What is quantum contextuality?

Daniel and Kelly dig into the mysterious concept of quantum contexuality: how measurements depend on each other. See omnystudio.com/listener https://omnystudio.com/listener for privacy information.

Speaker names marked ? are inferred from speaking time and the show’s known hosts — they are not voice-verified.

• 0:00Daniel Whiteson?

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• 1:43Daniel Whiteson?

  Imagine you're taking a test. You sit down, pencils sharpened, and your nice notepad, ready to bend your mind to the task. Your goal for each question is, of course, to find the answer. Because every question has an answer, one that just needs to be revealed or discovered. And whether you get question 17 right shouldn't depend on your answer to question 38, or whether the test writers included question 10 or cut it. Because that's just how tests work. They have fixed, predetermined answers. And that's how most of us think that the universe works. Something happens and it's our goal to figure out what happened and why.

• 2:28Daniel Whiteson?

  Doesn't matter what order you ask the questions or what other questions you asked. The answers are already set. Stuff happened. But the universe is quantum mechanical. It works differently. The answer to a question, the result of a physics measurement, does actually depend on which other measurements you've made. But this is not because of the famous Heisenberg uncertainty principle, or quantum fuzziness, or because measurements disturb the system. It's because fundamentally, quantum systems don't have a ground truth, a bedrock reality. Even if you avoid the Heisenberg uncertainty principle, quantum measurements are contextual.

• 3:12Daniel Whiteson?

  They depend on the context, the other measurements you've made, in a way that our classical brains really struggle to intuit. The answer to quantum question 17 does depend on your answer to question 38. Welcome to Daniel and Kelly's extraordinarily contextual universe.

• 3:45Kelly Weinersmith?

  Hello, I'm Kelly Wiener Smith. I study parasites and space. And today we are in for a really incredible explanation from Daniel.

• 3:56Kelly Weinersmith?

  Why are you laughing, Daniel?

• 4:00Daniel Whiteson?

  Wow, way to set me up so early in the episode.

• 4:03Kelly Weinersmith?

  Setting the bar high.

• 4:04Daniel Whiteson?

  Hi, I'm Daniel. I study particles and aliens. And I do my best to understand quantum mechanics and to explain all of it to you.

• 4:11Kelly Weinersmith?

  That's right. And quantum mechanics can be pretty tough to understand, but we are lucky to have Daniel to explain it to us. And so today we're talking a lot about measurements. And so I was wondering, as a scientist, Daniel, what is the hardest thing that you have had to try to measure?

• 4:29Daniel Whiteson?

  Oh, my gosh, the hardest thing that I've tried to measure.

• 4:34Kelly Weinersmith?

  I guess as a theory guy, have you?

• 4:36Daniel Whiteson?

  I'm not a theory guy. What? As a theory guy? Oh, that hurts. That hurts. I'm an experimentalist.

• 4:45Kelly Weinersmith?

  Okay, never mind. I pull it back. I pull back.

• 4:47Daniel Whiteson?

  No, well, that's fascinating because I get that a lot. Even some people in my department, I discovered, thought that I was a particle theorist. And I was like, what are you talking about? Remember that time I was away to CERN for two years to work on the experiment? I don't know what it is. I just give off theory vibes or something like, Daniel doesn't seem like he could work with his hands. Is that what's going on?

• 5:07Kelly Weinersmith?

  You know, okay, so in retrospect, I realize I, I don't know why I said that because I know you were concerned. You've had my family get a tour of CERN.

• 5:16Daniel Whiteson?

  Yes.

• 5:16Kelly Weinersmith?

  But I guess so in, in my field, though, when, when you mean, when we say we work with our hands, we mean we are up to our knees in mud and dirt. But when y'all work with your hands, you get like data sent through the internet and it shows up on your computer. And so I still feel like you're like theoretically dealing with particles.

• 5:38Daniel Whiteson?

  I see.

• 5:39Kelly Weinersmith?

  But that's not fair of me. Sorry.

• 5:41Daniel Whiteson?

  Would you be more impressed if I had to like pull on elbow length of gloves before I sat down at my computer to make a measurement?

• 5:49Kelly Weinersmith?

  I mean, at least then you're like imagining you could get messy, but I'm, I'm sorry. You're an experimentalist.

• 5:55Daniel Whiteson?

  No, it's fine. It's fine. Well, as an example, the measurement that I did when I was a postdoc, so after I got my PhD and before I was a professor, was trying to make a very precise measurement of the mass of the top quark. And that's hard because the top quark doesn't last very long. And so you never see it directly. You only see the stuff it blows up into. And you have to make measurements of that and then infer what was the top quark mass. And there's all sorts of stuff that makes that measurement fuzzy. And some of the work of experimental physics is how to make that measurement more clean, how to remove those sources of fuzziness so we get the most information from the universe. And so me and my colleagues invented a new statistical technique to extract as much information as possible from the data

• 6:39Daniel Whiteson?

  and to reduce our sensitivity to some sources. Of uncertainty, so we could force the universe to reveal information to us. And to me, that's the heart of experimental science. I mean, being a theorist requires cleverness and creativity and sort of mathematical chops. Being an experimentalist means figuring out ways to force the universe to reveal its answer to you. That's what an experiment is really, is setting up a situation where if the truth is A, then something happens. And if the truth is B, something else happens and you can tell the difference. So yeah, that's maybe the hardest measurement I ever did, and that's what got me my job here at Irvine.

• 7:17Kelly Weinersmith?

  But, but it still sounds to me like to get your answer, you needed mathematical or, or maybe statistical chops because what you did was figure out a new statistical technique. It wasn't like put on the gloves.

• 7:32Kelly Weinersmith?

  But it still counts. It still counts.

• 7:34Daniel Whiteson?

  Wow, I feel like I'm interviewing for my job all over again.

• 7:38Kelly Weinersmith?

  You get the job, Daniel.

• 7:39Daniel Whiteson?

