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Speaker 1: Hey, quick announcement everyone, we have just joined TikTok, So

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Speaker 1: head over there and follow us to see videos of

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Speaker 1: Daniel asking and answering science questions. All right, enjoy the pod.

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Speaker 2: Hey Daniel, does quantum mechanics really explain reality?

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Speaker 1: I mean I think so, even though it's pretty weird.

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Speaker 1: Are you sure? Well? Lots of experiments we've done over

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Speaker 1: the last century.

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Speaker 2: See yes, Yeah, But like, how can you be certain?

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Speaker 3: You know?

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Speaker 2: I thought quantum mechanics is everything is uncertain.

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Speaker 1: Well, we're very certain that quantum mechanics is uncertain, but

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Speaker 1: only about certain things.

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Speaker 2: I'm pretty certain that makes no sense.

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Speaker 1: I think it's curtains for certainty.

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Speaker 2: Are you sure about that?

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Speaker 1: Now? I'm not sure about anything.

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Speaker 2: I'm welcome to being a non physicist.

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Speaker 4: Hi.

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Speaker 2: I'm poor Hendrick Cartoonis and the author of Oliver's Great

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Speaker 2: Big Universe.

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Speaker 3: Hi.

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Speaker 1: I'm Daniel. I'm a particle physicist and a professor at

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Speaker 1: UC Irvine. Or at least I was certain of that

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Speaker 1: a moment ago.

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Speaker 2: Yeah, Now you're not sure that you have a job,

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Speaker 2: so he might have said something to get you fired here.

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Speaker 1: Yeah, that's one of those questions you shouldn't ask because

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Speaker 1: it might change the answer.

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Speaker 2: I thought ye had tenure that prevented them from firing you.

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Speaker 1: There are still limits to what we can do even

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Speaker 1: if we have tenure.

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Speaker 2: But anyways, welcome to our podcast Daniel and Jorge Explain

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Speaker 2: the Universe, a production of iHeartRadio.

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Speaker 1: In which we test the limits of our understanding of

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Speaker 1: the universe. How certain are we that the universe works

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Speaker 1: in a different way on a tiny scale, that there

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Speaker 1: are tiny quantum particles fluctuating in and out of existence,

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Speaker 1: that when we zoom down to the universe at its

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Speaker 1: smallest scale, different rules apply. On this podcast, we pushed

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Speaker 1: all those limits and we try to answer all of

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Speaker 1: your questions.

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Speaker 2: That's right, because it is a wonderful and amazing but

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Speaker 2: yet also a very mysterious universe that seems kind of

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Speaker 2: random at times, but also seems like a giant clock

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Speaker 2: that seems to be working precisely as it's supposed to be.

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Speaker 1: And the big goal of physics is not just to

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Speaker 1: reassure us that the universe works the way our intuition suggests,

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Speaker 1: but to discover the truth. Science is a knowledge building mechanism, right,

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Speaker 1: It's a way to figure out how the universe actually works,

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Speaker 1: even if it's deeply in contradiction with the way we

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Speaker 1: thought it worked.

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Speaker 2: Wait, I thought philosophers thought that you can never uncover

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Speaker 2: the real truth of things. It's impossible to be completely

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Speaker 2: certain about the truth.

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Speaker 1: Philosophers don't even agree about what you mean by the

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Speaker 1: real truth.

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Speaker 2: Well, I see, it's about I guess vocabulary.

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Speaker 4: Man.

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Speaker 1: Every philosophy argument in the end comes down to vocabulary. Like,

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Speaker 1: what do you mean when you say vocabulary? Anyway?

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Speaker 2: Oh, you can get a few inception levels deep into

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Speaker 2: this discussion.

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Speaker 1: What do you mean by what do you mean exactly?

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Speaker 1: What do you mean?

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Speaker 2: What is meaning?

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Speaker 1: Yes? What is meaning? What is a question?

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Speaker 2: Anyway? What is a what?

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Speaker 1: And I'd laugh at all these jokes, not to laugh

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Speaker 1: at philosophy, but out of deep respect for the way

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Speaker 1: philosophy forces us to figure out what we mean by

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Speaker 1: our questions? What is it? In the end, we're asking

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Speaker 1: what kind of answers do we expect? All this kind

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Speaker 1: of stuff? These are hard questions.

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Speaker 2: Wait, does that mean that philosophers don't think you actually

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Speaker 2: have a job as a physicist?

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Speaker 1: I mean, philosophers definitely recognize the physics is building a

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Speaker 1: set of facts, and those facts like power the world.

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Speaker 1: There is a reason that technology works, for example, But

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Speaker 1: exactly what it means about the universe, what is the

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Speaker 1: real story? What is real depends a little bit on

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Speaker 1: the questions we're asking, and it's not even clear that

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Speaker 1: there is an objective truth about it. It might just

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Speaker 1: be our perception of it answers to the kind of

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Speaker 1: questions we would ask.

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Speaker 2: Well, I guess the elusive quests for the real truth

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Speaker 2: of the universe is kind of what signs. It's all about,

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Speaker 2: you know, even if we don't get there, it's all

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Speaker 2: about trying to get there.

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Speaker 1: Exactly, and we can all work together to get there,

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Speaker 1: even if we're not in agreement about what there is.

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Speaker 1: Some of us think we are revealing the true underlying

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Speaker 1: mechanism of reality, something that like alien scientists would also

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Speaker 1: be revealing. Other folks don't care about that. They say, hey, look,

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Speaker 1: we're just getting something that works, something that predicts the

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Speaker 1: outcomes of experiments and lets us build technology. Who even

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Speaker 1: cares if it's real or what aliens would think about it.

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Speaker 1: You can totally disagree with the lofty philosophical goals of

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Speaker 1: science and still work hand in hand and get concrete results.

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Speaker 2: I feel like maybe that'sis's favorite part of the job.

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Speaker 2: It's arguing about the job, you know.

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Speaker 1: I think that there's a division early on, and people

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Speaker 1: who like to argue about it more end up in philosophy,

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Speaker 1: and the people who just want to like get in

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Speaker 1: the lab and learn stuff about the world end up

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Speaker 1: in physics.

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Speaker 2: You just want to get in there and blow stuff.

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Speaker 1: But there's always this tension, right. The juiciest questions in

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Speaker 1: physics are the ones that when we get the answer,

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Speaker 1: we go, hmmm, well, but why is it like that?

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Speaker 1: What does that mean about the world. The best physics

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Speaker 1: questions have philosophical implications.

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Speaker 2: Yeah, and so there's a lot of uncertainty about what

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Speaker 2: we do know or what we don't know, or what

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Speaker 2: we can know about the universe. But even deeper than that,

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Speaker 2: there seems to be a uncertainty about the universe itself.

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Speaker 1: Something shocking, something very difficult to understand about the quantum

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Speaker 1: picture of the world is that the world itself might

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Speaker 1: be limited in its precision, not just in our ability

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Speaker 1: to measure it or to extract that knowledge, but there

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Speaker 1: could be a fundamental fuzziness to the universe, a lack

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Speaker 1: of determination about reality.

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Speaker 2: It's not just me getting older and needing reading glasses.

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Speaker 1: It's that also. Yes, those two effects are combining.

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Speaker 2: I mean, have quantum vision.

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Speaker 5: Now.

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Speaker 2: I think we should start that company. Quantum laser surgery. Yeah,

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Speaker 2: quantum reading glasses. Yeah, I'm parably the only coast of dollars,

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Speaker 2: so we make a killer profit.

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Speaker 1: You can only read one word at a time.

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Speaker 2: But anyways, Yeah, there seems to be this interesting nugget

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Speaker 2: of strangeness to quantum mechanics which tries to explain the

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Speaker 2: entire universe. And so today on the podcast, we'll be

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Speaker 2: asking the question why is there quantum uncertainty? I feel

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Speaker 2: like we're asking a question about uncertainty.

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Speaker 1: We are uncertain about why there's uncertainty.

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Speaker 2: That's what I mean.

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Speaker 1: It's meta uncertainty.

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Speaker 2: We get very meta here. Well, if it helps, I'm

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Speaker 2: pretty sure. I'm a cartoonist, that's one thing I know.

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Speaker 1: Yeah, Well, this is exactly the kind of difficult philosophical

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Speaker 1: question because you know, I even sure like what kind

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Speaker 1: of answer we're looking for, Like, are we hoping to

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Speaker 1: reveal that the universe could have only ever been this way?

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Speaker 1: Or to argue that look, we could be in lots

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Speaker 1: of different universes. This one happens to have this quantum uncertainty.

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Speaker 1: You know, there's lots of different ways to attack this

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Speaker 1: sort of philosophical problem.

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Speaker 2: Well, hopefully it's more than just a philosophical problem, right, Eventually,

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Speaker 2: the hope, the goal is to find kind of physics,

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Speaker 2: math based answers to these questions, isn't it to me?

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Speaker 1: I think the sort of highest level process would be

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Speaker 1: go out and look at the universe, see what it's like,

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Speaker 1: boiling that down to like a few essential facts, build

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Speaker 1: a theory that describes how that works, why that works,

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Speaker 1: the mathematics to describe it, and then look at that

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Speaker 1: theory and ask philosophical questions like did it have to

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Speaker 1: be this way? Could you have a universe that was different?

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Speaker 1: Could we have built a different theory of the universe

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Speaker 1: that didn't have this feature or that feature about it?

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Speaker 1: So in the end, it's mathematical, but it's really rooted

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Speaker 1: in explaining what we see out there in the universe.

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Speaker 2: But couldn't you answer those questions you just asked in

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Speaker 2: a mathematical way. Maybe in the future. We don't know

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Speaker 2: for certain they can't be answered, right.

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Speaker 1: We don't know for certain they can't be answered. I

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Speaker 1: think a great analog that's going to help us understand

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Speaker 1: this question today is the question of like the speed

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Speaker 1: of light. You know, we live in a universe where

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Speaker 1: the speed of light is constant for all observers, and

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Speaker 1: if you start from that, you can build special relativity

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Speaker 1: and you can explain the whole universe. But you have

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Speaker 1: to start from that assumption. That's something we've seen in

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Speaker 1: the universe, something we know is true, we've measured it,

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Speaker 1: we've done the experiments, we've now coded it into our theory,

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Speaker 1: but we don't have an answer for why that is true.

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Speaker 1: And one day maybe people will have a deeper understanding

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Speaker 1: of the nature of space from which that bubbles up.

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Speaker 1: You might be able to explain that someday, but currently

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Speaker 1: we don't have an answer to why. It's just sort

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Speaker 1: of like the foundational assumption that we need to explain

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Speaker 1: everything we see in the universe.

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Speaker 4: Right.

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Speaker 2: Well, as you said, hopefully maybe someday somebody will answer

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Speaker 2: this deep question, but that person doesn't seem to be

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Speaker 2: out there, because Daniel went out there and asked this

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Speaker 2: question of folks and we got some pretty interesting answers back.

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Speaker 1: Yeah. Thanks, everybody who answers these questions as wacky and

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Speaker 1: as crazy as they are, without having any chance to

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Speaker 1: prepare yourself. Really appreciate your participation, and I'd love to

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Speaker 1: hear your voice on the podcast. That's right, I'm talking

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Speaker 1: to you. We haven't heard from you yet, and we

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Speaker 1: want your voice on the air.

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Speaker 2: Well, there's a bunch of people who have heard we

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Speaker 2: have heard from BOM. Right, you just totally snubbed them,

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Speaker 2: I feel.

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Speaker 1: I said, thanks to all those folks.

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Speaker 2: Also, Oh, you meant the other people.

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Speaker 1: It's a shockingly small group of people who volunteer for

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Speaker 1: these which is why you hear the same voices over

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Speaker 1: and over again.

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Speaker 2: Oh, I never noticed. You didn't have to tell me.

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Speaker 1: I should have maintained your quantumuncertainty.

