Daniel and Kelly’s Extraordinary Universe - Why is there quantum uncertainty?

Episode Date: November 14, 2023

Daniel and Jorge wrestle with one of the fuzziest concepts in quantum mechanicsSee omnystudio.com/listener for privacy information.

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asking and answering science questions. All right, enjoy the pod. Hey, Daniel, does quantum mechanics really explain reality? I mean, I think so. even though it's pretty weird. Are you sure? Well, lots of experiments we've done over the last century say yes. Yeah, but like how can you be certain?

You know, I thought quantum mechanics says everything is uncertain. Well, we're very certain that quantum mechanics is uncertain, but only about certain things. I'm pretty certain that makes no sense. I think it's curtains for certainty. Are you sure about that? Now I'm not sure about anything. Welcome to being a non-physicist. Hi, I'm Jorge McCartunist and the author of Oliver's Great Big Universe.

Hi, I'm Daniel. I'm a particle physicist and a professor at UC Irvine, or at least I was certain of that a moment ago. Yeah, now you're not sure that you have a job. Is that what you mean? You might have said something to get you fired here. Yeah, it's one of those questions you shouldn't ask because it might change the answer. I thought you had tenure. I thought that prevented them from firing you. There are still limits to what we can do even if we have tenure.

But anyways, welcome to our podcast, Daniel and Jorge, Explain the Universe, a production of IHeart Radio. In which we test the limits of our understanding of the universe. How certain are we that the universe works in a different way on a tiny scale? That there are tiny quantum particles fluctuating in and out of existence. that when we zoom down to the universe at its smallest scale, different rules apply. On this podcast, we push all those limits

and we try to answer all of your questions. That's right, because it is a wonderful and amazing, but yet also very mysterious universe that seems kind of random at times, but also seems like a giant clock that seems to be working precisely as it's supposed to be. And the big goal of physics is not just to reassure us that the universe works the way our intuition suggests, But to discover the truth, science is a knowledge-building mechanism, right? It's a way to figure out how the universe actually works,

even if it's deeply in contradiction with the way we thought it worked. Wait, I thought philosophers thought that you can never uncover the real truth of things. It's impossible to be completely certain about the truth. Philosophers don't even agree about what you mean by the real truth. Oh, I see. It's about, I guess, vocabulary. Man, every philosophy argument in the end comes down to vocabulary. Like, what do you mean when you say vocabulary anyway? Oh, you can get a few inception levels deep into this discussion.

What do you mean by what do you mean? Exactly. What do you mean? What is meaning? Yes, what is meaning? What is a question anyway? What is a what? And I laugh at all these jokes, not to laugh at philosophy, but out of deep respect for the way philosophy forces us to figure out what we mean by our questions.

What is it in the end? We're asking, what kind of answers do we expect, all this kind of stuff? These are hard questions. Wait, does that mean that philosophers don't think you ask? actually have a job as a physicist? I mean, philosophers definitely recognize that physics is building a set of facts and those facts like power of the world. There's a reason that technology works, for example.

But exactly what it means about the universe, what is the real story, what is real? Depends a little bit on the questions we're asking. And it's not even clear that there is an objective truth about it. It might just be our perception of it answers to the kind of questions we would ask. Well, I guess the elusive quest for the real truth of the universe is kind of what science is all bad. You know, even if we don't get there, it's all about trying to get there. Exactly. And we can all work together to get there, even if we're not in agreement about what there is. Some of us think we are revealing the true underlying mechanism of reality, something that like alien

scientist would also be revealing. Other folks don't care about that. They say, hey, look, we're just getting something that works, something that predicts the outcomes of experiments and lets us build technology. Who even cares if it's real or what aliens would think about it? You can totally disagree with the lofty philosophical goals of science and still work hand in hand and get concrete results. I feel like maybe that's physicist's favorite part of the job. It's arguing about the job. You know, I think that there's a division early on. People who like to argue about it more end up in philosophy and the people who just want to like get in the lab and learn stuff about the world end up in physics. You just want to get in there and blow stuff up. But there's

always this tension, right? The juiciest questions in physics are the ones that when we get the answer, we go, hmm, well, but why is it like that? What does that mean about the world? The best physics questions have philosophical implications. Yeah, and so there's a lot of uncertainty about what we do know or what we don't know or what we can know about the universe, but even deeper than that, there seems to be a certain uncertainty about the universe itself. Something shocking, something very difficult to understand about the quantum picture of the world, is that the world itself might be limited in its precision, not just in our ability to measure it. or to extract that knowledge,

but there could be a fundamental fuzziness to the universe, a lack of determination about reality. It's not just me getting older and needing reading glasses. It's that also, yes, those two effects are combining. Does I mean have quantum vision now? I think we should start that company, quantum laser surgery. Yeah, quantum reading glasses. Apparently, you only cost a dollar, so we make a killer profit.

You can only read one word at a time. But anyways, yeah, there seems to be this interesting nugget. of strangeness to quantum mechanics, which tries to explain the entire universe. And so today on the podcast, we'll be asking the question, Why is there quantum uncertainty? I feel like we're asking a question about uncertainty. We are uncertain about why there's uncertainty.

That's what I mean. It's meta uncertainty. We're getting very meta here. Well, if it helps, I'm pretty certain. I'm a cartoon. That's one thing I know. Yeah, well, this is exactly the kind of difficult philosophical question because, you know, I even sure, like, what kind of answer we're looking for?

