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Speaker 1: Hey, quick announcement, everyone, we had 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 4: 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 4: Are you sure?

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Speaker 1: Well, lots of experiments we've done over the last century.

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Speaker 4: Say yes, yeah, But like, how can you be certain?

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Speaker 4: You know, 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 4: 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 4: Are you sure about that?

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

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Speaker 4: I'm welcome to being a non physicist.

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Speaker 5: Hi.

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Speaker 4: I'm fore head made Corctuonas and the author of Oliver's

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Speaker 4: Great Big Universe.

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Speaker 5: 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 4: Yeah, Now you're not sure that you have a job,

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Speaker 4: so he might have said something to get you fired here.

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Speaker 1: Yeah, it'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 4: 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 4: But anyways, welcome to our podcast. Daniel and Jorge Explain

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Speaker 4: 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 4: That's right, because it is a wonderful and amazing but

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Speaker 4: yet also a very mysterious universe that seems kind of

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Speaker 4: random at times, but also seems like a giant clock

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Speaker 4: 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 4: Wait, I thought philosophers thought that you can never uncover

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Speaker 4: the real truth of things. It's impossible to be completely

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Speaker 4: 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 4: Well, I see, it's about I guess vocabulary.

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

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

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Speaker 4: Oh, you can get a few inception levels deep into

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Speaker 4: this discussion. What do you mean by what do you mean?

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Speaker 1: Exactly? What do you mean?

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Speaker 4: What is meaning?

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

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Speaker 4: 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 4: Wait, does that mean that philosophers don't think you actually

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Speaker 4: 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's a reason that technology works, for example, But exactly

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Speaker 1: what it means about the universe, what is the real story?

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Speaker 1: What is real? Depends a little bit on the questions

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Speaker 1: we're asking. And it's not even clear that there is

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Speaker 1: an objective truth about it. It might just be our

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Speaker 1: perception of it answers to the kind of questions we

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Speaker 1: would ask.

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Speaker 4: Well, I guess the elusive quests for the real truth

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Speaker 4: of the universe is kind of what signs. It's all about,

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Speaker 4: you know, even if we don't get there, it's all

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Speaker 4: about trying to get.

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Speaker 1: There exactly, and we can all work together to get

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Speaker 1: there 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 4: I feel like maybe that's physicist's favorite part of the job.

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Speaker 4: It's arguing about.

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Speaker 1: The job, you know. I think that there's a division

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Speaker 1: early on and people who like to argue about it

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Speaker 1: more end of in philosophy, and people who just want

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Speaker 1: to like get in the lab and learn stuff about

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Speaker 1: the world. End up in.

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Speaker 4: Physics, you just want to get in there and blows 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 4: Yeah, and so there's a lot of uncertainty about what

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Speaker 4: we do know or what we don't know, or what

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Speaker 4: we can know about the universe. But even deeper than that,

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Speaker 4: there seems to be 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 4: 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 4: I mean to have quantum vision now, I.

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Speaker 1: Think we should start that company.

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Speaker 4: Quantum laser surgery, yeah, Quantum reading glasses, Yeah, I'm parently

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Speaker 4: the only clast of dollars, 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 4: But anyways, Yeah, there seems to be this interesting nugget

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Speaker 4: of strangeness to quantum mechanics, which tries to explain the

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Speaker 4: entire universe. And so today on the podcast, we'll be

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Speaker 4: asking the question why is there quantum uncertainty? I feel

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Speaker 4: 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 4: That's what I mean.

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Speaker 1: It's meta uncertainty.

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Speaker 4: We get very meta here. Well, if it helps, I'm

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Speaker 4: 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

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Speaker 1: way or to argue that, look, we could be in

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Speaker 1: lots of different universes, this one happens to have this

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Speaker 1: quantum uncertainty. You know, there's lots of different ways to

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Speaker 1: attack this sort of philosophical problem.

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Speaker 4: Well, hopefully it's more than just a philosophical problem, right, Eventually,

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Speaker 4: the hope. The goal is to find kind of physics,

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Speaker 4: math based answers to these questions, isn't.

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Speaker 1: It to me? I think the sort of highest level

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Speaker 1: process would be go out and look at the universe,

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Speaker 1: see what it's like, boiling that down to like a

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Speaker 1: few essential facts, build a theory that describes how that works,

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Speaker 1: why that works, the mathematics to describe it, and then

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Speaker 1: look at that theory and ask philosophical questions like did

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Speaker 1: it have to be this way? Could you have a

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Speaker 1: universe that was different? Could we have built a different

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Speaker 1: theory of the universe that didn't have this feature or

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Speaker 1: that feature about it? So in the end, it's mathematical,

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Speaker 1: but it's really rooted in explaining what we see out

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Speaker 1: there in the universe.

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Speaker 4: But couldn't you answer those questions you just asked in

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Speaker 4: a mathematical way. Maybe in the future. We don't know

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Speaker 4: 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 the speed of light.

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Speaker 1: You know, we live in a universe where the speed

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Speaker 1: of light is constant for all observers and if you

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

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Speaker 1: can explain the whole universe, but you have to start

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Speaker 1: from that assumption. That's something we've seen in the universe,

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

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

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Speaker 1: 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 some 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. Well, as you said, hopefully maybe somebody, somebody will

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Speaker 4: answer this deep question, but that person doesn't seem to

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Speaker 4: be out there, because Daniel went out there and asked

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Speaker 4: this question of folks and we got some pretty interesting

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Speaker 4: 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 4: Well, there's a bunch of people who have heard we

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Speaker 4: have heard from them, right, you just totally snubbed them,

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Speaker 4: I feel.

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

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Speaker 4: 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 4: Oh, I never noticed. You didn't have to tell me.

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Speaker 1: I should have maintained your quantum uncertainty.

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Speaker 4: She kept it a mystery of the universe. But anyway,

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Speaker 4: I think for a second, why do you think there

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Speaker 4: is quantum uncertainty in the universe. Here's what people had

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Speaker 4: to say.

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Speaker 6: I guess that both because we can't really have an

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Speaker 6: accurate measurement on that very timely scale, and because measuring

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Speaker 6: a quantum process interferes on that process.

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Speaker 7: There's quantum uncertainty because when we measure a particle, it

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Speaker 7: changes what the particle is doing, and when we're not

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Speaker 7: looking at the particle, we never quite know what it's

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Speaker 7: doing without measuring it, which changes the state and the particle.

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Speaker 7: So we can never quite know exactly what a particle's

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Speaker 7: doing without changing the state.

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Speaker 5: I know that if you measure something, it falls into

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Speaker 5: the wave function collapses, and you fall into one of

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Speaker 5: the states I guess is uncertainty, because there's a wave function.

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Speaker 4: All Right, some pretty deep answers here. I'm pretty certain

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Speaker 4: 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 from being able to measure things super

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Speaker 1: duper precise? 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 4: All Right, Well, let's dig into this topic, and let's

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Speaker 4: 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, it always has a velocity.

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

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

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

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

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Speaker 4: That's sort of like maybe a good way to explain

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Speaker 4: it is basically like up to high school physics, right,

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Speaker 4: like you know, predicting where the baseball that you throw

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Speaker 4: is going to land, or you know how things move

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Speaker 4: you shake him orver you swing them. There's classical physics, right,

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Speaker 4: like you can predict where the things are, what things

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Speaker 4: are going to do, like in those exams in high school,

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Speaker 4: there's no room for uncertainty, like there's a right answer,

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Speaker 4: there's a wrong answer that's.

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Speaker 1: Right, and there's an exactness to the answer. And even

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

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

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

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Speaker 1: 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 imagine, 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 4: 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 Einstein to develop relativity. They didn't

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

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Speaker 1: an exact position, all right.

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Speaker 4: So then that's Einstein and newtune. But then around the

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Speaker 4: beginning of the nineteen hundreds they figured out that things

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Speaker 4: 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 microscopically of the

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

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

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

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

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

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

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

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Speaker 4: I feel like, or I seem to recall it. Initially,

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Speaker 4: quantum mechanics didn't have this idea of uncertainty to it, right, Like,

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Speaker 4: didn't it start with people just noticing that like light

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Speaker 4: came in packets or that electrons then you know, fly

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Speaker 4: off unless you met certain minimum energy requirements and things

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Speaker 4: like that. There's no uncertain to your fuzziness to it

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Speaker 4: at the beginning, was there?

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Speaker 1: The roots of quantum mechanics are exactly as you described.

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Speaker 1: You know, there's like the black body radiation problem, and

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

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Speaker 1: podcast several times. And you're right, it was actually Einstein

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Speaker 1: who figured that out right, who connected the ideas of

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Speaker 1: Plank with the experiments that we were seeing and saw

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Speaker 1: that light had to come and pack it so it

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Speaker 1: can only interact with a single electron. Absolutely. So those

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Speaker 1: really those core ideas which then led to the formulation

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

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Speaker 1: wasn't an essential ingredient.

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Speaker 4: Right, That's where the word quantum comes from, right, like quanta,

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Speaker 4: like little quantity.

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Speaker 1: Little countable things. Right, you can have one electron or

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Speaker 1: two electrons or nine electrons, but you can't have one

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Speaker 1: point seven photons, for example. But then as people were

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Speaker 1: trying to apply these theories and these ideas to describing

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Speaker 1: the atom, they need to develop mathematics that work, mathematics

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Speaker 1: that explained what we saw. And Heisenberg developed this theory

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Speaker 1: of quantum mechanics. He used to make calculations and to

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Speaker 1: understand like why did the electron have this energy level

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Speaker 1: around the atom and not that energy level? Why did

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Speaker 1: we get this atomic spectrum from the atom. He developed

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Speaker 1: this whole theory of quantum mechanics, and you can see

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Speaker 1: inherent in the mathematics of his theory comes out this

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Speaker 1: basic idea of the quantum uncertainty sort of falls out

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Speaker 1: of the mathematics he needed to describe the world as

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Speaker 1: he saw it.

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Speaker 4: Can you describe that a little bit more? Like? Why

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Speaker 4: did it need to include that uncertainty into these formulations

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Speaker 4: in order to explain things like the little packets 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 4: I feel like maybe that's at the root of quantum uncertainty,

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Speaker 4: which is like it's really only uncertainly with regards to

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Speaker 4: two things at the same time, right, Like, it's not

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Speaker 4: like something has an inherent fuzziness about its location. You

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Speaker 4: can know its location sort of very precisely, but then

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Speaker 4: you lose out in some other quantities.

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Speaker 1: Right, exactly. 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 4: Well, I'm pretty certain that we're going to get into

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Speaker 4: this uncertainty and this idea of conjugate pairs and how

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Speaker 4: that figures into the uncertainty that we see quantum mechanics

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Speaker 4: that tries to explain the universe. And so let's dig

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Speaker 4: into those details. But first, let's take a quick break.

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Speaker 1: the dairy industry are. US Dairy has set themselves some

442
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443
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444
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445
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446
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447
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448
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450
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451
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457
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Speaker 4: All Right, we are uncertainly talking about uncertainty today, specifically

458
00:21:53,560 --> 00:21:56,840
Speaker 4: quantum uncertainty, or at least we're trying to understand here

459
00:21:56,880 --> 00:21:59,159
Speaker 4: where it comes from and how it manifests itself in

460
00:21:59,200 --> 00:22:03,520
Speaker 4: our everyday life. And so we talked about how quantum

461
00:22:03,560 --> 00:22:06,399
Speaker 4: mechanics kind of change things, and there's a certain uncertainty

462
00:22:06,440 --> 00:22:09,680
Speaker 4: about it that has to do with two things being

463
00:22:09,680 --> 00:22:11,720
Speaker 4: measured at the same time. That's kind of a key

464
00:22:11,800 --> 00:22:14,120
Speaker 4: to the concept of quantum uncertainty, right, first of all

465
00:22:14,160 --> 00:22:16,960
Speaker 4: measurements and second of all two things at the same

466
00:22:17,000 --> 00:22:17,879
Speaker 4: time exactly.