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Speaker 2: She'd kept that a mystery of the universe. But anyways,

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Speaker 2: think about it for a second. Why do you think

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Speaker 2: there is quantum uncertainty in the universe. Here's what people

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Speaker 2: had to say.

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Speaker 5: I guess that both because we can't really have an

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Speaker 5: accurate measurement on that very timey scale, and because measuring

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Speaker 5: a quantum process interferes on that process.

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Speaker 3: There's quantum uncertainty because when we measure a particle, it

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Speaker 3: changes what the particle's doing, and when we're not looking

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Speaker 3: at the particle, we never quite know what it's doing

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Speaker 3: without measuring it, which changes the state and the particle.

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Speaker 3: So we can never quite know exactly what a particle's

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Speaker 3: doing without changing the state.

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Speaker 4: I know that if you measure something, it falls into

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Speaker 4: the wave function collapses, and you fall into one of

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Speaker 4: the states. I guess is uncertainty, because there's a wave function.

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Speaker 2: All right, and pretty deep answers here, I'm pretty certain

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Speaker 2: of that.

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Speaker 1: Yeah, a lot of these folks are developing like a

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Speaker 1: microphysical picture, like what's happening when you make a measurement?

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Speaker 1: What prevents you for being able to measure things super

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Speaker 1: duper precisely? And that's helpful, but I think it's only

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Speaker 1: really part of the story.

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Speaker 2: All right, Well, let's dig into this topic, and let's

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Speaker 2: start with the basic question, Daniel, what is quantum uncertainty?

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Speaker 1: There's so many weird things about quantum mechanics that we

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Speaker 1: could dig into for hours and hours, but I just

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Speaker 1: want to zoom in on this one thing, this quantum uncertainty,

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Speaker 1: which is different from other weird aspects of quantum mechanics,

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Speaker 1: and quantum uncertainty is a very specific thing. But let's

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Speaker 1: start off by talking about classical physics, because quantum uncertainty

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Speaker 1: is basically a rejection of that. So classical physics, the

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Speaker 1: physics of Newton, and even the physics of Einstein, says

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Speaker 1: that we live in a universe where you can know

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Speaker 1: everything about an object, like take a particle or a

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Speaker 1: banana or whatever. You can know everything about its location,

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Speaker 1: you can know everything about its velocity, you can know

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Speaker 1: its entire history that it moves in these smooth paths.

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Speaker 1: It always has a position, always has a velocity that

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Speaker 1: to reality, there is no fuzziness that there's an exactness

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Speaker 1: to this information, and you can know all of it

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Speaker 1: simultaneously because it's well defined. That's the classic physics picture

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Speaker 1: of like how things move in the universe. Right.

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Speaker 2: That's sort of like maybe a good way to explain

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Speaker 2: it is basically like up to high school physics, right,

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Speaker 2: like you know, predicting where the baseball that you throw

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Speaker 2: is going to land, or you know how things move

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Speaker 2: you shake him orver you swing them. That's classical physics, right,

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Speaker 2: Like you can predict where the things are, what things

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Speaker 2: are going to do. Like you in those exams in

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Speaker 2: high school, there's no room for uncertainty, Like there's a

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Speaker 2: right answer, there's a wrong answer.

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Speaker 1: That's right, and there's an exactness to the answer, and

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Speaker 1: even well past high school physics, I guess, depending on

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Speaker 1: your high school you know, Einstein's physics is also classical

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Speaker 1: in that sense. I mean, Einstein was a huge revolution

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Speaker 1: compared to Newtonian physics. Relativity is a whole other brain twister.

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Speaker 1: But Einstein's picture of the universe fundamentally is the same

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Speaker 1: in that there's no uncertainty. He imagined you could know

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Speaker 1: where a particle is that had an exact position, and

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Speaker 1: you could simultaneously know its position and its momentum and

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Speaker 1: all sorts of other things about.

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Speaker 2: It, even like light.

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Speaker 1: Yeah, the classical theory of electrodynamics, you know, which comes

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Speaker 1: from Maxwell and inspired Stein to develop relativity, didn't have

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Speaker 1: any sort of quantum uncertainty to it. Photons had an

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Speaker 1: exact position, all.

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Speaker 2: Right, So then that's Einstein and newtune. But then around

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Speaker 2: the beginning of the nineteen hundreds they figured out that

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Speaker 2: things are kind of strange and weird.

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Speaker 1: Yeah, basically, quantum mechanics looks at that and says, yeah, no,

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Speaker 1: you can't know all of these things simultaneously. And the

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Speaker 1: history of it's really fascinating. It comes around in the

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Speaker 1: nineteen twenties when people were trying to understand how the

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Speaker 1: atom worked and what was the picture of microscopically of

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Speaker 1: the electron and the nucleus. Was this sort of like

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Speaker 1: an orbital picture like bor was suggesting, or was there

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Speaker 1: something funnier and more complicated going on? And it was

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Speaker 1: really Heisenberg of the famous Heisenberg uncertainty principle, who developed

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Speaker 1: the sort of first theory of quantum mechanics that describe

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Speaker 1: how the atom worked in a way different from boor

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Speaker 1: that had like a fundamental different mathematics underneath it.

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Speaker 2: I feel like, or I seem to recall that initially

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Speaker 2: quantum mechanics didn't have this idea of uncertainty to it, right,

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Speaker 2: Like didn't it start with people just noticing that like

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Speaker 2: light case and packets, or that electrons wouldn't you know,

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Speaker 2: fly off unless you met certain minimum energy requirements and

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Speaker 2: things like that. There's no uncertain to your fuzziness to

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Speaker 2: it at the beginning.

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Speaker 1: Was there the roots of quantum mechanics are exactly as

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Speaker 1: you described. You know, there's like the black body radiation problem,

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Speaker 1: and there's the photoelectric effect that we dug into on

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Speaker 1: the podcast several times, and you're right, it was actually

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Speaker 1: Einstein who figured that out.

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Speaker 4: Right.

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Speaker 1: You connected the ideas of Plank with the experiments that

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Speaker 1: we were seeing and saw that light had to come

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Speaker 1: and packet, so it can only interact with a single electron. Absolutely.

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Speaker 1: So those really those core ideas which then led to

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Speaker 1: the formulation of quantum mechanics. Those didn't have uncertainty in them.

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Speaker 1: That wasn't an essential ingredient.

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Speaker 2: Right, That's where the word quantum comes from, right, like quanta,

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Speaker 2: like little quantity, little countable things.

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Speaker 1: Right, you can have one electron or two electrons or

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Speaker 1: nine electrons, but you can't have one point seven photons,

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Speaker 1: for example. But then as people were trying to apply

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Speaker 1: these theories and these ideas to describing the atom, they

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Speaker 1: need to develop mathematics that work, mathematics that explained what

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Speaker 1: we saw. And Heisenberg developed this theory of quantum mechanics

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Speaker 1: that he used to make calculations and to understand like

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Speaker 1: why did the electron have this energy level? Around the

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Speaker 1: atom and not that energy level. Why did we get

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Speaker 1: this atomic spectrum from the atom? He developed this whole

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Speaker 1: theory of quantum mechanics, and you can see inherent in

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Speaker 1: the mathematics of his theory comes out this basic idea

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Speaker 1: of the quantum uncertainty sort of falls out of the mathematics.

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Speaker 1: He needed to describe the world as he saw it.

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Speaker 2: Can you describe that a little bit more?

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Speaker 1: Like?

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Speaker 2: Why did it need to include that uncertainty into these

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Speaker 2: formulations in order to explain things like the little packets

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Speaker 2: of light?

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Speaker 1: Well, Heisenberg developed his theory of quant mechanics, and it

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Speaker 1: was based on a certain kind of mathematical object called

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Speaker 1: matrix's that we don't have to dig into. But what

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Speaker 1: he noticed about the structure of his theory was that

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Speaker 1: it seemed to matter the order in which you make measurements.

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Speaker 1: Like if you measure one thing, it changes the state

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Speaker 1: of the system, and then if you measure something else

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Speaker 1: you'll get a different answer. And so quantu uncertainty is

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Speaker 1: all about this. It's about recognizing that the order of

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Speaker 1: the measurements you makes matter for some pairs of quantities,

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Speaker 1: measuring one thing can change something else.

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Speaker 2: I feel like maybe that's at the root of quantum uncertainty,

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Speaker 2: which is like, it's really only uncertainly with regards to

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Speaker 2: two things at the same time, right, Like, it's not

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Speaker 2: like something has an inherent fuzziness, but its location you

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Speaker 2: can know its location sort of very precisely, but then

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Speaker 2: you lose out in some other quantities, right Exactly.

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Speaker 1: It's about simultaneous knowledge of specific pairs of quantities, right,

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Speaker 1: And it's really very specific. It's not like general and

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Speaker 1: broad and say you can't ever know the position very well,

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Speaker 1: or you can't ever know the momentum very well. You

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Speaker 1: can know the position as well as you like, but

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Speaker 1: it comes at a cost for one specific other quantity,

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Speaker 1: the momentum. And there are other things that are paired

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Speaker 1: in this way. If you dig deeper into this in physics,

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Speaker 1: you discover that these things are called conjugate variables. And

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Speaker 1: this came out of the mathematics that Heisenberg was using

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Speaker 1: to describe his theory of quantum mechanics.

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Speaker 2: Well, I'm pretty certain that we're going to get into

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Speaker 2: this uncertainty and this idea of conjugate pairs, and how

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Speaker 2: that figures into the uncertainty that we see in quantum

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Speaker 2: mechanics that tries to explain the universe, and so let's

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Speaker 2: dig into those details. But first let's take a quick break.

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Speaker 2: All right, we are uncertainly talking about uncertainty today, specifically

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Speaker 2: quantum uncertainty, or at least we're trying to understand here

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Speaker 2: where it comes from and how it manifests itself in

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Speaker 2: our everyday lives. And so we talked about how quantum

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Speaker 2: mechanics kind of change things, and there's a certain uncertainty

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Speaker 2: about it that has to do with two things being

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Speaker 2: measured at the same time. That's kind of a key

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Speaker 2: to the concept of quantum uncertainty, right, first of all

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Speaker 2: measurements and second of all two things at the same

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Speaker 2: time exactly.

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Speaker 1: And there's lots of fuzziness about quantum mechanics, but this

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Speaker 1: is what we're talking about right now, is this uncertainly

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Speaker 1: about simultaneous knowledge. There's a whole other issue in quantum

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Speaker 1: mechanics about indeterminism, you know, laws of quantum mechanics determining

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Speaker 1: probabilities rather than outcomes. That's a whole separate issue, super fascinating,

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Speaker 1: but different from quantum uncertainty. Right, So quantum indeterminism is

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Speaker 1: different from quantum uncertainty, which tells us about like how

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Speaker 1: much we can know simultaneously about a particle or an object.

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Speaker 2: Wait, what that's different. There's two kinds of uncertainties.

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Speaker 1: Well, one of them is uncertainty. The other one is indeterminism.

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Speaker 2: Well, that's what you call it, but it's basically another

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Speaker 2: word for uncertainty, Isn't it Like you're not certain of

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Speaker 2: what the outcome is going to be. So today we're

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Speaker 2: not talking about like if I throw an electron at

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Speaker 2: a magnetic field, I don't know if it's going to

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Speaker 2: be your rider left. That's a different kind of uncertainty.

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Speaker 2: What are you saying?

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Speaker 1: So in quantum mechanics, we talk about randomness to describe

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Speaker 1: predictions that are probabilistic. If you put a particle in

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Speaker 1: a box and you ask where is it, you don't

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Speaker 1: get a specific prediction the way you do for classical mechanics.

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Speaker 1: You get predictions for where it's likely to be. You

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Speaker 1: get predictions for the probability distribution, so that if you

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Speaker 1: do it like a thousand times and measure its location,

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Speaker 1: you then get a distribution of measurements that follow the

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Speaker 1: predicted probability distribution. That's inherent in most of the quantum

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Speaker 1: mechanics we're used to thinking about due to the story

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Speaker 1: it tells us about how the universe works. It's not

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Speaker 1: a particle that's following equations of motion that are fundamental.