Like, are we hoping to reveal that the universe could have only ever been this way? Or to argue that, look, we could be in lots of different universes. This one happens to have this quantum uncertainty. You know, there's lots of different ways to attack this sort of philosophical problem. Well, hopefully it's more than just a philosophical problem, right? Eventually, the hope, the goal is to find kind of physics, math-based answers to these questions, isn't it? To me, I think the sort of highest level process would be go out and look at the universe, see what it's like, boil that down to like a few essential facts, build a theory that describes how that works, why that works, the mathematics to describe it, and then look at that theory and ask philosophical questions like, did it have to be this way? Could you have a universe that was different?

Could we have built a different theory of the universe that didn't have this feature or that feature about it? So in the end, it's mathematical, but it's really rooted in explaining what we see out there in the universe. But couldn't you answer those questions? You just asked in a mathematical way, maybe in the future? We don't know for certain they can't be answered, right? We don't know for certain they can't be answered. I think a great analog that's going to help us understand this question today is the question of like the speed of light. You know, we live in a universe where the speed of light is constant for all observers.

And if you start from that, you can build special relativity and you can explain the whole universe. But you have to start from that assumption. That's something we've seen in the universe, something we know is true. We've measured it. We've done the experiments. We've now coded it into our theory. But we don't have an answer for why that is true. And one day, maybe people will have a deeper understanding of the nature of space from which that bubbles up.

You might be able to explain that someday. But currently, we don't have an answer to why. It's just sort of like the foundational assumption that we need to explain everything we see the universe. Right. Well, as you said, hopefully maybe somebody, somebody will answer this deep questions, but that person doesn't seem to be out there because Daniel went out there and asked this question of folks and we got some pretty interesting answers back. Yeah. Thanks everybody who answers these questions as wacky and as crazy as they are without having any chance to prepare yourself. Really appreciate your participation. And I'd love to hear your voice

on the podcast. That's right. I'm talking to you. We haven't heard from you yet and we want your voice on the air. There's a bunch of people who have heard we have heard from though, right? You just totally snub them, I feel. I said thanks to all those folks also. Oh, I see.

You meant the other people. It's a shockingly small group of people who volunteer for these, which is why you hear the same voices over and over again. Oh, I never noticed. You didn't have to tell me. I should have maintained

your quantum uncertainty. That's right. You should have kept that a mystery of the universe. But anyways, think about it for a second. Why do you think there is quantum uncertainty in the universe? Here's what people had to say. I guess that both because we can't really have an accurate measurement on that very tiny scale

and because measuring a quantum process interferes on that process. There's quantum uncertainty because when we measure a particle, it changes what the particle is doing. When we're not looking at the particle, we never quite know what it's doing without measuring it, which changes the state of the particle. So we can never quite know exactly what a particle is doing without changing the state. I know that if you measure something, it falls into the wave function collapses and you fall into one of the states, I guess there's uncertainty because there's a wave function. All right. Some pretty deep answers here.

I'm pretty certain of that. Yeah, a lot of these folks are developing like a microphysical picture. Like what's happening when you make a measurement? What prevents you from being able to measure things super duper precisely? And that's helpful, but I think it's only really part of the story. All right, well, let's dig into this topic and let's start with the basic question, Daniel. What is quantum uncertainty? There's so many weird things about quantum mechanics that we could dig into for hours and hours.

But I just want to zoom in on this one thing, this quantum uncertainty, which is different from other weird aspects of quantum mechanics. And quantum uncertainty is a very specific thing. But let's start out by talking about classical physics because quantum uncertainty is basically a rejection of that. So classical physics, the physics of Newton and even the physics of Einstein says that we live in a universe. where you can know everything about an object, like take a particle or a banana or whatever. You can know everything about its location. You can know everything about its velocity.

You can know its entire history, that it moves in these smooth paths. It always has a position. It always has a velocity. That to reality, there is no fuzziness. There's an exactness to this information, and you can know all of it simultaneously because it's well defined.

That's a classical physics picture of how things move in the universe. Right. That's sort of like maybe a good way to explain it. is basically like up to high school physics, right? Like, you know, predicting where the baseball that you throw is going to land or, you know, how things move. You shake them, wherever you swing them. That's classical physics, right?

Like, you can predict where things are, what things are going to do. Like, in those exams in high school, there's no room for uncertainty. Like, there's the right answer or there's a wrong answer. That's right. And there's an exactness to the answer. And even well past high school physics, I guess, depending on your high school, you know, Einstein's physics is also classical in that sense. I mean, Einstein was a huge revolution compared to Newtonian physics. Relativity is a whole other brain twister. But Einstein's picture of the universe fundamentally

is the same in that there's no uncertainty. He imagined you could know where a particle is that had an exact position and you could simultaneously know its position and its momentum and all sorts of other things about it. Even like light? Yeah, the classical theory of electrodynamics, you know, which comes from Maxwell and inspired Einstein to develop relativity, didn't have any sort of quantum uncertainty to it. Photons had an exact position. All right. So then that's Einstein and Newton. But then around the beginning of the 1900s, they figured out that things are kind of strange and weird. Yeah, basically quantum mechanics looks at that and says, yeah, no. You can't know all of these things simultaneously. And the history