467
00:22:18,200 --> 00:22:20,479
Speaker 1: And there's lots of fuzziness about quantum mechanics, but this

468
00:22:20,520 --> 00:22:22,560
Speaker 1: is what we're talking about right now, is this uncertainty

469
00:22:22,600 --> 00:22:26,240
Speaker 1: about simultaneous knowledge. There's a whole other issue in quantum

470
00:22:26,240 --> 00:22:30,200
Speaker 1: mechanics about indeterminism. You know, laws of quantum mechanics determining

471
00:22:30,200 --> 00:22:34,200
Speaker 1: probabilities rather than outcomes. That's a whole separate issue, super fascinating,

472
00:22:34,440 --> 00:22:38,320
Speaker 1: but different from quantum uncertainty. Right, So quantum indeterminism is

473
00:22:38,359 --> 00:22:41,040
Speaker 1: different from quantum uncertainty, which tells us about like how

474
00:22:41,119 --> 00:22:45,120
Speaker 1: much we can know simultaneously about a particle or an object.

475
00:22:45,480 --> 00:22:48,880
Speaker 4: Wait, wait, what that's different. There's two kinds of uncertainties.

476
00:22:49,040 --> 00:22:51,639
Speaker 1: Well, one of them is uncertainty. The other one is indeterminism.

477
00:22:51,760 --> 00:22:54,560
Speaker 4: Well that's what you call it, but it's basically another

478
00:22:54,600 --> 00:22:56,800
Speaker 4: word for uncertainty, Isn't it Like you're not certain of

479
00:22:56,920 --> 00:22:59,480
Speaker 4: what the outcome is going to be. So today we're

480
00:22:59,480 --> 00:23:01,960
Speaker 4: not talking about like if I throw an electron at

481
00:23:02,000 --> 00:23:03,639
Speaker 4: a magnetic field, I don't know if it's going to

482
00:23:03,680 --> 00:23:05,800
Speaker 4: veer rider left. That's a different kind of insertinty what

483
00:23:05,800 --> 00:23:06,280
Speaker 4: are you saying?

484
00:23:06,400 --> 00:23:09,800
Speaker 1: So in quantum mechanics we talk about randomness to describe

485
00:23:09,800 --> 00:23:13,199
Speaker 1: predictions that are probabilistic. If you put a particle in

486
00:23:13,200 --> 00:23:15,359
Speaker 1: a box and you ask where is it, you don't

487
00:23:15,359 --> 00:23:18,640
Speaker 1: get a specific prediction the way you do for classical mechanics.

488
00:23:18,640 --> 00:23:21,280
Speaker 1: You get predictions for where it's likely to be. You

489
00:23:21,320 --> 00:23:24,159
Speaker 1: get predictions for the probability distribution, so that if you

490
00:23:24,200 --> 00:23:26,800
Speaker 1: do it like a thousand times and measure its location,

491
00:23:27,240 --> 00:23:30,239
Speaker 1: you then get a distribution of measurements that follow the

492
00:23:30,240 --> 00:23:34,000
Speaker 1: predicted probability distribution. That's inherent in most of the quantum

493
00:23:34,040 --> 00:23:36,240
Speaker 1: mechanics we're used to thinking about due to the story

494
00:23:36,280 --> 00:23:39,480
Speaker 1: it tells us about how the universe works. It's not

495
00:23:39,560 --> 00:23:42,719
Speaker 1: a particle that's following equations of motion that are fundamental.

496
00:23:42,880 --> 00:23:45,320
Speaker 1: It's the wave function or the quantum field, which is

497
00:23:45,359 --> 00:23:48,679
Speaker 1: inherently probabilistic about the measurements you'll make of it. Now,

498
00:23:48,760 --> 00:23:52,880
Speaker 1: quantum uncertainty is related, but actually quite distinct. You can

499
00:23:52,920 --> 00:23:55,960
Speaker 1: think of it as another source of randomness, but it

500
00:23:56,080 --> 00:23:59,840
Speaker 1: says that specific pairs of measurements are linked that if

501
00:23:59,880 --> 00:24:01,919
Speaker 1: you measure one, it makes the other one have a

502
00:24:02,000 --> 00:24:07,240
Speaker 1: wider spread of probabilities. So it's like it induces more indeterminacy,

503
00:24:07,680 --> 00:24:11,120
Speaker 1: but it's linked to specific pairs of variables rather than

504
00:24:11,160 --> 00:24:13,359
Speaker 1: the probabilistic nature of the wave function.

505
00:24:14,280 --> 00:24:17,680
Speaker 4: I see. So today we're not talking about quantum randomness

506
00:24:17,800 --> 00:24:21,080
Speaker 4: at all. We're just talking about like our ability to

507
00:24:21,240 --> 00:24:22,960
Speaker 4: know where things are and where they're going.

508
00:24:23,040 --> 00:24:25,400
Speaker 1: Yeah, we're not talking about quantum randomness except for talking

509
00:24:25,440 --> 00:24:27,119
Speaker 1: about how we're not talking about it, which is the

510
00:24:27,119 --> 00:24:28,640
Speaker 1: first rule of quantum randness.

511
00:24:29,200 --> 00:24:32,000
Speaker 4: That's right. FIRSTU, all of physics club is talk about

512
00:24:32,119 --> 00:24:33,919
Speaker 4: what it means to be in a physics club and

513
00:24:33,960 --> 00:24:37,080
Speaker 4: what a club is. But I guess the question is, like,

514
00:24:37,480 --> 00:24:40,320
Speaker 4: are those two things related or are they totally separate

515
00:24:40,440 --> 00:24:44,560
Speaker 4: ideas In quantum mechanics, the randomness and the inability to

516
00:24:44,680 --> 00:24:47,160
Speaker 4: be certain about precision and velocity and things like that.

517
00:24:47,440 --> 00:24:48,600
Speaker 4: You can have one without the other.

518
00:24:48,880 --> 00:24:53,480
Speaker 1: So indeterminacy and uncertainty are different ideas. Because remember that

519
00:24:53,520 --> 00:24:56,280
Speaker 1: there are some theories of quantum mechanics which don't have

520
00:24:56,560 --> 00:25:02,000
Speaker 1: randomness and indeterminacy as inherent features. Example Bomian mechanics, where

521
00:25:02,040 --> 00:25:05,679
Speaker 1: the spread of outcomes isn't due to some randomness, but

522
00:25:05,720 --> 00:25:09,320
Speaker 1: it's due to slide variations in the initial conditions of

523
00:25:09,359 --> 00:25:12,280
Speaker 1: how you set up your experiment, of how exactly you

524
00:25:12,320 --> 00:25:14,679
Speaker 1: put that particle in a box, And so in those

525
00:25:14,760 --> 00:25:18,520
Speaker 1: theories like Boemian mechanics, uncertainty doesn't come from randomness. It

526
00:25:18,600 --> 00:25:21,600
Speaker 1: actually comes from the measuring device being part of the

527
00:25:21,680 --> 00:25:24,880
Speaker 1: experiment that's being measured, which keeps it out of total

528
00:25:24,960 --> 00:25:28,600
Speaker 1: quantum equilibrium, which causes uncertainty. So you don't actually need

529
00:25:28,720 --> 00:25:32,000
Speaker 1: randomness to have uncertainty in your quantum theory overall, though

530
00:25:32,040 --> 00:25:35,840
Speaker 1: there's a connection between uncertainty and indeterminacy in most of

531
00:25:35,880 --> 00:25:38,199
Speaker 1: the theories of quantum mechanics, though not at all, and

532
00:25:38,280 --> 00:25:40,760
Speaker 1: even to the one where there is a connection. Uncertainty

533
00:25:40,920 --> 00:25:44,119
Speaker 1: is a special kind of randomness because it relates to

534
00:25:44,200 --> 00:25:47,639
Speaker 1: specific pairs of quantities, not a general randomness.

535
00:25:48,040 --> 00:25:49,960
Speaker 4: Oh interesting, I don't think I ever knew that.

536
00:25:50,200 --> 00:25:52,480
Speaker 1: And the history of this is really fascinating, like how

537
00:25:52,520 --> 00:25:55,760
Speaker 1: it developed. And Heisenberg really was a pioneer, and he

538
00:25:55,840 --> 00:25:58,879
Speaker 1: developed this calculational tool that allowed him to predict you know,

539
00:25:59,000 --> 00:26:01,960
Speaker 1: energy levels, et cetera. But it was a little bit opaque,

540
00:26:02,000 --> 00:26:04,639
Speaker 1: Like he had these matrices and he was operating on

541
00:26:04,760 --> 00:26:06,520
Speaker 1: vectors with them, and people were like, all right, but

542
00:26:06,680 --> 00:26:09,200
Speaker 1: what does that mean? Like what are you talking about?

543
00:26:09,200 --> 00:26:13,520
Speaker 1: What's happening inside? What is the electron doing? And Heisenberg

544
00:26:13,600 --> 00:26:15,879
Speaker 1: was really kind of annoyed by this question, and he

545
00:26:15,920 --> 00:26:18,040
Speaker 1: wrote a whole paper about like what it means and

546
00:26:18,080 --> 00:26:20,640
Speaker 1: what is real and the title that paper I can't

547
00:26:20,680 --> 00:26:23,080
Speaker 1: translate for you because nobody agrees about how to translate

548
00:26:23,119 --> 00:26:25,600
Speaker 1: this one German word in the title, there's like a

549
00:26:25,720 --> 00:26:28,720
Speaker 1: quantum uncertainty about one of the early papers of quantum mechanics.

550
00:26:29,119 --> 00:26:30,439
Speaker 4: What do you mean? What is this title?

551
00:26:31,160 --> 00:26:34,520
Speaker 1: So the title of the paper is on the Acholich

552
00:26:34,760 --> 00:26:39,280
Speaker 1: content of quantum theoretical kinematics and mechanics, and German speakers

553
00:26:39,280 --> 00:26:43,760
Speaker 1: say that word means either like the visualization, which word anschulich,

554
00:26:45,840 --> 00:26:49,720
Speaker 1: which I'm sure I'm mispronouncing, thank you, And it might

555
00:26:49,800 --> 00:26:52,199
Speaker 1: mean like on the physical meaning of it or the

556
00:26:52,200 --> 00:26:55,760
Speaker 1: intelligibility of it or the visualization of it. There is this

557
00:26:55,920 --> 00:26:58,160
Speaker 1: concept in German which we don't have an exact word

558
00:26:58,200 --> 00:27:00,560
Speaker 1: for in English, but basically it's trying to get it,

559
00:27:00,600 --> 00:27:03,200
Speaker 1: like what does this mean? What is quantum mechanics saying

560
00:27:03,359 --> 00:27:04,320
Speaker 1: about what's happening?

561
00:27:04,920 --> 00:27:07,080
Speaker 4: It's like the zeitgeist of quantum mechanics.

562
00:27:07,240 --> 00:27:10,439
Speaker 1: Yeah, and Eisenberg's attitude was like, who cares you know?

