00:00:07
Speaker 1: It sure feels like a classical universe out there. Things move in paths, they don't seem to be uncertain. Everything I know about has a location and a velocity, and there doesn't seem to be any weird quantum mechanical effects going on. And yet we're told that's wrong. We're told that the deeper substrate of reality operates according to different rules, that things are not determined until you measure them, that they can be in a superposition, and that there's a true randomness to the universe. That feels weird, that feels alien, that feels counterintuitive. And so, as curious people, we want to know, how do you know? How could you tell? Often these things are hidden behind weird obstacles. Like, you can't see things when they're superpositioned. You could just measure them and get an outcome. That's unsatisfying. And the usual story is a series of experiments thought up by John Bell to prove that particles actually are determined randomly. that there's no local hidden information carried along with the particles that quietly determines what happens. But even these are still quite unsatisfying, because the answer to those experiments is in the patterns and the correlations. There's no smoking gun that says, here, this one experiment proves that quantum mechanics is a description of reality. And today on the pod, we're going to talk about an even more subtle, more complicated experiment that requires entangling three particles simultaneously and trying to get them to flash a series of lights in a certain pattern, which actually does definitively prove that quantum mechanics is the way our universe works. It provides the smoking gun you've always wanted. Welcome to Daniel and Kelly's Extraordinarily Quantum Universe.
00:02:13
Speaker 2: Hello, I'm Kelly Wiener-Smith. I study parasites and space and topics like entanglement make me wonder if physicists have the best slash worst pickup lines.
00:02:25
Speaker 1: Hi, I'm Daniel. I'm a particle physicist who likes to think about alien minds. And I also like to get tangled up in quantum mechanics, though I don't think that's a good pickup line.
00:02:35
Speaker 2: Okay, so here is, I was going to ask you about the worst physicist pickup lines, but I'm actually not sure that our audience wants to hear that. So when physicists have a party, what are physicist parties like?
00:02:47
Speaker 1: What are physicist parties like? Well, I can't generalize, but I can tell you my experience. Katrina and I were in grad school at the same time, and I went to a poor public school, Berkeley, and she went to a fancy private school, University of Chicago, and her department was flush with cash, which meant that if you threw a party at your house and invited the whole department of grad students, they would pay for the alcohol. What? So several times they gave us like $ 500 to throw a party, and of course we invited all the biologists, and then I invited all the physicists. So the physicists crashed all those biology parties. And it was fascinating to see the sort of cultural clash between the physics crew and the bio crew. Yeah, it was interesting. You know, we got some physics bio connections happening. You know, Katrina and I are one example. So, yeah, it was interesting to see how those folks approach a party differently. Right.
00:03:40
Speaker 2: So physicist parties are only good if they're organized by biologists is what I'm hearing.
00:03:43
Speaker 1: That's the story. Yes, exactly. And funded by the biologists. Right. Thank you, University of Chicago. We had some good times.
00:03:53
Speaker 2: Amazing. All right. Well, today we're not talking about entangling graduate students. We're talking about entangling particles.
00:03:59
Speaker 1: Yes, we are. And I got a question from Roger in Boston who heard about a fascinating set of experiments and wanted them explained. Here's his question. Hello, Daniel and Kelly.
00:04:12
Speaker 3: My name is Roger and I am reaching out from Boston, Massachusetts. I discovered your podcast a little while ago and I cannot get enough. Even though there's tons of stuff in there, I just don't seem to be able to wrap my head around. Fascinating stuff nonetheless. With a touch of makes my skin crawl. Down to my question now. Would you please explain how the Green Burger Horn Salinger Multi-particle entanglement experiment proves quantum entanglement. Please explain the hows and the whys of the experiment. I look forward to be blown away by your explanation. Thank you kindly and keep up the good work, guys.
00:05:02
Speaker 2: Greenberger, Horn, Zillinger. That's a mouthful.
00:05:05
Speaker 1: It's a mouthful. There's three smart guys who tangle themselves up thinking about triples of particles. And I started digging into this to answer Roger's question over email. And I was like, this is way too much for an email. Let's do a whole episode. Amazing. Yes, exactly. Because it also gives me an opportunity to talk again about some of my favorite experiments and then to talk about a super version of those experiments that's much cleaner, much crisper, sort of confusing in a different way about quantum mechanics. Oh, good.
00:05:34
Speaker 2: Layers of confusion.
00:05:36
Speaker 1: Yes.
00:05:36
Speaker 2: Fantastic. Entanglement is definitely one of those topics where every time I hear it, I'm still like, I think you guys are getting something wrong. But then you'd always tell me, no, we use this to predict other things and those predictions come true. This is useful information. And anyway, but it breaks my brain every time.
00:05:54
Speaker 1: But that's the point of experiment, right? Is that you go out and explore the universe so that it can change your intuition. So it can teach you how the universe actually works instead of how we think it might or the way we hope it should work. The universe follows its rules and the only way to learn it is to follow the data. And so today we're going to talk about that and we're going to talk about some fascinating entanglement experiments that rely on entangling three particles at the same time. Because entangling two is not complicated enough. No, no. We are going to three particles.
00:06:25
Speaker 2: Okay, but we're starting at two. But all right, keep going.
00:06:26
Speaker 1: We're starting at two. We're going to work up to it, yeah. But before we get there, I wanted to know what people thought about entangling three particles and where their sort of mental potholes were. So I went out and I asked our group of extraordinaries, can you entangle three particles? What is involved? Here's what folks had to say. But I'm suspecting it's a trick question and three can actually be entangled. Yes, you can, in fact, entangle multiple particles. That's what they're trying to do in quantum computing. I think we can somehow.
00:07:01
Speaker 3: Actually, I have no idea at all, but I also don't fully understand what quantum entanglement is.
00:07:09
Speaker 1: So I'll let Daniel take this one. I would think that you would need a particle with three different states, like spin.
00:07:17
Speaker 2: The idea of quantum entanglement always seemed to me to be binary.
00:07:21
Speaker 1: A left spin and a right spin, up or down, whatever. So having a threesome would be very odd. This almost broke my brain, but I guess.
00:07:30
Speaker 2: If there's a particle with a superposition that has three possible outcomes, then theoretically, yes, is how my logic would work.
00:07:38
Speaker 1: But quantum physics is not logic.
00:07:40
Speaker 2: There might be some super clever way you can entangle three together all at once, where some of them has to equal something, but you're not sure how it's distributed. Hmm. I've only heard of entanglement of a pair of particles. So I would say that doing it with three particles is not possible. Nice mix of answers here.
00:08:04
Speaker 1: Yeah. So there are definitely some misunderstandings here about entanglement and how it works and the limitations. And we're going to dig into all of that today. So thanks very much to The Extraordinaries for giving me clues as to where we need to go in this episode if you would like to participate for future episodes we would love to hear from you Please don't be shy. Write to us to questions at danielandkelly.org. And you too can get tough physics questions in your inbox. Didn't you always dream of that?
00:08:30
Speaker 2: The list is going to be a million people long, Daniel. What are we going to do?
00:08:36
Speaker 1: Email all at earth.
00:08:38
Speaker 2: That's right.
00:08:38
Speaker 1: That's right. All right.
00:08:41
Speaker 2: Well, let's start at the very beginning. Forget entangling three particles. Let's just entangle two. What is going on when two particles are entangled?
00:08:50
Speaker 1: Yeah. So first, what is entanglement anyway, right? Let's focus with two particles and understand what it is we're talking about. What entanglement is not is some magical connection between distant particles that binds their fate together. I think some people imagine entanglement the way it's often seen in science fiction. It's like you have a particle here and a particle there, and they have some connection. And anything you do to one particle affects the other one. And that sounds awesome, but that's not what entanglement is at all. That's like Bad pop-sci version, that's the science fiction version that allows you to communicate information across space and time instantly. If you had such a particle, like if I had one and Kelly had one and I could poke it and then Kelly's particle got poked, then yeah, I could send information along that wire, right? Because I could do stuff to my particle that would happen to her particle and she could read it out. That would be incredible. That is not what entanglement is at all, unfortunately, right? Physics as the wet blanket.
00:09:48
Speaker 2: Well, longtime DKEU listeners will not be laboring under that misconception because we have talked about this a few times. but let's definitely do it again to make sure it's fresh.
00:09:57
Speaker 1: The way you should think about entanglement is that you have to think about the two particles together. It's a correlation in the outcomes because it's really a single state. It's always created locally. Two particles are entangled when they interact, and then they maintain that correlation even if you separate them. And that's not too hard to understand. You know, Let's say you have two particles, and there's one property you want to measure about them, their spin. It's either up or it's down. So particle one can be up or down. Particle two can be up or down, right? So then how many possible outcomes are there for your measurement, Kelly?
00:10:34
Speaker 3: Four.
00:10:34
Speaker 1: Four, exactly.
00:10:35
Speaker 2: Thanks for making an outline ahead of time.
00:10:38
Speaker 1: Don't tip them off that you cheated. I wanted to give you some points there.
00:10:42
Speaker 2: I think I could have figured that one out. It's a small number of options, but thanks.
00:10:45
Speaker 1: So two for particle one, two for particle two. And you can enumerate them. It's up, up, down, down, up, down, or down, up. Those are the possible outcomes, right? If the particles are totally free to do whatever they like. Entanglement says, let's only allow some of those outcomes. We have some physics process that has created these particles in such a way that only some outcomes are allowed. For example, maybe there's a conservation of spin. And so we need zero spin for the whole state because it was made from a zero spin state and spin is conserved. And so the spin has to be zero afterwards, which means you either need up-down or down-up. The up-up would have too much spin and the down-down would have too much negative spin. So they're not allowed. So if instead of just having two particles free and willy-nilly to have any spin, if instead you create them together in a correlated way, right, from some interaction, and then separate them, then you know that they're either in up-down or in down-up. So entanglement is just those correlations. It just says, of the matrix of possibilities, you're going to cross some out. And you're imposing a condition that say only some of them are allowed, right? Mm-hmm. Now, that seems very obvious. You're like, hold on a second. Where's all the quantum weirdness, right? And the quantum weirdness comes in when you add superposition. When you say, well, which of those states are we in? In a classical version of this problem, say you have like a bag with two balls in it and one is labeled up and one is labeled down. And I take a ball and Kelly takes a ball and we go 10 miles apart and we haven't looked at our balls, right? Then if you look at your ball, you could say, oh, I have the up ball. Cool. That means I know instantly already that Daniel has the down ball because there was one up and there was one down. There's a correlation. So I know mine, therefore I know yours.
00:12:27
Speaker 3: Okay.
00:12:28
Speaker 1: And in that classical version, it's still not mysterious because you know how it happened. You know that the fact that you have up and I had down was determined when we pulled the balls out of the bag, right? So the fact that we walked 10 miles away, nothing interesting happens there, nothing special. This is predetermined by some properties on the ball. We call that hidden local variables. There's some feature of the ball that is literally the U on it or the D on it It tells you which one it's going to be, right? It's determined in advance. So that's the classical version of entanglement. Still with me?