  Well, let me say a couple of things about that. Particle physics has really big collaborations, which means that everybody does their bit and they all get to do their favorite bit. So there's some folks who really like climbing around the detector with bolts and screwdrivers and getting dirty and wearing gloves, and they get to do their bit. And they think that's the most important bit. And some of us get to nerd out about the statistics and we think that's the most important bit. And so, you know, I think specialization is progress and I'm a fan of that. And so I get to work on the thing that to me is the most interesting and everybody else gets to work on the thing that they think is the most interesting. So yeah, that's my contribution and it is statistical and it is computational, but I think it's also still experimental.

• 8:23Kelly Weinersmith?

  Yes, I, and I'm not going to argue with you at all. I'm totally giving you that. Just, just for comparison, though.

• 8:30Daniel Whiteson?

  Your tone is the tone that you use when you're like talking to a crazy old man and you don't want to anger him.

• 8:36Kelly Weinersmith?

  No, no. Maybe when I'm talking to my kids, but no.

• 8:42Daniel Whiteson?

  There you go. I'm definitely getting Kelly's mom voice.

• 8:46Kelly Weinersmith?

  Well, I think this is just a culture difference.

• 8:49Daniel Whiteson?

  Okay.

• 8:50Kelly Weinersmith?

  But so, so let me, let me tell, okay, the hardest thing I ever had to measure.

• 8:53Daniel Whiteson?

  Yes, tell us.

• 8:53Kelly Weinersmith?

  So you, you might remember in the zombie fish episode, I talked about how there's a free living stage of the parasite I studied that emerges from snails in salt marshes and swims around to look for fish. I was trying to figure out if there were parts of a salt marsh where you'd find more of those parasites, like, were they clumping and forming dense clouds at the top of the water, were they kind of near the bottom, were they in some parts of the salt marsh more than others? And so some engineering students had developed this device that would like suck little bits of water out of different heights of the water column. And I was supposed to move it from one part of the salt marsh to another and like suck

• 9:33Kelly Weinersmith?

  little water samples out and then sieve it and dye what I got and try to find and count the parasites. So I could figure out, well, where are the parasites? Where do you find the most of them? Where is it riskiest for the fish?

• 9:45Daniel Whiteson?

  So what was especially hard about this measurement?

• 9:47Kelly Weinersmith?

  Anytime I would try to, to take a little water sample, I was creating too much turbulence. These parasites are very delicate and they would get ripped to shreds. And so I could never get them intact enough so that I could count them. And the other problem is that I needed iodine to try to dye them. And it turns out iodine is a controlled substance.

• 10:08Daniel Whiteson?

  Oh.

• 10:09Kelly Weinersmith?

  In very high quantities, which I didn't know. And so I had to get all of this like security access and I couldn't get it done by the end of the summer. So anyway, I was in salt marshes trying to count parasites and it just wasn't working for me. And so I imagine measurements require like mud and security clearance and stuff like that.

• 10:28Daniel Whiteson?

  Okay, well, I can tell you a similar story. Before I became a particle physicist, I was trying to be a condensed matter physicist and I spent a summer in a basement working with a laser. And this laser has like 75 components to it, each of which works like 98% of the time, which means the laser never works.

• 10:46Kelly Weinersmith?

  Oh, no.

• 10:47Daniel Whiteson?

  Because there's always something broken. I spent the whole summer repairing this laser and tweaking this and then tweaking that and the other thing. And I think we got like 19 seconds in the whole. All summer when everything was working and we got a little bit of data.

• 10:59Kelly Weinersmith?

  Ah.

• 11:00Daniel Whiteson?

  And some people love that and they're like, oh, this is really fun. We get to debug the laser. But my reaction was like, this is really frustrating and annoying, which is why I didn't go into condensed matter experiment. And I prefer, you know, digital puzzles and I don't say that to be negative about people who do that kind of experiment. Just as an example of like, hey, this is very personal. What's frustrating and no fun for one person is an exciting challenge for somebody else. And that's why curiosity and science is so personal. And we have people who go into parasites and other people who go into particles and that's wonderful.

• 11:31Kelly Weinersmith?

  I totally agree and Daniel is super excited about quantum mechanics and measuring quantum phenomena. And he's going to tell us all about it today. And so today we're going to learn about quantum contextuality.

• 11:44Daniel Whiteson?

  Exactly. An excellent job with the transition. Thank you very much, Kelly, for keeping us on track.

• 11:49Kelly Weinersmith?

  I can do it too sometimes.

• 11:49Daniel Whiteson?

  Look at that.

• 11:50Kelly Weinersmith?

  Thanks. Yes. I mean, I took us about 10 minutes off, off path, but I'm bringing us back eventually.

• 11:56Daniel Whiteson?

  But I'm very excited to talk about this topic today because it's something very few people have heard about. I think at the pop side level, you know, we've heard about quantum mechanics. We've heard about measurement in quantum mechanics. We've heard about uncertainty and the challenge of how one measurement can upset another measurement. That's not what quantum contextuality is about. It's a deeper concept in quantum mechanics, which you probably learned about without realizing about it when we talked about Bell's theorem. But we're going to go to the heart of the matter today and it's going to show you something fundamental about quantum mechanics beyond the Heisenberg uncertainty principle.

• 12:30Kelly Weinersmith?

  Is this the kind of thing where folks should go back and listen to our episode on Bell's theorem before listening to this one? Or are we going to summarize it enough that they'll be fine?

• 12:38Daniel Whiteson?

  We'll give an encapsulated explanation of Bell's experiment, but Bell's experiment is just one example of quantum contextuality. But it's not actually the greatest example of it. So we're going to talk about other measurements. But before we dig into it, I was wondering how much people knew about quantum contextuality. It's always wonderful for me to get sort of a level of understanding out there. What do people think? What do they already know? So we can aim these episodes at the right level and get you the best possible understanding. If you'd like to participate for future episodes, please don't be shy. Write to us, [email protected]. You can throw your guesses into the mix. So think about it for a minute. Do you know what quantum contextuality is? Here's what listeners had to say.

• 13:20Speaker 06

  Wow, I have no idea. It sounds like the name for a new book. I have no idea what quantum contextuality is.