of it's really fascinating. It comes around in the 1920s when people were trying to understand how the atom worked and what was the picture microscopically of the electron and the nucleus. Was this sort of like an orbital picture like Bohr was suggesting, or is there something funnier and more complicated going on? And it was really Heisenberg of the famous Heisenberg Uncertainty Principle, who developed the sort of first theory of quantum mechanics that described how the atom worked in a way different from Bohr that had like a fundamental different mathematics underneath it. I feel like or I seem to recall that initially quantum mechanics didn't have this idea of uncertainty to it, right? Like didn't it start with people just noticing that like light came in packets or that

electrons wouldn't, you know, fly off unless you met certain minimum energy requirements and things like that. There's no uncertainty or fuzziness to it at the beginning, was there? The roots of quantum mechanics are exactly as you described. You know, there's like the black body radiation problem and there's the photoelectric effect that we dug into on the podcast several times. And you're right, it was actually Einstein who figured that out, right, who connected the ideas of plank with the experiments that we were seeing and saw that light had to come in packet, it can only interact with a single electron. Absolutely. So those really those core ideas which then led to the formulation of quantum mechanics, those didn't have uncertainty in

them. That wasn't an essential ingredient. Right, because that's where the word quantum comes from, right? Like quanta, like little quantity. Little countable things, right? You can have one electron or two electrons or nine electrons, but you can't have 1.7 photons, for example. But then as people were trying to apply these theories and these ideas to describing the atom, they need to develop mathematics that work, mathematics that explained what we saw. And Heisenberg developed this theory of quantum mechanics that he used to make calculations and to understand, like, why did the electron have this energy level around the atom and not that energy level? Why did we get this atomic spectrum from the atom? He developed this whole theory of quantum mechanics, and you can

see inherent in the mathematics of his theory comes out this basic idea of the quantum uncertainty, sort of falls out of the mathematics. He needed to describe the world as he saw it. Can you describe that a little bit more? Like, why did he need to include that uncertainty into these formulations in order to explain things like the little packets of light. Well, Heisenberg developed his theory of quantum mechanics and it was based on a certain kind of mathematical object called matrices that we don't have to dig into. But what he noticed about the structure of his theory was that it seemed to matter the order in which you make measurements. Like if you measure one thing, it changes the state of the system and then if you measure something else, you'll get a

different answer. And so quantum uncertainty is all about this. It's about recognizing that the order of the measurements you make matter for some pairs of quantities measuring one thing can change something else. I feel like maybe that's at the root of quantum uncertainty, which is like it's really only uncertainly with regards to two things at the same time, right? Like, it's not like something has an inherent fuzziness, but it's location. You can know its location, sort of very precisely, but then you lose out in some other quantities, right? Exactly. It's about simultaneous knowledge of specific pairs of quantities, right? And it's. really very specific. It's not like general and broad and say you can't ever know the position

very well or you can't ever know the momentum very well. You can know the position as well as you like, but it comes at a cost for one specific other quantity, the momentum. And there are other things that are paired in this way. If you dig deeper into this in physics, you discover that these things are called conjugate variables. And this came out of the mathematics that Heisenberg was using to describe his theory of quantum mechanics. Well, I'm pretty certain that we're going to get into this uncertainty and this idea of conjugate pairs and how that figures into the uncertainty that we see in quantum mechanics that tries to explain the universe. And so let's dig into those details. But first, let's take a quick break.

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And so we talked about how quantum mechanics kind of change things, and there's a certain uncertainty about it that has to do with two things being measured at the same time. That's kind of a key to the concept of quantum uncertainty, right? First of all, measurements, and second of all, two things at the same time. Exactly. And there's lots of fuzziness about quantum mechanics, but this is what we're talking about right now, is this uncertainty about simultaneous knowledge. There's a whole other issue in quantum mechanics about indeterminism,

you know, laws of quantum mechanics determining probabilities rather than outcomes. That's a whole separate issue, super fascinating, but different from quantum uncertainty. So quantum indeterminism is different from quantum uncertainty, which tells us about, like, how much we can know simultaneously about, a particle or an object. Wait, wait, wait, what? That's different? There's two kinds of uncertainties.

Well, one of them is uncertainty. The other one is indeterminism. Well, that's what you call it, but it's basically another word for uncertainty, isn't it? Like, you're not certain of what the outcome is going to be. So today we're not talking about, like, if I throw an electron at a magnetic field, I don't know if it's going to be right or left. That's a different kind of uncertainty, are you saying? So in quantum mechanics, we talk about randomness to describe predictions that are probabilistic.

If you put a particle in a box and you ask, where is it? You don't get a specific prediction the way you do for classical mechanics. You get predictions for where it's likely to be. You get predictions for the probability distribution. So that if you do it like a thousand times and measure its location, you then get a distribution of measurements that follow the predicted probability distribution. That's inherent in most of the quantum mechanics we're used to thinking about. Due to the story, it tells us about how the universe works.

It's not a particle that's following equations of motion. that are fundamental, it's the wave function or the quantum field, which is inherently probabilistic about the measurements you'll make of it. Now quantum uncertainty is related but actually quite distinct. You can think of it as another source of randomness, but it says that specific pairs of measurements are linked, that if you measure one, it makes the other one have a wider spread of probabilities. So it's like it induces more in determinacy, but it's linked to specific pairs of variables rather than the probabilistic nature of the wave function.

I see. So today we're not talking about quantum randomness at all. We're just talking about our ability to know where things are and where they're going. Yeah. We're not talking about quantum randomness except for talking about how we're not talking about it, which is the first rule of quantum readiness. That's right.