563
00:27:10,600 --> 00:27:13,240
Speaker 1: I have this mathematical tool and it makes predictions. I

564
00:27:13,240 --> 00:27:15,040
Speaker 1: can predict how your measurements are going to come out,

565
00:27:15,440 --> 00:27:17,639
Speaker 1: and so we're all good. People didn't really like that,

566
00:27:17,800 --> 00:27:21,000
Speaker 1: and at the same time, Schrodinger developed a completely alternative

567
00:27:21,080 --> 00:27:23,639
Speaker 1: view of quantum mechanics which is now more famous and

568
00:27:23,680 --> 00:27:26,919
Speaker 1: well known, you know, the Schrodinger equation. And because he

569
00:27:27,000 --> 00:27:29,600
Speaker 1: was using like a wave equation, it sort of allowed

570
00:27:29,640 --> 00:27:32,480
Speaker 1: people to more easily visualize what's going on. You know,

571
00:27:32,520 --> 00:27:35,840
Speaker 1: people have this like concept of a blob of probability

572
00:27:36,000 --> 00:27:38,360
Speaker 1: around the atom, et cetera, et cetera. And this really

573
00:27:38,440 --> 00:27:39,760
Speaker 1: kind of pissed Heisenberg off.

574
00:27:40,520 --> 00:27:44,119
Speaker 4: You mean he was annoyed the philosophers and Singer.

575
00:27:44,400 --> 00:27:47,560
Speaker 1: Yeah. He actually wrote in a letter once to another physicist, Polly,

576
00:27:47,640 --> 00:27:50,120
Speaker 1: he said, quote, the more I think about the physical

577
00:27:50,160 --> 00:27:53,199
Speaker 1: part of Schrodinger's theory, the more disgusting I find it.

578
00:27:53,600 --> 00:27:55,520
Speaker 4: Whoa yao wouch.

579
00:27:56,560 --> 00:27:58,600
Speaker 1: And then he said I consider it. And then he

580
00:27:58,680 --> 00:28:02,120
Speaker 1: used this German word must. And I try to look

581
00:28:02,160 --> 00:28:04,760
Speaker 1: up some translations to this German word, and again there's

582
00:28:04,760 --> 00:28:06,920
Speaker 1: a lot of uncertainties. Some people say it means junk,

583
00:28:07,080 --> 00:28:09,560
Speaker 1: some people say it means poppy cock, some people say

584
00:28:09,600 --> 00:28:12,000
Speaker 1: it means rubbish. And there's other less safe for work

585
00:28:12,080 --> 00:28:13,480
Speaker 1: translations of this word as well.

586
00:28:14,800 --> 00:28:17,560
Speaker 4: I think it means that Heisenberg had some saucy words

587
00:28:17,560 --> 00:28:17,840
Speaker 4: for Shu.

588
00:28:18,960 --> 00:28:22,000
Speaker 1: But the point is that in Heisenberg's view, this question

589
00:28:22,119 --> 00:28:25,439
Speaker 1: of like where is the electron was the wrong question.

590
00:28:26,119 --> 00:28:29,520
Speaker 1: In Heisenberg's quantum mechanics, there is like no true position

591
00:28:29,560 --> 00:28:32,360
Speaker 1: of a particle. There's only the outcome of a measurement,

592
00:28:32,400 --> 00:28:35,040
Speaker 1: and there's only if you measure something what's going to happen.

593
00:28:35,200 --> 00:28:38,920
Speaker 1: And inherent in Heisenberg's quantum mechanics was this idea that

594
00:28:38,920 --> 00:28:41,400
Speaker 1: if you measure one thing and then measure another thing,

595
00:28:41,640 --> 00:28:44,960
Speaker 1: the order matters. That like reversing the order will change

596
00:28:45,000 --> 00:28:48,560
Speaker 1: the outcome, which is sort of confusing. Like imagine measuring

597
00:28:48,600 --> 00:28:51,480
Speaker 1: the width and the height of a table. You don't

598
00:28:51,480 --> 00:28:54,160
Speaker 1: think about measuring them in a certain order because you figure, like, well,

599
00:28:54,160 --> 00:28:56,000
Speaker 1: the with and the height are things, I can measure

600
00:28:56,000 --> 00:28:58,360
Speaker 1: them in what order I want. But in this case,

601
00:28:58,400 --> 00:29:01,560
Speaker 1: in Heisenberg's quantum mechanics, some things the order does matter.

602
00:29:01,680 --> 00:29:04,640
Speaker 4: Well, let maybe let's break it down into a concrete example,

603
00:29:05,240 --> 00:29:08,960
Speaker 4: Like let's say that this table had quantum uncertainty about

604
00:29:09,000 --> 00:29:11,160
Speaker 4: its width and its length. Now what would that mean?

605
00:29:11,200 --> 00:29:13,120
Speaker 4: It means I can measure one but not the other,

606
00:29:13,280 --> 00:29:15,200
Speaker 4: or I can sort of measure one and sort of

607
00:29:15,240 --> 00:29:16,880
Speaker 4: measure the other or what does that mean?

608
00:29:16,960 --> 00:29:19,840
Speaker 1: So it would mean that measuring its width would change

609
00:29:19,880 --> 00:29:23,280
Speaker 1: its length, right, and measuring its length would change its width,

610
00:29:23,320 --> 00:29:26,480
Speaker 1: Which would mean the outcome of those measurements depended on

611
00:29:26,520 --> 00:29:28,800
Speaker 1: the order you made them. That measuring it's with then

612
00:29:28,840 --> 00:29:31,320
Speaker 1: its length, or measuring its length that it's with would

613
00:29:31,360 --> 00:29:32,520
Speaker 1: give you different answers.

614
00:29:32,760 --> 00:29:35,440
Speaker 4: Wait, it would change like if I measured the width,

615
00:29:35,560 --> 00:29:39,040
Speaker 4: it would change the length of it, like physically, or

616
00:29:39,160 --> 00:29:42,040
Speaker 4: it would maybe make me less able to measure the length.

617
00:29:42,240 --> 00:29:45,960
Speaker 1: It would change the uncertainty, the fundamental uncertainty of that quantity,

618
00:29:46,000 --> 00:29:47,880
Speaker 1: which would affect what you measure later.

619
00:29:48,040 --> 00:29:50,120
Speaker 4: Yeah, what do you mean the uncertainty? What would be

620
00:29:50,120 --> 00:29:52,200
Speaker 4: the uncertainty of its length? Like I can't predict what

621
00:29:52,280 --> 00:29:54,800
Speaker 4: its length it's going to be, or it can actually

622
00:29:54,840 --> 00:29:55,280
Speaker 4: measure it.

623
00:29:55,320 --> 00:29:57,600
Speaker 1: You can still make a measurement of its length, but

624
00:29:57,640 --> 00:30:00,360
Speaker 1: the outcome that measurement depends on the fundamental uncertain of

625
00:30:00,400 --> 00:30:03,600
Speaker 1: that object. That quantity is not well known, that quantity

626
00:30:03,640 --> 00:30:06,680
Speaker 1: is not like defined. It depends on the inherent uncertainty

627
00:30:06,760 --> 00:30:10,520
Speaker 1: of the object itself. And so if you affect that

628
00:30:10,600 --> 00:30:12,200
Speaker 1: uncertainty affects your measurement.

629
00:30:12,280 --> 00:30:13,760
Speaker 4: Right, So Let's say I measure the table and I

630
00:30:13,760 --> 00:30:17,200
Speaker 4: measure that it's thirty six inches wide. What does it

631
00:30:17,200 --> 00:30:19,360
Speaker 4: mean to that it changes its length? That I'm going

632
00:30:19,400 --> 00:30:21,640
Speaker 4: to measure it and I can't measure it, or I'm

633
00:30:21,640 --> 00:30:23,080
Speaker 4: going to measure it and it's going to sometimes it's

634
00:30:23,120 --> 00:30:24,920
Speaker 4: going to be twenty, sometimes going to be forty, or

635
00:30:25,280 --> 00:30:27,080
Speaker 4: it's like I'm going to measure it and it's going

636
00:30:27,160 --> 00:30:28,920
Speaker 4: to be fifty when I thought it was forty. What

637
00:30:28,960 --> 00:30:30,680
Speaker 4: does it mean that it changes you know what I mean? Like,

638
00:30:30,680 --> 00:30:31,840
Speaker 4: what are you trying to say?

639
00:30:31,920 --> 00:30:34,200
Speaker 1: Well, what I'm saying is that it changes the distribution

640
00:30:34,280 --> 00:30:36,720
Speaker 1: of possible measurements you're going to make for the length.

641
00:30:36,760 --> 00:30:39,080
Speaker 1: If you measure the width first, it changes the quantum

642
00:30:39,080 --> 00:30:41,320
Speaker 1: state of the particle. So now when you go to

643
00:30:41,360 --> 00:30:44,280
Speaker 1: measure the length, you're measuring like a different system than

644
00:30:44,280 --> 00:30:47,640
Speaker 1: you were measuring before you measured the width. You've perturbed it.

645
00:30:47,840 --> 00:30:50,280
Speaker 1: You're saying, it's changing the randomness of the length. There

646
00:30:50,320 --> 00:30:54,120
Speaker 1: is a random element there because the possible outcomes of

647
00:30:54,160 --> 00:30:57,080
Speaker 1: the length are now determined by a probability distribution, and

648
00:30:57,120 --> 00:30:59,440
Speaker 1: that is wider. You can think about it that way.

649
00:30:59,520 --> 00:31:02,880
Speaker 4: Yeah, Oh, I see, So it's like more random, Like

650
00:31:02,920 --> 00:31:04,800
Speaker 4: if I measure the width of the table, then the

651
00:31:04,880 --> 00:31:08,400
Speaker 4: length gets more random, like before it could maybe be

652
00:31:08,440 --> 00:31:10,920
Speaker 4: you know, between five and six feet. But now and

653
00:31:10,960 --> 00:31:14,240
Speaker 4: that I measured the width, now suddenly like this magical table,

654
00:31:14,280 --> 00:31:16,320
Speaker 4: it's like whoa, Now, now the length of it can

655
00:31:16,360 --> 00:31:18,040
Speaker 4: be one inch or it can be a million inches.

656
00:31:18,120 --> 00:31:20,520
Speaker 1: Yeah. And it's very counterintuitive when you think about a table,

657
00:31:20,520 --> 00:31:22,320
Speaker 1: because first of all, the table is a classical object

658
00:31:22,360 --> 00:31:24,560
Speaker 1: doesn't have any of these properties, and because we think

659
00:31:24,560 --> 00:31:27,360
Speaker 1: of a table as having like specific length and width,

660
00:31:27,600 --> 00:31:30,280
Speaker 1: and that's also true of quantum objects. Right, This uncertainty

661
00:31:30,360 --> 00:31:32,920
Speaker 1: only applies to very specific pairs of things that you

662
00:31:32,960 --> 00:31:35,480
Speaker 1: can measure, not to everything. So for a particle, for example,

663
00:31:35,560 --> 00:31:39,040
Speaker 1: it applies to position and momentum, not to like its

664
00:31:39,160 --> 00:31:41,840
Speaker 1: X position and its why position. You can measure something

665
00:31:41,880 --> 00:31:44,600
Speaker 1: in X really precisely and then measure and why really

666
00:31:44,600 --> 00:31:47,720
Speaker 1: precisely with no problem and the order doesn't matter. But

667
00:31:47,760 --> 00:31:50,240
Speaker 1: if you measure its position in X really precisely, it

668
00:31:50,240 --> 00:31:53,520
Speaker 1: messes up your potential knowledge of its momentum in X.

669
00:31:53,800 --> 00:31:56,040
Speaker 4: I see, but I guess for our magical table, I

670
00:31:56,080 --> 00:31:58,160
Speaker 4: can still measure the length, right, Like if I measured

671
00:31:58,160 --> 00:32:00,200
Speaker 4: the width. That doesn't mean I can't measure the length.