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Speaker 1: It's the wave function or the quantum field, which is

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Speaker 1: inherently probabilistic about the measurements you'll make of it. Now,

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Speaker 1: quantum uncertainty is related but actually quite distinct. You can

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Speaker 1: think of it as another source of randomness, but it

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Speaker 1: says that specific pairs of measurements are linked that if

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Speaker 1: you measure one, it makes the other one have a

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Speaker 1: wider spread of probabilities. So it's like it induces more indeterminacy,

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Speaker 1: but it's linked to specific pairs of variables rather than

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Speaker 1: the probabilistic nature of the wave function.

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Speaker 2: I see. So today we're not talking about quantum randomness

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Speaker 2: at all. We're just talking about our ability to know

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Speaker 2: where things are and where they're going.

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Speaker 1: Yeah, we're not talking about quantum randomness except for talking

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Speaker 1: about how we're not talking about it, which is the

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Speaker 1: first rule of quantum randomness.

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Speaker 2: That's right. Firstrule of physics club is talk about what

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Speaker 2: it means to be in a physics club and what

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Speaker 2: a club is. But I guess the question is, like,

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Speaker 2: are those two things related or are they totally separate

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Speaker 2: ideas In quantum mechanics, the randomness and the inability to

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Speaker 2: be certain about precision and velocity and things like that,

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Speaker 2: you can have one without the other.

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Speaker 1: So indeterminacy and uncertainty are different ideas because remember that

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Speaker 1: there are some theories of quantum mechanics which don't have

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Speaker 1: randomness and indeterminacy as inherent features, for example Bomian mechanics,

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Speaker 1: where the spread of outcomes isn't due to some randomness,

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Speaker 1: but it's due to slide variations in the initial conditions

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Speaker 1: of how you set up your experiment, of how exactly

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Speaker 1: you put that particle in a box, and so in

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Speaker 1: those theories like Boemian mechanics, uncertainty doesn't come from randomness.

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Speaker 1: It actually comes from the measuring device being part of

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Speaker 1: the experiment that's being measured, which keeps it out of

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Speaker 1: total quantum equilibrium, which causes uncertain So you don't actually

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Speaker 1: need randomness to have uncertainty in your quantum theory. Overall,

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Speaker 1: though there's a connection between uncertainty and indeterminacy in most

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Speaker 1: of the theories of quantum mechanics, though not at all,

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Speaker 1: and even to the one where there is a connection.

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Speaker 1: Uncertainty is a special kind of randomness because it relates

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Speaker 1: to specific pairs of quantities, not a general randomness.

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Speaker 2: Oh interesting, I don't think I ever knew that.

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Speaker 1: And the history of this is really fascinating, like how

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Speaker 1: it developed. And Heisenberg really was a pioneer, and he

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Speaker 1: developed this calculational tool that allowed him to predict you know,

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Speaker 1: energy levels, et cetera. But it was a little bit opaque,

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Speaker 1: like he had these matrices and he was operating on

442
00:20:37,520 --> 00:20:39,280
Speaker 1: vectors with them, and people were like, all right, but

443
00:20:39,440 --> 00:20:41,960
Speaker 1: what does that mean? Like what are you talking about?

444
00:20:41,960 --> 00:20:46,240
Speaker 1: What's happening inside? What is the electron doing? And Heisenberg

445
00:20:46,359 --> 00:20:48,639
Speaker 1: was really kind of annoyed by this question, and he

446
00:20:48,680 --> 00:20:50,760
Speaker 1: wrote a whole paper about like what it means and

447
00:20:50,840 --> 00:20:53,400
Speaker 1: what is real? And the title that paper I can't

448
00:20:53,440 --> 00:20:55,840
Speaker 1: translate for you because nobody agrees about how to translate

449
00:20:55,880 --> 00:20:58,359
Speaker 1: this one German word in the title, there's like a

450
00:20:58,520 --> 00:21:00,639
Speaker 1: quantum uncertainty about one of the earth. The papers of

451
00:21:00,720 --> 00:21:01,440
Speaker 1: quantum mechanics.

452
00:21:01,880 --> 00:21:03,160
Speaker 2: What do you mean? What is this title?

453
00:21:03,920 --> 00:21:07,280
Speaker 1: So the title of The paper is on the aich

454
00:21:07,520 --> 00:21:12,000
Speaker 1: content of quantum theoretical kinematics and mechanics, and German speakers

455
00:21:12,040 --> 00:21:16,480
Speaker 1: say that word means either like the visualization, which word anschulich,

456
00:21:18,640 --> 00:21:22,439
Speaker 1: which I'm sure I'm mispronouncing, thank you, and it might

457
00:21:22,600 --> 00:21:24,920
Speaker 1: mean like on the physical meaning of it or the

458
00:21:24,960 --> 00:21:28,520
Speaker 1: intelligibility of it or the visualization of it. There's this

459
00:21:28,680 --> 00:21:30,880
Speaker 1: concept in German which we don't have an exact word

460
00:21:31,000 --> 00:21:33,399
Speaker 1: for in English, but basically it's trying to get it like,

461
00:21:33,720 --> 00:21:36,399
Speaker 1: what does this mean? What is quantum mechanics saying about

462
00:21:36,400 --> 00:21:37,040
Speaker 1: what's happening?

463
00:21:37,720 --> 00:21:39,720
Speaker 2: It's like the zeitgeist of quantum mechanics.

464
00:21:40,000 --> 00:21:43,159
Speaker 1: Yeah, and Eisenberg's attitude is like, who cares? You know?

465
00:21:43,359 --> 00:21:45,960
Speaker 1: I have this mathematical tool and it makes predictions. I

466
00:21:46,040 --> 00:21:47,719
Speaker 1: can predict how your measurements are going to come out,

467
00:21:48,200 --> 00:21:50,359
Speaker 1: and so we're all good. People didn't really like that,

468
00:21:50,560 --> 00:21:53,760
Speaker 1: And at the same time, Schrodinger developed a completely alternative

469
00:21:53,840 --> 00:21:56,399
Speaker 1: view of quantum mechanics which is now more famous and

470
00:21:56,480 --> 00:21:59,600
Speaker 1: well known, you know, the Schrodinger equation. And because he

471
00:21:59,760 --> 00:22:02,320
Speaker 1: was you like a wave equation, it sort of allowed

472
00:22:02,400 --> 00:22:05,200
Speaker 1: people to more easily visualize what's going on. You know,

473
00:22:05,280 --> 00:22:08,480
Speaker 1: people have this like concept of a blob of probability

474
00:22:08,800 --> 00:22:11,120
Speaker 1: around the atom, et cetera, et cetera, And this really

475
00:22:11,200 --> 00:22:12,480
Speaker 1: kind of pissed Heisenberg off.

476
00:22:13,280 --> 00:22:15,320
Speaker 2: You mean he was annoyed to philosophers.

477
00:22:15,320 --> 00:22:19,119
Speaker 1: And yeah, he actually wrote in a letter once to

478
00:22:19,240 --> 00:22:22,120
Speaker 1: another physicist, Polly, he said, quote, the more I think

479
00:22:22,119 --> 00:22:25,280
Speaker 1: about the physical part of Schrodinger's theory, the more disgusting

480
00:22:25,400 --> 00:22:25,920
Speaker 1: I find it.

481
00:22:26,400 --> 00:22:28,280
Speaker 2: Whoa yaouch?

482
00:22:29,320 --> 00:22:31,359
Speaker 1: And then he said I consider it, And then he

483
00:22:31,480 --> 00:22:34,880
Speaker 1: used this German word must. And I try to look

484
00:22:34,960 --> 00:22:37,560
Speaker 1: up some translations to this German word, and again there's

485
00:22:37,560 --> 00:22:39,680
Speaker 1: a lot of uncertainties. Some people say it means junk.

486
00:22:39,840 --> 00:22:42,280
Speaker 1: Some people say it means poppy cock, some people say

487
00:22:42,359 --> 00:22:44,720
Speaker 1: it means rubbish, and the other less safe for work

488
00:22:44,840 --> 00:22:46,200
Speaker 1: translations of this word as.

489
00:22:46,119 --> 00:22:50,040
Speaker 2: Well, I think it means that Heisenberg had some saucy

490
00:22:50,080 --> 00:22:50,800
Speaker 2: words for Schroder.

491
00:22:51,720 --> 00:22:54,720
Speaker 1: But the point is that in Heisenberg's view, this question

492
00:22:54,880 --> 00:22:58,160
Speaker 1: of like where is the electron was the wrong question.

493
00:22:58,880 --> 00:23:02,240
Speaker 1: In Heisenberg's quant mechanics, there is like no true position

494
00:23:02,359 --> 00:23:05,080
Speaker 1: of a particle. There's only the outcome of a measurement,

495
00:23:05,160 --> 00:23:07,760
Speaker 1: and there's only if you measure something what's going to happen.

496
00:23:07,960 --> 00:23:11,639
Speaker 1: And inherent in Heisenberg's quantum mechanics was this idea that

497
00:23:11,680 --> 00:23:14,160
Speaker 1: if you measure one thing and then measure another thing,

498
00:23:14,400 --> 00:23:17,600
Speaker 1: the order matters that like reversing the order will change

499
00:23:17,760 --> 00:23:21,280
Speaker 1: the outcome, which is sort of confusing. Like imagine measuring

500
00:23:21,400 --> 00:23:24,240
Speaker 1: the width and the height of a table. You don't

501
00:23:24,280 --> 00:23:26,920
Speaker 1: think about measuring them in a certain order because you figure, like, well,

502
00:23:26,960 --> 00:23:28,760
Speaker 1: but with and the height are things, I can measure

503
00:23:28,800 --> 00:23:31,120
Speaker 1: them in what order I want. But in this case,

504
00:23:31,160 --> 00:23:34,280
Speaker 1: in Heisenberg's quantum mechanics, for some things the order does matter.

505
00:23:34,440 --> 00:23:37,360
Speaker 2: Well, let maybe let's break it down into a concrete example,

506
00:23:38,000 --> 00:23:41,720
Speaker 2: Like let's say that this table had quantum uncertainty about

507
00:23:41,760 --> 00:23:43,879
Speaker 2: its width and its length. Now what would that mean.

508
00:23:43,960 --> 00:23:45,880
Speaker 2: It means I can measure one but not the other,

509
00:23:46,080 --> 00:23:47,960
Speaker 2: or I can sort of measure one and sort of

510
00:23:48,000 --> 00:23:49,600
Speaker 2: measure the other, or what does that mean?

511
00:23:49,720 --> 00:23:52,520
Speaker 1: So it would mean that measuring its width would change

512
00:23:52,640 --> 00:23:56,040
Speaker 1: its length, right, and measuring its length would change its width,

513
00:23:56,080 --> 00:23:59,159
Speaker 1: which would mean the outcome of those measurements depended on

514
00:23:59,280 --> 00:24:01,560
Speaker 1: the order you make them. That measuring it's with then

515
00:24:01,600 --> 00:24:04,080
Speaker 1: it's length, or measuring its length and it's with would

516
00:24:04,119 --> 00:24:05,280
Speaker 1: give you different answers.

517
00:24:05,560 --> 00:24:08,120
Speaker 2: Wait, it would change, like if I measured the width,

518
00:24:08,359 --> 00:24:11,560
Speaker 2: it would change the length of it, like physically, or

519
00:24:11,920 --> 00:24:14,760
Speaker 2: it would maybe make me less able to measure the length.

520
00:24:15,000 --> 00:24:18,680
Speaker 1: It would change the uncertainty, the fundamental uncertainty of that quantity,

521
00:24:18,760 --> 00:24:20,640
Speaker 1: which would affect what you measure later.

