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

• 0:00
  Speaker 1: Hey, quick announcement everyone, we have just joined TikTok, So
• 0:03
  Speaker 1: head over there and follow us to see videos of
• 0:05
  Speaker 1: Daniel asking and answering science questions. All right, enjoy the pod.
• 0:18
  Speaker 2: Hey Daniel, does quantum mechanics really explain reality?
• 0:22
  Speaker 1: I mean I think so, even though it's pretty weird.
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  Speaker 1: Are you sure? Well? Lots of experiments we've done over
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  Speaker 1: the last century.
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  Speaker 2: See yes, Yeah, But like, how can you be certain?
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  Speaker 3: You know?
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  Speaker 2: I thought quantum mechanics is everything is uncertain.
• 0:35
  Speaker 1: Well, we're very certain that quantum mechanics is uncertain, but
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  Speaker 1: only about certain things.
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  Speaker 2: I'm pretty certain that makes no sense.
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  Speaker 1: I think it's curtains for certainty.
• 0:45
  Speaker 2: Are you sure about that?
• 0:47
  Speaker 1: Now? I'm not sure about anything.
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  Speaker 2: I'm welcome to being a non physicist.
• 1:06
  Speaker 4: Hi.
• 1:06
  Speaker 2: I'm poor Hendrick Cartoonis and the author of Oliver's Great
• 1:09
  Speaker 2: Big Universe.
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  Speaker 3: Hi.
• 1:10
  Speaker 1: I'm Daniel. I'm a particle physicist and a professor at
• 1:13
  Speaker 1: UC Irvine. Or at least I was certain of that
• 1:15
  Speaker 1: a moment ago.
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  Speaker 2: Yeah, Now you're not sure that you have a job,
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  Speaker 2: so he might have said something to get you fired here.
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  Speaker 1: Yeah, that's one of those questions you shouldn't ask because
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  Speaker 1: it might change the answer.
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  Speaker 2: I thought ye had tenure that prevented them from firing you.
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  Speaker 1: There are still limits to what we can do even
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  Speaker 1: if we have tenure.
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  Speaker 2: But anyways, welcome to our podcast Daniel and Jorge Explain
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  Speaker 2: the Universe, a production of iHeartRadio.
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  Speaker 1: In which we test the limits of our understanding of
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  Speaker 1: the universe. How certain are we that the universe works
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  Speaker 1: in a different way on a tiny scale, that there
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  Speaker 1: are tiny quantum particles fluctuating in and out of existence,
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  Speaker 1: that when we zoom down to the universe at its
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  Speaker 1: smallest scale, different rules apply. On this podcast, we pushed
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  Speaker 1: all those limits and we try to answer all of
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  Speaker 1: your questions.
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  Speaker 2: That's right, because it is a wonderful and amazing but
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  Speaker 2: yet also a very mysterious universe that seems kind of
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  Speaker 2: random at times, but also seems like a giant clock
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  Speaker 2: that seems to be working precisely as it's supposed to be.
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  Speaker 1: And the big goal of physics is not just to
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  Speaker 1: reassure us that the universe works the way our intuition suggests,
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  Speaker 1: but to discover the truth. Science is a knowledge building mechanism, right,
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  Speaker 1: It's a way to figure out how the universe actually works,
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  Speaker 1: even if it's deeply in contradiction with the way we
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  Speaker 1: thought it worked.
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  Speaker 2: Wait, I thought philosophers thought that you can never uncover
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  Speaker 2: the real truth of things. It's impossible to be completely
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  Speaker 2: certain about the truth.
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  Speaker 1: Philosophers don't even agree about what you mean by the
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  Speaker 1: real truth.
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  Speaker 2: Well, I see, it's about I guess vocabulary.
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  Speaker 4: Man.
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  Speaker 1: Every philosophy argument in the end comes down to vocabulary. Like,
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  Speaker 1: what do you mean when you say vocabulary? Anyway?
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  Speaker 2: Oh, you can get a few inception levels deep into
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  Speaker 2: this discussion.
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  Speaker 1: What do you mean by what do you mean exactly?
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  Speaker 1: What do you mean?
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  Speaker 2: What is meaning?
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  Speaker 1: Yes? What is meaning? What is a question?
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  Speaker 2: Anyway? What is a what?
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  Speaker 1: And I'd laugh at all these jokes, not to laugh
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  Speaker 1: at philosophy, but out of deep respect for the way
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  Speaker 1: philosophy forces us to figure out what we mean by
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  Speaker 1: our questions? What is it? In the end, we're asking
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  Speaker 1: what kind of answers do we expect? All this kind
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  Speaker 1: of stuff? These are hard questions.
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  Speaker 2: Wait, does that mean that philosophers don't think you actually
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  Speaker 2: have a job as a physicist?
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  Speaker 1: I mean, philosophers definitely recognize the physics is building a
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  Speaker 1: set of facts, and those facts like power the world.
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  Speaker 1: There is a reason that technology works, for example, But
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  Speaker 1: exactly what it means about the universe, what is the
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  Speaker 1: real story? What is real depends a little bit on
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  Speaker 1: the questions we're asking, and it's not even clear that
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  Speaker 1: there is an objective truth about it. It might just
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  Speaker 1: be our perception of it answers to the kind of
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  Speaker 1: questions we would ask.
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  Speaker 2: Well, I guess the elusive quests for the real truth
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  Speaker 2: of the universe is kind of what signs. It's all about,
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  Speaker 2: you know, even if we don't get there, it's all
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  Speaker 2: about trying to get there.
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  Speaker 1: Exactly, and we can all work together to get there,
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  Speaker 1: even if we're not in agreement about what there is.
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  Speaker 1: Some of us think we are revealing the true underlying
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  Speaker 1: mechanism of reality, something that like alien scientists would also
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  Speaker 1: be revealing. Other folks don't care about that. They say, hey, look,
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  Speaker 1: we're just getting something that works, something that predicts the
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  Speaker 1: outcomes of experiments and lets us build technology. Who even
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  Speaker 1: cares if it's real or what aliens would think about it.
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  Speaker 1: You can totally disagree with the lofty philosophical goals of
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  Speaker 1: science and still work hand in hand and get concrete results.
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  Speaker 2: I feel like maybe that'sis's favorite part of the job.
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  Speaker 2: It's arguing about the job, you know.
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  Speaker 1: I think that there's a division early on, and people
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  Speaker 1: who like to argue about it more end up in philosophy,
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  Speaker 1: and the people who just want to like get in
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  Speaker 1: the lab and learn stuff about the world end up
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  Speaker 1: in physics.
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  Speaker 2: You just want to get in there and blow stuff.
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  Speaker 1: But there's always this tension, right. The juiciest questions in
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  Speaker 1: physics are the ones that when we get the answer,
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  Speaker 1: we go, hmmm, well, but why is it like that?