First rule of physics club is talk about what it means to be in a physics club and what a club is. But I guess the question is like, are those two things related or are they totally separate ideas in quantum mechanics, the randomness and the inability to be certain about position and velocity and things like that.

But you can have one without the other. So indeterminacy and uncertainty are different ideas because remember that there are some theories of quantum mechanics which don't have randomness and indeterminacy as inherent features. For example, Bohemian mechanics where the spread of outcomes isn't due to some randomness, but it's due to slide variations in the initial conditions of how you set up your experiment, of how exactly you put that particle in a box. And so in those theories like Bohemian mechanics, uncertainty doesn't come from randomness.

It actually comes from the measuring device being part of the experiment that's being measured, which keeps it out of total quantum equilibrium, which causes uncertainty. So you don't actually need randomness to have uncertainty in your quantum theory. Overall, though, there's a connection between uncertainty and indeterminacy in most of the theories of quantum mechanics,

though not in all. And even in the one where there is a connection, and uncertainty is a special kind of randomness because it relates to specific pairs of quantities, not a general randomness. Oh, interesting. I don't think I ever knew that. And the history of this is really fascinating,

like how it developed when Heisenberg really was a pioneer and he developed this calculational tool that allowed him to predict, you know, energy levels, et cetera. But it was a little bit opaque. Like he had these matrices and he was operating on vectors with them and people were like, all right, but what does that mean? Like, what are you talking about? What's happening?

inside. What is the electron doing? And Heisenberg was really kind of annoyed by this question and he wrote a whole paper about like what it means and what is real. And the title of that paper, I can't translate for you because nobody agrees about how to translate this one German word in the title. There's like a quantum uncertainty about one of the early papers of quantum mechanics. What do you mean? What is this title? So the title of the paper is on the enschelich content of quantum theoretical kinematics and mechanics. And German speakers say that word means. either like the visualization. Which word?

Anshulich. Which I'm sure I'm mispronouncing. Gezenheit. Thank you. And it might mean like on the physical meaning of it or the intelligibility of it or the visualization of it. This is concept in German, which we don't have an exact word for in English. But basically it's trying to get it like, what is this mean? What is quantum mechanics saying about what's happening?

It's like the zeitgeist of quantum mechanics. Yeah. And Heisenberg's attitude was like, who cares? You know, I have this mathematical tool and it makes predictions. I can predict how your measurements are going to come out. And so we're all good. People didn't really like that. And at the same time, Schrodinger developed a completely alternative view of quantum mechanics,

which is now more famous and well known, you know, the Schrodinger equation. And because he was using like a wave equation, it sort of allowed people to more easily visualize what's going on. You know, people have this like concept of a blob of probability around the atom, et cetera, et cetera. And this really kind of pissed Heisenberg off. You mean he was annoyed to philosophers

and Schroggendger? Yeah, he actually wrote in a letter once to another physicist, Polly. He said, quote, the more I think about the physical part of Schrodinger's theory, the more disgusting I find it. Whoa.

Yow. Ouch. And then he said, I consider it. And then he used this German word must. And I try to look up some translations to this German word. And again, there's a lot of uncertainty.

Some people say it means junk. Some people say it means poppy cock. Some people say it means rubbish and there's other less safe for work translations of this word as well. I think it means that Heisenberg had some saucy words for shrugden. But the point is that in Heisenberg's view, this question of like, where is the electron? Was the wrong question? In Heisenberg's quantum mechanics, there is like no true position of a particle.

There's only the outcome of a measurement. And there's only if you measure something, what's going to happen? And inherent in Heisenberg's quantum mechanics was this idea that if you measure one thing, and then measure another thing, the order matters. That, like, reversing the order will change the outcome, which is sort of confusing. Like, imagine measuring the width and the height of a table. You don't think about measuring them in a certain order

because you figure, like, well, the width and the height are things. I can measure them in what order I want. But in this case, in Heisenberg's quantum mechanics, for some things, the order does matter. Well, maybe let's break it down into a concrete example. Like, let's say that this table had quantum uncertainty about its width and its length. length. No, what would that mean? It means I can measure one but not the other, or I can

sort of measure one and sort of measure the other, or what does that mean? So it would mean that measuring its width would change its length, right? And measuring its length would change its width, which would mean the outcome of those measurements depended on the order you made them. That measuring its width and its length, or measuring its length and its width would give you different answers. Wait, it would change, like if I measure the width, it would change the length of it, like physically, or it would maybe make me less able to measure the length? It would change the uncertainty, the fundamental uncertainty of that quantity, which would affect what you measure later, yeah.

What do you mean the uncertainty? What would be the uncertainty of its length? Like, I can't predict what its length is going to be or I can actually measure it. You can still make a measurement of its length, but the outcome that measurement depends on the fundamental uncertainty of that object. That quantity is not well known. The quantity is not like defined. It depends on the inherent uncertainty.

of the object itself. And so if you affect that uncertainty, it affects your measurement. Right. So let's say I measure the table and I measure that it's 36 inches wide. What does it mean that it changes its length? That I'm going to measure it and I can't measure it or I'm going to measure it. And sometimes it's going to be 20, sometimes it's going to be 40 or it's like I'm going to measure it and it's going to be 50 when I thought it was 40.

What does it mean that it changes? You know what I mean? Like what are you trying to say? Well, what I'm saying is that it changes the distribution of possible measurements you're going to make for the length. If you measure the width first, it changes the quantum state of the particle. So now when you go to measure the length, you're measuring like a different system than you were measuring before you measured the width. You've perturbed it. You're saying it's changing the randomness of the length?