672
00:32:00,240 --> 00:32:01,880
Speaker 4: I can still measure the length. It's just going to

673
00:32:01,960 --> 00:32:04,720
Speaker 4: be extra random. So that if I had like a

674
00:32:04,760 --> 00:32:06,840
Speaker 4: million of these magical tables, I'm going to think the

675
00:32:06,920 --> 00:32:07,880
Speaker 4: length is all over the place.

676
00:32:07,960 --> 00:32:09,560
Speaker 1: Mm hmm, Yeah, that's exactly right.

677
00:32:09,640 --> 00:32:11,760
Speaker 4: That means that there is an element of randomness to

678
00:32:12,160 --> 00:32:14,840
Speaker 4: the idea of uncertainty, Like how could you have uncertainty

679
00:32:15,320 --> 00:32:16,040
Speaker 4: without randomness?

680
00:32:16,120 --> 00:32:16,880
Speaker 1: Yeah, that's a good point.

681
00:32:16,920 --> 00:32:20,240
Speaker 4: Okay, So that's the magical table, and if quantum uncertainty

682
00:32:20,280 --> 00:32:22,000
Speaker 4: applied to that table, that's how it would be for

683
00:32:22,040 --> 00:32:25,200
Speaker 4: the table. But now let's maybe take a more physical example.

684
00:32:25,280 --> 00:32:27,840
Speaker 4: You were talking about precision and momentum.

685
00:32:27,920 --> 00:32:30,680
Speaker 1: Yeah, because it's important to understand quantumuncertainty doesn't just apply

686
00:32:30,720 --> 00:32:33,200
Speaker 1: willing nearly to everything. It doesn't say the whole universe

687
00:32:33,240 --> 00:32:36,680
Speaker 1: is fasting. No matter what it says. Specific pairs of

688
00:32:36,760 --> 00:32:39,680
Speaker 1: things can't be known at the same time. So you

689
00:32:39,720 --> 00:32:42,040
Speaker 1: can know the X and the why of a particle,

690
00:32:42,120 --> 00:32:44,280
Speaker 1: but you can't know it's X and it's momentum also

691
00:32:44,400 --> 00:32:45,000
Speaker 1: in X.

692
00:32:45,160 --> 00:32:47,440
Speaker 4: Wait, I can know it or I can measure it,

693
00:32:47,480 --> 00:32:49,680
Speaker 4: because like the table, I can measure the with and

694
00:32:49,720 --> 00:32:52,640
Speaker 4: the length right, Or are you saying that if I

695
00:32:52,680 --> 00:32:54,240
Speaker 4: measure the width, I can measure the length.

696
00:32:54,280 --> 00:32:56,000
Speaker 1: You can always measure it. But in the case of

697
00:32:56,040 --> 00:32:58,160
Speaker 1: the table, if you measure the width, you get a number.

698
00:32:58,240 --> 00:33:00,120
Speaker 1: You measure the length, you get a number. But now

699
00:33:00,160 --> 00:33:02,400
Speaker 1: you no longer know the width because you messed up

700
00:33:02,400 --> 00:33:04,400
Speaker 1: the width when you measure the length. These two things

701
00:33:04,440 --> 00:33:05,080
Speaker 1: are connected.

702
00:33:05,240 --> 00:33:06,920
Speaker 4: I see. I think maybe what you mean by no

703
00:33:07,320 --> 00:33:10,240
Speaker 4: is you actually mean predict, Like if I measure the width,

704
00:33:10,640 --> 00:33:12,640
Speaker 4: then it makes it harder for me to predict what

705
00:33:12,760 --> 00:33:14,480
Speaker 4: the length is going to be of this table. Because

706
00:33:14,480 --> 00:33:16,160
Speaker 4: I can know what the length of the table is,

707
00:33:16,200 --> 00:33:17,840
Speaker 4: I can measure it, right, That's how we know it.

708
00:33:18,400 --> 00:33:20,320
Speaker 4: But it's more about like being able to know it

709
00:33:20,360 --> 00:33:21,160
Speaker 4: before you measure it.

710
00:33:21,160 --> 00:33:22,840
Speaker 1: Well, I'd say, when you measure it, you measure it

711
00:33:22,880 --> 00:33:24,880
Speaker 1: with some uncertainty. Even if you know it, you know

712
00:33:24,960 --> 00:33:27,400
Speaker 1: with some uncertainty. There's like error bars on it.

713
00:33:27,720 --> 00:33:30,920
Speaker 4: Oh, it's about error bars. That's different, though, isn't it.

714
00:33:31,000 --> 00:33:31,160
Speaker 9: Well?

715
00:33:31,200 --> 00:33:32,800
Speaker 1: You know it depends on how you interpret the er

716
00:33:32,880 --> 00:33:35,440
Speaker 1: bars and the randomness. But like repeated measurements which probe

717
00:33:35,440 --> 00:33:39,360
Speaker 1: that probability distribution will give different outcomes. It doesn't fundamentally

718
00:33:39,520 --> 00:33:42,000
Speaker 1: have a specific length that has a distribution, and if

719
00:33:42,040 --> 00:33:45,520
Speaker 1: you measure it multiple times, you'll get different answers according

720
00:33:45,560 --> 00:33:46,960
Speaker 1: to the width of that distribution.

721
00:33:47,240 --> 00:33:50,000
Speaker 4: Oh, I see, I feel like you're saying kind of like,

722
00:33:50,040 --> 00:33:52,400
Speaker 4: the table has the length and with, but then there's

723
00:33:52,480 --> 00:33:54,520
Speaker 4: our measurement of the length and with which might not

724
00:33:54,640 --> 00:33:56,480
Speaker 4: be what it's real length and with this.

725
00:33:56,880 --> 00:33:59,000
Speaker 1: In the case of the magical table, which follows this

726
00:33:59,080 --> 00:34:02,800
Speaker 1: quantum uncertainty. So obviously tables don't really right. If we

727
00:34:02,840 --> 00:34:05,560
Speaker 1: say that it has this quantumuncertainty attached to the length

728
00:34:05,600 --> 00:34:07,360
Speaker 1: and the width, then the length and the width are

729
00:34:07,400 --> 00:34:10,759
Speaker 1: not determined simultaneously. It's not that it exists and it's

730
00:34:10,760 --> 00:34:13,200
Speaker 1: written in a gold tablet by God somewhere. We just

731
00:34:13,200 --> 00:34:15,600
Speaker 1: don't have access to seeing it. It's just that it's

732
00:34:15,640 --> 00:34:16,320
Speaker 1: not defined.

733
00:34:16,400 --> 00:34:18,279
Speaker 4: Oh, I think I see what like you're saying. I

734
00:34:18,320 --> 00:34:21,719
Speaker 4: think that if I measure this table with like a

735
00:34:21,800 --> 00:34:24,239
Speaker 4: super precise ruler, and I measured the width and I

736
00:34:24,280 --> 00:34:27,240
Speaker 4: get that it's three feet wide and I'm super certain

737
00:34:27,239 --> 00:34:30,080
Speaker 4: about that, that means that no matter what I do

738
00:34:30,200 --> 00:34:33,440
Speaker 4: to measure the length, I have to assign a certain

739
00:34:33,640 --> 00:34:36,320
Speaker 4: uncertainty or a certain error to it. I might measure

740
00:34:36,360 --> 00:34:38,120
Speaker 4: the length of the table. I might say, oh, I

741
00:34:38,239 --> 00:34:40,120
Speaker 4: measure it to be six feet, But in the back

742
00:34:40,160 --> 00:34:43,080
Speaker 4: of my head I have to be like, well, that's

743
00:34:43,120 --> 00:34:45,319
Speaker 4: probably not actually six feet. Is that kind of what

744
00:34:45,360 --> 00:34:46,520
Speaker 4: you mean by uncertainty?

745
00:34:46,760 --> 00:34:49,239
Speaker 1: Yeah, And then if you go back to measure the

746
00:34:49,280 --> 00:34:50,799
Speaker 1: withth you're going to get a different answer than you

747
00:34:50,840 --> 00:34:54,240
Speaker 1: did before, because measuring the length has now changed the width.

748
00:34:54,280 --> 00:34:55,720
Speaker 4: Well, no, i'm it's still the same table.

749
00:34:55,800 --> 00:34:58,120
Speaker 1: No, it's not still the same table, right, because you've

750
00:34:58,120 --> 00:35:00,000
Speaker 1: made a measurement to it and measuring things change.

751
00:35:00,880 --> 00:35:02,719
Speaker 4: Oh but what if I mentioned at the same time.

752
00:35:02,840 --> 00:35:05,080
Speaker 1: Yeah, great question, But you can't do that, right. You

753
00:35:05,120 --> 00:35:07,080
Speaker 1: make a measurement of a quantum system. You can measure

754
00:35:07,120 --> 00:35:10,440
Speaker 1: a thing, right, and these two things you can't measure simultaneously.

755
00:35:10,560 --> 00:35:12,640
Speaker 4: Oh see that. I feel like that's another concept. Then

756
00:35:12,640 --> 00:35:15,799
Speaker 4: in quantum chacs, why can't I measure this table at

757
00:35:15,800 --> 00:35:16,319
Speaker 4: the same time?

758
00:35:16,520 --> 00:35:19,440
Speaker 1: In heisimbers quantum mechanics, the way you make a measurement

759
00:35:19,560 --> 00:35:22,400
Speaker 1: is that you operate on that quantum state, operating, and

760
00:35:22,400 --> 00:35:24,480
Speaker 1: the quantum state will change it. And you can't do

761
00:35:24,640 --> 00:35:26,400
Speaker 1: two operations simultaneously.

762
00:35:26,600 --> 00:35:28,239
Speaker 4: Maybe for those of us that are not familiar with

763
00:35:28,320 --> 00:35:31,000
Speaker 4: quantum states, what does that mean? That means that, like

764
00:35:31,160 --> 00:35:33,799
Speaker 4: in a system, there are some variables that you just

765
00:35:33,840 --> 00:35:34,960
Speaker 4: can't measure at the same time.

766
00:35:35,000 --> 00:35:36,840
Speaker 1: I'll try. All measurements have to be made in a

767
00:35:36,880 --> 00:35:40,600
Speaker 1: certain order because potentially measurements could mess up later measurements.

768
00:35:40,760 --> 00:35:42,960
Speaker 1: In some cases they don't right, Like, you can measure

769
00:35:42,960 --> 00:35:45,160
Speaker 1: the X and then you can measure the Y, and

770
00:35:45,200 --> 00:35:47,399
Speaker 1: the answer you get for why doesn't depend on whether

771
00:35:47,440 --> 00:35:50,000
Speaker 1: you already measured x. But if you measure X and

772
00:35:50,040 --> 00:35:52,359
Speaker 1: then you measure momentum and X, then you will get

773
00:35:52,400 --> 00:35:54,840
Speaker 1: a different answer. And the order does matter, like measuring

774
00:35:55,040 --> 00:35:58,080
Speaker 1: x and then momentum or measuring momentum and then position

775
00:35:58,200 --> 00:36:00,600
Speaker 1: in X will change the answers that you get.

776
00:36:01,239 --> 00:36:03,680
Speaker 4: I see. It's kind of part of the magical properties

777
00:36:03,680 --> 00:36:06,160
Speaker 4: of my table. Like a regular table, I can definitely

778
00:36:06,200 --> 00:36:08,160
Speaker 4: get to people to measure it within the length at

779
00:36:08,160 --> 00:36:11,400
Speaker 4: the same time, But a quantum uncertain table you just can't.