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  Speaker 1: What does that mean about the world. The best physics
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  Speaker 1: questions have philosophical implications.
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  Speaker 2: Yeah, and so there's a lot of uncertainty about what
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  Speaker 2: we do know or what we don't know, or what
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  Speaker 2: we can know about the universe. But even deeper than that,
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  Speaker 2: there seems to be a uncertainty about the universe itself.
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  Speaker 1: Something shocking, something very difficult to understand about the quantum
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  Speaker 1: picture of the world is that the world itself might
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  Speaker 1: be limited in its precision, not just in our ability
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  Speaker 1: to measure it or to extract that knowledge, but there
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  Speaker 1: could be a fundamental fuzziness to the universe, a lack
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  Speaker 1: of determination about reality.
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  Speaker 2: It's not just me getting older and needing reading glasses.
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  Speaker 1: It's that also. Yes, those two effects are combining.
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  Speaker 2: I mean, have quantum vision.
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  Speaker 5: Now.
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  Speaker 2: I think we should start that company. Quantum laser surgery. Yeah,
• 5:36
  Speaker 2: quantum reading glasses. Yeah, I'm parably the only coast of dollars,
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  Speaker 2: so we make a killer profit.
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  Speaker 1: You can only read one word at a time.
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  Speaker 2: But anyways, Yeah, there seems to be this interesting nugget
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  Speaker 2: of strangeness to quantum mechanics which tries to explain the
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  Speaker 2: entire universe. And so today on the podcast, we'll be
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  Speaker 2: asking the question why is there quantum uncertainty? I feel
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  Speaker 2: like we're asking a question about uncertainty.
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  Speaker 1: We are uncertain about why there's uncertainty.
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  Speaker 2: That's what I mean.
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  Speaker 1: It's meta uncertainty.
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  Speaker 2: We get very meta here. Well, if it helps, I'm
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  Speaker 2: pretty sure. I'm a cartoonist, that's one thing I know.
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  Speaker 1: Yeah, Well, this is exactly the kind of difficult philosophical
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  Speaker 1: question because you know, I even sure like what kind
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  Speaker 1: of answer we're looking for, Like, are we hoping to
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  Speaker 1: reveal that the universe could have only ever been this way?
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  Speaker 1: Or to argue that look, we could be in lots
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  Speaker 1: of different universes. This one happens to have this quantum uncertainty.
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  Speaker 1: You know, there's lots of different ways to attack this
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  Speaker 1: sort of philosophical problem.
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  Speaker 2: Well, hopefully it's more than just a philosophical problem, right, Eventually,
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  Speaker 2: the hope, the goal is to find kind of physics,
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  Speaker 2: math based answers to these questions, isn't it to me?
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  Speaker 1: I think the sort of highest level process would be
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  Speaker 1: go out and look at the universe, see what it's like,
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  Speaker 1: boiling that down to like a few essential facts, build
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  Speaker 1: a theory that describes how that works, why that works,
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  Speaker 1: the mathematics to describe it, and then look at that
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  Speaker 1: theory and ask philosophical questions like did it have to
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  Speaker 1: be this way? Could you have a universe that was different?
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  Speaker 1: Could we have built a different theory of the universe
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  Speaker 1: that didn't have this feature or that feature about it?
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  Speaker 1: So in the end, it's mathematical, but it's really rooted
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  Speaker 1: in explaining what we see out there in the universe.
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  Speaker 2: But couldn't you answer those questions you just asked in
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  Speaker 2: a mathematical way. Maybe in the future. We don't know
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  Speaker 2: for certain they can't be answered, right.
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  Speaker 1: We don't know for certain they can't be answered. I
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  Speaker 1: think a great analog that's going to help us understand
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  Speaker 1: this question today is the question of like the speed
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  Speaker 1: of light. You know, we live in a universe where
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  Speaker 1: the speed of light is constant for all observers, and
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  Speaker 1: if you start from that, you can build special relativity
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  Speaker 1: and you can explain the whole universe. But you have
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  Speaker 1: to start from that assumption. That's something we've seen in
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  Speaker 1: the universe, something we know is true, we've measured it,
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  Speaker 1: we've done the experiments, we've now coded it into our theory,
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  Speaker 1: but we don't have an answer for why that is true.
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  Speaker 1: And one day maybe people will have a deeper understanding
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  Speaker 1: of the nature of space from which that bubbles up.
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  Speaker 1: You might be able to explain that someday, but currently
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  Speaker 1: we don't have an answer to why. It's just sort
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  Speaker 1: of like the foundational assumption that we need to explain
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  Speaker 1: everything we see in the universe.
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  Speaker 4: Right.
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  Speaker 2: Well, as you said, hopefully maybe someday somebody will answer
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  Speaker 2: this deep question, but that person doesn't seem to be
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  Speaker 2: out there, because Daniel went out there and asked this
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  Speaker 2: question of folks and we got some pretty interesting answers back.
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  Speaker 1: Yeah. Thanks, everybody who answers these questions as wacky and
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  Speaker 1: as crazy as they are, without having any chance to
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  Speaker 1: prepare yourself. Really appreciate your participation, and I'd love to
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  Speaker 1: hear your voice on the podcast. That's right, I'm talking
• 8:33
  Speaker 1: to you. We haven't heard from you yet, and we
• 8:35
  Speaker 1: want your voice on the air.
• 8:37
  Speaker 2: Well, there's a bunch of people who have heard we
• 8:39
  Speaker 2: have heard from BOM. Right, you just totally snubbed them,
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  Speaker 2: I feel.
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  Speaker 1: I said, thanks to all those folks.
• 8:44
  Speaker 2: Also, Oh, you meant the other people.
• 8:48
  Speaker 1: It's a shockingly small group of people who volunteer for
• 8:50
  Speaker 1: these which is why you hear the same voices over
• 8:52
  Speaker 1: and over again.
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  Speaker 2: Oh, I never noticed. You didn't have to tell me.
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  Speaker 1: I should have maintained your quantumuncertainty.
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  Speaker 2: She'd kept that a mystery of the universe. But anyways,
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  Speaker 2: think about it for a second. Why do you think
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  Speaker 2: there is quantum uncertainty in the universe. Here's what people
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  Speaker 2: had to say.
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  Speaker 5: I guess that both because we can't really have an
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  Speaker 5: accurate measurement on that very timey scale, and because measuring
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  Speaker 5: a quantum process interferes on that process.
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  Speaker 3: There's quantum uncertainty because when we measure a particle, it
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  Speaker 3: changes what the particle's doing, and when we're not looking
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  Speaker 3: at the particle, we never quite know what it's doing
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  Speaker 3: without measuring it, which changes the state and the particle.
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  Speaker 3: So we can never quite know exactly what a particle's
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  Speaker 3: doing without changing the state.