• 13:28Speaker 07

  When you finally explain quantum mechanics in a way that all of us can understand. I have never heard the phrase quantum contextuality, but taking from context, I would imagine it is a theory that talks about how the rules governing quantum systems can change depending on the context that system finds itself in. I have no idea, but I think I would say that it's something that you try to imagine at the quantum level. I think that would be my best guess. Maybe it's trying to find the line between quantum and classical, like when it's in which context.

• 14:10Speaker 07

  I'm just gonna guess that it's a way to specify what quantum someone's talking about in science fiction movies.

• 14:17Kelly Weinersmith?

  All right, well, if listener questions are meant to help you understand where you should start, it sounds like you should start at the beginning. And I appreciate that the listeners are at the same point that I am. Thank you, everybody. And so, yeah, Daniel, where do we start?

• 14:33Daniel Whiteson?

  Let's start by remembering what measurement is and focusing in on this. You know, every time we dig into the philosophy of something, you always gotta start with crisp definitions. So we know what are we talking about? Let's use language in a clear way. And let's start with something that's intuitive, which is measurement in classical systems, just like in your ordinary, everyday life. When you go out to measure something, you're measuring the number of parasites or the amount of seawater or something, you imagine that there's an answer there. The world is a certain way and you're just measuring it. You're observing it. Observation and measurement in a classical world is sort of passive. You're just gathering information. You're not changing the world. It's revelation. It's not interaction, right? You're not messing with it.

• 15:16Daniel Whiteson?

  Like if you go out and you measure somebody's height, right? Okay, Daniel is five, 10 or whatever. And then you measure Daniel's weight, right? The order in which you make these measurements doesn't matter. It doesn't matter if you measure weight first and then height or height and then weight, because there's an answer to each of them, right? There is a number that reflects my height. There's a number that reflects my weight. And all we're doing is trying to measure it. Maybe somebody comes along and invents a new statistical technique to make it more precise or whatever. But there is a truth there that we are aiming for. All right, still with me?

• 15:48Kelly Weinersmith?

  Totally intuitive, yep.

• 15:50Daniel Whiteson?

  Okay, yes. So that's the way classical systems work, right? Measurements are non-contextual in a classical system. It doesn't matter the context, what other measurements you've made, the order in which you make the measurements, right? Classical systems are non-contextual. All right, now let's talk about quantum systems. In the quantum system, measurement requires interaction. It's not like you can just sit back and gather information about a quantum system. In order to gather information, you have to probe the system. You have an electron flying along. You want information about that electron. You have to gather up particles that have been emitted by that electron or have bounced off of that electron. Like maybe the electron is turning and so it emits photons which you gather and then

• 16:34Daniel Whiteson?

  you can use that to know something about where the electron was or what its velocity was. Or you can shoot photons at the electron to deflect it, right? In every case, you're interacting with the system in order to gather information from it.

• 16:48Kelly Weinersmith?

  So I'm gonna go ahead and try to make this way more complicated, just in case there are other people out there like me who are trying to overcomplicate things. But you know, like so when I'm, when I go to the doctor's office and they make me stand on the thing to get my height, like, you know, there are photons that are, you know, like bouncing off of the meter stick and into the eyes of the person who's making the measurement.

• 17:11Daniel Whiteson?

  Yeah.

• 17:11Kelly Weinersmith?

  Is that in any way analogous to what you're talking about? Or no, because it's much more interactive in the second case?

• 17:19Daniel Whiteson?

  No, it's a great question and it goes to the heart of like the quantum mechanical measurement problem because essentially you're saying, hey, can't I think about the classical measurement in a quantum way? Isn't it really the same? Because even a classical measurement requires photons bouncing off of things. Like if I'm reading off the scale, somebody has to shine a light on the scale, right? And you're absolutely right. And because everything is quantum in the end. But in the classical system, we're assuming that all of those quantum effects cancel out, that they average out, that your height or your weight is not affected by the measurement at all. And that's mostly true for classical systems, right? Like, yes, photons do push on the scale and that might change the measurement,

• 18:02Daniel Whiteson?

  but not within the level at which we're talking about. So those quantum effects can be ignored for a classical system because when you zoom out, they average out and they go away. But for a tiny system, they're really important and they cannot be ignored. So that's really the distinction.

• 18:17Kelly Weinersmith?

  Okay, great. What's next?

• 18:19Daniel Whiteson?

  Cool. And so when you dig into these quantum systems, you have to give up your classical intuition, this feeling that you're just observing passively the universe. You're interacting with it, you're changing it, right? And so you can't measure something without changing it. And we're used to this because we already know about things like the Heisenberg uncertainty principle, that if you measure the position of an electron, that you can't also know its momentum very precisely, because those two things are coupled in quantum mechanics. And that's not what we mean by contextuality. It's not the topic of today's episode, but let's just explain it really briefly so that people understand what the Heisenberg uncertainty principle does and doesn't say, so we don't get confused later. You know, the Heisenberg

• 19:02Daniel Whiteson?

  uncertainty principle says that certain pairs of measurements, the order does matter. So like position and momentum. If you measure momentum, it changes the position. If you measure the position, it changes the momentum. These things are coupled. And they're coupled in this very specific way, like also energy is coupled to time, or spin in one axis is coupled to spin in another axis. And the Heisenberg uncertainty principle doesn't say like, you measure- Or one of these things and they all change. It says that there's specific relationships. So you measure position and momentum changes. It doesn't change spin or it doesn't change energy. It doesn't change time. Position and momentum are linked. Energy and time are linked. There are these Heisenberg pairs. Okay. And that's a fuzziness that's inherent in quantum mechanics.

• 19:47Daniel Whiteson?

  And it's another example of how classical measurements are different from quantum measurements. Right? And it gets you part of the way sort of philosophically or intuitive to accepting that quantum mechanics describes a world that sort of can't be pinned down. But there's another layer to that. The sense that quantum measurements are contextual. Even if you remove Heisenberg uncertainty, or if you avoid making measurements of quantities that are paired by Heisenberg uncertainty principle, even if you avoid all of that uncertainty, there's still a contextual nature to quantum measurements, meaning that the measurements you make depend on the other measurements you have made. The answer to question 18 on the test depends on the answer to 16 and to 14,

• 20:31Daniel Whiteson?

  not because of Heisenberg uncertainty principle, but because quantum mechanics does not describe a bedrock ground truth to the universe. The answer you get follows a bunch of rules and constraints, but there's no way to satisfy all of the constraints simultaneously. There is no ground truth that's being revealed. You're just interacting with the system and you're getting one view of it.