00:13:01
Speaker 2: Yeah, I'm still with you. The whole time, the ball was either up or down.
00:13:04
Speaker 1: Exactly. Yes. And all that makes sense, right? So now let's get to the quantum version. We have the whole setup ready. So in the quantum version, there is no local hidden information that determines whether the ball is up or down. It's in a superposition, which is a fancy quantum word for saying there's two possibilities in and neither are determined yet. So both possibilities are live. The up and the down are live on my ball until I look. So I pick out the ball from the bag. It can be up or down. I haven't looked yet. I walk 10 miles. It can still be up or down. I haven't looked yet. Kelly's ball can still be up or down. She hasn't looked yet, right? So that's the difference between the quantum version and the classical version. The classical version is local information that's encoded in the ball. It's predetermined. You learn about the other person's ball, but it was determined in advance. And the quantum version, it's uncertain. So what happens when I look is my ball goes from either up or down, from being in an uncertain state of those two, to being specifically up or specifically down, right? Whatever the universe chooses. And then the weird quantum part is the same thing has to happen to your ball, right? Now, we had two possibilities. Either I have up and you have down, or I have down and you have up. One of those has gotten crossed off the list, right? So now we only have one possibility. So just like in the classical version, seeing mine means I know yours, right? The fascinating thing is that when I measure mine, it's the same quantum state as yours. It's just non-local, it's extended. So the whole quantum state collapses from being in both options to being one specific option where I have up and you have down. So you haven't looked at your ball yet, but me looking at mine collapses your state also. That's the weird quantum thing, that over space and time, your state also collapses when I look at mine. Does that make sense?
00:14:53
Speaker 2: Yeah, I think so. I'm going to hopefully not get us too far off track with this question, okay? So when you said it's a superposition of up and down, that made me think about Schrodinger's cat, which is a superposition of alive and dead. Whereas I think in PopSci, they're usually like, it's dead until you take it out of the box and then maybe it's alive or something like that.
00:15:10
Speaker 1: No, they say it's both alive and dead. Right.
00:15:13
Speaker 2: It's a superposition.
00:15:14
Speaker 1: Okay.
00:15:14
Speaker 2: But so the difference is there, you're talking about one cat that's in a box, but that's what superposition is. And entanglement is when you have two things in superposition, but what happens to them is correlated.
00:15:24
Speaker 1: Yes, that's exactly right. Ding, ding, ding. You're a quantum mechanic. Yeah, exactly. Exactly. And the thing that often trips people up is this feeling like I've done something to my ball. I've measured my ball. I've seen that it's up. And that does something to your ball over there. And that's true. Your ball goes from in a superposition to only in one state, right? And so that feels like you should be able to use that somehow to send information. I am affecting your ball. I measure my ball. It affects your ball. Can I use that to do something? Answer, no. Because you can't tell that I've done that. You have your ball. You haven't looked at it. All you can do is look at it and measure up or down. When you look at it and measure down, you don't know if I've already collapsed it into down by looking at mine or if by measuring it, you collapsed it. There's no test you can do to say like, hey, are you collapsed or not? Did Daniel collapse it? And that's the loophole people usually try to use to build some device that can send information across space and time. But you can't, unfortunately.
00:16:25
Speaker 2: Boo.
00:16:25
Speaker 1: It's also unsatisfying because you don't sort of see the magic happening. Like, all you do is you look at your ball and you see up or you see down. Okay, but how do you know that it wasn't determined, right? How do you know that it wasn't? How do you know that there isn't some piece of information that's hidden from you you just didn't know about, some feature of this electron and that electron that really did determine it? Like you can't tell that it was in superposition, can you? That's the big puzzle, right? How do you know that this story we're telling about how the universe keeps both options live until you look, how do we know? And that's Bell's experiment, which we've talked about before. I'm going to get into again today. But Bell's experiment is unsatisfying, right? It's a statistical pattern. You measure these things, you count the numbers. There's no smoking gun.
00:17:08
Speaker 2: But it's clever.
00:17:09
Speaker 1: Oh yeah. Oh, it's genius. Absolutely.
00:17:11
Speaker 3: No, no.
00:17:12
Speaker 1: I don't mean to say, you know, the guy's not a smart person. It's just like, As somebody who's learning physics and wanting to see a clear and crisp smoking gun example of how there can't be local hidden information, how things really are random, it's a little unsatisfying. And that's where three-particle entanglement comes in. So these guys, Greenberger, Horn, Zellinger... came up with a way by entangling three particles together to make a smoking gun experiment showing that no set of pre-written local answers can reproduce the results. It just absolutely cannot be in a single result from the experiment. So that's exciting.
00:17:51
Speaker 2: Hold on, hold on. So how can you entangle three particles? I can imagine how like you can have an up and a down and the other.
00:17:57
Speaker 1: Yeah.
00:17:58
Speaker 2: Do you have to have three options for their states in order for this to work?
00:18:01
Speaker 3: Right.
00:18:01
Speaker 1: And this was the kind of thing that the listeners were confused about. So I want to explain it briefly before we get into the experiments. You know, there's the number two in this example. You have two states and you have two particles. But that's a coincidence. The fact that there are two states doesn't limit you to having two particles. You know, in that example, you had the initial state with spin zero and it turned into two particles with spin up and down and up plus down equals zero. So it all worked out. But you could very easily extend that to three particles. you could start with an initial state that was up instead of zero, and then turn that into three particles, and then you'd have to require that the three particles were up, down, up, so they all added up to the initial state. So there's no limit to the number of particles you can entangle, and you can just keep interacting. Entanglement comes from interactions. So you have a two-particle system, you interact it with another particle, now you have three particles entangled. Or you can create the entanglement from a single interaction from the beginning. And you can also... have particles with multiple spin states. There are particles with three spin states, like the W boson can be up, down, or zero, right? So you have all that freedom.
00:19:10
Speaker 2: Are you limited by features of the things that you're working with? Like, do they have to have three spin states? Or how the heck do you tell particles that we're starting with up and you have to equal zero at the end? And like, how do you convey that information to particles?
00:19:29
Speaker 1: You don't convey to the particles the rules of physics limit you to certain outcomes. You know, like when a photon decays to an electron and positron, the rules of angular momentum say that some of those spin states are allowed and some of them are not. And so some of them just never appear because they would violate a law of physics. And so if you create... three particles at once from a single state, then some of the spin outcomes just are not allowed. They will never happen because they violate some law of physics. And that's something we've reverse engineered. We've like watched this happen and we'd notice, huh, this never happens. That never happens. There must be some rule that prevents it. And we've reverse engineered that and now we call that a law of physics. But the reality is you just don't see that in the universe. And we describe that with our laws.
00:20:15
Speaker 2: So then it sounds like features of the particles determine how many combinations of particles you could have.
00:20:22
Speaker 1: Yeah, but particles have lots of features. You know, we're talking about spins, but also they can be entangled in their like linear momentum. You know, for example, if you have a Higgs boson at rest and then it turns into two particles flying off in either direction... then their linear momentum has to sum to the original Higgs boson momentum. So, you know, they have to be like going in opposite directions, which makes sense intuitively. Like if a particle explodes into two, they're back to back, which means you measure the direction of one, you automatically know the direction of the other, even if the direction of one has some randomness to it, right? And so that's another example of a correlation between the outcomes that really is a quantum superposition. It's because those two particles are entangled. And so they're entangled in many ways, not just their spin, also their momentum and all sorts of stuff. Yeah. So entanglement is no limitations, basically. Wow.
00:21:12
Speaker 2: Awesome. I have absorbed that, but I would still like to hear more about Bell's experiment to make sure I'm really following everything. So let's take a break. And when we get back, we're going to dig into Bell's experiment with two particles and then expand your mind out to three particles. Okay, we're back. We are talking about entanglement today. We have managed to mostly keep away from physicist pickup lines. I'm very proud of us. Let's go ahead and jump into Bell's experiments.
00:21:56
Speaker 1: Yeah, but I consider today's episode basically a party between physics and biology because here we are, right?
00:22:01
Speaker 2: That's right. That's right.
00:22:02
Speaker 1: It's a Friday morning coffee party.
00:22:05
Speaker 2: That's right. Parties don't have to have pickup lines. In fact, they're much better when they don't have pickup lines. So let's party the particle way.
00:22:13
Speaker 1: That's right. Let's pick up Bell's experiment. So the idea here is to figure out how do we know that the universe really is random, that it's not predetermined in some way we couldn't tell in advance. And that sounds like a tall order because you're trying to rule out basically not just a specific theory for like how the particles could be predetermined, what could be fixing their outcome, but any theory, any theory which ever could have the local information that would determine the outcome of your experiment, right? And so that seems like a tall order, like how do you tell if the universe was random and how do you rule out every possible theory? And so Bell's experiment is really genius. This guy invented this way of distinguishing between these two outcomes. And it's very clever, but it's also complicated and a little hard to follow. And the outcome is not really a smoking gun. But as a way to contrast it with a three-particle experiment, I think it's a useful warm-up.
00:23:15
Speaker 2: After that intro, I can't wait. Let's dig in.
00:23:19
Speaker 1: It's really worth understanding. And all the nuances are really fun. So the idea is, just like the example we started with before... you have two entangled electrons, right? That means if one is spin up in one direction, the other one has to be spin down in that same direction. Okay, but now we're gonna complicate things a little bit because before we were talking about the electrons having spin up and spin down as if there's only one kind of spin they can have, right? Just like spin up or spin down. But the truth is electrons are three-dimensional objects. And so when you measure their spin, you have to ask in which direction, right? Like think about the earth. The Earth is spinning around its axis, right? But it could have been spinning around a different axis. In fact, because there are three dimensions of space, you can imagine three different ways the Earth could be spinning, right? It could be spinning around the axis that goes between the North and the South Pole, like it does. Or you could stick an axis through the equator, right? And it could spin that way. Or another axis through the equator at 90 degrees to that, and it could spin that way. It's not, right? There are three different ways that the Earth could spin. Or in reality, it could be any mixture of those three, right? So the Earth is spinning around one axis, but there are more complicated ways to spin. And the same is true also for quantum particles. When you measure their spin, you have to say, I'm measuring your spin along this axis or along that axis or along the other axis. And the weird thing about quantum spin is that no matter what you ask, you either get up or down. There's no intermediate values. Like if you try to measure the Earth's spin using an axis that was not aligned with the North and South Pole axis, you would get some intermediate value. Say, oh yeah, it's spinning along that axis a little bit. It's also spinning along another axis a little bit. But that's not true for quantum particles. You either just get up or down. The answers are related, but they're always either up or down.
00:25:05
Speaker 2: Can I back you up real quick?
00:25:06
Speaker 1: Yeah, please.