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  Speaker 4: I know that if you measure something, it falls into
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  Speaker 4: the wave function collapses, and you fall into one of
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  Speaker 4: the states. I guess is uncertainty, because there's a wave function.
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  Speaker 2: All right, and pretty deep answers here, I'm pretty certain
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  Speaker 2: of that.
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  Speaker 1: Yeah, a lot of these folks are developing like a
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  Speaker 1: microphysical picture, like what's happening when you make a measurement?
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  Speaker 1: What prevents you for being able to measure things super
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  Speaker 1: duper precisely? And that's helpful, but I think it's only
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  Speaker 1: really part of the story.
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  Speaker 2: All right, Well, let's dig into this topic, and let's
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  Speaker 2: start with the basic question, Daniel, what is quantum uncertainty?
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  Speaker 1: There's so many weird things about quantum mechanics that we
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  Speaker 1: could dig into for hours and hours, but I just
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  Speaker 1: want to zoom in on this one thing, this quantum uncertainty,
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  Speaker 1: which is different from other weird aspects of quantum mechanics,
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  Speaker 1: and quantum uncertainty is a very specific thing. But let's
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  Speaker 1: start off by talking about classical physics, because quantum uncertainty
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  Speaker 1: is basically a rejection of that. So classical physics, the
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  Speaker 1: physics of Newton, and even the physics of Einstein, says
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  Speaker 1: that we live in a universe where you can know
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  Speaker 1: everything about an object, like take a particle or a
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  Speaker 1: banana or whatever. You can know everything about its location,
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  Speaker 1: you can know everything about its velocity, you can know
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  Speaker 1: its entire history that it moves in these smooth paths.
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  Speaker 1: It always has a position, always has a velocity that
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  Speaker 1: to reality, there is no fuzziness that there's an exactness
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  Speaker 1: to this information, and you can know all of it
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  Speaker 1: simultaneously because it's well defined. That's the classic physics picture
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  Speaker 1: of like how things move in the universe. Right.
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  Speaker 2: That's sort of like maybe a good way to explain
• 11:05
  Speaker 2: it is basically like up to high school physics, right,
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  Speaker 2: like you know, predicting where the baseball that you throw
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  Speaker 2: is going to land, or you know how things move
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  Speaker 2: you shake him orver you swing them. That's classical physics, right,
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  Speaker 2: Like you can predict where the things are, what things
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  Speaker 2: are going to do. Like you in those exams in
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  Speaker 2: high school, there's no room for uncertainty, Like there's a
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  Speaker 2: right answer, there's a wrong answer.
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  Speaker 1: That's right, and there's an exactness to the answer, and
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  Speaker 1: even well past high school physics, I guess, depending on
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  Speaker 1: your high school you know, Einstein's physics is also classical
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  Speaker 1: in that sense. I mean, Einstein was a huge revolution
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  Speaker 1: compared to Newtonian physics. Relativity is a whole other brain twister.
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  Speaker 1: But Einstein's picture of the universe fundamentally is the same
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  Speaker 1: in that there's no uncertainty. He imagined you could know
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  Speaker 1: where a particle is that had an exact position, and
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  Speaker 1: you could simultaneously know its position and its momentum and
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  Speaker 1: all sorts of other things about.
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  Speaker 2: It, even like light.
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  Speaker 1: Yeah, the classical theory of electrodynamics, you know, which comes
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  Speaker 1: from Maxwell and inspired Stein to develop relativity, didn't have
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  Speaker 1: any sort of quantum uncertainty to it. Photons had an
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  Speaker 1: exact position, all.
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  Speaker 2: Right, So then that's Einstein and newtune. But then around
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  Speaker 2: the beginning of the nineteen hundreds they figured out that
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  Speaker 2: things are kind of strange and weird.
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  Speaker 1: Yeah, basically, quantum mechanics looks at that and says, yeah, no,
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  Speaker 1: you can't know all of these things simultaneously. And the
• 12:22
  Speaker 1: history of it's really fascinating. It comes around in the
• 12:24
  Speaker 1: nineteen twenties when people were trying to understand how the
• 12:28
  Speaker 1: atom worked and what was the picture of microscopically of
• 12:30
  Speaker 1: the electron and the nucleus. Was this sort of like
• 12:32
  Speaker 1: an orbital picture like bor was suggesting, or was there
• 12:34
  Speaker 1: something funnier and more complicated going on? And it was
• 12:37
  Speaker 1: really Heisenberg of the famous Heisenberg uncertainty principle, who developed
• 12:41
  Speaker 1: the sort of first theory of quantum mechanics that describe
• 12:44
  Speaker 1: how the atom worked in a way different from boor
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  Speaker 1: that had like a fundamental different mathematics underneath it.
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  Speaker 2: I feel like, or I seem to recall that initially
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  Speaker 2: quantum mechanics didn't have this idea of uncertainty to it, right,
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  Speaker 2: Like didn't it start with people just noticing that like
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  Speaker 2: light case and packets, or that electrons wouldn't you know,
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  Speaker 2: fly off unless you met certain minimum energy requirements and
• 13:05
  Speaker 2: things like that. There's no uncertain to your fuzziness to
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  Speaker 2: it at the beginning.
• 13:09
  Speaker 1: Was there the roots of quantum mechanics are exactly as
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  Speaker 1: you described. You know, there's like the black body radiation problem,
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  Speaker 1: and there's the photoelectric effect that we dug into on
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  Speaker 1: the podcast several times, and you're right, it was actually
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  Speaker 1: Einstein who figured that out.
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  Speaker 4: Right.
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  Speaker 1: You connected the ideas of Plank with the experiments that
• 13:23
  Speaker 1: we were seeing and saw that light had to come
• 13:25
  Speaker 1: and packet, so it can only interact with a single electron. Absolutely.
• 13:29
  Speaker 1: So those really those core ideas which then led to
• 13:31
  Speaker 1: the formulation of quantum mechanics. Those didn't have uncertainty in them.
• 13:35
  Speaker 1: That wasn't an essential ingredient.
• 13:36
  Speaker 2: Right, That's where the word quantum comes from, right, like quanta,
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  Speaker 2: like little quantity, little countable things.
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  Speaker 1: Right, you can have one electron or two electrons or
• 13:45
  Speaker 1: nine electrons, but you can't have one point seven photons,
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  Speaker 1: for example. But then as people were trying to apply
• 13:50
  Speaker 1: these theories and these ideas to describing the atom, they
• 13:54
  Speaker 1: need to develop mathematics that work, mathematics that explained what
• 13:57
  Speaker 1: we saw. And Heisenberg developed this theory of quantum mechanics
• 14:01
  Speaker 1: that he used to make calculations and to understand like
• 14:04
  Speaker 1: why did the electron have this energy level? Around the
• 14:06
  Speaker 1: atom and not that energy level. Why did we get
• 14:08
  Speaker 1: this atomic spectrum from the atom? He developed this whole
• 14:11
  Speaker 1: theory of quantum mechanics, and you can see inherent in
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  Speaker 1: the mathematics of his theory comes out this basic idea
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  Speaker 1: of the quantum uncertainty sort of falls out of the mathematics.
