the development of quantum mechanics. And it happens to be a feature of the quantum mechanical algorithm that we've been talking about here, that there are certain circumstances in which there are pairs of particles. When you carry out a certain kind of measurement of particle number one, you should immediately change your description of particle number two. And the algorithm gives you the instruction that you should change your description of particle number two upon measuring particle number one in a way that looks strikingly non-local.
▶︎ 1:01:14 The instruction is that you should change your description of particle number two instantaneously, no matter how far apart particle one and particle two may happen to be, no matter what conditions might prevail, what physical conditions might prevail in the region between the two particles. It doesn't matter if that entire region is filled with lead that's so dense that even Superman can't see through it, or something like that. It's completely irrelevant what's going on in the region between the two of them. It's completely irrelevant how far apart they are. The time at which you're supposed to change your description of particle number two in order to go on with your calculations is exactly the moment when you carry out this measurement of particle number one.
▶︎ 1:02:09 This is the postulate of collapse, von Neumann's rule number two. This looks strikingly non-local, and Einstein noticed this. I don't know the history so well, but I suspect that Einstein was the first person to draw attention to the fact that this particular feature of the quantum mechanical algorithm, the quantum mechanical instructions for doing these calculations in order to predict the outcomes of future experiments, I believe that Einstein was the first person to draw attention to the fact that this algorithm contained a glaringly non-local instruction.
▶︎ 1:02:59 And what this suggested to Einstein, which given everything that physics had been through over the past 300 years, and given in particular what Einstein had been through over the previous 20 years, this suggested to Einstein that obviously we're dealing with another incomplete theory. We're dealing with another bad theory. We've seen this before. We know how this story ends. Every now and then, something comes up in physics which is calculationally useful, and which is formally non-local.
▶︎ 1:03:41 This is what happened with Newton's universal theory of gravitation. This is what happened with Coulomb's law of electrostatic repulsion and attraction. When you first write them down, you're writing them down in a crude way. The fact of their non-locality is a sure sign that that's not the end of the story. The fact of their non-locality is a reliable sign that there's more to be discovered here.
▶︎ 1:04:12 And like I said, Einstein in particular was someone who seemed to be in a position to say, "There's no reason to take this seriously. We've seen this happen before. We know how this story comes out." You work at it a little bit, and you discover that this non-locality is an artifact of an imperfect mathematical formalism, of an incomplete mathematical formalism. And it's a sign that we're gonna discover a deeper theory. And it's a sign that the quantum mechanical algorithm, as it stands in 1930 or so when Einstein is confronting this, just isn't the final, isn't the final theory.
▶︎ 1:05:06 And indeed, he hopes that whatever the final theory is, is not only gonna restore the locality of the world, but it's gonna get rid of all this weird stuff that's going on in quantum mechanics about superposition and so on and so forth. The amazing thing is that it
▶︎ 1:05:28 emerges 30 years later in the work of John Bell, that this time the story doesn't come out that way. That this time we have an argument, which I'm going to try to present here. It's a quite simple argument, that this quantum mechanical non-locality can't be eliminated. That is, that you can give a straightforward mathematical proof, as Bell does, that there couldn't be any algorithm for predicting the outcomes of experiments correctly, that is, which matches the quantum mechanical predictions, which as far as people knew at the time were correct. There can't be any theory which reproduces those descriptions without including, at one point or another, a non-local instruction of exactly this kind.
▶︎ 1:06:36 So this is an almost unbearably poignant way for this story to come out. An astonishing way for this story to come out. So now, we're in a position if Bell is right, I don't want to anticipate this too much, I want to go through the argument. But just to have it clear what's at stake, if Bell is right here, after all of this drama, about losing non-locality and regaining it and so on and so forth, it turns out that this deep primordial conviction about how the world works is wrong. Is demonstrably wrong.
▶︎ 1:07:22 Notwithstanding that it died and then got revived, and then died again, and then out, and then got revived again, and so on and so forth. At the end of the day, you didn't quite make it. And it turns out to be false. It turns out to be demonstrably false, and a lot of people have said, and I don't think this is any kind of crazy exaggeration, I'm not sure what the other candidates would be, but many people have said this is probably the most single shocking result of natural science since the scientific revolution of the 17th century.