522
00:24:20,800 --> 00:24:22,879
Speaker 2: Yeah, what do you mean the uncertainty? What would be

523
00:24:22,880 --> 00:24:24,920
Speaker 2: the uncertainty of its length? Like I can't predict what

524
00:24:25,040 --> 00:24:27,520
Speaker 2: its length it's going to be, or it can actually

525
00:24:27,600 --> 00:24:27,960
Speaker 2: measure it.

526
00:24:28,080 --> 00:24:30,320
Speaker 1: You can still make a measurement of its length, but

527
00:24:30,400 --> 00:24:33,080
Speaker 1: the outcome that measurement depends on the fundamental uncertainty of

528
00:24:33,160 --> 00:24:36,359
Speaker 1: that object. That quantity is not well known, that quantity

529
00:24:36,440 --> 00:24:39,359
Speaker 1: is not like defined. It depends on the inherent uncertainty

530
00:24:39,560 --> 00:24:43,240
Speaker 1: of the object itself. And so if you affect that

531
00:24:43,359 --> 00:24:44,919
Speaker 1: uncertainty affects your measurement.

532
00:24:45,040 --> 00:24:46,480
Speaker 2: Right, So let's say I measure the table and I

533
00:24:46,560 --> 00:24:49,920
Speaker 2: measure that it's thirty six inches wide. What does it

534
00:24:50,000 --> 00:24:52,119
Speaker 2: mean to the change is its length? That I'm going

535
00:24:52,200 --> 00:24:54,400
Speaker 2: to measure it and I can't measure it, or I'm

536
00:24:54,400 --> 00:24:55,840
Speaker 2: going to measure it and it's going to sometimes it's

537
00:24:55,880 --> 00:24:58,520
Speaker 2: going to be twenty somethings twenty forty or it's like

538
00:24:58,560 --> 00:25:00,399
Speaker 2: I'm going to measure it and it's gonna be fifty

539
00:25:00,680 --> 00:25:02,119
Speaker 2: when I thought it was forty. What does it mean

540
00:25:02,200 --> 00:25:03,480
Speaker 2: that it changes? You know what I mean? Like, what

541
00:25:03,920 --> 00:25:04,560
Speaker 2: are you trying to say?

542
00:25:04,680 --> 00:25:06,920
Speaker 1: Well, what I'm saying is that it changes the distribution

543
00:25:07,040 --> 00:25:09,440
Speaker 1: of possible measurements you're going to make for the length.

544
00:25:09,520 --> 00:25:11,800
Speaker 1: If you measure the width first, it changes the quantum

545
00:25:11,880 --> 00:25:14,040
Speaker 1: state of the particle. So now when you go to

546
00:25:14,160 --> 00:25:17,040
Speaker 1: measure the length, you're measuring like a different system than

547
00:25:17,080 --> 00:25:20,359
Speaker 1: you were measuring before you measured the width. You've perturbed it.

548
00:25:20,600 --> 00:25:22,840
Speaker 2: You're saying, it's changing the randomness of the length.

549
00:25:22,920 --> 00:25:26,119
Speaker 1: There is a random element there because the possible outcomes

550
00:25:26,680 --> 00:25:29,680
Speaker 1: of the length are now determined by a probability distribution,

551
00:25:29,800 --> 00:25:32,240
Speaker 1: and that is wider. You can think about it that way.

552
00:25:32,320 --> 00:25:35,600
Speaker 2: Yeah, Oh, I see, So it's like more random. Like

553
00:25:35,680 --> 00:25:37,560
Speaker 2: if I measured the width of the table, then the

554
00:25:37,680 --> 00:25:40,960
Speaker 2: length gets more random, like before it could maybe be

555
00:25:41,200 --> 00:25:43,639
Speaker 2: you know, between five and six feet. But now and

556
00:25:43,720 --> 00:25:46,960
Speaker 2: that I measured the width, now suddenly like this magical table,

557
00:25:47,040 --> 00:25:49,040
Speaker 2: it's like whoa, Now, now the length of it can

558
00:25:49,119 --> 00:25:50,800
Speaker 2: be one inchry it can be a million inches.

559
00:25:50,920 --> 00:25:53,240
Speaker 1: Yeah, And it's very counterintuitive when you think about a table,

560
00:25:53,320 --> 00:25:55,080
Speaker 1: because first of all, the table is a classical object,

561
00:25:55,119 --> 00:25:57,359
Speaker 1: doesn't have any these properties, and because we think of

562
00:25:57,440 --> 00:26:00,399
Speaker 1: a table as having like specific length and width, and

563
00:26:00,480 --> 00:26:03,280
Speaker 1: that's also true of quantum objects. Right. This uncertainty only

564
00:26:03,359 --> 00:26:06,240
Speaker 1: applies to very specific pairs of things that you can measure,

565
00:26:06,359 --> 00:26:08,359
Speaker 1: not to everything. So for a particle, for example, it

566
00:26:08,400 --> 00:26:12,000
Speaker 1: applies to position and momentum, not to like its ex

567
00:26:12,080 --> 00:26:14,680
Speaker 1: position and its why position. You can measure something in

568
00:26:14,960 --> 00:26:17,840
Speaker 1: X really precisely and then measure and why really precisely

569
00:26:18,160 --> 00:26:20,639
Speaker 1: with no problem, and the order doesn't matter. But if

570
00:26:20,680 --> 00:26:23,320
Speaker 1: you measure its position in X really precisely, it messes

571
00:26:23,400 --> 00:26:26,240
Speaker 1: up your potential knowledge of its momentum in X.

572
00:26:26,560 --> 00:26:28,800
Speaker 2: I see, but I guess for our magical table, I

573
00:26:28,840 --> 00:26:30,920
Speaker 2: can still measure the length, right, Like if I measured

574
00:26:30,920 --> 00:26:32,960
Speaker 2: the width, that doesn't mean I can't measure the length.

575
00:26:32,960 --> 00:26:34,680
Speaker 2: I can still measure the length. It's just going to

576
00:26:34,720 --> 00:26:37,440
Speaker 2: be exper random, so that if I had like a

577
00:26:37,560 --> 00:26:39,600
Speaker 2: million of these magical tables, I'm going to think the

578
00:26:39,680 --> 00:26:40,640
Speaker 2: length is all over the place.

579
00:26:40,760 --> 00:26:42,359
Speaker 1: M Yeah, that's exactly right.

580
00:26:42,400 --> 00:26:44,520
Speaker 2: That means that there is an element of randomness to

581
00:26:44,920 --> 00:26:47,520
Speaker 2: the idea of uncertainty, Like, how could you have uncertainty

582
00:26:48,080 --> 00:26:48,800
Speaker 2: without randomness?

583
00:26:48,880 --> 00:26:49,600
Speaker 1: Yeah, that's a good point.

584
00:26:49,680 --> 00:26:53,040
Speaker 2: Okay, So that's the magical table, and if quantum uncertainty

585
00:26:53,040 --> 00:26:54,720
Speaker 2: applied to that table, that's how it would be for

586
00:26:54,800 --> 00:26:57,919
Speaker 2: the table. But now let's maybe take a more physical example.

587
00:26:58,040 --> 00:27:00,480
Speaker 2: You were talking about precision and momentum.

588
00:27:00,720 --> 00:27:03,440
Speaker 1: Yeah, because it's important to understand quantumuncertainty doesn't just apply

589
00:27:03,520 --> 00:27:05,920
Speaker 1: willing nearly to everything. It doesn't say the whole universe

590
00:27:06,040 --> 00:27:09,399
Speaker 1: is flascting no matter what it says. Specific pairs of

591
00:27:09,520 --> 00:27:12,399
Speaker 1: things can't be known at the same time. So you

592
00:27:12,480 --> 00:27:14,760
Speaker 1: can know the X and the why of a particle,

593
00:27:14,880 --> 00:27:17,000
Speaker 1: but you can't know it's X and it's momentum also

594
00:27:17,200 --> 00:27:17,720
Speaker 1: in X.

595
00:27:17,960 --> 00:27:20,200
Speaker 2: Wait, I can know it or I can measure it,

596
00:27:20,240 --> 00:27:22,440
Speaker 2: because like the table, I can measure the with and

597
00:27:22,480 --> 00:27:25,359
Speaker 2: the length, right, Or are you saying that if I

598
00:27:25,440 --> 00:27:27,000
Speaker 2: measure the width, I can measure the length.

599
00:27:27,080 --> 00:27:28,760
Speaker 1: You can always measure it. But in the case of

600
00:27:28,800 --> 00:27:30,880
Speaker 1: the table, if you measure the width, you get a number.

601
00:27:31,040 --> 00:27:32,800
Speaker 1: You measure the length, you get a number. But now

602
00:27:32,840 --> 00:27:35,159
Speaker 1: you no longer know the width because you messed up

603
00:27:35,160 --> 00:27:37,160
Speaker 1: the width when you measure the length. These two things

604
00:27:37,200 --> 00:27:37,800
Speaker 1: are connected.

605
00:27:38,000 --> 00:27:39,680
Speaker 2: I see. I think maybe what you mean by no

606
00:27:40,119 --> 00:27:42,960
Speaker 2: is you actually mean predict, Like if I measure the width,

607
00:27:43,400 --> 00:27:45,359
Speaker 2: then it makes it harder for me to predict what

608
00:27:45,520 --> 00:27:47,240
Speaker 2: the length is going to be of this table. Because

609
00:27:47,280 --> 00:27:48,920
Speaker 2: I can know what the length of the table is.

610
00:27:48,960 --> 00:27:50,520
Speaker 2: I can measure it, right, That's how we know it.

611
00:27:51,160 --> 00:27:53,040
Speaker 2: But it's more about like being able to know it

612
00:27:53,119 --> 00:27:53,879
Speaker 2: before you measure it.

613
00:27:53,920 --> 00:27:55,560
Speaker 1: Well, I'd say, when you measure it, you measure it

614
00:27:55,640 --> 00:27:57,600
Speaker 1: with some uncertainty. Even if you know it, you know,

615
00:27:57,720 --> 00:27:59,920
Speaker 1: with some uncertainty. There's like error bars on it.

616
00:28:00,480 --> 00:28:03,600
Speaker 2: Oh, it's about error bars. That's different, though, isn't it.

617
00:28:03,760 --> 00:28:05,440
Speaker 1: Well, you know, it depends on how you interpret the

618
00:28:05,480 --> 00:28:07,920
Speaker 1: air bars and the randomness. But like repeated measurements which

619
00:28:07,960 --> 00:28:11,560
Speaker 1: probe that probability distribution will give different outcomes. It doesn't

620
00:28:11,560 --> 00:28:14,600
Speaker 1: fundamentally have a specific length. It has a distribution, and

621
00:28:14,640 --> 00:28:17,320
Speaker 1: if you measure it multiple times, you'll get different answers

622
00:28:17,720 --> 00:28:19,680
Speaker 1: according to the width of that distribution.

623
00:28:20,040 --> 00:28:22,520
Speaker 2: Oh, I see, I feel like you're saying kind of

624
00:28:22,680 --> 00:28:24,919
Speaker 2: like the table has the length and with but then

625
00:28:24,960 --> 00:28:27,119
Speaker 2: there's our measurement of the length and with which might

626
00:28:27,200 --> 00:28:28,840
Speaker 2: not be what it's real length.

627
00:28:28,920 --> 00:28:30,960
Speaker 1: And with this in the case of the magical table,

628
00:28:31,040 --> 00:28:34,840
Speaker 1: which follows this quantum uncertainty though obviously tables don't really right.

629
00:28:35,240 --> 00:28:37,960
Speaker 1: If we say that it has this quantum uncertainty attached

630
00:28:37,960 --> 00:28:39,680
Speaker 1: to the length and the with, then the length and

631
00:28:39,680 --> 00:28:42,680
Speaker 1: the width are not determined simultaneously. It's not that it

632
00:28:42,840 --> 00:28:45,400
Speaker 1: exists and it's written in a gold tablet by God somewhere.

633
00:28:45,680 --> 00:28:48,000
Speaker 1: We just don't have access to seeing it. It's just

634
00:28:48,080 --> 00:28:49,040
Speaker 1: that it's not defined.