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  Speaker 1: He needed to describe the world as he saw it.
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  Speaker 2: Can you describe that a little bit more?
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  Speaker 1: Like?
• 14:26
  Speaker 2: Why did it need to include that uncertainty into these
• 14:29
  Speaker 2: formulations in order to explain things like the little packets
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  Speaker 2: of light?
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  Speaker 1: Well, Heisenberg developed his theory of quant mechanics, and it
• 14:36
  Speaker 1: was based on a certain kind of mathematical object called
• 14:39
  Speaker 1: matrix's that we don't have to dig into. But what
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  Speaker 1: he noticed about the structure of his theory was that
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  Speaker 1: it seemed to matter the order in which you make measurements.
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  Speaker 1: Like if you measure one thing, it changes the state
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  Speaker 1: of the system, and then if you measure something else
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  Speaker 1: you'll get a different answer. And so quantu uncertainty is
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  Speaker 1: all about this. It's about recognizing that the order of
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  Speaker 1: the measurements you makes matter for some pairs of quantities,
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  Speaker 1: measuring one thing can change something else.
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  Speaker 2: I feel like maybe that's at the root of quantum uncertainty,
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  Speaker 2: which is like, it's really only uncertainly with regards to
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  Speaker 2: two things at the same time, right, Like, it's not
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  Speaker 2: like something has an inherent fuzziness, but its location you
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  Speaker 2: can know its location sort of very precisely, but then
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  Speaker 2: you lose out in some other quantities, right Exactly.
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  Speaker 1: It's about simultaneous knowledge of specific pairs of quantities, right,
• 15:26
  Speaker 1: And it's really very specific. It's not like general and
• 15:29
  Speaker 1: broad and say you can't ever know the position very well,
• 15:31
  Speaker 1: or you can't ever know the momentum very well. You
• 15:33
  Speaker 1: can know the position as well as you like, but
• 15:36
  Speaker 1: it comes at a cost for one specific other quantity,
• 15:39
  Speaker 1: the momentum. And there are other things that are paired
• 15:41
  Speaker 1: in this way. If you dig deeper into this in physics,
• 15:44
  Speaker 1: you discover that these things are called conjugate variables. And
• 15:47
  Speaker 1: this came out of the mathematics that Heisenberg was using
• 15:50
  Speaker 1: to describe his theory of quantum mechanics.
• 15:53
  Speaker 2: Well, I'm pretty certain that we're going to get into
• 15:55
  Speaker 2: this uncertainty and this idea of conjugate pairs, and how
• 15:59
  Speaker 2: that figures into the uncertainty that we see in quantum
• 16:02
  Speaker 2: mechanics that tries to explain the universe, and so let's
• 16:05
  Speaker 2: dig into those details. But first let's take a quick break.
• 16:21
  Speaker 2: All right, we are uncertainly talking about uncertainty today, specifically
• 16:26
  Speaker 2: quantum uncertainty, or at least we're trying to understand here
• 16:29
  Speaker 2: where it comes from and how it manifests itself in
• 16:32
  Speaker 2: our everyday lives. And so we talked about how quantum
• 16:36
  Speaker 2: mechanics kind of change things, and there's a certain uncertainty
• 16:39
  Speaker 2: about it that has to do with two things being
• 16:42
  Speaker 2: measured at the same time. That's kind of a key
• 16:44
  Speaker 2: to the concept of quantum uncertainty, right, first of all
• 16:46
  Speaker 2: measurements and second of all two things at the same
• 16:49
  Speaker 2: time exactly.
• 16:50
  Speaker 1: And there's lots of fuzziness about quantum mechanics, but this
• 16:53
  Speaker 1: is what we're talking about right now, is this uncertainly
• 16:55
  Speaker 1: about simultaneous knowledge. There's a whole other issue in quantum
• 16:59
  Speaker 1: mechanics about indeterminism, you know, laws of quantum mechanics determining
• 17:03
  Speaker 1: probabilities rather than outcomes. That's a whole separate issue, super fascinating,
• 17:07
  Speaker 1: but different from quantum uncertainty. Right, So quantum indeterminism is
• 17:11
  Speaker 1: different from quantum uncertainty, which tells us about like how
• 17:13
  Speaker 1: much we can know simultaneously about a particle or an object.
• 17:18
  Speaker 2: Wait, what that's different. There's two kinds of uncertainties.
• 17:21
  Speaker 1: Well, one of them is uncertainty. The other one is indeterminism.
• 17:24
  Speaker 2: Well, that's what you call it, but it's basically another
• 17:27
  Speaker 2: word for uncertainty, Isn't it Like you're not certain of
• 17:29
  Speaker 2: what the outcome is going to be. So today we're
• 17:32
  Speaker 2: not talking about like if I throw an electron at
• 17:34
  Speaker 2: a magnetic field, I don't know if it's going to
• 17:36
  Speaker 2: be your rider left. That's a different kind of uncertainty.
• 17:38
  Speaker 2: What are you saying?
• 17:39
  Speaker 1: So in quantum mechanics, we talk about randomness to describe
• 17:42
  Speaker 1: predictions that are probabilistic. If you put a particle in
• 17:46
  Speaker 1: a box and you ask where is it, you don't
• 17:48
  Speaker 1: get a specific prediction the way you do for classical mechanics.
• 17:51
  Speaker 1: You get predictions for where it's likely to be. You
• 17:54
  Speaker 1: get predictions for the probability distribution, so that if you
• 17:57
  Speaker 1: do it like a thousand times and measure its location,
• 18:00
  Speaker 1: you then get a distribution of measurements that follow the
• 18:03
  Speaker 1: predicted probability distribution. That's inherent in most of the quantum
• 18:06
  Speaker 1: mechanics we're used to thinking about due to the story
• 18:09
  Speaker 1: it tells us about how the universe works. It's not
• 18:12
  Speaker 1: a particle that's following equations of motion that are fundamental.
• 18:15
  Speaker 1: It's the wave function or the quantum field, which is
• 18:18
  Speaker 1: inherently probabilistic about the measurements you'll make of it. Now,
• 18:21
  Speaker 1: quantum uncertainty is related but actually quite distinct. You can
• 18:25
  Speaker 1: think of it as another source of randomness, but it
• 18:28
  Speaker 1: says that specific pairs of measurements are linked that if
• 18:32
  Speaker 1: you measure one, it makes the other one have a
• 18:34
  Speaker 1: wider spread of probabilities. So it's like it induces more indeterminacy,
• 18:40
  Speaker 1: but it's linked to specific pairs of variables rather than
• 18:43
  Speaker 1: the probabilistic nature of the wave function.