▶︎ 1:08:05 So let's talk about this result. The experiments that are actually done here are easier to do with photons than they are with electrons, but the logic is exactly the same in the case of electrons. I'm going to describe a version of this Bell reasoning that has to do with electrons. The experimental scenario that Bell considers involves three different measurable properties of electrons. Let's call one of those properties property A, one of them property B, and one of them property C.
▶︎ 1:08:48 These three properties, just like the hardness and color properties that we discussed earlier, are properties that always come in one of two possible values. The value of property A for every electron is either plus one or minus one. The same is true for property B. The same is true for property C.
▶︎ 1:09:10 Here's how the argument starts out. It turns out, this is also something that was first noticed by Einstein and two of his collaborators, Podolsky and Rosen, that if quantum mechanics is right, there's a way to prepare a pair of particles, a so-called EPR pair, such that if you follow these preparation instructions, let's call these preparation instructions P, if you follow these laboratory instructions, you're gonna get a pair of particles that has the following feature. If you measure A on particle one and A on particle two, the results will always be opposite. If particle one turns out to have A value plus one, particle two will have A value minus one. The same for property B and the same for property C.
▶︎ 1:10:13 There's a way of preparing a pair of particles such that if you follow those instructions, you will invariably get a pair of particles such that if you measure A on both, you'll get opposite results. If you measure B on both, you'll get opposite results 100% of the time. And if you measure C on both, you get opposite results.
▶︎ 1:10:37 Moreover, Einstein, Podolsky, and Rosen reasoned that no matter what quantum mechanics says, even if quantum mechanics says, "On measuring A, you should change your description. On measuring particle one, you should change your description of particle two," Einstein, Podolsky, Rosen reasoned if anything like a locality is true, and they're assuming that something like locality is true, if you get these two particles far enough apart from one another, measuring A on particle one can't affect anything about particle two. And measuring A on particle two can't affect anything about particle one.
▶︎ 1:11:20 So if it's a feature of this pair of particles that when you prepare them, according to these instructions, the value of A on particle one always turns out to be the opposite of the value of A on particle two, and similarly for B and C, that must already have been the case as soon as you prepared them. They must have had definite values of A, B, and C already. Because if you deny that, the only alternative is that you're measuring A on particle one somehow produced this opposite value in particle two, and that would be a violation of locality.
▶︎ 1:12:02 So if we're assuming that locality is true, whenever I prepare a pair of particles like this, I'm preparing a pair of particles, for each of which there is already, as soon as the preparation is done, a fact of the matter, a perfectly determinate fact of the matter about what the value of their A property is and what the value of their B property is, and what the value of their C property is. In fact, let's make that, it'll be useful to write down the possible values of these properties. Let's make a list of these possible values. This is particle number one. This is particle number two.
▶︎ 1:12:58 Here's A value. Excuse, yeah, A value, B value, C value for particle number one. Here's A value, B value, C value for particle number two. What EPR have argued is that once we follow these preparation instructions, never mind exactly what those instructions are, but we have a definite set of instructions, there are eight possibilities about what the values of A, B, and C for particles one and two might be. We know that if particle one has a value one for A, then particle two must have a value minus one for A. And we know that if particle one has a value one for B, particle two must have a value minus one for B, and similarly for C.
▶︎ 1:14:03 Whoops. Another way this could happen is if particle one has these values, say, and particle two has these values. I hope I'm gonna have room here. There are eight possibilities altogether, and I'm probably gonna forget some, so you have to tell me. Here's a third one, one, minus one, minus one, minus one, one, one, one, minus one, one, minus one, one, minus one. Two, three, four, we need four more. Minus one, minus one, minus one, one, one, one. Wow, we're not gonna have room. I'll write them smaller. Which ones am I forgetting? Minus one, minus one, one. Minus one, minus one, one, so that's gonna be one, one, minus one, and then we need two more over here.
▶︎ 1:15:20 Yeah? Minus one, one, one. Minus one, one, one. I think you're right. Minus one, one, one, and then for particle two, it's one, minus one, minus one. One, two, three, four, five, six. We need one more. Minus one, one, minus one? Minus one, I think you're right. Minus one, one, minus one, and one, minus one, one.