• 20:54Kelly Weinersmith?

  Let me just, okay, for the ground truthing thing, let me just try to understand. So like, you know, in quantum mechanics, things could be in a couple of different states. And so when you say there's not like a ground truth, but when you look at something at one moment, it collapses to one state. Aren't you seeing like the ground truth of what's happening like at that moment? After you've interacted with it, even if you're only seeing one piece of the whole truth? Is that still not a truth? Why is that not a ground truth? Or am I just getting tied up in the language?

• 21:30Daniel Whiteson?

  That's a really good point, and let's pull that apart. You're right that once you've collapsed the state, once you've made a measurement, there is a state in which the system is in, right? But the point of quantum contextuality is that measurement you've made depends on other measurements that have already been made. And there's no ground truth before you make the measurement that determines the measurement, right? The measurement depends not on the ground truth, but on the other measurements you've made. And we'll dig into that in more detail when we talk about Bell's experiment and non-locality and how that's an example of contextuality in quantum mechanics.

• 22:04Kelly Weinersmith?

  Well, then, let's take a break and go ahead and jump right into that when we get back.

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• 24:48Kelly Weinersmith?

  And we're back. And let's go ahead and start by jumping into a refresher on Bell's experiments.

• 24:54Daniel Whiteson?

  Right, so Bell's theorem and the experiments to test it are a great example of how we know that quantum mechanics is non-local and really random. If you remember, the setup is that you have a particle and it decays into two particles. And because the two particles were produced together, they're correlated. They have to satisfy some constraints. Like if one has been up, the other one has been down. Or if one is charged plus, the other one has to be charged minus. You know, there's some quantum mechanical rule that's applied there that says there's a connection between the two. And that correlation is local when the two particles are created. But then the particles can drift apart, right? And they can be miles away, one in California and one in Virginia. But that correlation is preserved if you

• 25:37Daniel Whiteson?

  Been really careful about keeping them isolated. And the confusing thing about quantum mechanics is that it says that the particle's actual state doesn't exist. It's not like my particle is spin up and Kelly's is spin down and it's just waiting for us to measure it. That would be the classical view, that there's some thing that has determined it. But that instead, my particle has a chance to be spin up or a chance to be spin down. And Kelly's has a chance to be spin up and a chance to be spin down. And it's not till I make my measurement that Kelly's particle is determined, right? This is what Bell's experiment is all about. Is it really true that there's no hidden information there really controlling the outcome? There is no ground truth that just depends on the measurement?

• 26:21Daniel Whiteson?

  And so in the language of contextuality, does Kelly's measurement depend on my measurement? There's no like actual truth to her particle? Or is there some hidden variable that we just haven't measured yet? And Bell's theorem is a way to test that, to distinguish between the two hypotheses. One, that there's some hidden variable, some ground truth to the experiment that's controlling everything. We just haven't sensed it, or there isn't. And Bell's experiment is really clever, but a little bit subtle. Because there's no like one-shot experiment, a smoking gun that proves that the particles were not determined, that there's no hidden variable there. It's instead about correlations. Bell's experiment works because you can't just measure it along one axis.

• 27:05Daniel Whiteson?

  Where it'd be hard to tell, like, was my particle actually determined before I measured it? Or does it depend on whether or not Kelly has made her measurement? You pick three different axes and it relies on the correlations of the measurements across those axes. So Kelly and I both pick three axes and then at random, we choose which axis we're going to measure. And then we compare results. And quantum mechanics gives one prediction for how correlated our answer should be. And hidden variables, a classical theory, gives a different prediction. And so again, it's not like one measurement you're making, where like, I got up, you got down. What does that mean? Nothing. It's about the patterns of ups and downs when we measure along different axes or similar axes or related axes.

• 27:49Daniel Whiteson?

  That's why the experiment is so subtle and so powerful and so clever.

• 27:53Kelly Weinersmith?

  Okay, and? The results suggest that there aren't hidden variables when it's all said and done.

• 28:00Daniel Whiteson?

  That's right.

• 28:01Kelly Weinersmith?

  And so does that suggest that there is not contextuality? Is that the connection here?

• 28:06Daniel Whiteson?

  So that suggests the opposite. It suggests that there is contextuality, right?

• 28:10Kelly Weinersmith?

  Bang.

• 28:11Daniel Whiteson?

  It tells you that there's no way to preassign spin to all the particles that are going to satisfy all of the measurements, right? There's no like actual value of these things that you can preassign in advance that's going to say, here, I can determine without knowing what Daniel measures, I can determine what Kelly's going to measure, right? There's no information that's carried along with the particles that's going to determine what Kelly's going to measure. It depends on Daniel's measurement. Has he made his measurement or not? What is the outcome of Daniel's measurement? There's no local hidden variable that can meet all the requirements, right? So what this tells us is that the measurement is non-local. That's usually the focus of understanding Bell's experiment. The weirdness of quantum mechanics that Kelly's measurement depends on Daniel's measurement.

• 28:55Daniel Whiteson?

  And that's really cool, but in the context of this conversation, let's reinterpret that. Let's interpret it as Kelly's measurement depends on its quantum context. And in this case, its quantum context is Daniel's measurement, right? And that's this question of contextuality. Your measurement depends on other measurements because of constraints. You know, like one has to be spin up and the other has to be spin down. And in a classical world, you can satisfy these constraints just by like, well, I'm going to assign one to be spin up and another one to be spin down. But in these systems, there's no way to satisfy all of the measurements by making these pre-assigned values. Just like in Bell's experiment, any individual test you could explain by assigning a spin up or spin down in advance.

• 29:39Daniel Whiteson?