00:25:06
Speaker 2: I'm not sure the Earth thing was helping. I think it might've confused me. So you've said there's three ways that it could spin. So say you've got an axis. Earth can spin the way it's spinning now. It could go exactly backwards from the way that it's going, like spin in the opposite direction. And then what is the third way that it could spin?
00:25:21
Speaker 1: Oh, I see. Spinning the opposite direction is still spinning around the same axis.
00:25:25
Speaker 2: Oh, but you said direction matters, but that doesn't count as changing direction?
00:25:31
Speaker 1: Right. So, you know, imagine spinning the way that we're spinning around the north-south pole. Call that, you know, positive.
00:25:38
Speaker 2: Yeah, okay.
00:25:38
Speaker 1: Yeah. And spinning the other direction around that same pole, that would be negative. But it's around the same axis. I'm talking about measuring its spin along a different line. Like, is it spinning around a line that goes through the equator? So, like, take your Earth and stick a bar through it horizontally. And imagine the Earth spinning around that line instead of spinning around a vertical line. That would be a different axis.
00:26:00
Speaker 2: But then couldn't you have infinite kinds of spin then? Because that axis could be anywhere?
00:26:05
Speaker 1: Yes, absolutely. There's infinite number of axes you could choose. And if you have a 3D physical classical object, then as you change the axis, you get more or less of that spin captured by that axis, right?
00:26:16
Speaker 2: Okay, I'm with you now.
00:26:17
Speaker 3: Mm-hmm.
00:26:18
Speaker 1: Okay. All right. Thanks. And so you can also do that for an electron. So for example, if you have two electrons and I measure mine to be up and you measure yours to be down and we could say, well, let's flip the axis we're measuring, right? Let's just turn it 180 degrees. Then we're going to get the opposite results. If I got up and you got down, then I'll now get down and you'll get up, right? Okay. That's easy. Now, if we flip the axis a little bit, like by some angle, instead of all the way, 180 degrees, then we get some different results up and down, but it depends on the angle. And so Bell's axis does this. It says, let's pick three spin directions in advance at random. We'll call them A, B, and C, okay? And then I'm gonna choose randomly which axis to measure my electron, and you're gonna choose randomly which axis to measure your electron. And then we're gonna ask, how often do we get the opposite spin? Now, if we choose the same axis, We get the opposite spin because one has to be up, the other one has to be down. If we choose axes that are upside down, then we'll always get the same spin, right? I'll measure up and you're measuring down along my axis. But if your axis is reversed, you're going to get an up also. And if you choose an axis that's like at some weird crazy angle, you're sometimes going to get up, sometimes going to get down. So you do this a bunch of times and you measure how often do we get opposite spins, right? A third of the time, you use the same axis, so you're going to get opposite spins. And this is where the two ideas separate. Remember, we're trying to distinguish between quantum mechanics that says, look, everything is random and it's determined only when you measure it, and the hidden variable theory that says, no, it's predetermined. There's some information on the particles that tells you all along which one was up and which one was down. And so the hidden variable theory says, well, We know the answer is all in advance. We can just make a table of the outcomes. And if you do that calculation, you can see that you can't get the same spin more than two thirds of the time. Like one third, you're going to get the same spin because we flip axes. And then sometimes you get the same axis because the angles. But if you do the math, you get the same spin less than two thirds of the time. But quantum mechanics disagrees. Quantum mechanics says, no, you can get the same spin up to 75% of the time. because of the correlations between these two particles. And so this feels a little fuzzy. I just sort of like said that and it is a little bit fuzzy. It comes out of the math and I've never found a great like intuitive way to explain like why the quantum mechanics predicts something different from the hidden variables. It just sort of comes out of the math and you do the experiment and you get an answer that's like 75% and that tells you, okay, it's quantum mechanics. And you can't point to any individual experiment and say, like, look, this one was up and that one was down, and that's impossible by hidden variables. It's just the pattern of the measurements that you've made that tells you you've seen them get opposite spin more often than you would expect from hidden variables. And it's just the rate you would expect from quantum mechanics. Okay.
00:29:22
Speaker 2: And so just to confirm, so you're measuring, for example, are the particles up or down? And the only thing that's changing is the axis along which you make that measurement.
00:29:31
Speaker 3: Yes.
00:29:32
Speaker 2: So you're not measuring multiple things about these particles. You're just looking at it from a different like angle.
00:29:37
Speaker 1: That's right. Yeah. Okay. And in the case of. quantum mechanics like if you adjust the angles correctly so the angles are like all 120 degrees apart then you get this weird behavior and you know i can give a little bit more intuition the reason that quantum mechanics gives a different prediction from hidden variables is comes from the interference of the possibilities, right? Which is something that quantum mechanics has and the hidden variables theory doesn't. Hidden variables is just like, look, everything's determined in advance. You can write down before you look at the particles, the possible outcomes and know which ones are going to happen. Quantum mechanics says you can't, there are these various possibilities and they interfere with each other. The way you see like interference in the double slit experiment, right? If you do not collapse the possibilities, then those various possibilities can interfere with each other and give a change in the actual prediction. And that's what's happening here. But again, it's kind of subtle, right? It does tell you something amazing about the universe. It tells you that it really is quantum mechanical. There isn't any secret information that fixes the outcome, right? That this really does happen at a distance. Quantum mechanics is non-local. Like you measure one particle over here, And it determines, it helps cross things off the list for the other particle. And in that sense, determines stuff that's happening far away. And that's fascinating and bizarre. And there's all sorts of weird puzzles there about how to incorporate that with special relativity. Remember, special relativity tells us that what I mean by now and what somebody else means by now are different. And simultaneity is not guaranteed in special relativity. So if you're talking about two particles simultaneously collapsing over space-time, Then like, well, how does that simultaneous for me and simultaneous for Zach, who's flying by us at half the speed of light? And we have a whole episode digging into that and like retro causal theories of quantum mechanics. We're not going to get into that today, but it's amazing what it tells you about the universe. But still, it's kind of unsatisfying because like, yeah, you know, you're counting the numbers, you're getting a seven. And you know that if you get a seven, it's quantum mechanics. If you get a five, it's hidden variables. But like, show me the experiment that really proves it. And I always found this experiment to be kind of unsatisfying. And I think a lot of people did, which is why three smart folks came up with a more complicated version of the experiment that is more complex, but it does give a very crisp and clear smoking gun of quantum mechanics.
00:32:00
Speaker 2: But when Bell came up with this, did it, like, make a big wave?
00:32:03
Speaker 1: Oh, yeah. Absolutely, it did. But it took a little while. I mean, Bell was, like, not a big name at the time, and he published his theorem in in this little journal that not a lot of people read. And the reason he chose that is because it didn't charge you to publish. Like a lot of times when you submit a paper, they're like, great, we accept your paper. Please pay $ 4, 000 of publishing fees. And it's like, what? Oh my gosh. It's expensive to publish a paper.
00:32:31
Speaker 3: Yeah.
00:32:31
Speaker 1: But some journals are free. Like society journals tend to not charge as much. And so he actually published in a journal that paid the authors who published there. Amazing.
00:32:40
Speaker 2: That happens?
00:32:41
Speaker 1: Yeah.
00:32:41
Speaker 2: Yeah.
00:32:42
Speaker 1: But it also means that they were cheap in other ways. They didn't provide free reprints of the article. This is before you could just download any article online. And so he used the money he was paid to publish the article to buy copies of the article that he then sent to other physicists. So it took a little while for people to get the word. But once people read the paper, they were like, oh my gosh, this is a big deal. And then people went and did the experiments. And there's been a whole series of these experiments over the last few decades verifying Bell's predictions and closing loopholes. There's a bunch of assumptions in this experiment, like you have to get these particles far enough away that when they collapse, information can't travel from one to the other in time to communicate the collapse. So you have to get them far enough away and measure them quickly enough that you can verify that light doesn't have time to go from one particle to the other. Because otherwise, maybe somehow the information did sneak from one to the other. So you got better and better versions of this experiment that were further and further apart to close loopholes. And there are still loopholes. The experiment relies on choosing these axes randomly. And so what if you don't have a real random number generator? What if your choice of those axes is actually predetermined by some demon in the early universe who set up the whole universe so that it looks like it was quantum mechanical, but actually it's not? That's called superdeterminism. And That's technically a live option to explain this, though I find it kind of bonkers.
00:34:08
Speaker 2: The demon thing is superdeterminism? Yes.
00:34:11
Speaker 1: Superdeterminism says, let's set up the universe in advance in a way so that when humans do these experiments, they get results that look quantum mechanical, but we're just going to predetermine the quantum mechanical appearing outcome.
00:34:23
Speaker 3: Wow. Right?
00:34:24
Speaker 1: By tweaking with the random numbers so they're not really random. I mean, people think deeply about this stuff, and they should. It's like... we're drawing bonkers conclusions about the natures of reality. Let's make sure we didn't miss anything. You know, I get it. And so people have been doing these experiments, closing loopholes, winning Nobel prizes for that, and also inventing more complicated versions that are clear and crisper proofs that the universe really is quantum mechanical. All right.
00:34:50
Speaker 2: Well, now that we've got Bell's experiment and two entangled particles all entangled up in our brain, let's go ahead and jump to three particles. And we're going to do that after the break. So Welcome back to Daniel and Kelly's Extraordinary Universe. We are going to talk about entangling three particles now in the G-H-K experiment.
00:35:29
Speaker 1: G-H-K. Kelly, come on.
00:35:32
Speaker 2: All right.
00:35:35
Speaker 1: So Bell's experiment, very cool, but there's no smoking gun there. And so people were wondering, can we invent an experiment where there's an outcome from a single run of the experiment? that shows you that only quantum mechanics can explain this, right? Can it do something which is impossible under hidden variables? Bell's experiment does something which is like less likely under hidden variables. And if you run it often enough, you can exclude it and say, okay, the outcomes don't seem like hidden variables, but it doesn't do something which is impossible under hidden variables. So people are like, can we come up with an experiment where the universe does something which is just flat out impossible under hidden variables? And therefore, there must be quantum mechanics. And to do that, you need three entangled particles. And that's why we're doing this whole episode about three entangled particles, because this is what GHK came up with.
00:36:26
Speaker 2: But the payoff is now, people.