There is a random element there because the possible outcomes of the length are now determined by probability distribution and that is wider. You can think about it that way, yeah. Oh, I see. So it's like more random. Like if I measure the width of the table, then the length gets more random. Like before it could maybe be, you know, between five and six feet. But now that I measured the width, now suddenly like this magical table, it's like, whoa, now the length of it can be one inch or it can be a million inches. Yeah.

And it's very counterintuitive when you think about a table because, first of all, a table is a classical object doesn't have any of these properties. And because we think of a table as having like specific length and width. And that's also true of quantum objects, right? This uncertainty only applies to very specific pairs of things that you can measure, not to everything. So for a particle, for example, it applies to position and momentum, not to like its exposition and its Y position. You can measure something in X really precisely and then measure it in Y really precisely with no problem.

And the order doesn't matter. But if you measure its position in X really precisely, it messes up your potential knowledge of its momentum in X. I see. But I guess for our magical table, I can still measure the length, right? Like if I measure the width, that doesn't mean I can't measure the length. I can still measure the length. It's just going to be extra random. So that if I had like a million of these magical tables, I'm going to think the length is all over the place.

Yeah, that's exactly right. That means that there is an element of randomness to the idea of uncertainty. Like, how could you have uncertainty without randomness? Yeah, that's a good point. Okay, so that's the magical table. And if quantum uncertainty applied to that table, that's how it would be for the table. But now let's maybe take a more physical example. You were talking about precision and momentum.

Yeah, because it's important to understand quantum uncertainty doesn't just apply willingly to everything. It doesn't say the whole universe is fussy, no matter what. It says specific pairs of things can't be known at the same time. So you can know the X and the Y of a particle, but you can't know it's X and its momentum also in X. Wait, I can't know it or I can't measure it because like the table I can measure the width and the length, right? Or are you saying that if I measure the width, I can measure the length. You can always measure it. But in the case of the table, if you measure the width, you get a number.

You measure the length, you get a number. But now you no longer know the width. Because you messed up the width when you measured the length. These two things are connected. I see. I think maybe what you mean by no is you actually mean predict. Like if I measure the width, then it makes it harder for me to predict what the length is going to be on this table. Because I can know what the length of the table is.

I can measure it, right? That's how I would know it. But it's more about like being able to know it before you measure it. Well, I'd say when you measure it, you measure it with some uncertainty. Even if you know it, you know with some uncertainty. There's like error bars on it. Oh, it's about error bars. That's different though, isn't it?

Well, you know, it depends on how you interpret the error bars and the randomness, but like repeated measurements which probe that probability distribution will give different outcomes. It doesn't fundamentally have a specific length that has a distribution. And if you measure it multiple times, you'll get different answers according to the width of that distribution. Oh, I see. I feel like you're saying kind of like the table has a length and width. But then there's our measurement of the length and width, which might not be what it's real length and width is. In the case of the magical table, which follows this quantum uncertainty, though obviously

tables don't really, right? If we say that it has this quantum uncertainty attached to the length and the width, then the length and the width are not determined simultaneously. It's not that it exists and it's written in a gold tablet by God somewhere. We just don't have access to seeing it. It's just that it's not defined. Oh, I think I see what you're saying. I think that if I measure this table with like a super precise ruler and I measure the width and I get that it's three feet wide and I'm super certain about that that means that no matter what I do to measure the length I have to assign a certain uncertainty

or a certain error to it. I might measure the length of the table and might say, oh, I measure it to be six feet, but in the back of my head, I have to be like, well, that's probably not actually six feet. Is that kind of what you mean by uncertainty? Yeah, and then if you go back to measure the width, you're going to get a different answer than you did before

because measuring the length has now changed the width. But no, it's still the same. No, it's not still the same table, right? Because you've made a measurement to it and measuring things changes them. Oh, but what if I measure at the same time? Yeah, great question, but you can't do that, right? You make a measurement of a quantum system, you can measure a thing, right? And these two things, you can't measure simultaneously. Oh, see, I feel like that's another concept then in quantum mechanics. Why can't I measure this table at the same time? In Heisenberg's quantum mechanics, the way you make a measurement is that you operate on that quantum state. Operating on the quantum state will change it. And you can't do two operations. simultaneously.

Maybe for those of us that are not familiar with quantum states, what does that mean? That means that like in a system, there are some variables that you just can't measure at the same time. That's right. All measurements have to be made in a certain order because potentially measurements could mess up later measurements. In some cases, they don't, right? Like you can measure the X and then you can measure the Y.

And the answer you get for Y doesn't depend on whether you already measured X. But if you measure X and then you measure momentum in X, then you will get a different answer and the order does matter. Like measuring X and then momentum, or measuring momentum and then position in X will change the answers that you get. I see. It's kind of part of the magical properties of my table. Like a regular table, I can definitely get two people to measure its width and the length at the same time. But a quantum uncertain table, you just can't.

You can only do one at a time. Yeah. And it's sort of hard to understand that about a table because it doesn't seem to make any sense. And X and Y seem to be orthogonal, right? And that's why I suggested it as a ridiculous example because it's very counterintuitive. and quantum mechanics is counterintuitive in that way, but not quite as counterintuitive. I mean, you can't get some understanding of why measuring one thing messes up another.