635
00:28:49,160 --> 00:28:51,000
Speaker 2: Oh, I think I see what like you're saying. I

636
00:28:51,080 --> 00:28:54,440
Speaker 2: think that if I measure this table with like a

637
00:28:54,560 --> 00:28:56,920
Speaker 2: super precise ruler, and I measured the with and I

638
00:28:57,040 --> 00:28:59,920
Speaker 2: get that it's three feet wide and I'm super certain

639
00:29:00,040 --> 00:29:02,800
Speaker 2: about that, that means that no matter what I do

640
00:29:03,000 --> 00:29:06,160
Speaker 2: to measure the length, I have to assign a certain

641
00:29:06,440 --> 00:29:09,080
Speaker 2: uncertainty or a certain error to it. I might measure

642
00:29:09,120 --> 00:29:10,920
Speaker 2: the length of the table, I might say, oh, I

643
00:29:11,000 --> 00:29:12,880
Speaker 2: measure it to be six feet, but in the back

644
00:29:12,920 --> 00:29:15,600
Speaker 2: of my head I have to be like, well, that's

645
00:29:15,880 --> 00:29:18,000
Speaker 2: probably not actually six feet. Is that kind of what

646
00:29:18,120 --> 00:29:19,240
Speaker 2: you mean by uncertainty?

647
00:29:19,520 --> 00:29:22,200
Speaker 1: Yeah? And then if you go back to measure the width,

648
00:29:22,240 --> 00:29:23,719
Speaker 1: you're going to get a different answer than you did

649
00:29:23,760 --> 00:29:26,920
Speaker 1: before because measuring the length has now changed the width.

650
00:29:27,040 --> 00:29:28,440
Speaker 2: But no, i'm it's still the same table.

651
00:29:28,600 --> 00:29:30,840
Speaker 1: No, it's not still the same table, right, because you've

652
00:29:30,880 --> 00:29:33,280
Speaker 1: made a measurement to it and measuring things changes them.

653
00:29:33,640 --> 00:29:35,480
Speaker 2: Oh, but what if I mentioned it at the same time.

654
00:29:35,600 --> 00:29:37,800
Speaker 1: Yeah, great question, But you can't do that, right. You

655
00:29:37,880 --> 00:29:39,840
Speaker 1: make a measurement of a quantum system. You can measure

656
00:29:39,920 --> 00:29:43,120
Speaker 1: a thing, right, and these two things you can't measure simultaneously.

657
00:29:43,320 --> 00:29:45,360
Speaker 2: Oh see, that's I feel like that's another concept. Then

658
00:29:45,400 --> 00:29:48,520
Speaker 2: in quantum mechanics, why can't I measure this table at

659
00:29:48,560 --> 00:29:49,040
Speaker 2: the same time.

660
00:29:49,280 --> 00:29:52,160
Speaker 1: In Heisimber's quantum mechanics, the way you make a measurement

661
00:29:52,320 --> 00:29:55,160
Speaker 1: is that you operate on that quantum state. Operating on

662
00:29:55,160 --> 00:29:57,240
Speaker 1: the quantum state will change it, and you can't do

663
00:29:57,400 --> 00:29:59,080
Speaker 1: two operations simultaneously.

664
00:29:59,360 --> 00:30:01,680
Speaker 2: Maybe for those us that are not familiar with quantum states,

665
00:30:01,920 --> 00:30:04,520
Speaker 2: what does that mean? That means that, like in a system,

666
00:30:04,600 --> 00:30:07,280
Speaker 2: there are some variables that you just can't measure at

667
00:30:07,280 --> 00:30:07,720
Speaker 2: the same time.

668
00:30:07,800 --> 00:30:09,600
Speaker 1: I'll try. All measurements have to be made in a

669
00:30:09,640 --> 00:30:13,280
Speaker 1: certain order because potentially measurements could mess up later measurements.

670
00:30:13,520 --> 00:30:15,680
Speaker 1: In some cases they don't, right, Like you can measure

671
00:30:15,720 --> 00:30:17,920
Speaker 1: the X and then you can measure the Y, and

672
00:30:17,960 --> 00:30:20,160
Speaker 1: the answer you get for why doesn't depend on whether

673
00:30:20,200 --> 00:30:22,760
Speaker 1: you already measured x. But if you measure x and

674
00:30:22,800 --> 00:30:25,160
Speaker 1: then you measure momentum and X, then you will get

675
00:30:25,200 --> 00:30:27,560
Speaker 1: a different answer. And the order does matter, like measuring

676
00:30:27,800 --> 00:30:30,800
Speaker 1: x and then momentum or measuring momentum and then position

677
00:30:31,000 --> 00:30:33,320
Speaker 1: in X will change the answers that you get.

678
00:30:34,000 --> 00:30:36,400
Speaker 2: I see, it's kind of part of the magical properties

679
00:30:36,480 --> 00:30:38,960
Speaker 2: of my table. Like a regular table, I can definitely

680
00:30:39,000 --> 00:30:40,880
Speaker 2: get two people to measure it within the length at

681
00:30:40,920 --> 00:30:44,120
Speaker 2: the same time, but a quantum uncertain table you just can't.

682
00:30:44,200 --> 00:30:45,480
Speaker 2: You can only do one at a time.

683
00:30:45,640 --> 00:30:47,440
Speaker 1: Yeah, And it's sort of hard to understand that about

684
00:30:47,440 --> 00:30:49,080
Speaker 1: a table because it doesn't seem to make any sense.

685
00:30:49,120 --> 00:30:51,440
Speaker 1: And X and Y seem to be orthogonal, right, And

686
00:30:51,800 --> 00:30:54,920
Speaker 1: that's why I suggested it as a ridiculous example, because

687
00:30:55,040 --> 00:30:58,960
Speaker 1: it's very counterintuitive, and quantum mechanics is counterintuitive in that way,

688
00:30:59,040 --> 00:31:01,800
Speaker 1: but not quite as counterintuitive. I mean, you can't get

689
00:31:01,840 --> 00:31:04,880
Speaker 1: some understanding of why measuring one thing messes up another

690
00:31:05,200 --> 00:31:08,200
Speaker 1: if you think more specifically about, for example, momentum and

691
00:31:08,320 --> 00:31:10,880
Speaker 1: position instead of like table lengths and widths.

692
00:31:11,280 --> 00:31:13,640
Speaker 2: Right, I just think that, you know, for more less

693
00:31:13,640 --> 00:31:16,000
Speaker 2: of us saying that's what the mass says, and it's magic.

694
00:31:16,280 --> 00:31:20,600
Speaker 2: It's pretty much the same thing. It's magicmagical, mathemagical.

695
00:31:20,880 --> 00:31:23,320
Speaker 1: There you go. I mean you can think about it

696
00:31:23,400 --> 00:31:26,280
Speaker 1: in terms of like measuring a particle, right, say you

697
00:31:26,360 --> 00:31:28,640
Speaker 1: want to know its location, how would you actually make

698
00:31:28,720 --> 00:31:32,120
Speaker 1: that measurement? Well, in order to measure the location of

699
00:31:32,120 --> 00:31:34,200
Speaker 1: a particle, you got to like bounce something else off

700
00:31:34,240 --> 00:31:37,640
Speaker 1: of it. There's no passive observing of the universe. You

701
00:31:37,720 --> 00:31:39,880
Speaker 1: got to like bounce a photon off of it, for example,

702
00:31:39,960 --> 00:31:42,960
Speaker 1: to see where it is. And if you want to

703
00:31:43,000 --> 00:31:45,720
Speaker 1: know its precision really, really precisely, then you need a

704
00:31:45,800 --> 00:31:49,600
Speaker 1: really high energy photon because high energy photons have short

705
00:31:49,680 --> 00:31:52,720
Speaker 1: wavelengths and so they can tell you information about really

706
00:31:52,800 --> 00:31:55,960
Speaker 1: small distances. But if you bounce a really high energy

707
00:31:56,000 --> 00:31:58,600
Speaker 1: photon off of your electron, then you're going to totally

708
00:31:58,680 --> 00:32:00,760
Speaker 1: mess up its momentum. It'sent is going to be very

709
00:32:00,800 --> 00:32:03,640
Speaker 1: different now than before you measured it. So if you

710
00:32:03,720 --> 00:32:05,360
Speaker 1: go off to measure its momentum, you're going to get

711
00:32:05,360 --> 00:32:08,360
Speaker 1: a different answer than if you hadn't measured the position.

712
00:32:08,600 --> 00:32:10,360
Speaker 2: That's if you try to do it one after the other.

713
00:32:10,480 --> 00:32:14,160
Speaker 2: But I'm just throwing out an idea. What if you, like,

714
00:32:14,400 --> 00:32:17,440
Speaker 2: throw a photon at it and you measure how the

715
00:32:17,680 --> 00:32:20,600
Speaker 2: photeland bounces, and then that tells you both things at

716
00:32:20,600 --> 00:32:23,360
Speaker 2: the same time. Maybe right, Like if I catch a baseball,

717
00:32:23,760 --> 00:32:25,960
Speaker 2: I know its position and how fast it was going.

718
00:32:26,120 --> 00:32:28,040
Speaker 1: Yeah, and you can do that for a classical object,

719
00:32:28,120 --> 00:32:31,960
Speaker 1: and you can know simultaneously multiple things about quantum objects,

720
00:32:32,360 --> 00:32:35,480
Speaker 1: just not some things right, just in this case, like

721
00:32:35,800 --> 00:32:38,840
Speaker 1: not position and momentum simultaneously. And the reason that you

722
00:32:38,920 --> 00:32:41,880
Speaker 1: can't has to do with how this information is encoded

723
00:32:41,960 --> 00:32:44,080
Speaker 1: in the particle, which I think we can understand without

724
00:32:44,080 --> 00:32:45,200
Speaker 1: getting too mathematical.

725
00:32:45,320 --> 00:32:47,880
Speaker 2: All right, well, let's dig into some of this mathemagic

726
00:32:48,160 --> 00:32:51,040
Speaker 2: or not mathe physics, I guess, and the idea of

727
00:32:51,240 --> 00:32:53,560
Speaker 2: wave and the wave function, which is I think where

728
00:32:53,560 --> 00:32:55,760
Speaker 2: we're going with this, dig into that waving is. But

729
00:32:55,800 --> 00:33:11,360
Speaker 2: first let's take another quick break. All right, we're talking

730
00:33:11,480 --> 00:33:15,080
Speaker 2: about the hairy topic of quantum uncertainty and all the

731
00:33:15,200 --> 00:33:18,600
Speaker 2: uncertain details about it. Down to the nittigree to hear. Now, Daniel,

732
00:33:18,600 --> 00:33:20,360
Speaker 2: you think that maybe a good way to explain this

733
00:33:20,920 --> 00:33:24,800
Speaker 2: is using waves, and specifically sound waves, right as maybe

734
00:33:24,840 --> 00:33:27,520
Speaker 2: they relate to the wave function of quantum particles.

735
00:33:27,680 --> 00:33:29,880
Speaker 1: Yeah, if you're trying to think about position and momentum

736
00:33:29,920 --> 00:33:32,840
Speaker 1: of particles and how they're like encoded in the mathematical

737
00:33:32,880 --> 00:33:36,160
Speaker 1: description of the particle in quantum mechanics, truly helpful to

738
00:33:36,240 --> 00:33:38,680
Speaker 1: think about analogies we have in the classical world that

739
00:33:38,720 --> 00:33:40,760
Speaker 1: are a little bit more intuitive. And there actually is

740
00:33:40,840 --> 00:33:42,560
Speaker 1: one that a lot of people are familiar with, and

741
00:33:42,640 --> 00:33:46,360
Speaker 1: that's sound waves and songs and how words and music

742
00:33:46,440 --> 00:33:49,000
Speaker 1: can be broken up into very specific frequencies.

743
00:33:49,160 --> 00:33:51,640
Speaker 2: All right, let's dig into it. How is a quantum

744
00:33:51,720 --> 00:33:53,840
Speaker 2: uncertainty like a song?