780
00:36:11,440 --> 00:36:12,719
Speaker 4: You can only do one at a time.

781
00:36:12,880 --> 00:36:14,640
Speaker 1: Yeah, And it's sort of hard to understand that about

782
00:36:14,640 --> 00:36:16,319
Speaker 1: a table because it doesn't seem to make any sense.

783
00:36:16,320 --> 00:36:19,000
Speaker 1: An X and Y seem to be orthogonal, right, And

784
00:36:19,040 --> 00:36:22,200
Speaker 1: that's why I suggested it as a ridiculous example, because

785
00:36:22,280 --> 00:36:26,200
Speaker 1: it's very counterintuitive, and quant mechanics is counterintuitive in that way,

786
00:36:26,239 --> 00:36:29,080
Speaker 1: but not quite as counterintuitive. I mean, you can't get

787
00:36:29,080 --> 00:36:32,160
Speaker 1: some understanding of why measuring one thing messes up another

788
00:36:32,400 --> 00:36:35,480
Speaker 1: if you think more specifically about, for example, momentum and

789
00:36:35,560 --> 00:36:38,280
Speaker 1: position instead of like table lengths and widths.

790
00:36:38,480 --> 00:36:40,440
Speaker 4: Right, I just think that you know for more for

791
00:36:40,640 --> 00:36:42,600
Speaker 4: less of us saying that's what the mass says. And

792
00:36:42,680 --> 00:36:46,799
Speaker 4: it's magic. It's pretty much the same thing. It's magematical, yes,

793
00:36:46,800 --> 00:36:48,640
Speaker 4: it's right's mathemagical, you go.

794
00:36:49,680 --> 00:36:51,200
Speaker 1: I mean you can think about it in terms of

795
00:36:51,239 --> 00:36:54,000
Speaker 1: like measuring a particle, right, say you want to know

796
00:36:54,120 --> 00:36:57,359
Speaker 1: its location, how would you actually make that measurement? Well,

797
00:36:57,400 --> 00:36:59,920
Speaker 1: in order to measure the location of a particle, you

798
00:37:00,080 --> 00:37:02,239
Speaker 1: got to like bounce something else off of it. There's

799
00:37:02,280 --> 00:37:05,319
Speaker 1: no passive observing of the universe. You got to like

800
00:37:05,400 --> 00:37:07,600
Speaker 1: bounce a photon off of it, for example, to see

801
00:37:07,600 --> 00:37:10,480
Speaker 1: where it is. And if you want to know its

802
00:37:10,520 --> 00:37:13,680
Speaker 1: precision really really precisely, then you need a really high

803
00:37:13,800 --> 00:37:17,840
Speaker 1: energy photon because high energy photons have short wavelengths, and

804
00:37:17,920 --> 00:37:21,240
Speaker 1: so they can tell you information about really small distances.

805
00:37:21,800 --> 00:37:24,000
Speaker 1: But if you bounce a really high energy photon off

806
00:37:24,040 --> 00:37:26,239
Speaker 1: of your electron, then you're going to totally mess up

807
00:37:26,280 --> 00:37:28,360
Speaker 1: its momentum. It's momentum, it's going to be very different

808
00:37:28,400 --> 00:37:31,040
Speaker 1: now then before you measured it. So if you go

809
00:37:31,040 --> 00:37:32,640
Speaker 1: off to measure its momentum, you're going to get a

810
00:37:32,680 --> 00:37:35,600
Speaker 1: different answer than if you hadn't measured the position.

811
00:37:35,840 --> 00:37:37,640
Speaker 4: That's if you try to do it one after the other.

812
00:37:37,719 --> 00:37:41,440
Speaker 4: But I'm just throwing out an idea. What if you, like,

813
00:37:41,640 --> 00:37:44,719
Speaker 4: throw a photon at it and you measure how the

814
00:37:44,880 --> 00:37:47,839
Speaker 4: photland bounces, and then that tells you both things at

815
00:37:47,840 --> 00:37:50,640
Speaker 4: the same time, maybe right, Like if I catch a baseball,

816
00:37:51,000 --> 00:37:53,239
Speaker 4: I know its position and how fast it was going.

817
00:37:53,360 --> 00:37:55,280
Speaker 1: Yeah, and you can do that for a classical object,

818
00:37:55,320 --> 00:37:59,239
Speaker 1: and you can know simultaneously multiple things about quantum objects

819
00:38:00,280 --> 00:38:03,600
Speaker 1: some things right just in this case, like not position

820
00:38:03,760 --> 00:38:06,640
Speaker 1: a momentum simultaneously. And the reason that you can't has

821
00:38:06,680 --> 00:38:09,960
Speaker 1: to do with how this information is encoded in the particle,

822
00:38:10,000 --> 00:38:12,440
Speaker 1: which I think we can understand without getting too mathematical.

823
00:38:12,560 --> 00:38:15,160
Speaker 4: All right, well, let's dig into some of this mathemagic

824
00:38:15,400 --> 00:38:18,800
Speaker 4: or not mathaphysics, I guess, and the idea of wave

825
00:38:18,920 --> 00:38:20,960
Speaker 4: and the wave function, which is I think where we're

826
00:38:21,000 --> 00:38:23,360
Speaker 4: going with this dig into that waving as But first

827
00:38:23,680 --> 00:38:25,040
Speaker 4: let's take another quick break.

828
00:38:29,680 --> 00:38:31,480
Speaker 1: When you pop a piece of cheese into your mouth

829
00:38:31,560 --> 00:38:34,719
Speaker 1: or enjoy a rich spoonful of greeky yogurt, you're probably

830
00:38:34,760 --> 00:38:38,800
Speaker 1: not thinking about the environmental impact of each and every bite.

831
00:38:38,840 --> 00:38:41,440
Speaker 1: But the people in the dairy industry are. US Dairy

832
00:38:41,480 --> 00:38:45,799
Speaker 1: has set themselves some ambitious sustainability goals, including being greenhouse

833
00:38:45,800 --> 00:38:48,399
Speaker 1: gas neutral by twenty to fifty. That's why they're working

834
00:38:48,440 --> 00:38:50,800
Speaker 1: hard every day to find new ways to reduce waste,

835
00:38:50,840 --> 00:38:55,040
Speaker 1: conserve natural resources, and drive down greenhouse gas emissions. Take water,

836
00:38:55,080 --> 00:38:58,160
Speaker 1: for example, most dairy farms reuse water up to four

837
00:38:58,239 --> 00:39:01,720
Speaker 1: times the same water cools them well, clean's equipment, washes

838
00:39:01,760 --> 00:39:04,560
Speaker 1: the barn, and irrigates the crops. How is US dairy

839
00:39:04,560 --> 00:39:08,319
Speaker 1: tackling greenhouse gases? Many farms use anaerobic digestors that turn

840
00:39:08,360 --> 00:39:12,280
Speaker 1: the methane from maneure into renewable energy that can power farms, towns,

841
00:39:12,280 --> 00:39:14,400
Speaker 1: and electric cars. So the next time you grab a

842
00:39:14,400 --> 00:39:16,440
Speaker 1: slice of pizza or lick an ice cream cone, know

843
00:39:16,480 --> 00:39:19,200
Speaker 1: that dairy farmers and processors around the country are using

844
00:39:19,200 --> 00:39:22,719
Speaker 1: the latest practices and innovations to provide the nutrient dense

845
00:39:22,840 --> 00:39:25,560
Speaker 1: dairy products we love with less of an impact. Visit

846
00:39:25,640 --> 00:39:28,439
Speaker 1: usdairy dot com slash sustainability to learn more.

847
00:39:28,840 --> 00:39:31,880
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848
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Speaker 11: There are children, friends, and families walking, riding on paths

873
00:40:49,040 --> 00:40:51,480
Speaker 11: and roads every day. Remember they're real people with loved

874
00:40:51,520 --> 00:40:52,279
Speaker 11: ones who need them to.

875
00:40:52,239 --> 00:40:53,040
Speaker 1: Get home safely.

876
00:40:53,239 --> 00:40:55,839
Speaker 11: Protect our cyclists and pedestrians because they're people too.

877
00:40:56,120 --> 00:40:56,640
Speaker 1: Go safely.

878
00:40:56,719 --> 00:40:59,640
Speaker 11: California from the California Office of Traffic Safety and Caltrans.

879
00:41:07,640 --> 00:41:10,720
Speaker 4: All right, we're talking about the hairy topic of quantum

880
00:41:10,800 --> 00:41:13,920
Speaker 4: uncertainty and all the uncertain details about it down to

881
00:41:13,960 --> 00:41:16,439
Speaker 4: the nittigrie to hear now, Daniel, you think that maybe

882
00:41:16,480 --> 00:41:19,799
Speaker 4: a good way to explain this is using waves, and

883
00:41:20,160 --> 00:41:23,239
Speaker 4: specifically sound waves, right as maybe they relate to the

884
00:41:23,280 --> 00:41:24,680
Speaker 4: wave function of quantum particles.

885
00:41:24,800 --> 00:41:27,000
Speaker 1: Yeah, if you're trying to think about position and momentum

886
00:41:27,080 --> 00:41:30,000
Speaker 1: of particles and how they're like encoded in the mathematical

887
00:41:30,040 --> 00:41:33,360
Speaker 1: description of the particle in quantum Mechanics' trually helpful to

888
00:41:33,360 --> 00:41:35,840
Speaker 1: think about analogies we have in the classical world that

889
00:41:35,880 --> 00:41:37,960
Speaker 1: are a little bit more intuitive, And there actually is

890
00:41:37,960 --> 00:41:39,759
Speaker 1: one that a lot of people are familiar with, and

891
00:41:39,800 --> 00:41:43,520
Speaker 1: that's sound waves and songs and how words and music

892
00:41:43,600 --> 00:41:46,200
Speaker 1: can be broken up into very specific frequencies.

893
00:41:46,320 --> 00:41:48,760
Speaker 4: All right, let's dig into it. How is a quantum

894
00:41:48,840 --> 00:41:51,040
Speaker 4: uncertainty like a song?

895
00:41:51,120 --> 00:41:54,239
Speaker 1: Well, think about like your equalizer on your stereo when

896
00:41:54,280 --> 00:41:56,360
Speaker 1: you hear songs that has like a bass and a

897
00:41:56,440 --> 00:41:59,480
Speaker 1: trouble and whatever, and there's high frequencies and low frequencies,

898
00:41:59,719 --> 00:42:02,520
Speaker 1: and equalizer is telling you like how much bass is there,

899
00:42:02,760 --> 00:42:05,040
Speaker 1: or how many low frequency sounds are there, or how

900
00:42:05,120 --> 00:42:07,120
Speaker 1: many high frequency sounds are there.

901
00:42:06,960 --> 00:42:10,120
Speaker 4: Or more like how strong the song is in this

902
00:42:10,200 --> 00:42:11,000
Speaker 4: frequency range?

903
00:42:11,040 --> 00:42:13,319
Speaker 1: Right exactly, So we're going to think about the relationship

904
00:42:13,360 --> 00:42:17,640
Speaker 1: between frequencies pure notes of specific frequencies and how you

905
00:42:17,640 --> 00:42:19,920
Speaker 1: can use them to build up different kinds of sound.

906
00:42:20,360 --> 00:42:22,400
Speaker 1: That's going to give you a feeling for the physical

907
00:42:22,480 --> 00:42:26,040
Speaker 1: reason why there are some specific quantities that you can't

908
00:42:26,080 --> 00:42:29,400
Speaker 1: know at the same time how they're linked by quantum uncertainty.