If you think more specifically about, for example, momentum and position instead of like table lengths and widths. Right. I just think that, you know, for most of us saying that's what the math says and it's magic, it's pretty much the same thing. It's magimatical. Yeah, it's right. It's mathematical. There you go. I mean, you can think about it in terms of like measuring a particle, right?

Say you want to know its location. How would you actually make that measurement? Well, in order to measure the location of particle, you've got to like bounce something else off of it. There's no passive observing of the universe. You've got to like bounce a photon off of it, for example, to see where it is. And if you want to know its precision really, really precisely,

then you need a really high energy photon because high energy photons have short wavelengths. And so they can tell you information about really small distances. but if you bounce a really high-energy photon off of your electron, then you're going to totally mess up its momentum. Its momentum is going to be very different now than before you measured it. So if you go off to measure its momentum, you're going to get a different answer than if you hadn't measured the position.

That's if you try to do it one after the other, but I'm just throwing out an idea. What if you, like, throw a photon at it, and you measure how the photon bounces, and then that tells you both things at the same time, maybe? Right? Like if I catch a baseball, I know it's position and how fast it was going.

Yeah, and you can do that for a classical object. And you can know simultaneously multiple things about quantum objects, just not some things, right? Just in this case, like not position and momentum simultaneously. And the reason that you can't has to do with how this information is encoded in the particle, which I think we can understand without getting too mathematical. All right. Well, let's dig into some of this mathematics or not math physics, I guess. And the idea of wave and the wave function, which is I think we're,

where we're going with this. Let's dig into that waviness. But first, let's take another quick break. Your entire identity has been fabricated. Your beloved brother goes missing without a trace. You discover the depths of your mother's illness, the way it has echoed and reverberated throughout your life, impacting your very legacy. Hi, I'm Danny Shapiro. And these are just a few of the profound and powerful stories I'll be mining on our 12th season of Family Secrets. With over 37 million downloads, we continue to be moved and inspired by our guests and their courageously told stories. I can't wait to share 10 powerful new episodes with you, stories of tangled up identities, concealed truths, and the way in which family secrets almost always need to be told. I hope you'll

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an Iheart women's sports production in partnership with deep blue sports and entertainment on the Iheart radio app, Apple Podcasts, or wherever you get your podcasts. Presented by Capital One, founding partner of IHart Women's Sports. All right, we're talking about the hairy topic of quantum uncertainty and all of the uncertain details about it. down to the nitty-gritty here. Now, Daniel, you think that maybe a good way to explain this is using waves and specifically sound waves, right, as maybe they relate to the wave function of quantum particles.

Yeah, if you're trying to think about position and momentum of particles and how they're like encoded in the mathematical description of the particle in quantum mechanics, it's really helpful to think about analogies we have in the classical world that are a little bit more intuitive. And there actually is one that a lot of people are familiar with. And that's sound waves and songs and how words and music can. be broken up into very specific frequencies. All right.

Let's dig into it. How is a quantum uncertainty like a song? Well, think about like your equalizer on your stereo. When you hear songs, they have like a bass and a treble and whatever and there's high frequencies and low frequencies. And your equalizer is telling you like how much bass is there or how many low frequency sounds are there or how many high frequency sounds are there. Or more like how strong the song is in this frequency range, right?

Exactly. So we're going to think about the relationship between. frequencies, pure notes of specific frequencies, and how you can use them to build up different kinds of sound, that's going to give you a feeling for the physical reason why there are some specific quantities that you can't know at the same time, how they're linked by quantum uncertainty. So start with a pure note, like an opera singer singing high C. That's just one frequency. On your equalizer or on a spectrograph, it's going to give you a single spike at that frequency. And there's very little uncertainty in the frequency, right? You hear the sound, you know the

frequency, there's only one frequency to the sound. Now think about the corresponding quantity, the shape. If she hits the high C, then where is that sine wave? That sign wave is everywhere in the room. It goes up and down. It doesn't really have a shape. It's a sign wave everywhere. It fills the room or the opera house or whatever it is. So you know a lot about the frequency of her note. The spectrograph is a spike, but the sound wave itself is very spread out in position. It's filled the whole room. It's everywhere. Well, what if we wanted our opera singer? to create a sound that you could only hear in part of the room. And you know that you can get different sounds in different parts of the room.

If you take advantage of how they can interfere, that's why they very carefully designed acoustics in opera houses, etc. But we can get our singer to make a sound that you can only hear in one part of the room. Like in only one spot can you hear it. In the other spots, it'll be totally silent. She can do this if she adds more frequencies, right? So if she has just one frequency, just the high seat, it's everywhere. Now add another singer singing a different.

frequency and those two sign waves have different frequencies and so they'll cancel out in some places of the room and add up in others that's constructive and destructive interference at a third singer with another frequency and you can shape the total effect further the more frequencies you add the more you can shape that sound and if you add an infinite number of singers crowded onto that stage you can make any sound shape you want in the room including a very very narrow spike so that the sound can only be heard at one spot in the room. So in this scenario, the sound has a huge spread of frequencies,

but a single very well-determined location. All the sound is in one place. So maybe now you see the trade-off. Either you can have a single frequency, the one high C note, but the position is very broad. It's anywhere in the room. Or you can have a broad range of frequencies, lots of singers on the stage,