• 18:47
  Speaker 2: I see. So today we're not talking about quantum randomness
• 18:50
  Speaker 2: at all. We're just talking about our ability to know
• 18:54
  Speaker 2: where things are and where they're going.
• 18:55
  Speaker 1: Yeah, we're not talking about quantum randomness except for talking
• 18:58
  Speaker 1: about how we're not talking about it, which is the
• 18:59
  Speaker 1: first rule of quantum randomness.
• 19:02
  Speaker 2: That's right. Firstrule of physics club is talk about what
• 19:05
  Speaker 2: it means to be in a physics club and what
• 19:06
  Speaker 2: a club is. But I guess the question is, like,
• 19:10
  Speaker 2: are those two things related or are they totally separate
• 19:13
  Speaker 2: ideas In quantum mechanics, the randomness and the inability to
• 19:17
  Speaker 2: be certain about precision and velocity and things like that,
• 19:20
  Speaker 2: you can have one without the other.
• 19:21
  Speaker 1: So indeterminacy and uncertainty are different ideas because remember that
• 19:26
  Speaker 1: there are some theories of quantum mechanics which don't have
• 19:29
  Speaker 1: randomness and indeterminacy as inherent features, for example Bomian mechanics,
• 19:34
  Speaker 1: where the spread of outcomes isn't due to some randomness,
• 19:38
  Speaker 1: but it's due to slide variations in the initial conditions
• 19:42
  Speaker 1: of how you set up your experiment, of how exactly
• 19:44
  Speaker 1: you put that particle in a box, and so in
• 19:47
  Speaker 1: those theories like Boemian mechanics, uncertainty doesn't come from randomness.
• 19:51
  Speaker 1: It actually comes from the measuring device being part of
• 19:54
  Speaker 1: the experiment that's being measured, which keeps it out of
• 19:57
  Speaker 1: total quantum equilibrium, which causes uncertain So you don't actually
• 20:01
  Speaker 1: need randomness to have uncertainty in your quantum theory. Overall,
• 20:04
  Speaker 1: though there's a connection between uncertainty and indeterminacy in most
• 20:08
  Speaker 1: of the theories of quantum mechanics, though not at all,
• 20:10
  Speaker 1: and even to the one where there is a connection.
• 20:12
  Speaker 1: Uncertainty is a special kind of randomness because it relates
• 20:16
  Speaker 1: to specific pairs of quantities, not a general randomness.
• 20:20
  Speaker 2: Oh interesting, I don't think I ever knew that.
• 20:23
  Speaker 1: And the history of this is really fascinating, like how
• 20:25
  Speaker 1: it developed. And Heisenberg really was a pioneer, and he
• 20:28
  Speaker 1: developed this calculational tool that allowed him to predict you know,
• 20:31
  Speaker 1: energy levels, et cetera. But it was a little bit opaque,
• 20:34
  Speaker 1: like he had these matrices and he was operating on
• 20:37
  Speaker 1: vectors with them, and people were like, all right, but
• 20:39
  Speaker 1: what does that mean? Like what are you talking about?
• 20:41
  Speaker 1: What's happening inside? What is the electron doing? And Heisenberg
• 20:46
  Speaker 1: was really kind of annoyed by this question, and he
• 20:48
  Speaker 1: wrote a whole paper about like what it means and
• 20:50
  Speaker 1: what is real? And the title that paper I can't
• 20:53
  Speaker 1: translate for you because nobody agrees about how to translate
• 20:55
  Speaker 1: this one German word in the title, there's like a
• 20:58
  Speaker 1: quantum uncertainty about one of the earth. The papers of
• 21:00
  Speaker 1: quantum mechanics.
• 21:01
  Speaker 2: What do you mean? What is this title?
• 21:03
  Speaker 1: So the title of The paper is on the aich
• 21:07
  Speaker 1: content of quantum theoretical kinematics and mechanics, and German speakers
• 21:12
  Speaker 1: say that word means either like the visualization, which word anschulich,
• 21:18
  Speaker 1: which I'm sure I'm mispronouncing, thank you, and it might
• 21:22
  Speaker 1: mean like on the physical meaning of it or the
• 21:24
  Speaker 1: intelligibility of it or the visualization of it. There's this
• 21:28
  Speaker 1: concept in German which we don't have an exact word
• 21:31
  Speaker 1: for in English, but basically it's trying to get it like,
• 21:33
  Speaker 1: what does this mean? What is quantum mechanics saying about
• 21:36
  Speaker 1: what's happening?
• 21:37
  Speaker 2: It's like the zeitgeist of quantum mechanics.
• 21:40
  Speaker 1: Yeah, and Eisenberg's attitude is like, who cares? You know?
• 21:43
  Speaker 1: I have this mathematical tool and it makes predictions. I
• 21:46
  Speaker 1: can predict how your measurements are going to come out,
• 21:48
  Speaker 1: and so we're all good. People didn't really like that,
• 21:50
  Speaker 1: And at the same time, Schrodinger developed a completely alternative
• 21:53
  Speaker 1: view of quantum mechanics which is now more famous and
• 21:56
  Speaker 1: well known, you know, the Schrodinger equation. And because he
• 21:59
  Speaker 1: was you like a wave equation, it sort of allowed
• 22:02
  Speaker 1: people to more easily visualize what's going on. You know,
• 22:05
  Speaker 1: people have this like concept of a blob of probability
• 22:08
  Speaker 1: around the atom, et cetera, et cetera, And this really
• 22:11
  Speaker 1: kind of pissed Heisenberg off.
• 22:13
  Speaker 2: You mean he was annoyed to philosophers.
• 22:15
  Speaker 1: And yeah, he actually wrote in a letter once to
• 22:19
  Speaker 1: another physicist, Polly, he said, quote, the more I think
• 22:22
  Speaker 1: about the physical part of Schrodinger's theory, the more disgusting
• 22:25
  Speaker 1: I find it.
• 22:26
  Speaker 2: Whoa yaouch?
• 22:29
  Speaker 1: And then he said I consider it, And then he
• 22:31
  Speaker 1: used this German word must. And I try to look
• 22:34
  Speaker 1: up some translations to this German word, and again there's
• 22:37
  Speaker 1: a lot of uncertainties. Some people say it means junk.
• 22:39
  Speaker 1: Some people say it means poppy cock, some people say
• 22:42
  Speaker 1: it means rubbish, and the other less safe for work
• 22:44
  Speaker 1: translations of this word as.
• 22:46
  Speaker 2: Well, I think it means that Heisenberg had some saucy
• 22:50
  Speaker 2: words for Schroder.