909
00:42:29,560 --> 00:42:31,880
Speaker 1: So start with a pure note, like an opera singer

910
00:42:32,000 --> 00:42:35,440
Speaker 1: singing a high see that's just one frequency on your

911
00:42:35,480 --> 00:42:37,840
Speaker 1: equalizer or on a spectrograph, it's going to give you

912
00:42:37,880 --> 00:42:40,919
Speaker 1: a single spike at that frequency. And there's very little

913
00:42:40,960 --> 00:42:43,000
Speaker 1: uncertainty in the frequency. Right, you hear the sound, you

914
00:42:43,040 --> 00:42:45,400
Speaker 1: know the frequency. There's only one frequency to the sound.

915
00:42:45,560 --> 00:42:49,759
Speaker 1: Now think about the corresponding quantity, the shape. If she

916
00:42:49,920 --> 00:42:52,560
Speaker 1: hits the high Sea, then where is that sine wave?

917
00:42:52,640 --> 00:42:54,920
Speaker 1: That sinwave is everywhere in the room. It goes up

918
00:42:54,960 --> 00:42:57,400
Speaker 1: and down. It doesn't really have a shape. It's a

919
00:42:57,480 --> 00:43:00,320
Speaker 1: sine wave everywhere. It fills the room or the opera

920
00:43:00,320 --> 00:43:02,399
Speaker 1: house or whatever it is. So you know a lot

921
00:43:02,400 --> 00:43:06,000
Speaker 1: about the frequency of her note. The spectrograph is a spike,

922
00:43:06,360 --> 00:43:09,160
Speaker 1: but the soundwave itself is very spread out in position.

923
00:43:09,239 --> 00:43:11,839
Speaker 1: It's filled the whole room, it's everywhere. Well, what if

924
00:43:11,840 --> 00:43:14,840
Speaker 1: we wanted our opera singer to create a sound that

925
00:43:14,880 --> 00:43:17,719
Speaker 1: you could only hear in part of the room. And

926
00:43:17,760 --> 00:43:19,520
Speaker 1: you know that you can get different sounds in different

927
00:43:19,520 --> 00:43:21,120
Speaker 1: parts of the room if you take advantage of how

928
00:43:21,120 --> 00:43:24,399
Speaker 1: they can interfere That's why they very carefully design acoustics

929
00:43:24,400 --> 00:43:26,799
Speaker 1: in opera houses, et cetera. But we can get our

930
00:43:26,920 --> 00:43:29,040
Speaker 1: singer to make a sound that you can only hear

931
00:43:29,120 --> 00:43:31,839
Speaker 1: in one part of the room, like in only one

932
00:43:31,840 --> 00:43:33,799
Speaker 1: spot can you hear it, and the other spots it'll

933
00:43:33,840 --> 00:43:36,040
Speaker 1: be totally silent. She can do this if she adds

934
00:43:36,120 --> 00:43:39,480
Speaker 1: more frequencies. Right, So if she has just one frequency,

935
00:43:39,560 --> 00:43:42,760
Speaker 1: just the high seats everywhere. Now add another singer singing

936
00:43:42,800 --> 00:43:46,960
Speaker 1: a different frequency, and those two sine waves have different frequencies,

937
00:43:46,960 --> 00:43:49,040
Speaker 1: and so they'll cancel out in some places of the

938
00:43:49,120 --> 00:43:52,160
Speaker 1: room and add up in others. That's constructive and destructive

939
00:43:52,200 --> 00:43:55,600
Speaker 1: interference at a third singer with another frequency, and you

940
00:43:55,640 --> 00:43:59,480
Speaker 1: can shape the total effect further. The more frequencies you add,

941
00:43:59,680 --> 00:44:02,239
Speaker 1: the more where you can shape that sound. And if

942
00:44:02,239 --> 00:44:04,719
Speaker 1: you add an infinite number of singers crowded on to

943
00:44:04,800 --> 00:44:07,359
Speaker 1: that stage, you can make any sound shape you want

944
00:44:07,400 --> 00:44:11,239
Speaker 1: in the room, including a very very narrow spike so

945
00:44:11,280 --> 00:44:13,920
Speaker 1: that the sound can only be heard at one spot

946
00:44:13,960 --> 00:44:16,680
Speaker 1: in the room. So in this scenario, the sound has

947
00:44:16,719 --> 00:44:19,959
Speaker 1: a huge spread of frequencies but a single very well

948
00:44:20,000 --> 00:44:24,120
Speaker 1: determined location. All the sound is in one place. So

949
00:44:24,160 --> 00:44:27,560
Speaker 1: maybe now you see the tradeoff. Either you can have

950
00:44:27,600 --> 00:44:30,400
Speaker 1: a single frequency the one high scene note, but the

951
00:44:30,440 --> 00:44:33,040
Speaker 1: position is very broad it's anywhere in the room. Or

952
00:44:33,719 --> 00:44:36,680
Speaker 1: you can have a broad range of frequencies lots of

953
00:44:36,680 --> 00:44:39,359
Speaker 1: singers on the stage, but the position is now very

954
00:44:39,440 --> 00:44:43,240
Speaker 1: very narrow. So because of the wavelike nature of sound,

955
00:44:43,640 --> 00:44:47,600
Speaker 1: you can't have narrowness in both frequency and in location.

956
00:44:47,960 --> 00:44:51,319
Speaker 1: Those two things are inherently linked by the nature of

957
00:44:51,400 --> 00:44:54,960
Speaker 1: the physical process of sound. You can't use a single

958
00:44:55,040 --> 00:44:58,440
Speaker 1: frequency to create a narrow spike a sound that exists

959
00:44:58,480 --> 00:45:02,680
Speaker 1: only one location in space. It's either narrow frequency in

960
00:45:02,760 --> 00:45:08,200
Speaker 1: broad position or broad frequency range and narrow position. Frequency

961
00:45:08,239 --> 00:45:11,399
Speaker 1: and position are conjugate variables. They're linked in that very

962
00:45:11,400 --> 00:45:15,080
Speaker 1: special way. And that also applies to quantum waves. For

963
00:45:15,160 --> 00:45:17,479
Speaker 1: a particle in a box, the frequency of the wave

964
00:45:17,480 --> 00:45:20,560
Speaker 1: function tells you its momentum. So if you want your

965
00:45:20,560 --> 00:45:23,640
Speaker 1: particle to have little uncertainty in position, you have to

966
00:45:23,760 --> 00:45:27,359
Speaker 1: use lots of frequencies, lots of possible momenta which add

967
00:45:27,440 --> 00:45:29,360
Speaker 1: up to give you that spike. And because you have

968
00:45:29,440 --> 00:45:32,359
Speaker 1: lots of possible momentum now in your wave function, that

969
00:45:32,520 --> 00:45:37,799
Speaker 1: means a large momentum uncertainty, so small uncertainty position requires

970
00:45:37,880 --> 00:45:41,120
Speaker 1: a large momentum uncertainty. And on the other direction, if

971
00:45:41,120 --> 00:45:44,640
Speaker 1: you want your particle to have little uncertainty in momentum,

972
00:45:44,840 --> 00:45:47,960
Speaker 1: then you can only use a narrow range of frequencies,

973
00:45:48,000 --> 00:45:50,840
Speaker 1: which means you'll get a very broad blob in position.

974
00:45:51,360 --> 00:45:54,480
Speaker 1: You can't build a quantum wave function out of just

975
00:45:54,520 --> 00:45:58,239
Speaker 1: a few frequencies that also localized in position, for the

976
00:45:58,280 --> 00:46:01,160
Speaker 1: same reason that the oppera singer can't sing a single

977
00:46:01,239 --> 00:46:03,520
Speaker 1: note and have it be localized in the room.

978
00:46:03,800 --> 00:46:06,080
Speaker 4: Yeah, I think that maybe a way that I've seen

979
00:46:06,120 --> 00:46:08,400
Speaker 4: it explain is a little bit talking about like the

980
00:46:08,520 --> 00:46:11,600
Speaker 4: with of things are you saying can be described by

981
00:46:11,640 --> 00:46:15,000
Speaker 4: wave functions, Right, Like something that has like a really

982
00:46:15,080 --> 00:46:18,560
Speaker 4: wide wave means that it's it's really fuzzy and you

983
00:46:18,600 --> 00:46:20,920
Speaker 4: don't know where quite where it is. Whereas something that

984
00:46:21,239 --> 00:46:24,160
Speaker 4: is really narrow you can sort of know its position,

985
00:46:25,040 --> 00:46:26,760
Speaker 4: but it's also going really fast.

986
00:46:26,800 --> 00:46:29,200
Speaker 1: Maybe exactly for something you know really really well, and

987
00:46:29,239 --> 00:46:31,200
Speaker 1: its wave function is going to be super duper narrow,

988
00:46:31,239 --> 00:46:34,160
Speaker 1: like a spike. But to build a spike in terms

989
00:46:34,200 --> 00:46:37,640
Speaker 1: of frequencies, in terms of like various possible momenta requires

990
00:46:37,640 --> 00:46:39,760
Speaker 1: a very large number of them. You need like lots

991
00:46:39,760 --> 00:46:41,840
Speaker 1: of them to add up and cancel out in just

992
00:46:41,880 --> 00:46:43,960
Speaker 1: the right way to give you that spike. Whereasf you

993
00:46:44,000 --> 00:46:46,400
Speaker 1: want something really big and fat as a blob, then

994
00:46:46,440 --> 00:46:49,279
Speaker 1: you need fewer different frequencies to add up to give

995
00:46:49,320 --> 00:46:52,120
Speaker 1: you that big fat blob. Something that's very uncertain. So

996
00:46:52,200 --> 00:46:55,040
Speaker 1: a wave function that's really narrow needs lots of different

997
00:46:55,040 --> 00:46:58,040
Speaker 1: frequencies to add up, which means lots of different possible

998
00:46:58,080 --> 00:47:00,160
Speaker 1: momentum because frequency and moment are the same in for

999
00:47:00,200 --> 00:47:03,280
Speaker 1: a particle, which means a lot of uncertainty in its momentum,

1000
00:47:03,320 --> 00:47:05,960
Speaker 1: Whereas if you have a lot of uncertainty in his position,

1001
00:47:06,280 --> 00:47:09,520
Speaker 1: you only need a few frequencies, which means less uncertainty

1002
00:47:09,760 --> 00:47:11,759
Speaker 1: in its momentum. That gives you a little bit of

1003
00:47:11,760 --> 00:47:15,160
Speaker 1: the flavor of why position and momentum have this special relationship.

1004
00:47:15,239 --> 00:47:18,640
Speaker 1: Quantumncerurnity is all about very specific pairs of things you

1005
00:47:18,680 --> 00:47:20,840
Speaker 1: can measure that have this relationship. It's not just like

1006
00:47:20,880 --> 00:47:21,960
Speaker 1: any two things that you.

1007
00:47:21,960 --> 00:47:24,600
Speaker 4: Measure, right, and so maybe it might help to get

1008
00:47:24,600 --> 00:47:27,000
Speaker 4: into some of these other things. So you're saying that

1009
00:47:27,080 --> 00:47:30,320
Speaker 4: position of momentum are linked together in this quantum uncertainty

1010
00:47:30,440 --> 00:47:33,000
Speaker 4: because of its wave nature. Right. For example, if you

1011
00:47:33,000 --> 00:47:36,239
Speaker 4: take to measure the velocity of a wave, somehow it's

1012
00:47:36,280 --> 00:47:39,000
Speaker 4: related also to its frequency, which that's where the fuzziness

1013
00:47:39,120 --> 00:47:41,000
Speaker 4: maybe it comes from. So maybe talk about some of

1014
00:47:41,040 --> 00:47:44,719
Speaker 4: these other variables in quantum mechanics that are also linked

1015
00:47:44,760 --> 00:47:45,840
Speaker 4: together by uncertainty.