745
00:33:54,000 --> 00:33:57,080
Speaker 1: Well, think about like your equalizer on your stereo when

746
00:33:57,120 --> 00:33:59,200
Speaker 1: you hear songs that has like a bass and a

747
00:33:59,280 --> 00:34:02,240
Speaker 1: trouble and whatever, and the high frequencies and low frequencies,

748
00:34:02,600 --> 00:34:04,920
Speaker 1: and your equalizer is telling you like how much bass

749
00:34:05,040 --> 00:34:07,640
Speaker 1: is there, or how many low frequency sounds are there,

750
00:34:07,720 --> 00:34:09,759
Speaker 1: or how many high frequency sounds are there.

751
00:34:09,840 --> 00:34:12,960
Speaker 2: Or more like how strong the song is in this

752
00:34:13,040 --> 00:34:13,839
Speaker 2: frequency range?

753
00:34:13,880 --> 00:34:16,120
Speaker 1: Right exactly, So we're going to think about the relationship

754
00:34:16,200 --> 00:34:20,440
Speaker 1: between frequencies, pure notes of specific frequencies and how you

755
00:34:20,520 --> 00:34:22,720
Speaker 1: can use them to build up different kinds of sound.

756
00:34:23,239 --> 00:34:25,200
Speaker 1: That's going to give you a feeling for the physical

757
00:34:25,320 --> 00:34:28,799
Speaker 1: reason why there are some specific quantities that you can't

758
00:34:28,920 --> 00:34:32,200
Speaker 1: know at the same time how they're linked by quantum uncertainty.

759
00:34:32,440 --> 00:34:34,680
Speaker 1: So start with a pure note, like an opera singer

760
00:34:34,840 --> 00:34:38,279
Speaker 1: singing a high seed. That's just one frequency on your

761
00:34:38,320 --> 00:34:40,640
Speaker 1: equalizer or on a spectrograph. It's going to give you

762
00:34:40,719 --> 00:34:43,759
Speaker 1: a single spike at that frequency, and there's very little

763
00:34:43,800 --> 00:34:45,840
Speaker 1: uncertainty in the frequency. Right you hear the sound, you

764
00:34:45,880 --> 00:34:48,200
Speaker 1: know the frequency. There's only one frequency to the sound.

765
00:34:48,440 --> 00:34:52,560
Speaker 1: Now think about the corresponding quantity, the shape. If she

766
00:34:52,760 --> 00:34:55,520
Speaker 1: hits the high sea, then where is that sindwave? That

767
00:34:55,600 --> 00:34:58,120
Speaker 1: sinwave is everywhere in the room. It goes up and down.

768
00:34:58,239 --> 00:35:01,440
Speaker 1: It doesn't really have a shape. It's a sine wave everywhere.

769
00:35:01,520 --> 00:35:03,840
Speaker 1: It fills the room or the opera house or whatever

770
00:35:03,920 --> 00:35:06,319
Speaker 1: it is. So you know a lot about the frequency

771
00:35:06,560 --> 00:35:09,440
Speaker 1: of her note. The spectrograph is a spike, but the

772
00:35:09,560 --> 00:35:12,640
Speaker 1: soundwave itself is very spread out in position. It's filled

773
00:35:12,680 --> 00:35:15,280
Speaker 1: the whole room. It's everywhere. Well, what if we wanted

774
00:35:15,320 --> 00:35:18,040
Speaker 1: our opera singer to create a sound that you could

775
00:35:18,080 --> 00:35:20,800
Speaker 1: only hear in part of the room. And you know

776
00:35:20,840 --> 00:35:22,600
Speaker 1: that you can get different sounds in different parts of

777
00:35:22,640 --> 00:35:24,720
Speaker 1: the room if you take advantage of how they can interfere.

778
00:35:24,840 --> 00:35:28,000
Speaker 1: That's why they very carefully designed acoustics in opera houses,

779
00:35:28,040 --> 00:35:30,399
Speaker 1: et cetera. But we can get our singer to make

780
00:35:30,440 --> 00:35:32,960
Speaker 1: a sound that you can only hear in one part

781
00:35:33,080 --> 00:35:35,239
Speaker 1: of the room, like in only one spot can you

782
00:35:35,320 --> 00:35:37,440
Speaker 1: hear it, and the other spots it'll be totally silent.

783
00:35:37,600 --> 00:35:40,680
Speaker 1: She can do this if she adds more frequencies, right,

784
00:35:40,760 --> 00:35:42,799
Speaker 1: So if she has just one frequency, just the high

785
00:35:42,800 --> 00:35:46,840
Speaker 1: seats everywhere, Now add another singer singing a different frequency,

786
00:35:47,080 --> 00:35:49,960
Speaker 1: and those two sine waves have different frequencies, and so

787
00:35:50,000 --> 00:35:52,239
Speaker 1: they'll cancel out in some places of the room and

788
00:35:52,320 --> 00:35:55,920
Speaker 1: add up in others. That's constructive and destructive interference at

789
00:35:55,920 --> 00:35:59,080
Speaker 1: a third singer with another frequency, and you can shape

790
00:35:59,120 --> 00:36:02,640
Speaker 1: the total effect further. The more frequencies you add, the

791
00:36:02,719 --> 00:36:05,399
Speaker 1: more you can shape that sound. And if you add

792
00:36:05,400 --> 00:36:08,320
Speaker 1: an infinite number of singers crowded onto that stage, you

793
00:36:08,360 --> 00:36:10,680
Speaker 1: can make any sound shape you want. In the room,

794
00:36:11,000 --> 00:36:14,680
Speaker 1: including a very very narrow spike, so that the sound

795
00:36:14,760 --> 00:36:17,279
Speaker 1: can only be heard at one spot in the room.

796
00:36:17,520 --> 00:36:20,360
Speaker 1: So in this scenario, the sound has a huge spread

797
00:36:20,400 --> 00:36:24,640
Speaker 1: of frequencies but a single very well determined location. All

798
00:36:24,719 --> 00:36:27,520
Speaker 1: the sound is in one place. So maybe now you

799
00:36:27,600 --> 00:36:31,759
Speaker 1: see the tradeoff. Either you can have a single frequency

800
00:36:31,920 --> 00:36:34,040
Speaker 1: the one high scene note, but the position is very

801
00:36:34,120 --> 00:36:36,920
Speaker 1: broad it's anywhere in the room. Or you can have

802
00:36:37,040 --> 00:36:40,560
Speaker 1: a broad range of frequencies lots of singers on the stage,

803
00:36:40,880 --> 00:36:43,680
Speaker 1: but the position is now very very narrow. So because

804
00:36:43,760 --> 00:36:48,000
Speaker 1: of the wavelike nature of sound, you can't have narrowness

805
00:36:48,120 --> 00:36:51,880
Speaker 1: in both frequency and in location. Those two things are

806
00:36:51,960 --> 00:36:55,880
Speaker 1: inherently linked by the nature of the physical process of sound.

807
00:36:56,480 --> 00:36:59,960
Speaker 1: You can't use a single frequency to create a narrow spike,

808
00:37:00,360 --> 00:37:03,399
Speaker 1: a sound that exists only one location in space. It's

809
00:37:03,520 --> 00:37:08,640
Speaker 1: either narrow frequency in broad position or broad frequency range

810
00:37:08,760 --> 00:37:13,239
Speaker 1: and narrow position. Frequency and position are conjugate variables, they're

811
00:37:13,320 --> 00:37:16,200
Speaker 1: linked in that very special way, and that also applies

812
00:37:16,280 --> 00:37:19,239
Speaker 1: to quantum waves. For a particle in a box, the

813
00:37:19,320 --> 00:37:22,719
Speaker 1: frequency of the wave function tells you its momentum. So

814
00:37:22,800 --> 00:37:25,800
Speaker 1: if you want your particle to have little uncertainty, in position,

815
00:37:26,160 --> 00:37:29,200
Speaker 1: you have to use lots of frequencies, lots of possible

816
00:37:29,280 --> 00:37:31,680
Speaker 1: momenta which add up to give you that spike. And

817
00:37:31,760 --> 00:37:34,319
Speaker 1: because you have lots of possible momentum now in your

818
00:37:34,320 --> 00:37:38,640
Speaker 1: wave function, that means a large momentum uncertainty, So small

819
00:37:38,760 --> 00:37:42,719
Speaker 1: uncertainty position requires a large momentum uncertainty. And in the

820
00:37:42,840 --> 00:37:45,879
Speaker 1: other direction, if you want your particle to have little

821
00:37:45,960 --> 00:37:49,360
Speaker 1: uncertainty in momentum, then you can only use a narrow

822
00:37:49,640 --> 00:37:52,400
Speaker 1: range of frequencies, which means you'll get a very broad

823
00:37:52,560 --> 00:37:56,200
Speaker 1: blob in position. You can't build a quantum wave function

824
00:37:56,840 --> 00:38:00,680
Speaker 1: out of just a few frequencies that also localize in position,

825
00:38:00,880 --> 00:38:03,480
Speaker 1: for the same reason that the opera singer can't sing

826
00:38:03,560 --> 00:38:06,359
Speaker 1: a single note and have it be localized in the room.

827
00:38:06,680 --> 00:38:08,919
Speaker 2: Yeah, I think that maybe a way that I've seen

828
00:38:08,960 --> 00:38:11,239
Speaker 2: it explain is a little bit talking about like the

829
00:38:11,360 --> 00:38:14,280
Speaker 2: with of things are you saying they can be described

830
00:38:14,320 --> 00:38:17,480
Speaker 2: by wave functions? Right, Like something that has like a

831
00:38:17,560 --> 00:38:21,239
Speaker 2: really wide wave means that it's it's really fuzzy and

832
00:38:21,320 --> 00:38:23,560
Speaker 2: you don't know where quite where it is, whereas something

833
00:38:23,640 --> 00:38:27,000
Speaker 2: that is really narrow you can sort of know its position,

834
00:38:27,880 --> 00:38:29,800
Speaker 2: but it's also going really fast.

835
00:38:29,640 --> 00:38:32,000
Speaker 1: Maybe exactly for something you know really really well, and

836
00:38:32,120 --> 00:38:34,000
Speaker 1: it's wave function is going to be super duper narrow,

837
00:38:34,120 --> 00:38:37,000
Speaker 1: like a spike. But to build a spike in terms

838
00:38:37,040 --> 00:38:40,440
Speaker 1: of frequencies, in terms of like various possible momenta requires

839
00:38:40,480 --> 00:38:42,600
Speaker 1: a very large number of them. You need like lots

840
00:38:42,640 --> 00:38:44,640
Speaker 1: of them to add up and cancel out in just

841
00:38:44,719 --> 00:38:46,800
Speaker 1: the right way to give you that spike. Whereas you

842
00:38:46,840 --> 00:38:49,239
Speaker 1: want something really big and fat as a blob, then

843
00:38:49,280 --> 00:38:52,120
Speaker 1: you need fewer different frequencies to add up to give

844
00:38:52,160 --> 00:38:54,960
Speaker 1: you that big, fat blob. Something that's very uncertain. So

845
00:38:55,040 --> 00:38:57,880
Speaker 1: a wave function that's really narrow needs lots of different

846
00:38:57,920 --> 00:39:01,680
Speaker 1: frequencies to add up, which means different possible momentum because

847
00:39:01,719 --> 00:39:03,719
Speaker 1: frequency and momentum are the same for a particle, which

848
00:39:03,800 --> 00:39:06,560
Speaker 1: means a lot of uncertainty in its momentum, Whereas if

849
00:39:06,560 --> 00:39:09,160
Speaker 1: you have a lot of uncertainty in its position, you

850
00:39:09,239 --> 00:39:12,640
Speaker 1: only need a few frequencies, which means less uncertainty in

851
00:39:12,800 --> 00:39:14,640
Speaker 1: its momentum. That gives you a little bit of the

852
00:39:14,719 --> 00:39:18,000
Speaker 1: flavor of why position and momentum have this special relationship.