  But the pattern across these many experiments, that smoking gun of no hidden variables of the quantum nature, cannot be explained by any assignment of hidden variables. There's no ground truth there. The measurements depend not on some bedrock reality, but on the other measurements that have been made.

• 29:59Kelly Weinersmith?

  Okay, I understand that. And so now to take a step back and connect what you said about the Heisenberg uncertainty principle being sort of an example of contextuality, but not being an example of contextuality.

• 30:12Daniel Whiteson?

  No, that's a good point, though, because here, there's no Heisenberg uncertainty principle. This is not an issue of measurements commuting, one fuzzing the other. My measurement of my particle is not coupled by the Heisenberg uncertainty to yours. It doesn't mess up your measurement the way like measuring position messes up momentum, right? These two things we can both know. I can know my particle spin and you can know your particle spin. They're not fuzzed up by the Heisenberg uncertainty principle. The bizarren is here, quantum mechanics is not about the Heisenberg uncertainty principle. It's about how my measurement depends on your measurement. So Bell's experiment is the most familiar example of contextuality, but it's a little bit hard to tease out the contextuality from that

• 30:53Daniel Whiteson?

  one. So let's take a step back and try to build a classical intuition for contextuality. And I think there are useful examples that are easier to think about, maybe even familiar, that are geographical, that I think help people understand what we mean by contextuality.

• 31:09Kelly Weinersmith?

  Okay, I have a feeling I'm gonna end up thinking, we should have started here.

• 31:14Daniel Whiteson?

  Okay, maybe.

• 31:16Kelly Weinersmith?

  And then we can, and then we can say, Kelly, why didn't you realize that when you read the outline earlier? But let's go, okay, let's go ahead and let's, let's go ahead and start with the easy example then, Daniel.

• 31:25Daniel Whiteson?

  Because it's context dependent, right? You have to hear it first. It depends on what I said.

• 31:29Kelly Weinersmith?

  Okay.

• 31:30Daniel Whiteson?

  So imagine your job is to take a world map and you have the outlines of all the countries and to color them. Okay. And you only have three colors, right? You have blue, red, and green. Okay. And there are no rules other than you have to color every country. It doesn't matter what color you give the United States, green, red, blue, whatever. Doesn't matter if adjacent countries have the same color, right? The easy version of this game is you go and you color, right? And that's not a problem. You can assign every country a color. You can make the whole world green. You can make the whole world blue. You can do whatever you like. Not a problem. You can give every country a color, right? Still with me?

• 32:10Kelly Weinersmith?

  Yeah, this is real easy.

• 32:11Daniel Whiteson?

  All right, easy so far. Now, quantum mechanics adds constraints, right? If we're gonna make this a quantum measurement, there's always some rules here, like the way that my particle is spin up, then yours has to be spin down, have to be opposites, right? And so let's add some constraints. And the typical constraint when you're coloring a map is you don't want adjacent countries to have the same color. It's confusing.

• 32:33Kelly Weinersmith?

  Yeah.

• 32:33Daniel Whiteson?

  Right? If a country is red, you want none of its neighbors to be red, because otherwise it's hard to tell when it ends, right? And this is a famous problem in map coloring, right? How many colors does it take to color a two dimensional map and have no adjacent countries have the same color, right? Really fun math puzzle that actually, as a kid, I spent a lot of time trying to come up with maps that required more than four colors. But it's an interesting thing that with four colors, you can color every single country and have no neighbors have the same color. Okay, so you need four colors. Still with me?

• 33:05Kelly Weinersmith?

  You're the right kind of nerd, Daniel.

• 33:09Daniel Whiteson?

  It's just so fun as a puzzle, because one example will misprove it, right? There's this theorem that says four colors is enough to color any map. So if any little seven year old nerd comes with a map that you can't color, boom, you disprove the whole theorem. So that seems to me like an easy challenge. And I spent a lot of time in the afternoons just like, what if I bend this one and make a really narrow thing over here and it loops around it? Anyway, obviously, I never figured it out or it'd be much more famous. But in this example, let's say somebody gives you the impossible task of coloring a map with only three colors. So now you have a map. No adjacent countries can have the same color, but you only have three colors, right? So you can start by like, okay, this one's green. I'm gonna make its neighbors red and blue. But eventually, you're gonna run into a problem, right?

• 33:54Daniel Whiteson?

  There's no way to color this map using only three colors. And so every time you color a new country, you're gonna have to change a previous country, right? And there's no global assignment you can make. There's no solution. There's no perfect truth where you can assign the right color to every country. And then later, Kelly comes along and asks Daniel, oh, what'd you color Turkmenistan? And I can tell you, right? The answer to Turkmenistan depends on its neighbors.

• 34:20Kelly Weinersmith?

  Right. Quantum mechanics is impossible. Stop trying.

• 34:25Kelly Weinersmith?

  No? No.

• 34:27Daniel Whiteson?

  No, what this tells you is that if you have this constraint that adjacent countries can't have the same color and you only have three colors, then there is no way to color the map, right? There is no solution.

• 34:38Kelly Weinersmith?

  Okay.

• 34:39Daniel Whiteson?

  Now, you can have little local solutions. You can say, well, I'm going to color this one red and I'm going to color its neighbors differently. And that'll work for this over here. But then if we want to color a different part of the globe, we're going to have to switch it up, right? I can't just give this country a fixed color because there's no way to make a global assignment to all the countries where every country has one of three colors and no neighboring countries have the same color. It takes four colors to do that. So if you're given only three, you just can't do it.

• 35:08Kelly Weinersmith?

  Okay, so now there's no one answer that works for everything. And so you can get a local answer. But as soon as you start looking somewhere else, then the local answer that you had before changed. So if Turkmenistan was green before, you understood what was happening with the electrons that were over in the above the part of your map where Turkmenistan was. And then you go over and you look at what was happening above America. Does that change the electrons? Or, you know, change what was happening over above Turkmenistan? I'm like mixing metaphors now, but like, does this make sense? Every time you measure electrons, does that change everything about all the other electrons you've ever looked at?

• 35:50Daniel Whiteson?