1016
00:47:45,960 --> 00:47:49,080
Speaker 1: Yeah, and a tiny little quibble there is that it

1017
00:47:49,120 --> 00:47:52,040
Speaker 1: can be explained in terms of like shirting or wave mechanics.

1018
00:47:52,320 --> 00:47:55,080
Speaker 1: But Heisenberg can also explain it without any waves at all.

1019
00:47:55,480 --> 00:47:58,040
Speaker 1: He has a completely different formulation of quant mechanics that

1020
00:47:58,120 --> 00:48:00,840
Speaker 1: uses matrices. And for those of you who like know

1021
00:48:00,960 --> 00:48:04,720
Speaker 1: matrix mechanics, you know, like multiplication of matrices doesn't commute

1022
00:48:04,719 --> 00:48:07,280
Speaker 1: that you like, it matters what you order you multiply

1023
00:48:07,400 --> 00:48:10,120
Speaker 1: things by with your matrices. So like it comes out

1024
00:48:10,120 --> 00:48:13,200
Speaker 1: of quantum mechanics no matter what mathematical formulation you use,

1025
00:48:13,360 --> 00:48:16,839
Speaker 1: matrices or waves or whatever. It's like really deep in there.

1026
00:48:16,880 --> 00:48:19,600
Speaker 1: But you're right, it's not just position and momentum that

1027
00:48:19,600 --> 00:48:22,200
Speaker 1: this affects. There's lots of other things that are paired.

1028
00:48:22,320 --> 00:48:26,400
Speaker 1: Another famous example is energy and time of what like

1029
00:48:26,440 --> 00:48:28,840
Speaker 1: of a particle. So, for example, a particle might have

1030
00:48:28,880 --> 00:48:32,960
Speaker 1: a specific mass, and that affects how long it lasts. So,

1031
00:48:33,040 --> 00:48:36,719
Speaker 1: for example, an electron which lasts forever has a very

1032
00:48:36,719 --> 00:48:40,680
Speaker 1: specific mass. Every electron out there has the same mass exactly,

1033
00:48:40,719 --> 00:48:43,640
Speaker 1: because electrons live for an infinite number of years. But

1034
00:48:43,680 --> 00:48:46,400
Speaker 1: if you have particles whose lifetime is shorter, there's a

1035
00:48:46,440 --> 00:48:49,160
Speaker 1: quant mechanical uncertainty to how long they're going to live,

1036
00:48:49,520 --> 00:48:52,680
Speaker 1: then their mass is more uncertain. So for example, a

1037
00:48:52,760 --> 00:48:55,400
Speaker 1: top quark, it might be one hundred and seventy three GV,

1038
00:48:55,640 --> 00:48:57,319
Speaker 1: might be one hundred and sixty five, might be one

1039
00:48:57,360 --> 00:49:00,520
Speaker 1: hundred and eighty one. There's a huge variation there in

1040
00:49:00,560 --> 00:49:03,400
Speaker 1: the possible masses the top quark would have because it

1041
00:49:03,440 --> 00:49:04,920
Speaker 1: doesn't live for very long.

1042
00:49:05,280 --> 00:49:07,320
Speaker 4: So when you say like it lasts, meaning like it

1043
00:49:07,719 --> 00:49:11,080
Speaker 4: might at any point break down into other things, right,

1044
00:49:11,239 --> 00:49:14,040
Speaker 4: lower energy things, and so it has a lifespan and

1045
00:49:14,080 --> 00:49:16,400
Speaker 4: you're saying, like, how long we expect it to be

1046
00:49:16,480 --> 00:49:19,280
Speaker 4: around hole is tied to its mass exactly.

1047
00:49:19,640 --> 00:49:22,640
Speaker 1: Electrons, we think their lifetime is basically infinity. You could

1048
00:49:22,640 --> 00:49:25,040
Speaker 1: wait infinite number of years, the electron just sitting out

1049
00:49:25,040 --> 00:49:27,520
Speaker 1: there in space would still be an electron. Top quark

1050
00:49:27,600 --> 00:49:30,120
Speaker 1: lasts for like ten to the minus twenty three seconds.

1051
00:49:30,239 --> 00:49:32,759
Speaker 1: So there's a lot less uncertainty about how long a

1052
00:49:32,840 --> 00:49:34,440
Speaker 1: top quark is going to be in the universe just

1053
00:49:34,480 --> 00:49:38,080
Speaker 1: because its lifetime is shorter, which means there's more uncertainty

1054
00:49:38,120 --> 00:49:40,560
Speaker 1: about its energy, and that comes down to uncertainty about

1055
00:49:40,600 --> 00:49:43,760
Speaker 1: its mass. So there's like a whole distribution of possible

1056
00:49:43,840 --> 00:49:46,400
Speaker 1: masses you could measure for a top quark, of masses

1057
00:49:46,440 --> 00:49:49,239
Speaker 1: that it actually has. It's like a fundamental uncertainty and

1058
00:49:49,320 --> 00:49:52,520
Speaker 1: like how much energy there is in this thing because

1059
00:49:52,520 --> 00:49:55,080
Speaker 1: there's very little uncertainty about how long it's going to last.

1060
00:49:55,160 --> 00:49:56,799
Speaker 1: It's not going to last very long at all.

1061
00:49:57,480 --> 00:49:59,400
Speaker 4: It's not just like uncertainty about where it is and

1062
00:49:59,400 --> 00:50:02,560
Speaker 4: where it's going. It's like done sorry about it's actual

1063
00:50:02,760 --> 00:50:05,000
Speaker 4: like being right, like what it is, how much of

1064
00:50:05,040 --> 00:50:06,280
Speaker 4: it is there exactly?

1065
00:50:06,680 --> 00:50:09,040
Speaker 1: And there's a really deep connection between these two variables

1066
00:50:09,160 --> 00:50:12,320
Speaker 1: energy and time, position and momentum. We talked about this

1067
00:50:12,360 --> 00:50:15,400
Speaker 1: philosophical connection in another episode. It all comes out of

1068
00:50:15,400 --> 00:50:18,200
Speaker 1: this theorem no Other's theorem, which tells us like relationships

1069
00:50:18,239 --> 00:50:22,000
Speaker 1: between symmetries and conservation laws. We know the fact that

1070
00:50:22,080 --> 00:50:25,320
Speaker 1: space is the same everywhere in the universe means momentum

1071
00:50:25,360 --> 00:50:28,759
Speaker 1: is conserved. So another connection there between position and momentum.

1072
00:50:29,120 --> 00:50:32,799
Speaker 1: Other's law also tells us that energy is conserved if

1073
00:50:32,840 --> 00:50:35,840
Speaker 1: space is the same across time. There's a connection between

1074
00:50:35,920 --> 00:50:38,600
Speaker 1: energy and time, and so you see that there's a

1075
00:50:38,640 --> 00:50:41,200
Speaker 1: really deep connection between these variables. Some of these things

1076
00:50:41,200 --> 00:50:45,200
Speaker 1: are just sort of fundamentally paired physically, position and momentum,

1077
00:50:45,520 --> 00:50:49,160
Speaker 1: energy and time. There's also weird properties of the spins

1078
00:50:49,160 --> 00:50:51,319
Speaker 1: of particles that have these kind of relationships.

1079
00:50:51,840 --> 00:50:52,760
Speaker 4: What do you mean by spin?

1080
00:50:53,040 --> 00:50:55,759
Speaker 1: So particles can have quantum spin right, spin up or

1081
00:50:55,800 --> 00:50:58,640
Speaker 1: spin down, but it depends on how you measure it.

1082
00:50:58,760 --> 00:51:01,040
Speaker 1: Like if you try to measure the spin of a particle,

1083
00:51:01,320 --> 00:51:03,080
Speaker 1: you can do so by putting it in a magnetic

1084
00:51:03,080 --> 00:51:06,239
Speaker 1: field and it will align one way or the other way. Well,

1085
00:51:06,280 --> 00:51:08,960
Speaker 1: that's a spin along one axis, the axis of that

1086
00:51:09,000 --> 00:51:11,880
Speaker 1: magnetic field. You could also try to measure its spin

1087
00:51:12,120 --> 00:51:14,880
Speaker 1: like at we using a perpendicular setup, like take another

1088
00:51:14,960 --> 00:51:18,239
Speaker 1: magnet and rotated ninety degrees, try to measure it spin

1089
00:51:18,280 --> 00:51:20,160
Speaker 1: in another way. So you have like spin in X

1090
00:51:20,160 --> 00:51:22,719
Speaker 1: and spin and y. It turns out these two things

1091
00:51:22,719 --> 00:51:25,120
Speaker 1: are related. You can't know the spin of a particle

1092
00:51:25,160 --> 00:51:29,080
Speaker 1: in two directions simultaneously, Like you measure it spin in X,

1093
00:51:29,280 --> 00:51:31,640
Speaker 1: that will mess up its spin and y. If you

1094
00:51:31,640 --> 00:51:33,520
Speaker 1: measure it spin and why, that will mess up its

1095
00:51:33,520 --> 00:51:35,879
Speaker 1: spin in X. These two things are linked the same

1096
00:51:35,880 --> 00:51:38,080
Speaker 1: way position and momentum are linked. Right.

1097
00:51:38,200 --> 00:51:42,080
Speaker 4: Well, by mess up, you mean like it changes its probability, right,

1098
00:51:42,160 --> 00:51:42,920
Speaker 4: like what it can be.

1099
00:51:43,120 --> 00:51:45,520
Speaker 1: Yeah, there's this famous experiment where they take a bunch

1100
00:51:45,520 --> 00:51:47,359
Speaker 1: of atoms and they put them through a magnetic field

1101
00:51:47,400 --> 00:51:49,680
Speaker 1: so they're either spin up or spin down. Then use

1102
00:51:49,680 --> 00:51:51,719
Speaker 1: a fancy device to filter all them out so they

1103
00:51:51,800 --> 00:51:54,000
Speaker 1: like only take the spin up ones. Then they send

1104
00:51:54,000 --> 00:51:55,920
Speaker 1: them through the experiment again, but rotate it, so now

1105
00:51:55,960 --> 00:51:58,520
Speaker 1: they're measuring it like along another axis. And when they

1106
00:51:58,560 --> 00:52:01,160
Speaker 1: send it back through the first device again, they're now

1107
00:52:01,280 --> 00:52:03,839
Speaker 1: both spin up and spin down. So you've taken a

1108
00:52:03,840 --> 00:52:06,200
Speaker 1: beam that are only spin up. You measure it in

1109
00:52:06,280 --> 00:52:10,319
Speaker 1: an orthogonal way. That messes up your original distribution in

1110
00:52:10,360 --> 00:52:13,120
Speaker 1: the first direction. So measuring in one direction messes up

1111
00:52:13,120 --> 00:52:15,520
Speaker 1: the measurement in the other direction. Because these two things

1112
00:52:15,560 --> 00:52:18,640
Speaker 1: are linked fundamentally, you can't know them simultaneously.

1113
00:52:18,880 --> 00:52:22,360
Speaker 4: It kind of feels like maybe these things are paired

1114
00:52:22,400 --> 00:52:28,319
Speaker 4: together by kind of the constraints that measuring those things have.