853
00:39:18,080 --> 00:39:21,359
Speaker 1: Quantum manternity is all about very specific pairs of things

854
00:39:21,440 --> 00:39:23,640
Speaker 1: you can measure that have this relationships, not just like

855
00:39:23,760 --> 00:39:26,120
Speaker 1: any two things that you measure, right, And so.

856
00:39:26,200 --> 00:39:28,120
Speaker 2: Maybe it might help to get into some of these

857
00:39:28,200 --> 00:39:31,000
Speaker 2: other things. So you're saying that position of momentum are

858
00:39:31,080 --> 00:39:35,160
Speaker 2: linked together in this quantum uncertainty because of its wave nature. Right.

859
00:39:35,200 --> 00:39:37,400
Speaker 2: For example, if you take to measure the velocity of

860
00:39:37,760 --> 00:39:40,799
Speaker 2: a wave, somehow it's related also to its frequency, which

861
00:39:40,920 --> 00:39:43,120
Speaker 2: that's where the fuzziness maybe it comes from. So maybe

862
00:39:43,160 --> 00:39:46,280
Speaker 2: talk about some of these other variables in quantum mechanics

863
00:39:46,360 --> 00:39:48,640
Speaker 2: that are also linked together by uncertainty.

864
00:39:48,800 --> 00:39:51,840
Speaker 1: Yeah, And a tiny little quibble there is that it

865
00:39:52,000 --> 00:39:54,840
Speaker 1: can be explained in terms of like shirting or wave mechanics,

866
00:39:55,160 --> 00:39:57,879
Speaker 1: but Heisenberg can also explain it without any waves at all.

867
00:39:58,360 --> 00:40:01,840
Speaker 1: He has a completely different formulation quant mechanics that uses matrices.

868
00:40:02,320 --> 00:40:04,640
Speaker 1: And for those of you who like know matrix mechanics,

869
00:40:04,680 --> 00:40:07,880
Speaker 1: you know, like multiplication of matrices doesn't commute that you like,

870
00:40:08,120 --> 00:40:10,880
Speaker 1: it matters what you order you multiply things by with

871
00:40:11,000 --> 00:40:13,680
Speaker 1: your matrices, So like it comes out of quantum mechanics.

872
00:40:13,760 --> 00:40:17,560
Speaker 1: No matter what mathematical formulation you use, matrices or waves

873
00:40:17,680 --> 00:40:20,160
Speaker 1: or whatever. It's like really deep in there. But you're right,

874
00:40:20,239 --> 00:40:23,399
Speaker 1: it's not just position and momentum that this affects. There's

875
00:40:23,440 --> 00:40:26,240
Speaker 1: lots of other things that are paired. Another famous example

876
00:40:26,680 --> 00:40:30,239
Speaker 1: is energy and time of what like of a particle. So,

877
00:40:30,320 --> 00:40:33,480
Speaker 1: for example, a particle might have a specific mass, and

878
00:40:33,640 --> 00:40:36,480
Speaker 1: that affects how long it lasts. So, for example, an

879
00:40:36,520 --> 00:40:40,680
Speaker 1: electron which lasts forever has a very specific mass. Every

880
00:40:40,719 --> 00:40:44,320
Speaker 1: electron out there has the same mass exactly, because electrons

881
00:40:44,360 --> 00:40:46,719
Speaker 1: live for an infinite number of years. But if you

882
00:40:46,760 --> 00:40:49,480
Speaker 1: have particles whose lifetime is shorter and there's a quant

883
00:40:49,520 --> 00:40:52,520
Speaker 1: mechanical uncertainty to how long they're going to live, then

884
00:40:52,560 --> 00:40:56,200
Speaker 1: their mass is more uncertain. So for example, a top quark,

885
00:40:56,520 --> 00:40:58,600
Speaker 1: it might be one hundred and seventy three GV might

886
00:40:58,600 --> 00:41:01,040
Speaker 1: be one hundred and sixty five one hundred and eighty one.

887
00:41:01,360 --> 00:41:04,520
Speaker 1: There's a huge variation there in the possible masses a

888
00:41:04,600 --> 00:41:07,719
Speaker 1: top quark would have because it doesn't live for very long.

889
00:41:08,160 --> 00:41:10,200
Speaker 2: So when you say like it lasts, meaning like it

890
00:41:10,400 --> 00:41:13,879
Speaker 2: it might at any point break down into other things, right,

891
00:41:14,120 --> 00:41:16,840
Speaker 2: lower energy things, and so it has a lifespan and

892
00:41:16,920 --> 00:41:19,640
Speaker 2: you're saying, like, how long we expect it to be around?

893
00:41:19,760 --> 00:41:22,040
Speaker 2: Hole is tied to its mass exactly.

894
00:41:22,520 --> 00:41:25,480
Speaker 1: Electrons, we think their lifetime is basically infinity. You could

895
00:41:25,480 --> 00:41:27,880
Speaker 1: wait infinite number of years the electron just sitting out

896
00:41:27,880 --> 00:41:30,359
Speaker 1: there in space would still be an electron. Top quark

897
00:41:30,440 --> 00:41:32,880
Speaker 1: lasts for like ten to the minus twenty three seconds,

898
00:41:33,120 --> 00:41:35,640
Speaker 1: So there's a lot less uncertainty about how long a

899
00:41:35,680 --> 00:41:37,279
Speaker 1: top quark is going to be in the universe just

900
00:41:37,320 --> 00:41:40,880
Speaker 1: because its lifetime is shorter, which means there's more uncertainty

901
00:41:41,000 --> 00:41:43,439
Speaker 1: about its energy, and that comes down to uncertainty about

902
00:41:43,440 --> 00:41:46,600
Speaker 1: its mass. So there's like a whole distribution of possible

903
00:41:46,719 --> 00:41:49,240
Speaker 1: masses you could measure for a top quark of masses

904
00:41:49,280 --> 00:41:52,080
Speaker 1: that it actually has. It's like a fundamental uncertainty and

905
00:41:52,200 --> 00:41:55,360
Speaker 1: like how much energy there is in this thing, because

906
00:41:55,400 --> 00:41:57,839
Speaker 1: there's very little uncertainty about how long it's going to last.

907
00:41:58,000 --> 00:41:59,600
Speaker 1: It's not going to last very long at all.

908
00:42:00,360 --> 00:42:02,239
Speaker 2: It's not just like uncertainty about where it is and

909
00:42:02,280 --> 00:42:05,640
Speaker 2: where it's going. It's like concertainty about it's actual like

910
00:42:05,760 --> 00:42:07,960
Speaker 2: being right, like what it is, how much of it.

911
00:42:08,080 --> 00:42:11,080
Speaker 1: Is there exactly. And there's a really deep connection between

912
00:42:11,120 --> 00:42:14,640
Speaker 1: these two variables energy and time, position and momentum. We

913
00:42:14,719 --> 00:42:17,680
Speaker 1: talked about this philosophical connection in another episode. It all

914
00:42:17,760 --> 00:42:19,919
Speaker 1: comes out of this theorem No Other's theorem, which tells

915
00:42:19,960 --> 00:42:24,320
Speaker 1: us like relationships between symmetries and conservation laws. We know

916
00:42:24,400 --> 00:42:26,360
Speaker 1: the fact that space is the same everywhere in the

917
00:42:26,480 --> 00:42:30,320
Speaker 1: universe means momentum is conserved. It's another connection there between

918
00:42:30,360 --> 00:42:33,640
Speaker 1: position and momentum. No Other's law also tells us that

919
00:42:33,960 --> 00:42:37,440
Speaker 1: energy is conserved if space is the same across time.

920
00:42:37,640 --> 00:42:40,680
Speaker 1: There's a connection between energy and time. And so you

921
00:42:40,760 --> 00:42:43,440
Speaker 1: see that there's really a deep connection between these variables.

922
00:42:43,480 --> 00:42:46,520
Speaker 1: Some of these things are just sort of fundamentally paired physically,

923
00:42:46,920 --> 00:42:51,120
Speaker 1: position and momentum, energy and time. There's also weird properties

924
00:42:51,239 --> 00:42:54,120
Speaker 1: of the spins of particles that have these kind of relationships.

925
00:42:54,680 --> 00:42:55,600
Speaker 2: What do you mean by spin?

926
00:42:55,880 --> 00:42:58,600
Speaker 1: So particles can have quantum spin right, spin up or

927
00:42:58,680 --> 00:43:02,080
Speaker 1: spin down depends on how you measure it. Like if

928
00:43:02,120 --> 00:43:04,200
Speaker 1: you try to measure the spin of a particle, you

929
00:43:04,280 --> 00:43:06,200
Speaker 1: can do so by putting it in a magnetic field.

930
00:43:06,200 --> 00:43:09,040
Speaker 1: Then it will align one way or the other way. Well,

931
00:43:09,120 --> 00:43:11,680
Speaker 1: that's a spin along one axis the axis of that

932
00:43:11,880 --> 00:43:14,720
Speaker 1: magnetic field. You could also try to measure its spin

933
00:43:15,000 --> 00:43:17,680
Speaker 1: like at we're using a perpendicular setup. Like take another

934
00:43:17,840 --> 00:43:21,040
Speaker 1: magnet and rotated ninety degrees. Try to measure it spin

935
00:43:21,120 --> 00:43:23,080
Speaker 1: in another way, so you like spin in X and

936
00:43:23,160 --> 00:43:26,120
Speaker 1: spin and y. It turns out these two things are related.

937
00:43:26,160 --> 00:43:28,319
Speaker 1: You can't know the spin of a particle in two

938
00:43:28,400 --> 00:43:32,200
Speaker 1: directions simultaneously. Like you measure it spin in X, that

939
00:43:32,280 --> 00:43:34,759
Speaker 1: will mess up its spin and y. If you measure

940
00:43:34,800 --> 00:43:36,600
Speaker 1: it spin and why, that will mess up its spin

941
00:43:36,680 --> 00:43:38,920
Speaker 1: in X. These two things are linked the same way

942
00:43:38,960 --> 00:43:40,879
Speaker 1: position and momentum are linked. Right.

943
00:43:41,080 --> 00:43:44,839
Speaker 2: Well, by mess up, you mean like it changes its probability, right,

944
00:43:45,000 --> 00:43:45,759
Speaker 2: like what it can be.

945
00:43:45,960 --> 00:43:48,359
Speaker 1: Yeah, there's this famous experiment where they take a bunch

946
00:43:48,360 --> 00:43:50,200
Speaker 1: of atoms and they put them into a magnetic field

947
00:43:50,239 --> 00:43:52,520
Speaker 1: so they're either spin up or spin down. Then use

948
00:43:52,560 --> 00:43:54,520
Speaker 1: a fancy device to filter all them out so they

949
00:43:54,640 --> 00:43:56,839
Speaker 1: like only take the spin up ones. Then they send

950
00:43:56,880 --> 00:43:58,799
Speaker 1: this through the experiment again, but rotate it so now

951
00:43:58,840 --> 00:44:01,360
Speaker 1: they're measuring it like along another axis. And when they

952
00:44:01,400 --> 00:44:04,000
Speaker 1: send it back through the first device again, they're now

953
00:44:04,120 --> 00:44:06,640
Speaker 1: both spin up and spin down. So you've taken a

954
00:44:06,719 --> 00:44:09,000
Speaker 1: beam that are only spin up. You measure it in

955
00:44:09,120 --> 00:44:13,120
Speaker 1: an orthogonal way, that messes up your original distribution in

956
00:44:13,239 --> 00:44:15,960
Speaker 1: the first direction. So measuring in one direction messes up

957
00:44:16,000 --> 00:44:18,359
Speaker 1: the measurement in the other direction. Because these two things

958
00:44:18,400 --> 00:44:21,400
Speaker 1: are linked fundamentally, you can't know them simultaneously.