  Oh, yes, you are on the right track. Think again about Turkmenistan. Does it have a fixed ground truth color? Is there a color you can assign to it that satisfies all of the quantum rules when you look at its neighbors? Can you do that all the way across the globe so that every country just has a single color? No, you can't. Not if you only have three colors. So in that case, Turkmenistan doesn't have a single color. It might have to be blue in the context where you first colored its neighbor Afghanistan, or red if you first colored Kazakhstan, etc. There's no global solution for everyone. And so the answer, what is the color of Turkmenistan depends on what else you have already colored. It has to shift depending

• 36:35Daniel Whiteson?

  What colors you've already chosen. That's the context. That's why this is now a contextual issue.

• 36:41Kelly Weinersmith?

  Okay.

• 36:42Daniel Whiteson?

  So both sets of measurements satisfied the constraints where you can't get something that conflicts with itself. The way like if I get spin up, you have to get spin down. Right? Absolutely. But if I measure first or you measure first, we might get different answers.

• 36:56Kelly Weinersmith?

  Okay.

• 36:56Daniel Whiteson?

  But if I measure it and then you measure it, your measurement doesn't change my measurement. Right? Because we still have to have a consistent result that satisfies the quantum mechanical constraints.

• 37:06Kelly Weinersmith?

  And this only depends on whether or not the electrons are connected in some way. Right? Because they don't have to be.

• 37:15Daniel Whiteson?

  That's right. This only happens if there's a quantum mechanical constraint. Right? In our case, they're entangled and they come from the same origin. And when the case of the map analogy, we've imposed this artificial constraint. You're only allowed to use three colors because we knew that that made it impossible. And that made it a good analogy. If you didn't have that constraint, if you could do any color, whatever, you had an infinite number of colors, or you didn't care about the neighbors, then this wouldn't apply. Right?

• 37:40Kelly Weinersmith?

  Okay.

• 37:40Daniel Whiteson?

  But the idea here is to give you the intuition that there are some problems where there is no global solution. And the answer you get from one country depends on the countries you've done so far.

• 37:50Kelly Weinersmith?

  Got it. Got it. So, you know, I feel like this should be something that makes sense to all of us because Kelly has been saying it depends on the show for such a long time. We should have internalized this long ago. Okay. I feel like that map example has now totally clicked for me and let's take a break. And when we come back, let's do another example, looking at just a single particle to try to make this all click even more.

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• 40:51Kelly Weinersmith?

  All right, we are talking about quantum contextuality on the show today, and we are going through examples to try to make this complicated idea click. And so now we're going to go through a single particle example. Go for it.

• 41:06Daniel Whiteson?

  Yeah, so the cool thing about Bell's experiment, right, is this connection between the particles, and it's famous because of this business of entanglement. But contextuality doesn't require entanglement between two particles. The weird thing about Bell's experiment is the non-locality, the fact that the two particle measurements depend on each other. And you can actually set up quantum systems that exhibit this weird behavior where one measurement depends on another measurement, and it's just a single particle. It doesn't require entanglement across space and time. And that's helpful because it shows you that it's not about entanglement, it's actually something else. It's this contextuality.

• 41:45Kelly Weinersmith?

  Okay. And as a physics person who doesn't know all the ins and outs of the Heisenberg uncertainty principle, is the Heisenberg uncertainty principle about pairs of particles, or is that about one particle and not being able to measure multiple things about one particle?

• 42:02Daniel Whiteson?

  Yeah, it's about one particle, right? And not being able to measure the momentum and location of one particle, for example. But again, this contextuality thing is not about the Heisenberg uncertainty principle. So here, we're going to focus on multiple measurements of a single particle, but where the Heisenberg uncertainty principle does not apply. You know, the same way I can measure like, position, and then I can measure spin, and Heisenberg has nothing to say about that, right? Those are two measurements you can make in any order. We're going to remove Heisenberg from the conversation by only making measurements where the uncertainty principle does not apply. But there are going to be constraints about these measurements that shows us that the context in which you measure it changes the answer you get, that there's no true answer, there's no true state

• 42:47Daniel Whiteson?

  to this quantum system. The measurements you make depend on the other measurements you've made because of these quantum rules that do apply.

• 42:55Kelly Weinersmith?

  All right, set this up for me. And keep your mouth shut, Heisenberg.

• 43:01Daniel Whiteson?

  All right, so we're going to talk about a particle and we're going to talk about its spin. And in the past, we've talked about particles that can be spin up or spin down. But imagine instead a particle that has three possible spin states, up, zero, or down. And so this is like a spin one particle, like a Z or a photon or any kind of boson. It can have three possible spins, okay, instead of just two outcomes. Okay, so now you pick three random directions, X, Y, and Z, and those are your axes. And because, you know, space is relative, you can pick those in any way as long as they're perpendicular to each other. And then you make a measurement of the spin of this particle along X, along Y, and along Z. Okay, and listeners who know about the Heisenberg uncertainty principle will be like, hold on a second.

• 43:46Daniel Whiteson?

  Daniel, you said we're making measurements where Heisenberg does not apply, but it does apply to spins what's going on. And you're right, but if you make a tweak to this, you can lock Heisenberg out of the discussion. If you measure the spin and you don't ask, what is the spin? You just ask, is the spin zero, right? Like, is it zero or is it plus or minus? Turns out that that measurement, for complicated reasons we don't need to get into, can ignore the Heisenberg uncertainty principle. So you have your particle, you measure the spin along three axes and you ask, is it zero along X, is it zero along Y, is it zero along Z? Right, so you have three yes or no questions you're asking about this particle.

• 44:24Kelly Weinersmith?

  I am wondering if it is going to be intuitive to someone who's like a biologist to think of, like, what does it mean to say that you are negative along the Z axis and positive along the X axis in your spin?

• 44:37Daniel Whiteson?