1115
00:52:28,640 --> 00:52:31,719
Speaker 4: It's impossible to measure the spin of a particle in

1116
00:52:31,760 --> 00:52:34,440
Speaker 4: the up and down direction and in the site to

1117
00:52:34,480 --> 00:52:36,719
Speaker 4: side direction at the same time, and therefore those two

1118
00:52:36,840 --> 00:52:37,680
Speaker 4: things are linked.

1119
00:52:37,760 --> 00:52:40,520
Speaker 1: Yeah, those two things are definitely linked. You know. Why

1120
00:52:40,560 --> 00:52:43,120
Speaker 1: these two things are linked and not other two things

1121
00:52:43,600 --> 00:52:46,120
Speaker 1: is a really interesting and deep question. I think that's

1122
00:52:46,120 --> 00:52:48,440
Speaker 1: fundamentally a question of the episode, like why is there

1123
00:52:48,480 --> 00:52:52,080
Speaker 1: any quantum uncertainty in classical physics? All these things are

1124
00:52:52,080 --> 00:52:54,720
Speaker 1: totally separate and independent, and quant mechanics has like linked

1125
00:52:54,840 --> 00:52:57,320
Speaker 1: some certain pairs of quantities together and said there's a

1126
00:52:57,400 --> 00:53:00,960
Speaker 1: limited information in these things. And the pliosophical answer that

1127
00:53:01,040 --> 00:53:03,480
Speaker 1: question is a little bit slippery, you know, like we

1128
00:53:03,680 --> 00:53:07,000
Speaker 1: have this mathematical description that we can use to predict

1129
00:53:07,040 --> 00:53:10,520
Speaker 1: all these wonderful quantumic experiments, and those mathematics have this

1130
00:53:10,640 --> 00:53:13,680
Speaker 1: uncertainty built into them inherently. So you can then look

1131
00:53:13,719 --> 00:53:15,759
Speaker 1: at that theory and say, like, well, why you know,

1132
00:53:15,840 --> 00:53:18,480
Speaker 1: and oh, it's matrix mechanics or here's a frequency analysis

1133
00:53:18,520 --> 00:53:21,279
Speaker 1: of a wave function. Fundamentally, that's not really a satisfying

1134
00:53:21,360 --> 00:53:23,759
Speaker 1: answer because it doesn't tell us like, why we don't

1135
00:53:23,760 --> 00:53:26,480
Speaker 1: live in the universe without this uncertainty. Why couldn't you

1136
00:53:26,520 --> 00:53:29,200
Speaker 1: have built a classical universe without it? Why did the

1137
00:53:29,280 --> 00:53:32,080
Speaker 1: designers of the universe, whoever they are, give us the

1138
00:53:32,160 --> 00:53:34,640
Speaker 1: universe with this property instead of other properties?

1139
00:53:34,760 --> 00:53:37,279
Speaker 4: These things are not they're tied to each other, but

1140
00:53:37,320 --> 00:53:40,160
Speaker 4: they're not tied across different categories. Like, for example, you

1141
00:53:40,239 --> 00:53:42,920
Speaker 4: can know the position of a particle and it's mass,

1142
00:53:43,280 --> 00:53:46,400
Speaker 4: and it's been along the up and down direction right perfectly,

1143
00:53:46,480 --> 00:53:47,120
Speaker 4: those three things.

1144
00:53:47,160 --> 00:53:48,960
Speaker 1: Pick one in each category and you can know it

1145
00:53:49,000 --> 00:53:49,719
Speaker 1: as well as you.

1146
00:53:49,800 --> 00:53:52,160
Speaker 4: Like, all right, So then it sounds like we haven't

1147
00:53:52,560 --> 00:53:54,280
Speaker 4: answered the question of the episode.

1148
00:53:55,280 --> 00:53:57,120
Speaker 1: The answer to the question of the episode is we

1149
00:53:57,200 --> 00:53:59,600
Speaker 1: don't know, right. It's a feature of our universe, the

1150
00:53:59,640 --> 00:54:01,560
Speaker 1: way that the speed of light is a feature of

1151
00:54:01,600 --> 00:54:04,640
Speaker 1: our universe. We observe it, we can build mathematical theories

1152
00:54:04,680 --> 00:54:07,360
Speaker 1: to describe it. We can then scratch our heads and say, hm,

1153
00:54:07,360 --> 00:54:08,799
Speaker 1: does it have to be this way? And we don't

1154
00:54:08,800 --> 00:54:10,279
Speaker 1: have an answer to that. We don't know if it

1155
00:54:10,480 --> 00:54:14,440
Speaker 1: would have been possible to build a universe that was classical.

1156
00:54:14,560 --> 00:54:17,359
Speaker 1: We actually talked about that on a recent episode Philosophically

1157
00:54:17,400 --> 00:54:19,640
Speaker 1: and fundamentally and theoretically, you might have been able to

1158
00:54:19,640 --> 00:54:23,080
Speaker 1: build a classical universe without any quantum uncertainty, but ours

1159
00:54:23,160 --> 00:54:24,600
Speaker 1: seems to have this feature.

1160
00:54:24,880 --> 00:54:27,879
Speaker 4: But I think, as you said, you know, it's a process, right,

1161
00:54:27,880 --> 00:54:30,080
Speaker 4: We're in the middle of this process. And it might

1162
00:54:30,120 --> 00:54:32,040
Speaker 4: be that in the future we do know why the

1163
00:54:32,040 --> 00:54:34,200
Speaker 4: speed of light had to be a certain velocity, right.

1164
00:54:34,160 --> 00:54:36,440
Speaker 1: Yeah, and in the future and we understand quantum gravity

1165
00:54:36,480 --> 00:54:39,359
Speaker 1: and string theory, there might be a simple reason like, oh,

1166
00:54:39,360 --> 00:54:43,520
Speaker 1: the universe has this property and therefore you have quantum uncertainty,

1167
00:54:43,600 --> 00:54:46,320
Speaker 1: or the universe is this way, and therefore the speed

1168
00:54:46,320 --> 00:54:48,640
Speaker 1: of light is what it is. But you know, that's

1169
00:54:48,680 --> 00:54:51,080
Speaker 1: just going to generate more questions, right, whatever property that

1170
00:54:51,280 --> 00:54:53,680
Speaker 1: is that gives rise to quantum uncertainty, we're then going

1171
00:54:53,719 --> 00:54:55,520
Speaker 1: to ask, well, why that property?

1172
00:54:56,000 --> 00:54:58,879
Speaker 4: So basically it's a never ending story.

1173
00:55:00,600 --> 00:55:02,640
Speaker 1: I hope. So then I'll keep having a job.

1174
00:55:02,480 --> 00:55:04,640
Speaker 4: Well, assuming people want you to do it, or I

1175
00:55:04,680 --> 00:55:06,440
Speaker 4: guess you could do it. You can pay yourself, I

1176
00:55:06,440 --> 00:55:09,960
Speaker 4: guess it's still a job. If you pay yourself yourself.

1177
00:55:10,040 --> 00:55:11,440
Speaker 4: You can be self employed physicists.

1178
00:55:11,480 --> 00:55:13,719
Speaker 1: Yeah, there's lots of great self employed physicists out there.

1179
00:55:13,800 --> 00:55:15,919
Speaker 4: What if I just say that the answer is forty two.

1180
00:55:16,640 --> 00:55:18,799
Speaker 4: Is there a universe out there where the answer is.

1181
00:55:18,800 --> 00:55:21,480
Speaker 1: Forty two the answer to what question?

1182
00:55:21,800 --> 00:55:23,880
Speaker 4: I don't know, the answer of why the speed of

1183
00:55:23,960 --> 00:55:28,320
Speaker 4: light is the way it is, it's because the number

1184
00:55:28,320 --> 00:55:29,239
Speaker 4: forty two, I don't know.

1185
00:55:29,280 --> 00:55:31,120
Speaker 1: I'd love to live in a universe where that answer

1186
00:55:31,120 --> 00:55:33,160
Speaker 1: made sense for that question, but I don't think that's

1187
00:55:33,200 --> 00:55:33,920
Speaker 1: this universe.

1188
00:55:34,920 --> 00:55:37,120
Speaker 4: I wonder if them that universe they have the Hitchhiker's

1189
00:55:37,120 --> 00:55:40,160
Speaker 4: Guide to the Galaxy, or I guess in an infinite

1190
00:55:40,239 --> 00:55:44,319
Speaker 4: multiverse there is a universe where the answer is forty two.

1191
00:55:45,080 --> 00:55:46,799
Speaker 4: And also Douglas Adams.

1192
00:55:46,680 --> 00:55:48,920
Speaker 1: Was right, yes, and it all makes sense.

1193
00:55:49,280 --> 00:55:51,239
Speaker 4: Yes, and then and that one you'd be out of

1194
00:55:51,239 --> 00:55:54,040
Speaker 4: a job, but not cartoonists, because we can always draw

1195
00:55:54,080 --> 00:55:55,520
Speaker 4: cartoons of the number forty.

1196
00:55:55,280 --> 00:55:57,800
Speaker 1: Two, that's right, and cartoonists can always be self employed.

1197
00:55:57,920 --> 00:56:01,080
Speaker 4: All right, Well, hopefully that gives you a sense of

1198
00:56:01,160 --> 00:56:05,160
Speaker 4: how this universe still has a lot that can't be explained.

1199
00:56:05,600 --> 00:56:09,359
Speaker 4: You know, there's these fundamental uncertainties in it and what

1200
00:56:09,400 --> 00:56:12,239
Speaker 4: we can and cannot measure. At the same time, it

1201
00:56:12,320 --> 00:56:14,960
Speaker 4: is sort of a magical table kind of for now.

1202
00:56:14,880 --> 00:56:17,239
Speaker 1: Right, it is we can describe it mathematically, and we

1203
00:56:17,239 --> 00:56:19,440
Speaker 1: can give answers to like why the mathematics works this

1204
00:56:19,560 --> 00:56:22,239
Speaker 1: way and why these things bubble up from the mathematics,

1205
00:56:22,239 --> 00:56:24,400
Speaker 1: But we don't fundamentally know why we live in a

1206
00:56:24,480 --> 00:56:25,920
Speaker 1: universe with quantum uncertainty.

1207
00:56:26,600 --> 00:56:28,840
Speaker 4: Yeah, and if you eat out of a magical table,

1208
00:56:29,200 --> 00:56:31,160
Speaker 4: is that a good way to control your diet?

1209
00:56:33,440 --> 00:56:35,040
Speaker 1: If you don't know the lengthen with of your table,

1210
00:56:35,040 --> 00:56:36,319
Speaker 1: it's a good way to make a big mess on

1211
00:56:36,320 --> 00:56:36,760
Speaker 1: the floor.

1212
00:56:37,440 --> 00:56:40,040
Speaker 4: Yeah, there you go. You might be sitting down your

1213
00:56:40,040 --> 00:56:42,120
Speaker 4: food in empty space. All right, Well, we hope you

1214
00:56:42,200 --> 00:56:45,879
Speaker 4: enjoyed that. Thanks for joining us, See you next time.

1215
00:56:50,960 --> 00:56:53,840
Speaker 1: For more science and curiosity, come find us on social

1216
00:56:53,880 --> 00:56:58,840
Speaker 1: media where we answer questions and post videos. We're on Twitter, Discord, Instant,

1217
00:56:58,920 --> 00:57:02,120
Speaker 1: and now TikTok. And remember that Daniel and Jorge Explain

1218
00:57:02,200 --> 00:57:06,200
Speaker 1: the Universe is a production of iHeartRadio. For more podcasts

1219
00:57:06,200 --> 00:57:10,840
Speaker 1: from iHeartRadio, visit the iHeartRadio app, Apple Podcasts, or wherever

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