00:36:29
Speaker 1: All right. So thank you to everybody who's curious about this topic and stayed with us so far. We're about to get weirder, all right? Oh, yay. Yeah. And so this is a really strange explanation. What we're going to do is we're going to describe an experiment with detectors. And we're not going to explain how those detectors work. We're going to describe an experiment, and then we're going to design an outcome to that experiment that's possible in quantum mechanics and impossible in hidden variables, okay? Okay. Without being specific about how the detectors work, because we don't care. So imagine we have something which entangles three particles and then shoots them out in three different directions, okay? Okay. And those particles then hit detectors, and each detector has a switch on it. one or two. So you have like a switch on it. It can be either in state one or state two. And it also has two lights, red and green. So the particles are entangled. They shoot out, they get to each detector. And then each detector has some algorithm that says, based on how the switch is set, I'm going to either flash red or I'm going to flash green. Okay. Okay. So you might be wondering like, how does this detector work? Is it as simple as like, if the switch is set to one, it flashes green. And if a switch is set to two, it flashes red. Well, we haven't set that up yet. We're going to start instead from the outcome we want. We're going to devise an outcome of this experiment, and then we're going to see, can we build a hidden variables version that gives us that outcome? And can we build a quantum mechanical version that gives us that outcome? And somebody has already thought about this and come up with an outcome that's impossible for hidden variables and possible for quantum mechanics. That's where we're going to walk through. And so we need to think about what outcome do we want from this experiment? given any of the settings of the switches. So like, what if all the switches are one? What if all the switches are two? What if two of the switches are one and one of the switches is two? Okay, so we're gonna design the outcome of the experiment so that it's possible to do in quantum mechanics and not possible to do in hidden variables. And we're gonna start with what happens to this experiment. We have three detectors and three switches. What happens to this experiment if one detector has the switch set to one and two of them have the switches set to two, okay? And what we want is that in that scenario, we have three flashes, right? Three detectors with three lights. We want an odd number of them to be red. So we want like red, green, green, or green, green, red, or red, red, red. Okay, that's the possible outcomes. And then if all three switches are set to one, like one on one, we want an even number of reds. So if one of the detectors has a switch at one, we want an odd number of reds. If all three of them have switches at one, We want an even number of reds. And the other configurations don't matter. They're not interesting. So we've designed this outcome. It feels kind of weird. We're thinking about how the detectors will flash red and green given their lights, et cetera. And so now let's think about, can we make this happen in the hidden variables case? Can we design detectors? Is it even possible to design detectors that respond in this way if everything is predetermined? Remember, the particles can communicate. They're entangled, so they can have some correlation between them. And then they fly off to their detectors. And when they get to the detector in the hidden variables version, There has to be whatever information you need to flash the right way based on whatever the particle has. So in the hidden variables version, we can like write some instructions into the particle. We can say like, all right, if the switch is one, flash red. If the switch is two, flash green, right? So we can give little instructions to the particles. When they get to the detector, they know which light to flash.
00:40:08
Speaker 2: Sorry, I think I'm not totally following that. So the particle arrives at the detector.
00:40:12
Speaker 1: Yeah.
00:40:13
Speaker 2: What is it doing to the detector to make it flash a light?
00:40:15
Speaker 1: It gets to decide. The particle arrives at the detector and it gets to decide whether it flashes red or green.
00:40:20
Speaker 2: And it doesn't matter if it's on one or two?
00:40:22
Speaker 1: It decides based on whether the detector is at one or two when it gets there. And it can't know that in advance, right? Like, it gets to the detector and it sees, okay, you're set one, I'm going to flash red. Or set two, I'm going to flash green. So each particle, you have to give a little instruction set to say, when you get to the detector, here's what to do depending on how the switch is set. Here's which light to flash. Okay.
00:40:43
Speaker 2: And so then just to be clear, we're doing like a thought experiment that would help you understand what happened in a more complicated experiment because you can't give particles those kinds of instructions.
00:40:54
Speaker 1: And we're not being specific about like, how would you inscribe these instructions in the particle? Because we want to be very general. We want this to apply to any hidden variables theory, any way that you're inscribing this information. That's why we're being sort of vague about it. Okay. And so, you know, the particles don't know in advance, is the detector set to one or two? They have to be prepared for either outcome. And so they have to know which light to flash when they arrive. And so the question is, can you give each particle the instructions it needs so that when it gets to the detector, it satisfies our requirement? Our requirement was if only one detector has switched one, you get an odd number of reds. If all three have switched one, you get an even number of reds. So let's consider the first case where one detector is one and the other two are two. So like the switches are like one, two, two, or two, two, one. So you can devise a set of instructions to give all your little particles so that when they get there, they do the right thing. You know, for example, particle one, you can say, flash me a red if you see one and green if you see two. And the other particles get the opposite instructions. Green if you see one, red if you see two. And then for all the settings, one, two, two, two, one, two, two, two, one, you always get an odd number of reds. And you can sit down and work this out. And so that's cool. You can actually inscribe the instructions into the particles in the hidden variable theory. It works and you can get the desired outcome for the case where one switch is one and the other one are two. All right. Okay.
00:42:21
Speaker 2: And the particle doesn't know what's happening at the other detectors.
00:42:24
Speaker 1: That's right.
00:42:25
Speaker 2: It only knows, yeah, what's happening at its detector and you gave it instructions for what to do.
00:42:29
Speaker 1: Exactly. We gave it instructions for what to do. So we're devising some general hidden variable theory to give the desired outcome for this case. The one of the switches is one and the other two switches are two. And there's exactly eight sets of instructions you can give that make this work.
00:42:44
Speaker 3: Okay.
00:42:44
Speaker 1: And people went through and enumerated all of them. And like, you know, the instructions are very simple. It's like red if one, green if two or whatever. And you can give different instructions to each of the three particles. And so you have that freedom and there's eight different ways to do it. That's cool. All right. Now, what about the three switches or one case? Okay. Now the same set of instructions have to work because you don't know in advance how what the detectors are set to. And somebody could even flip the switches after the particles have been given their instructions and before they reach the detector. So the instructions have to work for both cases, okay? So in the three switches equals one case, you want an even number of reds. Problem is that none of the eight valid instructions that work for the other case work for this case. So in the example I gave you before where particle one gives a red, if you see switch one and particles two and three give a green if they see switch one, then that would give you red, green, green, which is an odd number of reds, which is wrong. We needed to give an even number of reds for the three switches case. And there is no way to write the instructions for the particles that satisfies the one switch is set to one and the three switches are set to one case. You can figure out all the valid instructions for the one, two, two case that works, but none of the valid instructions for that case also work for the one, one, one case, which means If you build this thing and you run it and you set the switches to 1, 1, 1, and you ever see an even number of reds, then you know that it's not hidden variables because it's impossible to write instructions for a hidden variable theory that ever gives you an even number of reds when the detectors are set to 1, 1, 1. It's just impossible. We just proved it. There's no way to devise that experiment. But fascinatingly, and this is why we started with this setup, It is possible in quantum mechanics. You can organize your particles and entangle them in the right way to maintain superposition and correlations where you choose one and that affects the other, right? The particles in the hidden variable theory can't talk to each other at all. They have the instructions and they go off and they do their thing. But in quantum mechanics, what happens to one particle can affect the other particles, right? Okay. So you can build a quantum mechanical version of this, which does have this outcome. which when you set all the detectors to 111, gives you an even number of reds. And it works on measuring particle spin in different directions. And you can have like little devices that measure their spin. If it's spin up, you get red. If it's spin down, you get green. And the key to the quantum mechanical setup is how you entangle those three particles. You have to create this special state where you have the possibility of them being up, up, up, and the possibility of them being down, down, down, but you combine those two states with a minus sign instead of a plus sign. And that gives you all the exact correlations that you need and gives you exactly the right behavior for all the conditions that we set up before, no matter what the detector switches are set to. And this was a theory first, like people came up with this idea. They're like, okay, it's possible to do this in quantum mechanics. It's impossible to do it with hidden variables. But it was just like a thought experiment. So these guys, Greenberger, Horn, and Zellinger are the first ones to think up this experiment. And it was really complicated. It was really hard to understand. A guy named David Merman, who's a physicist and an expert in quantum mechanics, he simplified it. He came up with this red-green detector switch one-two thing. And if you can believe it, that's the simpler version of the description. It's already like a lot to absorb. Then people actually went and did it. They built these devices. So guys named Pan, Baumister, Daniel, Weinfurter, and Zellinger of GHZ, who came up with this, actually built this thing and they made it work in the year 2000. And they got that outcome. They got an even number of reds when they set the detectors to 111, even though it's impossible for that to happen in the hidden variables theory. And then Zellinger won the Nobel Prize in 2022 for helping close some of these hidden variable loopholes And that's because of this smoking gun result. He made the universe do something that's proven to be impossible with hidden variables and only possible in quantum mechanics. And so you run the experiment, you get an even number of flashes. It's definitely impossible with hidden variables. That single run of the experiment shows you that there can't be hidden variables there.
00:47:17
Speaker 2: Was there a physics party when all the red lights lit up?
00:47:23
Speaker 1: I wonder what that moment was like because you've thought about the theory. You already think quantum mechanics does describe the universe. So this is just a demonstration. But to actually see it happen, it must be really thrilling. Those are the moments when you force the universe to reveal an answer to you. You know, that's what experimental science is all about. I think a lot of people underestimate the creativity required in experimental physics. They think theory is where the brains are at. But, you know, experiment requires a different kind of creativity. You have to conduct these experiments. You have to build these situations that force the universe to reveal option A or option B, right? And boy, this was complicated and creative. And I didn't think it was even possible. I thought Bell's experiment was it, that all we had was this sort of subtle pattern of correlations. And so for somebody to come up with this convoluted setup that's impossible for hidden variables, impossible for quantum mechanics, and then you have this moment. When you're like, you run the thing, you press the button, the lights flash, the universe is telling you how it works. Wow, what a thrill.
00:48:27
Speaker 2: Yeah, that does sound amazing. And I'll note that you might be able to force the universe to give up her secrets, but you can't force Daniel and Kelly to get names right. And so I'll note that we've referred to this idea as the GHK and the GHZ experiment. And I think it's the GHZ, right?
00:48:44
Speaker 1: It's definitely the GHZ. Yes, exactly.
00:48:47
Speaker 2: Okay.
00:48:48
Speaker 1: That must just be a typo on my part. Sorry. Apologies to Z and your Nobel Prize.
00:48:53
Speaker 2: I'm guessing that Z is sleeping just fine at night. Yeah.
00:48:56
Speaker 1: All right, everybody.
00:48:57
Speaker 2: Thank you so much for listening. And thank you so much for sharing your questions about the universe with us. If you'd like to share a question with Daniel, you can write at questions at danielandkelly.org. I will be taking biology questions again. Not until 2027, though, because I've gotten so many amazing questions from you all. I just need a moment to catch up. But we look forward to explaining another topic to you again next time.
00:49:24
Speaker 1: Thanks everybody for listening. Please go and do us a favor and rate the show on whatever podcast app you're using. It really helps people find us.
00:49:32
Speaker 2: Daniel and Kelly's Extraordinary Universe is edited by the amazing Matt Kesselman.
00:49:37
Speaker 1: He really is a wizard. You can also find us online on Blue Sky, Instagram, and X, D & K Universe. Come engage with us.
00:49:47
Speaker 2: You can email us at questions at danielandkelly.org. We really do want to hear from you.
00:49:52
Speaker 1: And you can find our website, www.danielandkelly.org, where you'll also find an invitation to join our Discord, where everybody comes and talks about the amazing universe.
00:50:03
Speaker 2: And we also have the most amazing moderators. This is an iHeart podcast. Thanks for joining us.