but the position is now very, very narrow. narrow. So because of the wave-like nature of sound, you can't have narrowness in both frequency and in location. Those two things are inherently linked by the nature of the physical process of sound. You can't use a single frequency to create a narrow spike, a sound that exists only one location in space. It's either narrow frequency and broad position or broad frequency range and narrow position. Frequency and position are conjugate variables. They're linked in that very special way. And that also applies to quantum waves. For a particle in a box, the frequency of the wave function tells you its momentum. So if you want your particle to have little uncertainty

in position, you have to use lots of frequencies, lots of possible momentum which add up to give you that spike. And because you have lots of possible momentum now in your wave function, that means a large momentum uncertainty. So small uncertainty position requires a large momentum uncertainty. And on the other direction, if you want your particle to have little uncertainty in momentum, then you can only use a narrow range of frequencies, which means you'll get a very broad blob in position. You can't build a quantum wave function out of just a few frequencies that's also localized in position for the same reason that the opera singer can't sing a single note and have it be localized in the room. Yeah, I think that maybe a way that I've seen it explain is a little bit talking about like the width of things.

Are you saying it can be described by wave functions, right? Like something that has like a really wide wave means that it's really fuzzy and you don't know quite where it is. Whereas something that is really narrow, you can sort of know its position, but it's also going really fast maybe. Exactly. For something you know really, really well, then its wave function is going to be super duper narrow like a spike. But to build a spike in terms of frequencies in terms of like various possible mementa requires a very large number of them. You need like lots of them to add up and cancel out in just the right way to give you that spike. Whereas if you want something really big and fat as a blob, then you need fewer different frequencies to add up to give you that big fat blob, something that's very uncertain.

So a wave function that's really narrow needs lots of different frequencies to add up, which means lots of different possible momentum because frequency and momentum are the same for a particle, which means a lot of unscounter. certainty in his momentum. Whereas if you have a lot of uncertainty in his position, you only need a few frequencies, which means less uncertainty in its momentum. That gives you a little bit of the flavor of why position and momentum have this special relationship. Quantum uncertainty is all about very specific pairs of things you can measure that have this relationship. It's not just like any two things that you measure. Right. And so maybe it might help to get into some of these other things. So you're saying that position and momentum are linked together in this quantum uncertainty because of its wave nature, right?

For example, if you take to measure the velocity of a wave, somehow it's related also to its frequency, which that's where the fuzziness maybe comes from. So maybe talk about some of these other variables in quantum mechanics that are also linked together by uncertainty. Yeah, and a tiny little quibble there is that it can be explained in terms of like Schrodinger wave mechanics, but Heisenberg can also explain it without any waves at all.

He has a completely different formulation of quantum mechanics that uses matrices. And for those of you who like no matrix mechanics, you know that like multiplication of matrices doesn't commute. Like it matters what order you multiply things by with your matrices. So like it comes out of quantum mechanics no matter what mathematical formulation you use, matrices or waves or whatever. It's like really deep in there.

But you're right. It's not just position and momentum that this affects. There's lots of other things that are paired. Another famous example is energy and time. Of what? Like of a particle. So for example, a particle might have. a specific mass and that affects how long it lasts.

So for example, an electron which lasts forever has a very specific mass. Every electron out there has the same mass exactly because electrons live for an infinite number of years. But if you have particles whose lifetime is shorter, there's a quantum mechanical uncertainty to how long they're going to live, then their mass is more uncertain. So for example, a top cork, it might be 173 GV, might be 165, might be 181, there's a huge huge variation there in the possible masses the top cork would have because it doesn't live for very long.

So when you say like it lasts, meaning like it might at any point break down into other things, right? Lower energy things. And so it has a lifespan. And you're saying like how long we expect it to be around whole is tied to its mass. Exactly. Electrons, we think their lifetime is basically infinity. You could wait an infinite number of years.

The electron is just sitting out there in space would still be an electron. Top cork lasts for like 10 to the minus. 23 seconds. So there's a lot less uncertainty about how long a top quark is going to be in the universe just because its lifetime is shorter, which means there's more uncertainty about its energy. And that comes down to uncertainty about its mass. So there's like a whole distribution of possible masses you could measure for a top quark of masses that it actually has. It's like a fundamental uncertainty in like how much energy there is in this thing because there's very little uncertainty about how long it's going to last. It's not going to last very long at all.

It's not just like uncertainty about where it is and where it's going. It's like uncertainty about it's actual like being, right? Like what it is. How much of it is there? Exactly. And there's a really deep connection between these two variables, energy and time, position and momentum. We talked about this philosophical connection in another episode. It all comes out of this theorem, Nother's theorem, which tells us like relationships between symmetries and conservation laws.

We know the fact that space is the same everywhere in the universe means momentum is conserved. There's another connection there between position and momentum. Nother's Law also tells us that energy is conserved if space is the same across time. There's a connection between energy and time. And so you see that there's a really deep connection between these variables. Some of these things are just sort of fundamentally paired physically. Position and momentum, energy, and time. There's also weird properties of the spins of particles that have these kind of relationships.

What do you mean by spin? So particles can have quantum spin, right? spin up or spin down. But it depends on how you measure it. Like if you try to measure the spin of a particle, you can do so by putting it in a magnetic field and it'll align one way or the other way. Well, that's a spin along one axis, the axis of that magnetic field. You could also try to measure its spin like we're using a perpendicular setup, like take another magnet and rotate at 90 degrees, try to measure its spin in another way. So you have like spin in X and spin in Y. Turns out these two things are related. You can't know the spin of a particle

in two directions simultaneously. Like you measure its spin in X, that will mess up its spin in Y. If you measure it spin in Y, that'll mess up its spin in X. These two things are linked the same way position and momentum are linked. Right.