  For biologists or people with classical intuition, you're probably thinking like, all right, the particle has some spin, it's spinning in some direction. So what do we mean by spin in some direction or positive or negative spin? This is a bit of a physics thing. We think of spin, even in classical systems like a planet, as being along the axis of rotation, the line around which it's spinning. So the Earth, for example, is spinning and it spins around the north-south pole, right? Draw a line between the north pole and The south pole. So that's the spin axis. And then there's a direction clockwise. Spin is positive and counterclockwise spin is negative. No spin is zero. So if you have an object that's spinning,

• 45:22Daniel Whiteson?

  you can define some axes and ask, how is it spinning along these axes? Or if you're a vector like kind of person, you can think about that spin is having a vector along the spin axis. And then if you define X, Y, and Z axes, you're asking, how much do those axes overlap with the spin vector? So back to the earth, if you lined up your X, Y, Z axes so that X was along the north, south pole, you'd say the earth has positive spin along X and zero along Y and Z. If the axes didn't line up with the north, south pole, they would like skewed somehow. You'd say the earth has spin along multiple axes. It has spin along some direction, north, south, and these axes are each capturing a part of it.

• 46:05Daniel Whiteson?

  All right. So that's what happens when you have an actual object that's really classically spinning. Just to think about like the math of spin. Now let's think about the quantum version and what it means to measure the spin of a particle.

• 46:16Kelly Weinersmith?

  Okay.

• 46:16Daniel Whiteson?

  And now I'm like measuring its spin along some axis. It's maybe capturing some fraction of it. And I want to imagine that there's a real answer here. It's really spinning in some direction and I'm just capturing it along some angle. But remember that number one, this is quantum spin. So these things are not like actually spinning. We call it spin because it has some relationship to spin. There's like the math of it is similar to the math of spin. But you shouldn't think of it as actually spinning. Just think about it as some weird quantum process. These things can do. The X, Y, and Z are important because that's where the quantum constraint comes in. Okay.

• 46:52Kelly Weinersmith?

  Okay.

• 46:52Daniel Whiteson?

  Quantum mechanics says that only one of these directions can have zero spin. So you can measure zero along X, you can measure zero along Y, or you can measure zero along Z. But you can't get zero along X and Z at the same time. That's the quantum constraint. So we make these three measurements along our X, Y, and Z. We ask, is it zero on X? Is it zero on Y? Is it zero on Z? We can only get a yes along one of those axes. Okay. So that's the equivalent of like the map coloring rule, right? There's some quantum constraint here.

• 47:23Kelly Weinersmith?

  Is it interesting to know why only one of those values can be zero? Or is that just an arbitrary thing in this example?

• 47:31Daniel Whiteson?

  It's totally not arbitrary. It comes like out of the mathematics of spin. It's sort of what spin one means. The mathematical details, I think, are not helpful, but it's not just a rule that we've chosen.

• 47:43Kelly Weinersmith?

  Okay.

• 47:43Daniel Whiteson?

  Right. This is the nature of spin one particles, that they can only have zero along one direction at a time. And so Kelly or the biologist or the hidden variable proponent might be like, okay, look, my particle has spin in some direction. And there are predetermined answers to the question of like, is it zero along X? Is it zero along Y? Is it zero along Z? And when I go make my measurements, it just reveals the secret pre-existing answer that the universe had all along, that there is a truth there. Right?

• 48:13Kelly Weinersmith?

  Okay.

• 48:13Daniel Whiteson?

  Problem is that you are not the only person making measurements.

• 48:17Kelly Weinersmith?

  All right. So I have an X, Y, and Z, and I've got my zero.

• 48:21Daniel Whiteson?

  Yeah.

• 48:22Kelly Weinersmith?

  And you have an X, Y, and Z, and you have a zero in a different spot.

• 48:25Daniel Whiteson?

  Yeah.

• 48:26Kelly Weinersmith?

  Is that because we have different particles that we're looking at? Or like, what, what do I know now that I know that we have different answers?

• 48:33Daniel Whiteson?

  Yeah. So we're looking at the same particle, right? You measure your X, Y, and Z. You have your zero. I measure my X, Y, and Z. I have a zero. And you might think, all right, well, there's some way to satisfy Kelly's answer and Daniel's answer simultaneously. There's some hidden truth here that they're both consistent with. But you can keep adding people who choose their X, Y, and Z. And for example, somebody might come along who has the same X as me and a different Y and Z. Right? So now X belongs to two different triples and has to satisfy two different constraints. Right? And it's not possible to have an assignment to all of these things that's consistent across all the triples that anybody might measure.

• 49:16Daniel Whiteson?

  And so whether I get a zero for X depends on the answer I got for Y and Z. And whether somebody else gets a zero for their X, which is the same as mine, depends on their Y and Z. And so even though our X is the same, I could get a zero and somebody else might not get a zero. Maybe they already have a zero for their Y. And so it's impossible to come up with an assignment that satisfies all of the triples simultaneously, that all the triples only have one zero.

• 49:43Daniel Whiteson?

  The answer you get always depends on the other Y and Z you chose, the measurements you made in the other directions.

• 49:49Kelly Weinersmith?

  And are we all looking at the same particle at the same time and getting different answers about it, or we're all looking at different?

• 49:55Daniel Whiteson?

  Yes.

• 49:56Kelly Weinersmith?

  Oh, how does that happen?

• 49:58Daniel Whiteson?

  We're all looking at the same particle at the same time, and we're making measurements that don't mess up the other measurements, right? Remember, we locked Heisenberg out of this conversation. It's not like a momentum and location thing. The fact is that the quantum system doesn't have a ground truth that we're probing. The answers you get depend on the other answers you got, because it has to satisfy these quantum rules. And the quantum rules are such that there is no global solution that you can satisfy. It's like making an impossible requirement on a system, like saying, look, I'm going to color this map with only three colors, and I know adjacent country is going to have the same color. It's an impossible constraint, right? Quantum mechanics says, okay, that's no problem. I'm just going to give everybody who asks a different color, right? There is no true color to Turkmenistan, right?

• 50:43Daniel Whiteson?

  I'm just going to say, well, depending on what you color its neighbors, I'm going to tell you what you need to know to satisfy the constraints, right? But there is no true global assignment for everybody. And so the properties of quantum systems are contextual. They depend on other measurements you have made to satisfy the quantum constraints.