Speaker 1: It sure feels like a classical universe out there. Things move in paths, they don't seem to be uncertain. Everything I know about has a location and a velocity, and there doesn't seem to be any weird quantum mechanical effects going on. And yet we're told that's wrong. We're told that the deeper substrate of reality operates according to different rules, that things are not determined until you measure them, that they can be in a superposition, and that there's a true randomness to the universe. That feels weird, that feels alien, that feels counterintuitive. And so, as curious people, we want to know, how do you know? How could you tell? Often these things are hidden behind weird obstacles. Like, you can't see things when they're superpositioned. You could just measure them and get an outcome. That's unsatisfying. And the usual story is a series of experiments thought up by John Bell to prove that particles actually are determined randomly. that there's no local hidden information carried along with the particles that quietly determines what happens. But even these are still quite unsatisfying, because the answer to those experiments is in the patterns and the correlations. There's no smoking gun that says, here, this one experiment proves that quantum mechanics is a description of reality. And today on the pod, we're going to talk about an even more subtle, more complicated experiment that requires entangling three particles simultaneously and trying to get them to flash a series of lights in a certain pattern, which actually does definitively prove that quantum mechanics is the way our universe works. It provides the smoking gun you've always wanted. Welcome to Daniel and Kelly's Extraordinarily Quantum Universe.
00:02:13
Speaker 2: Hello, I'm Kelly Wiener-Smith. I study parasites and space and topics like entanglement make me wonder if physicists have the best slash worst pickup lines.
00:02:25
Speaker 1: Hi, I'm Daniel. I'm a particle physicist who likes to think about alien minds. And I also like to get tangled up in quantum mechanics, though I don't think that's a good pickup line.
00:02:35
Speaker 2: Okay, so here is, I was going to ask you about the worst physicist pickup lines, but I'm actually not sure that our audience wants to hear that. So when physicists have a party, what are physicist parties like?
00:02:47
Speaker 1: What are physicist parties like? Well, I can't generalize, but I can tell you my experience. Katrina and I were in grad school at the same time, and I went to a poor public school, Berkeley, and she went to a fancy private school, University of Chicago, and her department was flush with cash, which meant that if you threw a party at your house and invited the whole department of grad students, they would pay for the alcohol. What? So several times they gave us like $ 500 to throw a party, and of course we invited all the biologists, and then I invited all the physicists. So the physicists crashed all those biology parties. And it was fascinating to see the sort of cultural clash between the physics crew and the bio crew. Yeah, it was interesting. You know, we got some physics bio connections happening. You know, Katrina and I are one example. So, yeah, it was interesting to see how those folks approach a party differently. Right.
00:03:40
Speaker 2: So physicist parties are only good if they're organized by biologists is what I'm hearing.
00:03:43
Speaker 1: That's the story. Yes, exactly. And funded by the biologists. Right. Thank you, University of Chicago. We had some good times.
00:03:53
Speaker 2: Amazing. All right. Well, today we're not talking about entangling graduate students. We're talking about entangling particles.
00:03:59
Speaker 1: Yes, we are. And I got a question from Roger in Boston who heard about a fascinating set of experiments and wanted them explained. Here's his question. Hello, Daniel and Kelly.
00:04:12
Speaker 3: My name is Roger and I am reaching out from Boston, Massachusetts. I discovered your podcast a little while ago and I cannot get enough. Even though there's tons of stuff in there, I just don't seem to be able to wrap my head around. Fascinating stuff nonetheless. With a touch of makes my skin crawl. Down to my question now. Would you please explain how the Green Burger Horn Salinger Multi-particle entanglement experiment proves quantum entanglement. Please explain the hows and the whys of the experiment. I look forward to be blown away by your explanation. Thank you kindly and keep up the good work, guys.
00:05:02
Speaker 2: Greenberger, Horn, Zillinger. That's a mouthful.
00:05:05
Speaker 1: It's a mouthful. There's three smart guys who tangle themselves up thinking about triples of particles. And I started digging into this to answer Roger's question over email. And I was like, this is way too much for an email. Let's do a whole episode. Amazing. Yes, exactly. Because it also gives me an opportunity to talk again about some of my favorite experiments and then to talk about a super version of those experiments that's much cleaner, much crisper, sort of confusing in a different way about quantum mechanics. Oh, good.
00:05:34
Speaker 2: Layers of confusion.
00:05:36
Speaker 1: Yes.
00:05:36
Speaker 2: Fantastic. Entanglement is definitely one of those topics where every time I hear it, I'm still like, I think you guys are getting something wrong. But then you'd always tell me, no, we use this to predict other things and those predictions come true. This is useful information. And anyway, but it breaks my brain every time.
00:05:54
Speaker 1: But that's the point of experiment, right? Is that you go out and explore the universe so that it can change your intuition. So it can teach you how the universe actually works instead of how we think it might or the way we hope it should work. The universe follows its rules and the only way to learn it is to follow the data. And so today we're going to talk about that and we're going to talk about some fascinating entanglement experiments that rely on entangling three particles at the same time. Because entangling two is not complicated enough. No, no. We are going to three particles.
00:06:25
Speaker 2: Okay, but we're starting at two. But all right, keep going.
00:06:26
Speaker 1: We're starting at two. We're going to work up to it, yeah. But before we get there, I wanted to know what people thought about entangling three particles and where their sort of mental potholes were. So I went out and I asked our group of extraordinaries, can you entangle three particles? What is involved? Here's what folks had to say. But I'm suspecting it's a trick question and three can actually be entangled. Yes, you can, in fact, entangle multiple particles. That's what they're trying to do in quantum computing. I think we can somehow.
00:07:01
Speaker 3: Actually, I have no idea at all, but I also don't fully understand what quantum entanglement is.
00:07:09
Speaker 1: So I'll let Daniel take this one. I would think that you would need a particle with three different states, like spin.
00:07:17
Speaker 2: The idea of quantum entanglement always seemed to me to be binary.
00:07:21
Speaker 1: A left spin and a right spin, up or down, whatever. So having a threesome would be very odd. This almost broke my brain, but I guess.
00:07:30
Speaker 2: If there's a particle with a superposition that has three possible outcomes, then theoretically, yes, is how my logic would work.
00:07:38
Speaker 1: But quantum physics is not logic.
00:07:40
Speaker 2: There might be some super clever way you can entangle three together all at once, where some of them has to equal something, but you're not sure how it's distributed. Hmm. I've only heard of entanglement of a pair of particles. So I would say that doing it with three particles is not possible. Nice mix of answers here.
00:08:04
Speaker 1: Yeah. So there are definitely some misunderstandings here about entanglement and how it works and the limitations. And we're going to dig into all of that today. So thanks very much to The Extraordinaries for giving me clues as to where we need to go in this episode if you would like to participate for future episodes we would love to hear from you Please don't be shy. Write to us to questions at danielandkelly.org. And you too can get tough physics questions in your inbox. Didn't you always dream of that?
00:08:30
Speaker 2: The list is going to be a million people long, Daniel. What are we going to do?
00:08:36
Speaker 1: Email all at earth.
00:08:38
Speaker 2: That's right.
00:08:38
Speaker 1: That's right. All right.
00:08:41
Speaker 2: Well, let's start at the very beginning. Forget entangling three particles. Let's just entangle two. What is going on when two particles are entangled?
00:08:50
Speaker 1: Yeah. So first, what is entanglement anyway, right? Let's focus with two particles and understand what it is we're talking about. What entanglement is not is some magical connection between distant particles that binds their fate together. I think some people imagine entanglement the way it's often seen in science fiction. It's like you have a particle here and a particle there, and they have some connection. And anything you do to one particle affects the other one. And that sounds awesome, but that's not what entanglement is at all. That's like Bad pop-sci version, that's the science fiction version that allows you to communicate information across space and time instantly. If you had such a particle, like if I had one and Kelly had one and I could poke it and then Kelly's particle got poked, then yeah, I could send information along that wire, right? Because I could do stuff to my particle that would happen to her particle and she could read it out. That would be incredible. That is not what entanglement is at all, unfortunately, right? Physics as the wet blanket.
00:09:48
Speaker 2: Well, longtime DKEU listeners will not be laboring under that misconception because we have talked about this a few times. but let's definitely do it again to make sure it's fresh.
00:09:57
Speaker 1: The way you should think about entanglement is that you have to think about the two particles together. It's a correlation in the outcomes because it's really a single state. It's always created locally. Two particles are entangled when they interact, and then they maintain that correlation even if you separate them. And that's not too hard to understand. You know, Let's say you have two particles, and there's one property you want to measure about them, their spin. It's either up or it's down. So particle one can be up or down. Particle two can be up or down, right? So then how many possible outcomes are there for your measurement, Kelly?
00:10:34
Speaker 3: Four.
00:10:34
Speaker 1: Four, exactly.
00:10:35
Speaker 2: Thanks for making an outline ahead of time.
00:10:38
Speaker 1: Don't tip them off that you cheated. I wanted to give you some points there.
00:10:42
Speaker 2: I think I could have figured that one out. It's a small number of options, but thanks.
00:10:45
Speaker 1: So two for particle one, two for particle two. And you can enumerate them. It's up, up, down, down, up, down, or down, up. Those are the possible outcomes, right? If the particles are totally free to do whatever they like. Entanglement says, let's only allow some of those outcomes. We have some physics process that has created these particles in such a way that only some outcomes are allowed. For example, maybe there's a conservation of spin. And so we need zero spin for the whole state because it was made from a zero spin state and spin is conserved. And so the spin has to be zero afterwards, which means you either need up-down or down-up. The up-up would have too much spin and the down-down would have too much negative spin. So they're not allowed. So if instead of just having two particles free and willy-nilly to have any spin, if instead you create them together in a correlated way, right, from some interaction, and then separate them, then you know that they're either in up-down or in down-up. So entanglement is just those correlations. It just says, of the matrix of possibilities, you're going to cross some out. And you're imposing a condition that say only some of them are allowed, right? Mm-hmm. Now, that seems very obvious. You're like, hold on a second. Where's all the quantum weirdness, right? And the quantum weirdness comes in when you add superposition. When you say, well, which of those states are we in? In a classical version of this problem, say you have like a bag with two balls in it and one is labeled up and one is labeled down. And I take a ball and Kelly takes a ball and we go 10 miles apart and we haven't looked at our balls, right? Then if you look at your ball, you could say, oh, I have the up ball. Cool. That means I know instantly already that Daniel has the down ball because there was one up and there was one down. There's a correlation. So I know mine, therefore I know yours.
00:12:27
Speaker 3: Okay.
00:12:28
Speaker 1: And in that classical version, it's still not mysterious because you know how it happened. You know that the fact that you have up and I had down was determined when we pulled the balls out of the bag, right? So the fact that we walked 10 miles away, nothing interesting happens there, nothing special. This is predetermined by some properties on the ball. We call that hidden local variables. There's some feature of the ball that is literally the U on it or the D on it It tells you which one it's going to be, right? It's determined in advance. So that's the classical version of entanglement. Still with me?