• 22:51
  Speaker 1: But the point is that in Heisenberg's view, this question
• 22:54
  Speaker 1: of like where is the electron was the wrong question.
• 22:58
  Speaker 1: In Heisenberg's quant mechanics, there is like no true position
• 23:02
  Speaker 1: of a particle. There's only the outcome of a measurement,
• 23:05
  Speaker 1: and there's only if you measure something what's going to happen.
• 23:07
  Speaker 1: And inherent in Heisenberg's quantum mechanics was this idea that
• 23:11
  Speaker 1: if you measure one thing and then measure another thing,
• 23:14
  Speaker 1: the order matters that like reversing the order will change
• 23:17
  Speaker 1: the outcome, which is sort of confusing. Like imagine measuring
• 23:21
  Speaker 1: the width and the height of a table. You don't
• 23:24
  Speaker 1: think about measuring them in a certain order because you figure, like, well,
• 23:26
  Speaker 1: but with and the height are things, I can measure
• 23:28
  Speaker 1: them in what order I want. But in this case,
• 23:31
  Speaker 1: in Heisenberg's quantum mechanics, for some things the order does matter.
• 23:34
  Speaker 2: Well, let maybe let's break it down into a concrete example,
• 23:38
  Speaker 2: Like let's say that this table had quantum uncertainty about
• 23:41
  Speaker 2: its width and its length. Now what would that mean.
• 23:43
  Speaker 2: It means I can measure one but not the other,
• 23:46
  Speaker 2: or I can sort of measure one and sort of
• 23:48
  Speaker 2: measure the other, or what does that mean?
• 23:49
  Speaker 1: So it would mean that measuring its width would change
• 23:52
  Speaker 1: its length, right, and measuring its length would change its width,
• 23:56
  Speaker 1: which would mean the outcome of those measurements depended on
• 23:59
  Speaker 1: the order you make them. That measuring it's with then
• 24:01
  Speaker 1: it's length, or measuring its length and it's with would
• 24:04
  Speaker 1: give you different answers.
• 24:05
  Speaker 2: Wait, it would change, like if I measured the width,
• 24:08
  Speaker 2: it would change the length of it, like physically, or
• 24:11
  Speaker 2: it would maybe make me less able to measure the length.
• 24:15
  Speaker 1: It would change the uncertainty, the fundamental uncertainty of that quantity,
• 24:18
  Speaker 1: which would affect what you measure later.
• 24:20
  Speaker 2: Yeah, what do you mean the uncertainty? What would be
• 24:22
  Speaker 2: the uncertainty of its length? Like I can't predict what
• 24:25
  Speaker 2: its length it's going to be, or it can actually
• 24:27
  Speaker 2: measure it.
• 24:28
  Speaker 1: You can still make a measurement of its length, but
• 24:30
  Speaker 1: the outcome that measurement depends on the fundamental uncertainty of
• 24:33
  Speaker 1: that object. That quantity is not well known, that quantity
• 24:36
  Speaker 1: is not like defined. It depends on the inherent uncertainty
• 24:39
  Speaker 1: of the object itself. And so if you affect that
• 24:43
  Speaker 1: uncertainty affects your measurement.
• 24:45
  Speaker 2: Right, So let's say I measure the table and I
• 24:46
  Speaker 2: measure that it's thirty six inches wide. What does it
• 24:50
  Speaker 2: mean to the change is its length? That I'm going
• 24:52
  Speaker 2: to measure it and I can't measure it, or I'm
• 24:54
  Speaker 2: going to measure it and it's going to sometimes it's
• 24:55
  Speaker 2: going to be twenty somethings twenty forty or it's like
• 24:58
  Speaker 2: I'm going to measure it and it's gonna be fifty
• 25:00
  Speaker 2: when I thought it was forty. What does it mean
• 25:02
  Speaker 2: that it changes? You know what I mean? Like, what
• 25:03
  Speaker 2: are you trying to say?
• 25:04
  Speaker 1: Well, what I'm saying is that it changes the distribution
• 25:07
  Speaker 1: of possible measurements you're going to make for the length.
• 25:09
  Speaker 1: If you measure the width first, it changes the quantum
• 25:11
  Speaker 1: state of the particle. So now when you go to
• 25:14
  Speaker 1: measure the length, you're measuring like a different system than
• 25:17
  Speaker 1: you were measuring before you measured the width. You've perturbed it.
• 25:20
  Speaker 2: You're saying, it's changing the randomness of the length.
• 25:22
  Speaker 1: There is a random element there because the possible outcomes
• 25:26
  Speaker 1: of the length are now determined by a probability distribution,
• 25:29
  Speaker 1: and that is wider. You can think about it that way.
• 25:32
  Speaker 2: Yeah, Oh, I see, So it's like more random. Like
• 25:35
  Speaker 2: if I measured the width of the table, then the
• 25:37
  Speaker 2: length gets more random, like before it could maybe be
• 25:41
  Speaker 2: you know, between five and six feet. But now and
• 25:43
  Speaker 2: that I measured the width, now suddenly like this magical table,
• 25:47
  Speaker 2: it's like whoa, Now, now the length of it can
• 25:49
  Speaker 2: be one inchry it can be a million inches.
• 25:50
  Speaker 1: Yeah, And it's very counterintuitive when you think about a table,
• 25:53
  Speaker 1: because first of all, the table is a classical object,
• 25:55
  Speaker 1: doesn't have any these properties, and because we think of
• 25:57
  Speaker 1: a table as having like specific length and width, and
• 26:00
  Speaker 1: that's also true of quantum objects. Right. This uncertainty only
• 26:03
  Speaker 1: applies to very specific pairs of things that you can measure,
• 26:06
  Speaker 1: not to everything. So for a particle, for example, it
• 26:08
  Speaker 1: applies to position and momentum, not to like its ex
• 26:12
  Speaker 1: position and its why position. You can measure something in
• 26:14
  Speaker 1: X really precisely and then measure and why really precisely
• 26:18
  Speaker 1: with no problem, and the order doesn't matter. But if
• 26:20
  Speaker 1: you measure its position in X really precisely, it messes
• 26:23
  Speaker 1: up your potential knowledge of its momentum in X.
• 26:26
  Speaker 2: I see, but I guess for our magical table, I
• 26:28
  Speaker 2: can still measure the length, right, Like if I measured
• 26:30
  Speaker 2: the width, that doesn't mean I can't measure the length.
• 26:32
  Speaker 2: I can still measure the length. It's just going to
• 26:34
  Speaker 2: be exper random, so that if I had like a
• 26:37
  Speaker 2: million of these magical tables, I'm going to think the
• 26:39
  Speaker 2: length is all over the place.
• 26:40
  Speaker 1: M Yeah, that's exactly right.