▶︎ 1:15:57 We have an argument from EPR that whenever I prepare, whenever I follow these preparation instructions, what I'm left with is one of these conditions. How do I know? Because I know that the A, if I measure A on both sides, I get opposite results. If I measure B on both sides, I get opposite results. If I measure C on both sides, I get opposite results. So, whenever I follow these preparation instructions, I get one of these eight situations.
▶︎ 1:16:35 Which one do I get? Well, who knows how that works? Maybe it depends on the fine details of how I prepared it, or maybe there's some probabilistic situation where I get, if I prepare a large number of these in the same way, I get some statistical mixture, a certain percentage this, a certain percentage that, so on and so forth. Something like that must be going on. Bell takes up this argument of EPR, says they're right.
▶︎ 1:17:14 But Bell, unlike EPR, focuses on cases where we measure one variable for particle one and a different variable for particle two. What happens if we measure A for particle one and B for particle two, or A for particle one and C for particle two, or B for particle one and C for particle two? Good. Turns out the quantum mechanical algorithm will give you answers to those questions as well. The calculation is very straightforward.
▶︎ 1:17:50 It turns out that if you measure A for particle one and B for particle two, the probability of the... Remember, if you measure A for particle one and A for particle two, the probability that the results will be opposite is 100%. You can ask a similar question. Suppose I measure A for particle one and B for particle two, what's the probability that the results I get will be opposite? You ask quantum mechanics this question. Quantum mechanics makes a definite prediction. It turns out that the probability is a quarter that they'll be opposite, if you measure A for particle one and B for particle two.
▶︎ 1:18:32 And as a matter of fact, A and B and C are chosen in a sufficiently symmetrical way so that the predictions of quantum mechanics are that if you measure any variable on particle one and any other of these variables on particle two, the probability that the results will be opposite are exactly a quarter. So if you measure A on particle one and B on particle two, the probability that the results will be opposite is a quarter. If you measure A on particle one and C on particle two, the probability that the results will be opposite is a quarter, and if you measure B on particle one and C on particle two, the probability that the results will be opposite will be a quarter.
▶︎ 1:19:19 And now Bell says to himself, "But look, something's funny here. I'm gonna go down this list and I'm gonna put a check mark next to every situation where one of the following three things is true, either this is the opposite of this, or this is the opposite of this, or this is the opposite of this." Everybody with me? Good. Each of those is supposed to have probability a quarter, according to quantum mechanics.
▶︎ 1:19:50 So, let's see. In the first one, is this the opposite of this? Yes. Already gets a check mark. Second case. Is this the opposite of this? Yes. Already gets a check mark because just one of those has to be true in order to get a check. Third. Is this the opposite of this? No. Is this the opposite of this? No. Is this the opposite of this? Yes. Gets a check mark.
▶︎ 1:20:18 Fourth. Is this the opposite of this? Yes. Gets a check mark. Fifth. Or I don't know which this is. Is this the opposite of this? Yes. Gets a check mark. This one. Is this the opposite of this? Yes. Gets a check mark. Let's do the last two. Is this the opposite of this? No. Is this the opposite of this? No. Is this the opposite of this? Yes. Gets a check mark. Last one. Is this the opposite of this? Yes. Gets a check mark.
▶︎ 1:20:55 So, if the quantum mechanical predictions are that the probability that this is the opposite of this is a quarter, and the probability that this is the opposite of this is a quarter, and the probability that this is the opposite of this is a quarter, then the probability that any one of those is true can't exceed three quarters. But we've just gone down this list of possible states and every single one of them has at least one of those properties.
▶︎ 1:21:41 So, any statistical mixture of these that you might get by following the preparation instructions is gonna have the feature that no matter which of these states you end up with, or no matter what statistical mixture of these states you end up with, the percentage of times at which at least one of these is gonna be true is gonna be 100%, because every one of these possibilities has at least one of those features.