00:13:01
Speaker 2: Yeah, I'm still with you. The whole time, the ball was either up or down.
00:13:04
Speaker 1: Exactly. Yes. And all that makes sense, right? So now let's get to the quantum version. We have the whole setup ready. So in the quantum version, there is no local hidden information that determines whether the ball is up or down. It's in a superposition, which is a fancy quantum word for saying there's two possibilities in and neither are determined yet. So both possibilities are live. The up and the down are live on my ball until I look. So I pick out the ball from the bag. It can be up or down. I haven't looked yet. I walk 10 miles. It can still be up or down. I haven't looked yet. Kelly's ball can still be up or down. She hasn't looked yet, right? So that's the difference between the quantum version and the classical version. The classical version is local information that's encoded in the ball. It's predetermined. You learn about the other person's ball, but it was determined in advance. And the quantum version, it's uncertain. So what happens when I look is my ball goes from either up or down, from being in an uncertain state of those two, to being specifically up or specifically down, right? Whatever the universe chooses. And then the weird quantum part is the same thing has to happen to your ball, right? Now, we had two possibilities. Either I have up and you have down, or I have down and you have up. One of those has gotten crossed off the list, right? So now we only have one possibility. So just like in the classical version, seeing mine means I know yours, right? The fascinating thing is that when I measure mine, it's the same quantum state as yours. It's just non-local, it's extended. So the whole quantum state collapses from being in both options to being one specific option where I have up and you have down. So you haven't looked at your ball yet, but me looking at mine collapses your state also. That's the weird quantum thing, that over space and time, your state also collapses when I look at mine. Does that make sense?
00:14:53
Speaker 2: Yeah, I think so. I'm going to hopefully not get us too far off track with this question, okay? So when you said it's a superposition of up and down, that made me think about Schrodinger's cat, which is a superposition of alive and dead. Whereas I think in PopSci, they're usually like, it's dead until you take it out of the box and then maybe it's alive or something like that.
00:15:10
Speaker 1: No, they say it's both alive and dead. Right.
00:15:13
Speaker 2: It's a superposition.
00:15:14
Speaker 1: Okay.
00:15:14
Speaker 2: But so the difference is there, you're talking about one cat that's in a box, but that's what superposition is. And entanglement is when you have two things in superposition, but what happens to them is correlated.
00:15:24
Speaker 1: Yes, that's exactly right. Ding, ding, ding. You're a quantum mechanic. Yeah, exactly. Exactly. And the thing that often trips people up is this feeling like I've done something to my ball. I've measured my ball. I've seen that it's up. And that does something to your ball over there. And that's true. Your ball goes from in a superposition to only in one state, right? And so that feels like you should be able to use that somehow to send information. I am affecting your ball. I measure my ball. It affects your ball. Can I use that to do something? Answer, no. Because you can't tell that I've done that. You have your ball. You haven't looked at it. All you can do is look at it and measure up or down. When you look at it and measure down, you don't know if I've already collapsed it into down by looking at mine or if by measuring it, you collapsed it. There's no test you can do to say like, hey, are you collapsed or not? Did Daniel collapse it? And that's the loophole people usually try to use to build some device that can send information across space and time. But you can't, unfortunately.
00:16:25
Speaker 2: Boo.
00:16:25
Speaker 1: It's also unsatisfying because you don't sort of see the magic happening. Like, all you do is you look at your ball and you see up or you see down. Okay, but how do you know that it wasn't determined, right? How do you know that it wasn't? How do you know that there isn't some piece of information that's hidden from you you just didn't know about, some feature of this electron and that electron that really did determine it? Like you can't tell that it was in superposition, can you? That's the big puzzle, right? How do you know that this story we're telling about how the universe keeps both options live until you look, how do we know? And that's Bell's experiment, which we've talked about before. I'm going to get into again today. But Bell's experiment is unsatisfying, right? It's a statistical pattern. You measure these things, you count the numbers. There's no smoking gun.
00:17:08
Speaker 2: But it's clever.
00:17:09
Speaker 1: Oh yeah. Oh, it's genius. Absolutely.
00:17:11
Speaker 3: No, no.
00:17:12
Speaker 1: I don't mean to say, you know, the guy's not a smart person. It's just like, As somebody who's learning physics and wanting to see a clear and crisp smoking gun example of how there can't be local hidden information, how things really are random, it's a little unsatisfying. And that's where three-particle entanglement comes in. So these guys, Greenberger, Horn, Zellinger... came up with a way by entangling three particles together to make a smoking gun experiment showing that no set of pre-written local answers can reproduce the results. It just absolutely cannot be in a single result from the experiment. So that's exciting.
00:17:51
Speaker 2: Hold on, hold on. So how can you entangle three particles? I can imagine how like you can have an up and a down and the other.
00:17:57
Speaker 1: Yeah.
00:17:58
Speaker 2: Do you have to have three options for their states in order for this to work?
00:18:01
Speaker 3: Right.
00:18:01
Speaker 1: And this was the kind of thing that the listeners were confused about. So I want to explain it briefly before we get into the experiments. You know, there's the number two in this example. You have two states and you have two particles. But that's a coincidence. The fact that there are two states doesn't limit you to having two particles. You know, in that example, you had the initial state with spin zero and it turned into two particles with spin up and down and up plus down equals zero. So it all worked out. But you could very easily extend that to three particles. you could start with an initial state that was up instead of zero, and then turn that into three particles, and then you'd have to require that the three particles were up, down, up, so they all added up to the initial state. So there's no limit to the number of particles you can entangle, and you can just keep interacting. Entanglement comes from interactions. So you have a two-particle system, you interact it with another particle, now you have three particles entangled. Or you can create the entanglement from a single interaction from the beginning. And you can also... have particles with multiple spin states. There are particles with three spin states, like the W boson can be up, down, or zero, right? So you have all that freedom.
00:19:10
Speaker 2: Are you limited by features of the things that you're working with? Like, do they have to have three spin states? Or how the heck do you tell particles that we're starting with up and you have to equal zero at the end? And like, how do you convey that information to particles?
00:19:29
Speaker 1: You don't convey to the particles the rules of physics limit you to certain outcomes. You know, like when a photon decays to an electron and positron, the rules of angular momentum say that some of those spin states are allowed and some of them are not. And so some of them just never appear because they would violate a law of physics. And so if you create... three particles at once from a single state, then some of the spin outcomes just are not allowed. They will never happen because they violate some law of physics. And that's something we've reverse engineered. We've like watched this happen and we'd notice, huh, this never happens. That never happens. There must be some rule that prevents it. And we've reverse engineered that and now we call that a law of physics. But the reality is you just don't see that in the universe. And we describe that with our laws.
00:20:15
Speaker 2: So then it sounds like features of the particles determine how many combinations of particles you could have.
00:20:22
Speaker 1: Yeah, but particles have lots of features. You know, we're talking about spins, but also they can be entangled in their like linear momentum. You know, for example, if you have a Higgs boson at rest and then it turns into two particles flying off in either direction... then their linear momentum has to sum to the original Higgs boson momentum. So, you know, they have to be like going in opposite directions, which makes sense intuitively. Like if a particle explodes into two, they're back to back, which means you measure the direction of one, you automatically know the direction of the other, even if the direction of one has some randomness to it, right? And so that's another example of a correlation between the outcomes that really is a quantum superposition. It's because those two particles are entangled. And so they're entangled in many ways, not just their spin, also their momentum and all sorts of stuff. Yeah. So entanglement is no limitations, basically. Wow.
00:21:12
Speaker 2: Awesome. I have absorbed that, but I would still like to hear more about Bell's experiment to make sure I'm really following everything. So let's take a break. And when we get back, we're going to dig into Bell's experiment with two particles and then expand your mind out to three particles. Okay, we're back. We are talking about entanglement today. We have managed to mostly keep away from physicist pickup lines. I'm very proud of us. Let's go ahead and jump into Bell's experiments.
00:21:56
Speaker 1: Yeah, but I consider today's episode basically a party between physics and biology because here we are, right?
00:22:01
Speaker 2: That's right. That's right.
00:22:02
Speaker 1: It's a Friday morning coffee party.
00:22:05
Speaker 2: That's right. Parties don't have to have pickup lines. In fact, they're much better when they don't have pickup lines. So let's party the particle way.
00:22:13
Speaker 1: That's right. Let's pick up Bell's experiment. So the idea here is to figure out how do we know that the universe really is random, that it's not predetermined in some way we couldn't tell in advance. And that sounds like a tall order because you're trying to rule out basically not just a specific theory for like how the particles could be predetermined, what could be fixing their outcome, but any theory, any theory which ever could have the local information that would determine the outcome of your experiment, right? And so that seems like a tall order, like how do you tell if the universe was random and how do you rule out every possible theory? And so Bell's experiment is really genius. This guy invented this way of distinguishing between these two outcomes. And it's very clever, but it's also complicated and a little hard to follow. And the outcome is not really a smoking gun. But as a way to contrast it with a three-particle experiment, I think it's a useful warm-up.
00:23:15
Speaker 2: After that intro, I can't wait. Let's dig in.
00:23:19
Speaker 1: It's really worth understanding. And all the nuances are really fun. So the idea is, just like the example we started with before... you have two entangled electrons, right? That means if one is spin up in one direction, the other one has to be spin down in that same direction. Okay, but now we're gonna complicate things a little bit because before we were talking about the electrons having spin up and spin down as if there's only one kind of spin they can have, right? Just like spin up or spin down. But the truth is electrons are three-dimensional objects. And so when you measure their spin, you have to ask in which direction, right? Like think about the earth. The Earth is spinning around its axis, right? But it could have been spinning around a different axis. In fact, because there are three dimensions of space, you can imagine three different ways the Earth could be spinning, right? It could be spinning around the axis that goes between the North and the South Pole, like it does. Or you could stick an axis through the equator, right? And it could spin that way. Or another axis through the equator at 90 degrees to that, and it could spin that way. It's not, right? There are three different ways that the Earth could spin. Or in reality, it could be any mixture of those three, right? So the Earth is spinning around one axis, but there are more complicated ways to spin. And the same is true also for quantum particles. When you measure their spin, you have to say, I'm measuring your spin along this axis or along that axis or along the other axis. And the weird thing about quantum spin is that no matter what you ask, you either get up or down. There's no intermediate values. Like if you try to measure the Earth's spin using an axis that was not aligned with the North and South Pole axis, you would get some intermediate value. Say, oh yeah, it's spinning along that axis a little bit. It's also spinning along another axis a little bit. But that's not true for quantum particles. You either just get up or down. The answers are related, but they're always either up or down.
00:25:05
Speaker 2: Can I back you up real quick?
00:25:06
Speaker 1: Yeah, please.