• 26:42
  Speaker 2: That means that there is an element of randomness to
• 26:44
  Speaker 2: the idea of uncertainty, Like, how could you have uncertainty
• 26:48
  Speaker 2: without randomness?
• 26:48
  Speaker 1: Yeah, that's a good point.
• 26:49
  Speaker 2: Okay, So that's the magical table, and if quantum uncertainty
• 26:53
  Speaker 2: applied to that table, that's how it would be for
• 26:54
  Speaker 2: the table. But now let's maybe take a more physical example.
• 26:58
  Speaker 2: You were talking about precision and momentum.
• 27:00
  Speaker 1: Yeah, because it's important to understand quantumuncertainty doesn't just apply
• 27:03
  Speaker 1: willing nearly to everything. It doesn't say the whole universe
• 27:06
  Speaker 1: is flascting no matter what it says. Specific pairs of
• 27:09
  Speaker 1: things can't be known at the same time. So you
• 27:12
  Speaker 1: can know the X and the why of a particle,
• 27:14
  Speaker 1: but you can't know it's X and it's momentum also
• 27:17
  Speaker 1: in X.
• 27:17
  Speaker 2: Wait, I can know it or I can measure it,
• 27:20
  Speaker 2: because like the table, I can measure the with and
• 27:22
  Speaker 2: the length, right, Or are you saying that if I
• 27:25
  Speaker 2: measure the width, I can measure the length.
• 27:27
  Speaker 1: You can always measure it. But in the case of
• 27:28
  Speaker 1: the table, if you measure the width, you get a number.
• 27:31
  Speaker 1: You measure the length, you get a number. But now
• 27:32
  Speaker 1: you no longer know the width because you messed up
• 27:35
  Speaker 1: the width when you measure the length. These two things
• 27:37
  Speaker 1: are connected.
• 27:38
  Speaker 2: I see. I think maybe what you mean by no
• 27:40
  Speaker 2: is you actually mean predict, Like if I measure the width,
• 27:43
  Speaker 2: then it makes it harder for me to predict what
• 27:45
  Speaker 2: the length is going to be of this table. Because
• 27:47
  Speaker 2: I can know what the length of the table is.
• 27:48
  Speaker 2: I can measure it, right, That's how we know it.
• 27:51
  Speaker 2: But it's more about like being able to know it
• 27:53
  Speaker 2: before you measure it.
• 27:53
  Speaker 1: Well, I'd say, when you measure it, you measure it
• 27:55
  Speaker 1: with some uncertainty. Even if you know it, you know,
• 27:57
  Speaker 1: with some uncertainty. There's like error bars on it.
• 28:00
  Speaker 2: Oh, it's about error bars. That's different, though, isn't it.
• 28:03
  Speaker 1: Well, you know, it depends on how you interpret the
• 28:05
  Speaker 1: air bars and the randomness. But like repeated measurements which
• 28:07
  Speaker 1: probe that probability distribution will give different outcomes. It doesn't
• 28:11
  Speaker 1: fundamentally have a specific length. It has a distribution, and
• 28:14
  Speaker 1: if you measure it multiple times, you'll get different answers
• 28:17
  Speaker 1: according to the width of that distribution.
• 28:20
  Speaker 2: Oh, I see, I feel like you're saying kind of
• 28:22
  Speaker 2: like the table has the length and with but then
• 28:24
  Speaker 2: there's our measurement of the length and with which might
• 28:27
  Speaker 2: not be what it's real length.
• 28:28
  Speaker 1: And with this in the case of the magical table,
• 28:31
  Speaker 1: which follows this quantum uncertainty though obviously tables don't really right.
• 28:35
  Speaker 1: If we say that it has this quantum uncertainty attached
• 28:37
  Speaker 1: to the length and the with, then the length and
• 28:39
  Speaker 1: the width are not determined simultaneously. It's not that it
• 28:42
  Speaker 1: exists and it's written in a gold tablet by God somewhere.
• 28:45
  Speaker 1: We just don't have access to seeing it. It's just
• 28:48
  Speaker 1: that it's not defined.
• 28:49
  Speaker 2: Oh, I think I see what like you're saying. I
• 28:51
  Speaker 2: think that if I measure this table with like a
• 28:54
  Speaker 2: super precise ruler, and I measured the with and I
• 28:57
  Speaker 2: get that it's three feet wide and I'm super certain
• 29:00
  Speaker 2: about that, that means that no matter what I do
• 29:03
  Speaker 2: to measure the length, I have to assign a certain
• 29:06
  Speaker 2: uncertainty or a certain error to it. I might measure
• 29:09
  Speaker 2: the length of the table, I might say, oh, I
• 29:11
  Speaker 2: measure it to be six feet, but in the back
• 29:12
  Speaker 2: of my head I have to be like, well, that's
• 29:15
  Speaker 2: probably not actually six feet. Is that kind of what
• 29:18
  Speaker 2: you mean by uncertainty?
• 29:19
  Speaker 1: Yeah? And then if you go back to measure the width,
• 29:22
  Speaker 1: you're going to get a different answer than you did
• 29:23
  Speaker 1: before because measuring the length has now changed the width.
• 29:27
  Speaker 2: But no, i'm it's still the same table.
• 29:28
  Speaker 1: No, it's not still the same table, right, because you've
• 29:30
  Speaker 1: made a measurement to it and measuring things changes them.
• 29:33
  Speaker 2: Oh, but what if I mentioned it at the same time.
• 29:35
  Speaker 1: Yeah, great question, But you can't do that, right. You
• 29:37
  Speaker 1: make a measurement of a quantum system. You can measure
• 29:39
  Speaker 1: a thing, right, and these two things you can't measure simultaneously.
• 29:43
  Speaker 2: Oh see, that's I feel like that's another concept. Then
• 29:45
  Speaker 2: in quantum mechanics, why can't I measure this table at
• 29:48
  Speaker 2: the same time.
• 29:49
  Speaker 1: In Heisimber's quantum mechanics, the way you make a measurement
• 29:52
  Speaker 1: is that you operate on that quantum state. Operating on
• 29:55
  Speaker 1: the quantum state will change it, and you can't do
• 29:57
  Speaker 1: two operations simultaneously.
• 29:59
  Speaker 2: Maybe for those us that are not familiar with quantum states,
• 30:01
  Speaker 2: what does that mean? That means that, like in a system,
• 30:04
  Speaker 2: there are some variables that you just can't measure at
• 30:07
  Speaker 2: the same time.
• 30:07
  Speaker 1: I'll try. All measurements have to be made in a
• 30:09
  Speaker 1: certain order because potentially measurements could mess up later measurements.