▶︎ 1:22:12 But if these values, if they're supposed to be facts of the matter about these values as soon as the preparation is done, and if the quantum mechanical predictions are right, that the measurement of this turns out to be the opposite of this a quarter of the time, and this turns out to be the opposite of this a quarter of the time, and this turns out to be the opposite of this a quarter of the time, then the percentage of times that one of those is true couldn't exceed three quarters. We have a contradiction. Everybody with me?
▶︎ 1:22:49 We have a straightforward contradiction here. Only one assumption, well, two assumptions went into this. One, that the quantum mechanical predictions, these one-quarter predictions are correct. It was already known experimentally that the quantum mechanical predictions about what happens if you measure the same thing on both sides are correct. You get opposites 100% of the time. The question is, are these two conditions, that these are always opposite and that these are opposite a quarter of the time? The question is whether those two are mathematically compatible with one another, whether there's any arrangement of these properties that satisfies both of those statistical conditions. This argument shows that the answer to that question is no, is definitively no.
▶︎ 1:23:56 There are two assumptions that go into this argument. One is that the quantum mechanical probabilistic predictions are correct, especially these one-quarter predictions. The second assumption is locality. Because it's only if you assume locality that you can show that once the preparation is done, all these variables already have definite values. It's locality that's ruling out that by measuring A on particle one, I alter what's going on with particle two in such a way as to be able to explain this. So there are only two, we've got two assumptions here which jointly lead to a contradiction. Assumption number one is locality. Assumption number two is the correctness of the quantum mechanical predictions.
▶︎ 1:24:52 At this point, it becomes extremely urgent to run out and experimentally check these quantum mechanical predictions. And that's what people did. And oddly enough, we have a lot of Nobel Prizes coming up in this story. Oddly enough, it was these experiments that were awarded the Nobel Prize around two or three years ago. I forget exactly when. People ran out, did these experiments to confirm the quantum mechanical prediction that the percentage of time that the measurements would come out opposite if you measured different things on both sides would be a quarter. The quantum mechanical predictions turn out to be correct. So, locality must be false. Must be false.
▶︎ 1:25:50 There's no theory that's going to account for this, which is local. And we're done. And the story, this millennial, millennium old story, which got particularly intense over the last 300 years, ends this way. Locality turns out to be false. One has to, of course, tell a story, lots of stories about why we haven't noticed this before, why these circumstances are fairly exotic, physically, so on and so forth. One can tell all those stories very easily.
▶︎ 1:26:36 But once again, the situation here is very stark. And the situation makes it clear that no amount of inventiveness in concocting new theories of the kind that saved locality for gravitation and for electromagnetism is to be hoped for, in this case. If we assume locality, and if these quantum mechanical experimental predictions... So mind you, quantum mechanics doesn't have to be right in order to make this argument. It just has to be right about these specific predictions. Those are easy to test. You can go test them. You test them, it turns out that quantum mechanics is right about these, and then you win a Nobel Prize. As well you should.
▶︎ 1:27:34 It's now clear that we have these two claims that we've discovered contradict one another. One is locality. The second is this one fourth prediction of quantum mechanics. The one fourth prediction turns out to be true. There is no logical alternative anymore to locality being false. It turns out that this piece of the quantum mechanical algorithm, which tells you that the minute you measure particle number one, you have to alter your description of particle number two, this was not a disposable mathematical artifact of the formalism. There is no formalism that is not going to include a non-local instruction like that at one point or another that is going to make the empirically correct predictions. That's the end of this story. You've got a real non-locality here.
▶︎ 1:28:43 And this is something that a number of smart people have said is the single most shocking result of natural science since the 17th century. This is a very deep intuition that we have about how the world works. This is an intuition which is more or less the intuition that the world isn't magic. That the world isn't like voodoo. That there's got to be a story about how the effect gets from here to there. There's no story here. It's a prediction of quantum mechanics, and it's confirmed as well as we know that if you look in between these two and you look for any process of propagation, you're not going to find one. And that it doesn't depend on what's going on in the region between the two of them.
▶︎ 1:29:33 It's not a story about the effect of doing this getting over there. It's just a wrong way of thinking about it. It's somehow that doing this to particle one is doing something to particle two. Or that the effect doesn't get there by traveling across. The effect jumps. It has nothing to do with what's going on in between.