00:25:06
Speaker 2: I'm not sure the Earth thing was helping. I think it might've confused me. So you've said there's three ways that it could spin. So say you've got an axis. Earth can spin the way it's spinning now. It could go exactly backwards from the way that it's going, like spin in the opposite direction. And then what is the third way that it could spin?
00:25:21
Speaker 1: Oh, I see. Spinning the opposite direction is still spinning around the same axis.
00:25:25
Speaker 2: Oh, but you said direction matters, but that doesn't count as changing direction?
00:25:31
Speaker 1: Right. So, you know, imagine spinning the way that we're spinning around the north-south pole. Call that, you know, positive.
00:25:38
Speaker 2: Yeah, okay.
00:25:38
Speaker 1: Yeah. And spinning the other direction around that same pole, that would be negative. But it's around the same axis. I'm talking about measuring its spin along a different line. Like, is it spinning around a line that goes through the equator? So, like, take your Earth and stick a bar through it horizontally. And imagine the Earth spinning around that line instead of spinning around a vertical line. That would be a different axis.
00:26:00
Speaker 2: But then couldn't you have infinite kinds of spin then? Because that axis could be anywhere?
00:26:05
Speaker 1: Yes, absolutely. There's infinite number of axes you could choose. And if you have a 3D physical classical object, then as you change the axis, you get more or less of that spin captured by that axis, right?
00:26:16
Speaker 2: Okay, I'm with you now.
00:26:17
Speaker 3: Mm-hmm.
00:26:18
Speaker 1: Okay. All right. Thanks. And so you can also do that for an electron. So for example, if you have two electrons and I measure mine to be up and you measure yours to be down and we could say, well, let's flip the axis we're measuring, right? Let's just turn it 180 degrees. Then we're going to get the opposite results. If I got up and you got down, then I'll now get down and you'll get up, right? Okay. That's easy. Now, if we flip the axis a little bit, like by some angle, instead of all the way, 180 degrees, then we get some different results up and down, but it depends on the angle. And so Bell's axis does this. It says, let's pick three spin directions in advance at random. We'll call them A, B, and C, okay? And then I'm gonna choose randomly which axis to measure my electron, and you're gonna choose randomly which axis to measure your electron. And then we're gonna ask, how often do we get the opposite spin? Now, if we choose the same axis, We get the opposite spin because one has to be up, the other one has to be down. If we choose axes that are upside down, then we'll always get the same spin, right? I'll measure up and you're measuring down along my axis. But if your axis is reversed, you're going to get an up also. And if you choose an axis that's like at some weird crazy angle, you're sometimes going to get up, sometimes going to get down. So you do this a bunch of times and you measure how often do we get opposite spins, right? A third of the time, you use the same axis, so you're going to get opposite spins. And this is where the two ideas separate. Remember, we're trying to distinguish between quantum mechanics that says, look, everything is random and it's determined only when you measure it, and the hidden variable theory that says, no, it's predetermined. There's some information on the particles that tells you all along which one was up and which one was down. And so the hidden variable theory says, well, We know the answer is all in advance. We can just make a table of the outcomes. And if you do that calculation, you can see that you can't get the same spin more than two thirds of the time. Like one third, you're going to get the same spin because we flip axes. And then sometimes you get the same axis because the angles. But if you do the math, you get the same spin less than two thirds of the time. But quantum mechanics disagrees. Quantum mechanics says, no, you can get the same spin up to 75% of the time. because of the correlations between these two particles. And so this feels a little fuzzy. I just sort of like said that and it is a little bit fuzzy. It comes out of the math and I've never found a great like intuitive way to explain like why the quantum mechanics predicts something different from the hidden variables. It just sort of comes out of the math and you do the experiment and you get an answer that's like 75% and that tells you, okay, it's quantum mechanics. And you can't point to any individual experiment and say, like, look, this one was up and that one was down, and that's impossible by hidden variables. It's just the pattern of the measurements that you've made that tells you you've seen them get opposite spin more often than you would expect from hidden variables. And it's just the rate you would expect from quantum mechanics. Okay.
00:29:22
Speaker 2: And so just to confirm, so you're measuring, for example, are the particles up or down? And the only thing that's changing is the axis along which you make that measurement.
00:29:31
Speaker 3: Yes.
00:29:32
Speaker 2: So you're not measuring multiple things about these particles. You're just looking at it from a different like angle.
00:29:37
Speaker 1: That's right. Yeah. Okay. And in the case of. quantum mechanics like if you adjust the angles correctly so the angles are like all 120 degrees apart then you get this weird behavior and you know i can give a little bit more intuition the reason that quantum mechanics gives a different prediction from hidden variables is comes from the interference of the possibilities, right? Which is something that quantum mechanics has and the hidden variables theory doesn't. Hidden variables is just like, look, everything's determined in advance. You can write down before you look at the particles, the possible outcomes and know which ones are going to happen. Quantum mechanics says you can't, there are these various possibilities and they interfere with each other. The way you see like interference in the double slit experiment, right? If you do not collapse the possibilities, then those various possibilities can interfere with each other and give a change in the actual prediction. And that's what's happening here. But again, it's kind of subtle, right? It does tell you something amazing about the universe. It tells you that it really is quantum mechanical. There isn't any secret information that fixes the outcome, right? That this really does happen at a distance. Quantum mechanics is non-local. Like you measure one particle over here, And it determines, it helps cross things off the list for the other particle. And in that sense, determines stuff that's happening far away. And that's fascinating and bizarre. And there's all sorts of weird puzzles there about how to incorporate that with special relativity. Remember, special relativity tells us that what I mean by now and what somebody else means by now are different. And simultaneity is not guaranteed in special relativity. So if you're talking about two particles simultaneously collapsing over space-time, Then like, well, how does that simultaneous for me and simultaneous for Zach, who's flying by us at half the speed of light? And we have a whole episode digging into that and like retro causal theories of quantum mechanics. We're not going to get into that today, but it's amazing what it tells you about the universe. But still, it's kind of unsatisfying because like, yeah, you know, you're counting the numbers, you're getting a seven. And you know that if you get a seven, it's quantum mechanics. If you get a five, it's hidden variables. But like, show me the experiment that really proves it. And I always found this experiment to be kind of unsatisfying. And I think a lot of people did, which is why three smart folks came up with a more complicated version of the experiment that is more complex, but it does give a very crisp and clear smoking gun of quantum mechanics.
00:32:00
Speaker 2: But when Bell came up with this, did it, like, make a big wave?
00:32:03
Speaker 1: Oh, yeah. Absolutely, it did. But it took a little while. I mean, Bell was, like, not a big name at the time, and he published his theorem in in this little journal that not a lot of people read. And the reason he chose that is because it didn't charge you to publish. Like a lot of times when you submit a paper, they're like, great, we accept your paper. Please pay $ 4, 000 of publishing fees. And it's like, what? Oh my gosh. It's expensive to publish a paper.
00:32:31
Speaker 3: Yeah.
00:32:31
Speaker 1: But some journals are free. Like society journals tend to not charge as much. And so he actually published in a journal that paid the authors who published there. Amazing.
00:32:40
Speaker 2: That happens?
00:32:41
Speaker 1: Yeah.
00:32:41
Speaker 2: Yeah.
00:32:42
Speaker 1: But it also means that they were cheap in other ways. They didn't provide free reprints of the article. This is before you could just download any article online. And so he used the money he was paid to publish the article to buy copies of the article that he then sent to other physicists. So it took a little while for people to get the word. But once people read the paper, they were like, oh my gosh, this is a big deal. And then people went and did the experiments. And there's been a whole series of these experiments over the last few decades verifying Bell's predictions and closing loopholes. There's a bunch of assumptions in this experiment, like you have to get these particles far enough away that when they collapse, information can't travel from one to the other in time to communicate the collapse. So you have to get them far enough away and measure them quickly enough that you can verify that light doesn't have time to go from one particle to the other. Because otherwise, maybe somehow the information did sneak from one to the other. So you got better and better versions of this experiment that were further and further apart to close loopholes. And there are still loopholes. The experiment relies on choosing these axes randomly. And so what if you don't have a real random number generator? What if your choice of those axes is actually predetermined by some demon in the early universe who set up the whole universe so that it looks like it was quantum mechanical, but actually it's not? That's called superdeterminism. And That's technically a live option to explain this, though I find it kind of bonkers.
00:34:08
Speaker 2: The demon thing is superdeterminism? Yes.
00:34:11
Speaker 1: Superdeterminism says, let's set up the universe in advance in a way so that when humans do these experiments, they get results that look quantum mechanical, but we're just going to predetermine the quantum mechanical appearing outcome.
00:34:23
Speaker 3: Wow. Right?
00:34:24
Speaker 1: By tweaking with the random numbers so they're not really random. I mean, people think deeply about this stuff, and they should. It's like... we're drawing bonkers conclusions about the natures of reality. Let's make sure we didn't miss anything. You know, I get it. And so people have been doing these experiments, closing loopholes, winning Nobel prizes for that, and also inventing more complicated versions that are clear and crisper proofs that the universe really is quantum mechanical. All right.
00:34:50
Speaker 2: Well, now that we've got Bell's experiment and two entangled particles all entangled up in our brain, let's go ahead and jump to three particles. And we're going to do that after the break. So Welcome back to Daniel and Kelly's Extraordinary Universe. We are going to talk about entangling three particles now in the G-H-K experiment.
00:35:29
Speaker 1: G-H-K. Kelly, come on.
00:35:32
Speaker 2: All right.
00:35:35
Speaker 1: So Bell's experiment, very cool, but there's no smoking gun there. And so people were wondering, can we invent an experiment where there's an outcome from a single run of the experiment? that shows you that only quantum mechanics can explain this, right? Can it do something which is impossible under hidden variables? Bell's experiment does something which is like less likely under hidden variables. And if you run it often enough, you can exclude it and say, okay, the outcomes don't seem like hidden variables, but it doesn't do something which is impossible under hidden variables. So people are like, can we come up with an experiment where the universe does something which is just flat out impossible under hidden variables? And therefore, there must be quantum mechanics. And to do that, you need three entangled particles. And that's why we're doing this whole episode about three entangled particles, because this is what GHK came up with.
00:36:26
Speaker 2: But the payoff is now, people.