959
00:44:21,719 --> 00:44:25,200
Speaker 2: It kind of feels like maybe these things are paired

960
00:44:25,239 --> 00:44:31,160
Speaker 2: together by kind of the constraints that measuring those things have.

961
00:44:31,480 --> 00:44:34,560
Speaker 2: It's impossible to measure the spin of a particle in

962
00:44:34,600 --> 00:44:37,279
Speaker 2: the up and down direction and in the site to

963
00:44:37,320 --> 00:44:39,560
Speaker 2: side direction at the same time, and therefore those two

964
00:44:39,680 --> 00:44:40,520
Speaker 2: things are linked.

965
00:44:40,600 --> 00:44:43,239
Speaker 1: Yeah, those two things are definitely linked. You know, why

966
00:44:43,400 --> 00:44:45,880
Speaker 1: these two things are linked and not other two things

967
00:44:46,480 --> 00:44:48,960
Speaker 1: is a really interesting and deep question. I think that's

968
00:44:48,960 --> 00:44:51,239
Speaker 1: fundamentally a question of the episode, like why is there

969
00:44:51,360 --> 00:44:54,920
Speaker 1: any quantum uncertainty in classical physics? All these things are

970
00:44:54,960 --> 00:44:57,560
Speaker 1: totally separate and independent, and quant mechanics has like linked

971
00:44:57,680 --> 00:45:00,200
Speaker 1: some certain pairs of quantities together and said, is a

972
00:45:00,280 --> 00:45:03,359
Speaker 1: limited information in these things? And you know, the philosophical

973
00:45:03,400 --> 00:45:06,000
Speaker 1: answer to that question is a little bit slippery, you know,

974
00:45:06,120 --> 00:45:09,160
Speaker 1: like we have this mathematical description that we can use

975
00:45:09,280 --> 00:45:12,960
Speaker 1: to predict all these wonderful quantumic experiments, and those mathematics

976
00:45:13,120 --> 00:45:16,200
Speaker 1: have this uncertainty built into them inherently, So you can

977
00:45:16,200 --> 00:45:17,839
Speaker 1: then look at that theory and say like, well, why

978
00:45:18,440 --> 00:45:20,440
Speaker 1: you know, and no, it's matrix mechanics or here's a

979
00:45:20,480 --> 00:45:23,279
Speaker 1: frequency analysis of a wave function. Fundamentally, that's not really

980
00:45:23,320 --> 00:45:26,239
Speaker 1: a satisfying answer because it doesn't tell us like why

981
00:45:26,280 --> 00:45:28,600
Speaker 1: we don't live in the universe without this uncertainty. Why

982
00:45:28,840 --> 00:45:31,440
Speaker 1: couldn't you have built a classical universe without them? Why

983
00:45:31,760 --> 00:45:34,680
Speaker 1: did the designers of the universe, whoever they are, give

984
00:45:34,760 --> 00:45:37,400
Speaker 1: us the universe with this property instead of other properties?

985
00:45:37,600 --> 00:45:40,120
Speaker 2: These things are not They're tied to each other, but

986
00:45:40,160 --> 00:45:42,960
Speaker 2: they're not tied across different categories. Like, for example, you

987
00:45:43,080 --> 00:45:45,640
Speaker 2: can know the position of a particle and its mass

988
00:45:46,160 --> 00:45:49,200
Speaker 2: and it's been along the up and down direction right perfectly,

989
00:45:49,320 --> 00:45:49,920
Speaker 2: those three things.

990
00:45:50,000 --> 00:45:51,759
Speaker 1: Pick one in each category and you can know it

991
00:45:51,840 --> 00:45:52,680
Speaker 1: as well as you like.

992
00:45:52,840 --> 00:45:55,720
Speaker 2: All right, So then it sounds like we haven't answered

993
00:45:55,760 --> 00:45:56,800
Speaker 2: the question of the episode.

994
00:45:58,120 --> 00:45:59,880
Speaker 1: The answer to the question of the episode is we

995
00:46:00,120 --> 00:46:02,520
Speaker 1: don't know, right. It's a feature of our universe the

996
00:46:02,560 --> 00:46:04,400
Speaker 1: way like the speed of light is a feature of

997
00:46:04,440 --> 00:46:07,480
Speaker 1: our universe. We observe it, we can build mathematical theories

998
00:46:07,520 --> 00:46:10,000
Speaker 1: to describe it. We can then scratch our heads and say, hm,

999
00:46:10,239 --> 00:46:11,640
Speaker 1: does it have to be this way, and we don't

1000
00:46:11,640 --> 00:46:13,160
Speaker 1: have an answer to that. We don't know if it

1001
00:46:13,320 --> 00:46:17,239
Speaker 1: would have been possible to build a universe that was classical.

1002
00:46:17,400 --> 00:46:20,239
Speaker 1: We actually talked about that on a recent episode. Philosophically

1003
00:46:20,280 --> 00:46:22,719
Speaker 1: and fundamentally, theoretically, you might have been able to build

1004
00:46:22,719 --> 00:46:26,320
Speaker 1: a classical universe without any quantum uncertainty, but ours seems

1005
00:46:26,360 --> 00:46:27,400
Speaker 1: to have this feature.

1006
00:46:27,719 --> 00:46:30,680
Speaker 2: But I think, as you said, you know, it's a process, right,

1007
00:46:30,760 --> 00:46:32,880
Speaker 2: We're in the middle of this process, and it might

1008
00:46:32,960 --> 00:46:34,880
Speaker 2: be that in the future we do know why the

1009
00:46:34,920 --> 00:46:37,040
Speaker 2: speed of light had to be a certain velocity, right.

1010
00:46:37,000 --> 00:46:39,280
Speaker 1: Yeah, and in the future and we understand quantum gravity

1011
00:46:39,320 --> 00:46:42,200
Speaker 1: and string theory, there might be a simple reason like, oh,

1012
00:46:42,200 --> 00:46:46,360
Speaker 1: the universe has this property and therefore you have quantum uncertainty,

1013
00:46:46,480 --> 00:46:49,120
Speaker 1: or the universe is this way and therefore the speed

1014
00:46:49,200 --> 00:46:51,440
Speaker 1: of light is what it is. But you know that's

1015
00:46:51,520 --> 00:46:53,920
Speaker 1: just going to generate more questions, right, whatever property that

1016
00:46:54,160 --> 00:46:56,520
Speaker 1: is that gives rise to quantum uncertainty, we're then going

1017
00:46:56,560 --> 00:46:58,320
Speaker 1: to ask, well, why that property?

1018
00:46:58,880 --> 00:47:03,799
Speaker 2: So basically it's a never ending story, I hope.

1019
00:47:03,840 --> 00:47:05,200
Speaker 1: So then I'll keep having a job.

1020
00:47:05,320 --> 00:47:07,480
Speaker 2: Well, assuming people want you to do it, or I

1021
00:47:07,520 --> 00:47:09,239
Speaker 2: guess you could do it you can pay yourself. I

1022
00:47:09,320 --> 00:47:12,760
Speaker 2: guess it's still a job. If you pay yourself yourself,

1023
00:47:12,880 --> 00:47:14,280
Speaker 2: you can be a self employed physicists.

1024
00:47:14,320 --> 00:47:16,480
Speaker 1: Yeah, there's lots of great self employed physicists out there.

1025
00:47:16,640 --> 00:47:18,719
Speaker 2: What if I just say that the answer is forty two?

1026
00:47:19,520 --> 00:47:21,560
Speaker 2: Is there a universe out there where the answer is

1027
00:47:21,640 --> 00:47:22,080
Speaker 2: forty two?

1028
00:47:23,000 --> 00:47:24,280
Speaker 1: The answer to what question?

1029
00:47:24,640 --> 00:47:26,719
Speaker 2: I don't know the answer of why the speed of

1030
00:47:26,840 --> 00:47:31,120
Speaker 2: light is the way it is, it's because the number

1031
00:47:31,200 --> 00:47:32,040
Speaker 2: forty two, I don't know.

1032
00:47:32,120 --> 00:47:33,879
Speaker 1: I'd love to live in a universe where that answer

1033
00:47:34,000 --> 00:47:36,000
Speaker 1: made sense for that question, but I don't think that's

1034
00:47:36,040 --> 00:47:36,720
Speaker 1: this universe.

1035
00:47:37,719 --> 00:47:39,960
Speaker 2: I wonder if them that universe they have the Hitchhiker's

1036
00:47:40,000 --> 00:47:43,040
Speaker 2: Guide to the Galaxy. Or I guess in an infinite

1037
00:47:43,120 --> 00:47:47,200
Speaker 2: multiverse there is a universe for the answer is forty two.

1038
00:47:47,920 --> 00:47:49,200
Speaker 2: And also Douglas.

1039
00:47:48,920 --> 00:47:51,719
Speaker 1: Adams was right, yes, and it all makes sense.

1040
00:47:52,160 --> 00:47:54,399
Speaker 2: Yes, And then that one you'd be out of a job,

1041
00:47:54,840 --> 00:47:57,440
Speaker 2: but not cartoonist, because we can always draw cartoons of

1042
00:47:57,480 --> 00:47:58,440
Speaker 2: the number forty two.

1043
00:47:58,440 --> 00:48:00,600
Speaker 1: That's right, and cartoonists can always be self employed.

1044
00:48:00,760 --> 00:48:03,440
Speaker 2: All right, Well, I hopefully that gives you a sense

1045
00:48:03,600 --> 00:48:07,359
Speaker 2: of how this universe still has a lot that can't

1046
00:48:07,400 --> 00:48:11,600
Speaker 2: be explained. You know, there's these fundamental uncertainties in it

1047
00:48:11,760 --> 00:48:14,319
Speaker 2: and what we can and cannot measure. At the same time,

1048
00:48:15,000 --> 00:48:17,600
Speaker 2: it is sort of a magical table kind of for now,

1049
00:48:17,719 --> 00:48:18,239
Speaker 2: right it is.

1050
00:48:18,360 --> 00:48:20,680
Speaker 1: We can describe it mathematically, and we can give answers

1051
00:48:20,719 --> 00:48:23,319
Speaker 1: to like why the mathematics works this way and why

1052
00:48:23,400 --> 00:48:25,520
Speaker 1: these things bubble up from the mathematics, but we don't

1053
00:48:25,560 --> 00:48:28,719
Speaker 1: fundamentally know why we live in a universe with quantum uncertainty.

1054
00:48:29,480 --> 00:48:31,640
Speaker 2: Yeah, and if you eat out of a magical table,

1055
00:48:32,080 --> 00:48:34,000
Speaker 2: is that a good way to control your diet?

1056
00:48:36,280 --> 00:48:37,879
Speaker 1: If you don't know the lengthen with of your table,

1057
00:48:37,920 --> 00:48:39,160
Speaker 1: it's a good way to make a big mess on

1058
00:48:39,200 --> 00:48:39,520
Speaker 1: the floor.

1059
00:48:40,280 --> 00:48:42,880
Speaker 2: Yeah, there you go. You might be sitting down your

1060
00:48:42,920 --> 00:48:44,960
Speaker 2: food in empty space. All right, Well, we hope you

1061
00:48:45,080 --> 00:48:48,680
Speaker 2: enjoyed that. Thanks for joining us. See you next time.

1062
00:48:53,840 --> 00:48:56,680
Speaker 1: For more science and curiosity, come find us on social

1063
00:48:56,760 --> 00:49:01,680
Speaker 1: media where we answer questions and post videos on Twitter, Discord, Instant,

1064
00:49:01,760 --> 00:49:05,000
Speaker 1: and now TikTok. And remember that Daniel and Jorge Explain

1065
00:49:05,040 --> 00:49:09,000
Speaker 1: the Universe is a production of iHeartRadio. For more podcasts

1066
00:49:09,080 --> 00:49:13,640
Speaker 1: from iHeartRadio, visit the iHeartRadio app Apple Podcasts or wherever

1067
00:49:13,760 --> 00:49:15,480
Speaker 1: you listen to your favorite shows,