• 51:03Kelly Weinersmith?

  Okay, so now my brain is like going to the implications and like, how do you learn from a system where everybody looks at the same thing, but gets different outcomes? And I guess the answer is you just do it statistically and probabilistically? Or, ah!

• 51:21Daniel Whiteson?

  Yeah, no, I love that. And it turns out to not be important that systems have like fixed true values, right? The universe can just be undetermined in that way. It can be contextual, it still follows rules. And as long as it's following the rules, we can discover those rules, right? As long as we give up on our like sort of hidden philosophical assumptions that there is a singular hidden truth that we're probing, and accept that measurements are interactions, and those interactions are contextual. Textual in this really weird way, right? And this is not like the observers creating your reality or, you know, quantum mechanics is consciousness or the quantum mechanics is nonsensical,

• 52:06Daniel Whiteson?

  right? It comes actually out of quantum mechanics requiring constraints, right? Respecting conservation laws. And what's real here are the relationships, right? Properties of objects are not fixed. They depend on the context and they're determined by relationships. So the sort of the same way that like you don't have a velocity, your velocity depends on who's measuring. You have multiple velocities simultaneously, right? I have a velocity with respect to my chair and a different one with respect to the sun and a different one with respect to some asteroid in space. It's cool to have many velocities, right? It depends on the context, the observer who's making the measurement. In the same way, properties of particles are contextual. Even though we like to think of the universe as like having an answer,

• 52:50Daniel Whiteson?

  being a certain way, there are some properties of the universe that are not like that. They are just contextual. They are not fixed.

• 52:58Kelly Weinersmith?

  I feel like you had the nub of your like quantum self-help book in there somewhere, like the only thing that's real are the relationships. And, uh, and I think your million lies somewhere in the last five minutes of things that you said. Anyway, think, think about that.

• 53:14Daniel Whiteson?

  Well, my agent tells me that self-help books are all that's selling in the nonfiction category. So.

• 53:19Kelly Weinersmith?

  That's what I've heard as well. And so that's why I'm always listening for the next self-help book. Anyway, so what are some, some like misinterpretations? What are some things that, that doesn't mean that people get confused about?

• 53:32Daniel Whiteson?

  Yeah, this is not an open door to consciousness or to, you know, quantum woo or anything like that. This is a path to a deeper understanding of what quantum mechanics says about the universe, which is that there isn't a fixed assigned truth that we're observing, right? That the measurements we make depend on the other measurements. Question 18 depends on question 16 and the answer you gave. And that's just a different way of thinking about what's out there and what's real. If anything is real. And I think it tells you that we are not separate from the universe. We are part of it and that our interactions with the universe, our measurements of it, don't reveal some fundamental, objective reality.

• 54:16Daniel Whiteson?

  They reveal the laws that the universe follow. And those laws are quite different from the intuition that we've built up from like walking around on this earth and interacting with goats or whatever.

• 54:26Kelly Weinersmith?

  Which is one of the best things that you can do with this lifetime of ours.

• 54:32Daniel Whiteson?

  Especially quantum goats. So tell me, is your goat still in a superposition of having given birth and not having given birth? Or is that collapsed?

• 54:40Kelly Weinersmith?

  It hasn't collapsed yet. It hasn't collapsed yet, Daniel.

• 54:44Daniel Whiteson?

  And that is Kelly's context right now.

• 54:48Kelly Weinersmith?

  That's right. That's right. It's the only context in my life. Everything depends on whether or not Lottie has given birth yet.

• 54:57Kelly Weinersmith?

  So before we started this show, I knew that you could entangle particles. And what happens, you know, if you looked at one of them, what happened to the other one depended on what happened to this one. And so that's an example of contextuality.

• 55:12Daniel Whiteson?

  Yes, exactly.

• 55:14Kelly Weinersmith?

  And so the new thing in this case is that we're trying to tell people that there's lots of instances where what you see happening in the quantum worlds depends on what happened somewhere else.

• 55:27Daniel Whiteson?

  Or even other measurements of the same particle, not just somewhere else. Right?

• 55:31Kelly Weinersmith?

  Or even other measurements of the same particle, but not, we're not talking about a Heisenberg uncertainty principle.

• 55:38Daniel Whiteson?

  That's right.

• 55:38Kelly Weinersmith?

  We're talking about other people looking at the exact same particle.

• 55:43Daniel Whiteson?

  Exactly.

• 55:44Kelly Weinersmith?

  Not getting the same measurements.

• 55:46Daniel Whiteson?

  Exactly.

• 55:47Kelly Weinersmith?

  And these are just two examples of the many ways that contextuality happens? Or these are the examples of contextuality?

• 55:55Daniel Whiteson?

  These are two examples of a fundamental principle in quantum mechanics, which is contextuality.

• 56:00Kelly Weinersmith?

  All right, got it. Okay, so then I think that's what I got out of the episode. So it sounds like we did it.

• 56:06Daniel Whiteson?

  Thank you very much, Kelly, for describing in two minutes what I took an hour to explain.

• 56:11Kelly Weinersmith?

  Well, but I only was able to do that because you explained it so clearly over the hour. So hooray for Daniel.

• 56:19Kelly Weinersmith?

  Go Team D K E U.

• 56:21Daniel Whiteson?

  And thank you, everybody, for going on this crazy quantum journey with us, understanding the weird nature of quantum measurements.

• 56:29Kelly Weinersmith?

  Thanks, everybody. See you next time.

• 56:37Daniel Whiteson?

  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.

• 56:45Kelly Weinersmith?

  Daniel and Kelly's Extraordinary Universe is edited by the amazing Matt Kesselman.

• 56:50Daniel Whiteson?

  He really is a wizard. You can also find us online on Blue Sky, Instagram, and X, D and K Universe. Come engage with us.

• 57:00Kelly Weinersmith?

  You can email us at [email protected]. We really do want to hear from you.

• 57:05Daniel Whiteson?

  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.

• 57:17Kelly Weinersmith?

  And we also have the most amazing moderators. This is an iHeart Podcast. Thanks for joining us.

• 57:26Kelly Weinersmith?

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