00:36:29
Speaker 1: All right. So thank you to everybody who's curious about this topic and stayed with us so far. We're about to get weirder, all right? Oh, yay. Yeah. And so this is a really strange explanation. What we're going to do is we're going to describe an experiment with detectors. And we're not going to explain how those detectors work. We're going to describe an experiment, and then we're going to design an outcome to that experiment that's possible in quantum mechanics and impossible in hidden variables, okay? Okay. Without being specific about how the detectors work, because we don't care. So imagine we have something which entangles three particles and then shoots them out in three different directions, okay? Okay. And those particles then hit detectors, and each detector has a switch on it. one or two. So you have like a switch on it. It can be either in state one or state two. And it also has two lights, red and green. So the particles are entangled. They shoot out, they get to each detector. And then each detector has some algorithm that says, based on how the switch is set, I'm going to either flash red or I'm going to flash green. Okay. Okay. So you might be wondering like, how does this detector work? Is it as simple as like, if the switch is set to one, it flashes green. And if a switch is set to two, it flashes red. Well, we haven't set that up yet. We're going to start instead from the outcome we want. We're going to devise an outcome of this experiment, and then we're going to see, can we build a hidden variables version that gives us that outcome? And can we build a quantum mechanical version that gives us that outcome? And somebody has already thought about this and come up with an outcome that's impossible for hidden variables and possible for quantum mechanics. That's where we're going to walk through. And so we need to think about what outcome do we want from this experiment? given any of the settings of the switches. So like, what if all the switches are one? What if all the switches are two? What if two of the switches are one and one of the switches is two? Okay, so we're gonna design the outcome of the experiment so that it's possible to do in quantum mechanics and not possible to do in hidden variables. And we're gonna start with what happens to this experiment. We have three detectors and three switches. What happens to this experiment if one detector has the switch set to one and two of them have the switches set to two, okay? And what we want is that in that scenario, we have three flashes, right? Three detectors with three lights. We want an odd number of them to be red. So we want like red, green, green, or green, green, red, or red, red, red. Okay, that's the possible outcomes. And then if all three switches are set to one, like one on one, we want an even number of reds. So if one of the detectors has a switch at one, we want an odd number of reds. If all three of them have switches at one, We want an even number of reds. And the other configurations don't matter. They're not interesting. So we've designed this outcome. It feels kind of weird. We're thinking about how the detectors will flash red and green given their lights, et cetera. And so now let's think about, can we make this happen in the hidden variables case? Can we design detectors? Is it even possible to design detectors that respond in this way if everything is predetermined? Remember, the particles can communicate. They're entangled, so they can have some correlation between them. And then they fly off to their detectors. And when they get to the detector in the hidden variables version, There has to be whatever information you need to flash the right way based on whatever the particle has. So in the hidden variables version, we can like write some instructions into the particle. We can say like, all right, if the switch is one, flash red. If the switch is two, flash green, right? So we can give little instructions to the particles. When they get to the detector, they know which light to flash.
00:40:08
Speaker 2: Sorry, I think I'm not totally following that. So the particle arrives at the detector.
00:40:12
Speaker 1: Yeah.
00:40:13
Speaker 2: What is it doing to the detector to make it flash a light?
00:40:15
Speaker 1: It gets to decide. The particle arrives at the detector and it gets to decide whether it flashes red or green.
00:40:20
Speaker 2: And it doesn't matter if it's on one or two?
00:40:22
Speaker 1: It decides based on whether the detector is at one or two when it gets there. And it can't know that in advance, right? Like, it gets to the detector and it sees, okay, you're set one, I'm going to flash red. Or set two, I'm going to flash green. So each particle, you have to give a little instruction set to say, when you get to the detector, here's what to do depending on how the switch is set. Here's which light to flash. Okay.
00:40:43
Speaker 2: And so then just to be clear, we're doing like a thought experiment that would help you understand what happened in a more complicated experiment because you can't give particles those kinds of instructions.
00:40:54
Speaker 1: And we're not being specific about like, how would you inscribe these instructions in the particle? Because we want to be very general. We want this to apply to any hidden variables theory, any way that you're inscribing this information. That's why we're being sort of vague about it. Okay. And so, you know, the particles don't know in advance, is the detector set to one or two? They have to be prepared for either outcome. And so they have to know which light to flash when they arrive. And so the question is, can you give each particle the instructions it needs so that when it gets to the detector, it satisfies our requirement? Our requirement was if only one detector has switched one, you get an odd number of reds. If all three have switched one, you get an even number of reds. So let's consider the first case where one detector is one and the other two are two. So like the switches are like one, two, two, or two, two, one. So you can devise a set of instructions to give all your little particles so that when they get there, they do the right thing. You know, for example, particle one, you can say, flash me a red if you see one and green if you see two. And the other particles get the opposite instructions. Green if you see one, red if you see two. And then for all the settings, one, two, two, two, one, two, two, two, one, you always get an odd number of reds. And you can sit down and work this out. And so that's cool. You can actually inscribe the instructions into the particles in the hidden variable theory. It works and you can get the desired outcome for the case where one switch is one and the other one are two. All right. Okay.
00:42:21
Speaker 2: And the particle doesn't know what's happening at the other detectors.
00:42:24
Speaker 1: That's right.
00:42:25
Speaker 2: It only knows, yeah, what's happening at its detector and you gave it instructions for what to do.
00:42:29
Speaker 1: Exactly. We gave it instructions for what to do. So we're devising some general hidden variable theory to give the desired outcome for this case. The one of the switches is one and the other two switches are two. And there's exactly eight sets of instructions you can give that make this work.
00:42:44
Speaker 3: Okay.
00:42:44
Speaker 1: And people went through and enumerated all of them. And like, you know, the instructions are very simple. It's like red if one, green if two or whatever. And you can give different instructions to each of the three particles. And so you have that freedom and there's eight different ways to do it. That's cool. All right. Now, what about the three switches or one case? Okay. Now the same set of instructions have to work because you don't know in advance how what the detectors are set to. And somebody could even flip the switches after the particles have been given their instructions and before they reach the detector. So the instructions have to work for both cases, okay? So in the three switches equals one case, you want an even number of reds. Problem is that none of the eight valid instructions that work for the other case work for this case. So in the example I gave you before where particle one gives a red, if you see switch one and particles two and three give a green if they see switch one, then that would give you red, green, green, which is an odd number of reds, which is wrong. We needed to give an even number of reds for the three switches case. And there is no way to write the instructions for the particles that satisfies the one switch is set to one and the three switches are set to one case. You can figure out all the valid instructions for the one, two, two case that works, but none of the valid instructions for that case also work for the one, one, one case, which means If you build this thing and you run it and you set the switches to 1, 1, 1, and you ever see an even number of reds, then you know that it's not hidden variables because it's impossible to write instructions for a hidden variable theory that ever gives you an even number of reds when the detectors are set to 1, 1, 1. It's just impossible. We just proved it. There's no way to devise that experiment. But fascinatingly, and this is why we started with this setup, It is possible in quantum mechanics. You can organize your particles and entangle them in the right way to maintain superposition and correlations where you choose one and that affects the other, right? The particles in the hidden variable theory can't talk to each other at all. They have the instructions and they go off and they do their thing. But in quantum mechanics, what happens to one particle can affect the other particles, right? Okay. So you can build a quantum mechanical version of this, which does have this outcome. which when you set all the detectors to 111, gives you an even number of reds. And it works on measuring particle spin in different directions. And you can have like little devices that measure their spin. If it's spin up, you get red. If it's spin down, you get green. And the key to the quantum mechanical setup is how you entangle those three particles. You have to create this special state where you have the possibility of them being up, up, up, and the possibility of them being down, down, down, but you combine those two states with a minus sign instead of a plus sign. And that gives you all the exact correlations that you need and gives you exactly the right behavior for all the conditions that we set up before, no matter what the detector switches are set to. And this was a theory first, like people came up with this idea. They're like, okay, it's possible to do this in quantum mechanics. It's impossible to do it with hidden variables. But it was just like a thought experiment. So these guys, Greenberger, Horn, and Zellinger are the first ones to think up this experiment. And it was really complicated. It was really hard to understand. A guy named David Merman, who's a physicist and an expert in quantum mechanics, he simplified it. He came up with this red-green detector switch one-two thing. And if you can believe it, that's the simpler version of the description. It's already like a lot to absorb. Then people actually went and did it. They built these devices. So guys named Pan, Baumister, Daniel, Weinfurter, and Zellinger of GHZ, who came up with this, actually built this thing and they made it work in the year 2000. And they got that outcome. They got an even number of reds when they set the detectors to 111, even though it's impossible for that to happen in the hidden variables theory. And then Zellinger won the Nobel Prize in 2022 for helping close some of these hidden variable loopholes And that's because of this smoking gun result. He made the universe do something that's proven to be impossible with hidden variables and only possible in quantum mechanics. And so you run the experiment, you get an even number of flashes. It's definitely impossible with hidden variables. That single run of the experiment shows you that there can't be hidden variables there.
00:47:17
Speaker 2: Was there a physics party when all the red lights lit up?
00:47:23
Speaker 1: I wonder what that moment was like because you've thought about the theory. You already think quantum mechanics does describe the universe. So this is just a demonstration. But to actually see it happen, it must be really thrilling. Those are the moments when you force the universe to reveal an answer to you. You know, that's what experimental science is all about. I think a lot of people underestimate the creativity required in experimental physics. They think theory is where the brains are at. But, you know, experiment requires a different kind of creativity. You have to conduct these experiments. You have to build these situations that force the universe to reveal option A or option B, right? And boy, this was complicated and creative. And I didn't think it was even possible. I thought Bell's experiment was it, that all we had was this sort of subtle pattern of correlations. And so for somebody to come up with this convoluted setup that's impossible for hidden variables, impossible for quantum mechanics, and then you have this moment. When you're like, you run the thing, you press the button, the lights flash, the universe is telling you how it works. Wow, what a thrill.
00:48:27
Speaker 2: Yeah, that does sound amazing. And I'll note that you might be able to force the universe to give up her secrets, but you can't force Daniel and Kelly to get names right. And so I'll note that we've referred to this idea as the GHK and the GHZ experiment. And I think it's the GHZ, right?
00:48:44
Speaker 1: It's definitely the GHZ. Yes, exactly.
00:48:47
Speaker 2: Okay.
00:48:48
Speaker 1: That must just be a typo on my part. Sorry. Apologies to Z and your Nobel Prize.
00:48:53
Speaker 2: I'm guessing that Z is sleeping just fine at night. Yeah.
00:48:56
Speaker 1: All right, everybody.
00:48:57
Speaker 2: Thank you so much for listening. And thank you so much for sharing your questions about the universe with us. If you'd like to share a question with Daniel, you can write at questions at danielandkelly.org. I will be taking biology questions again. Not until 2027, though, because I've gotten so many amazing questions from you all. I just need a moment to catch up. But we look forward to explaining another topic to you again next time.
00:49:24
Speaker 1: Thanks everybody for listening. Please go and do us a favor and rate the show on whatever podcast app you're using. It really helps people find us.
00:49:32
Speaker 2: Daniel and Kelly's Extraordinary Universe is edited by the amazing Matt Kesselman.
00:49:37
Speaker 1: He really is a wizard. You can also find us online on Blue Sky, Instagram, and X, D & K Universe. Come engage with us.
00:49:47
Speaker 2: You can email us at questions at danielandkelly.org. We really do want to hear from you.
00:49:52
Speaker 1: And you can find our website, www.danielandkelly.org, where you'll also find an invitation to join our Discord, where everybody comes and talks about the amazing universe.
00:50:03
Speaker 2: And we also have the most amazing moderators. This is an iHeart podcast. Thanks for joining us.