Well, by mess up, you mean like it changes its probability, right? Like what it can be. Yeah, there's this famous experiment where they take a bunch of atoms and they put them through a magnetic field so they're either spin up or spin down. Then use a fancy device to filter all them out. So they like only take the spin up ones.

Then they send this through the experiment again, but rotated. So now they're measuring it like along another axis. And then they send it back through the first device again. They're now both spin up and spin down. So you've taken a beam that are only spin up. You measure it in an orthogonal way that messes up your original distribution in the first direction.

So measuring in one direction messes up the measurement in the other direction because these two things are linked. Fundamentally, you can't know them simultaneously. It kind of feels like maybe these things are paired together by kind of the constraints that measuring those things have. It's impossible to measure the spin of a particle in the up and down direction and in the side to side direction at the same time, and therefore those two things are linked. Yeah, those two things are definitely linked. You know, why these two things are linked and not other two things is a really interesting and deep question. I think that's

fundamentally the question of the episode. Like, why is there any quantum uncertainty? In classical physics, all these things are totally separate and independent. And quantum mechanics has like linked some certain pairs of quantities together and said, there's a limited information in these things. And, you know, the philosophical answer to that question is a little bit slippery. You know, like we have this mathematical description that we can use to predict all these wonderful quantum experiments. And those mathematics have this uncertainty built into them inherently. So you can then look at that theory and say like, well, why? You know, and oh, it's matrix mechanics or here's a frequency analysis of a wave function. Fundamentally, that's not really a satisfying

answer because it doesn't tell us like why we don't live in a universe without this uncertainty. Why couldn't you have built a classical universe without it? Why did the designers of the universe, whoever they are, give us a universe with this property instead of other properties? These things are not, they're tied to each other, but they're not tied across different categories. Like, for example, you can know the position of a particle and its mass and it's spin along the up and down direction, right?

Perfectly, those three things. Pick one in each category and you can know it as well as you like. All right. So then it sounds like we haven't really answered the question of the episode. The answer to the question of the episode is we don't know, right? It's a feature of our universe the way like the speed of light is a feature of our universe. We observe it. We can build mathematical theories to describe it. We can then scratch our heads and say, hmm, does it have to be this way? And we don't have an answer to that. We don't know if it would have been possible to build a universe that was classical. We actually talked about that on a recent episode. Philosophically and fundamentally and theoretically, you might have been able to build it. classical universe without any quantum uncertainty but ours seems to have this feature but i think as you said you know it's it's a process right we're in the middle of this process and it might be that in the future we do know why the speed of light had to be a certain velocity right yeah and in the future and we understand quantum gravity and string theory there might be a simple reason like oh the universe

has this property and therefore you have quantum uncertainty or the universe is this way and therefore the speed of light is what it is but you know that's just going to generate more questions Right, whatever property that is that gives rise to quantum uncertainty, we're then going to ask, well, why that property? So basically, it's a never-ending story. I hope so. Then I'll keep having a job. Well, so many people want you to do it.

Well, I guess you can do it. You can pay yourself, I guess. It's still a job if you pay yourself, isn't it? You can be a self-employed physicist. Yeah, there's lots of great self-employed physicists out there. What if I just say that the answer is 42? Is there a universe out there where the answer is 42? The answer to what question?

I don't know. The answer of why the speed of light is the way it is, it's because the number 42. I don't know. I'd love to live in a universe where that answer made sense for that question, but I don't think that's this universe. I wonder if in that universe, they have the hitchhiker's guide to the galaxy. Or I guess in an infinite multiverse, there is a universe where the answer is 42 and also Douglas Adams was right. Yes.

And it all makes sense. Yes. And then in that one, you'd be out of a job. But not cartoonist because we can always draw cartoons of the number 42. That's right. And cartoonists can always be self-employed. All right. Well, hopefully that gives you a sense of how this universe still has a lot that can't be explained.

You know, there's these fundamental uncertainties in it and what we can and cannot measure at the same time. It is sort of a magical table kind of for now, right? It is. We can describe it mathematically and we can give answers to like why the mathematics works this way. and why these things bubble up from the mathematics, but we don't fundamentally know why we live in a universe with quantum uncertainty. Yeah, and if you eat out of a magical table,

is that a good way to control your diet? If you don't know the length and width of your table, it's a good way to make a big mess on the floor. Yeah, there you go. You might be sitting down your food in empty space. All right, well, we hope you enjoyed that. Thanks for joining us. See you next time.

For more science and curiosity, come find us on social media where we answer questions and post videos. We're on Twitter, Discord, Insta, and now TikTok. And remember that Daniel and Jorge Explain the Universe is a production of IHeartRadio. For more podcasts from IHeartRadio, visit the IHeartRadio app, Apple Podcasts, or wherever you listen to your favorite shows. that is a cold case that has DNA. Right now, in a backlog, will be identified in our lifetime. On the new podcast, America's Crime Lab,

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And on my podcast, Good Game with Sarah Spain, I'm breaking down the players, the predictions, the pressure. And, of course, the honey deuses, the signature cocktail of the U.S. Open. The U.S. Open has gotten to be a very wonderfully experiential sporting event. To hear this and more, listen to Good Game with Sarah Spain, an Iheart women's sports production in partnership with Deep Blue Sports and Entertainment

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