• 30:13
  Speaker 1: In some cases they don't, right, Like you can measure
• 30:15
  Speaker 1: the X and then you can measure the Y, and
• 30:17
  Speaker 1: the answer you get for why doesn't depend on whether
• 30:20
  Speaker 1: you already measured x. But if you measure x and
• 30:22
  Speaker 1: then you measure momentum and X, then you will get
• 30:25
  Speaker 1: a different answer. And the order does matter, like measuring
• 30:27
  Speaker 1: x and then momentum or measuring momentum and then position
• 30:31
  Speaker 1: in X will change the answers that you get.
• 30:34
  Speaker 2: I see, it's kind of part of the magical properties
• 30:36
  Speaker 2: of my table. Like a regular table, I can definitely
• 30:39
  Speaker 2: get two people to measure it within the length at
• 30:40
  Speaker 2: the same time, but a quantum uncertain table you just can't.
• 30:44
  Speaker 2: You can only do one at a time.
• 30:45
  Speaker 1: Yeah, And it's sort of hard to understand that about
• 30:47
  Speaker 1: a table because it doesn't seem to make any sense.
• 30:49
  Speaker 1: And X and Y seem to be orthogonal, right, And
• 30:51
  Speaker 1: that's why I suggested it as a ridiculous example, because
• 30:55
  Speaker 1: it's very counterintuitive, and quantum mechanics is counterintuitive in that way,
• 30:59
  Speaker 1: but not quite as counterintuitive. I mean, you can't get
• 31:01
  Speaker 1: some understanding of why measuring one thing messes up another
• 31:05
  Speaker 1: if you think more specifically about, for example, momentum and
• 31:08
  Speaker 1: position instead of like table lengths and widths.
• 31:11
  Speaker 2: Right, I just think that, you know, for more less
• 31:13
  Speaker 2: of us saying that's what the mass says, and it's magic.
• 31:16
  Speaker 2: It's pretty much the same thing. It's magicmagical, mathemagical.
• 31:20
  Speaker 1: There you go. I mean you can think about it
• 31:23
  Speaker 1: in terms of like measuring a particle, right, say you
• 31:26
  Speaker 1: want to know its location, how would you actually make
• 31:28
  Speaker 1: that measurement? Well, in order to measure the location of
• 31:32
  Speaker 1: a particle, you got to like bounce something else off
• 31:34
  Speaker 1: of it. There's no passive observing of the universe. You
• 31:37
  Speaker 1: got to like bounce a photon off of it, for example,
• 31:39
  Speaker 1: to see where it is. And if you want to
• 31:43
  Speaker 1: know its precision really, really precisely, then you need a
• 31:45
  Speaker 1: really high energy photon because high energy photons have short
• 31:49
  Speaker 1: wavelengths and so they can tell you information about really
• 31:52
  Speaker 1: small distances. But if you bounce a really high energy
• 31:56
  Speaker 1: photon off of your electron, then you're going to totally
• 31:58
  Speaker 1: mess up its momentum. It'sent is going to be very
• 32:00
  Speaker 1: different now than before you measured it. So if you
• 32:03
  Speaker 1: go off to measure its momentum, you're going to get
• 32:05
  Speaker 1: a different answer than if you hadn't measured the position.
• 32:08
  Speaker 2: That's if you try to do it one after the other.
• 32:10
  Speaker 2: But I'm just throwing out an idea. What if you, like,
• 32:14
  Speaker 2: throw a photon at it and you measure how the
• 32:17
  Speaker 2: photeland bounces, and then that tells you both things at
• 32:20
  Speaker 2: the same time. Maybe right, Like if I catch a baseball,
• 32:23
  Speaker 2: I know its position and how fast it was going.
• 32:26
  Speaker 1: Yeah, and you can do that for a classical object,
• 32:28
  Speaker 1: and you can know simultaneously multiple things about quantum objects,
• 32:32
  Speaker 1: just not some things right, just in this case, like
• 32:35
  Speaker 1: not position and momentum simultaneously. And the reason that you
• 32:38
  Speaker 1: can't has to do with how this information is encoded
• 32:41
  Speaker 1: in the particle, which I think we can understand without
• 32:44
  Speaker 1: getting too mathematical.
• 32:45
  Speaker 2: All right, well, let's dig into some of this mathemagic
• 32:48
  Speaker 2: or not mathe physics, I guess, and the idea of
• 32:51
  Speaker 2: wave and the wave function, which is I think where
• 32:53
  Speaker 2: we're going with this, dig into that waving is. But
• 32:55
  Speaker 2: first let's take another quick break. All right, we're talking
• 33:11
  Speaker 2: about the hairy topic of quantum uncertainty and all the
• 33:15
  Speaker 2: uncertain details about it. Down to the nittigree to hear. Now, Daniel,
• 33:18
  Speaker 2: you think that maybe a good way to explain this
• 33:20
  Speaker 2: is using waves, and specifically sound waves, right as maybe
• 33:24
  Speaker 2: they relate to the wave function of quantum particles.
• 33:27
  Speaker 1: Yeah, if you're trying to think about position and momentum
• 33:29
  Speaker 1: of particles and how they're like encoded in the mathematical
• 33:32
  Speaker 1: description of the particle in quantum mechanics, truly helpful to
• 33:36
  Speaker 1: think about analogies we have in the classical world that
• 33:38
  Speaker 1: are a little bit more intuitive. And there actually is
• 33:40
  Speaker 1: one that a lot of people are familiar with, and
• 33:42
  Speaker 1: that's sound waves and songs and how words and music
• 33:46
  Speaker 1: can be broken up into very specific frequencies.
• 33:49
  Speaker 2: All right, let's dig into it. How is a quantum
• 33:51
  Speaker 2: uncertainty like a song?
• 33:54
  Speaker 1: Well, think about like your equalizer on your stereo when
• 33:57
  Speaker 1: you hear songs that has like a bass and a
• 33:59
  Speaker 1: trouble and whatever, and the high frequencies and low frequencies,
• 34:02
  Speaker 1: and your equalizer is telling you like how much bass
• 34:05
  Speaker 1: is there, or how many low frequency sounds are there,
• 34:07
  Speaker 1: or how many high frequency sounds are there.
• 34:09
  Speaker 2: Or more like how strong the song is in this
• 34:13
  Speaker 2: frequency range?
• 34:13
  Speaker 1: Right exactly, So we're going to think about the relationship
• 34:16
  Speaker 1: between frequencies, pure notes of specific frequencies and how you
• 34:20
  Speaker 1: can use them to build up different kinds of sound.
• 34:23
  Speaker 1: That's going to give you a feeling for the physical
• 34:25
  Speaker 1: reason why there are some specific quantities that you can't
• 34:28
  Speaker 1: know at the same time how they're linked by quantum uncertainty.
• 34:32
  Speaker 1: So start with a pure note, like an opera singer
• 34:34
  Speaker 1: singing a high seed. That's just one frequency on your
• 34:38
  Speaker 1: equalizer or on a spectrograph. It's going to give you
• 34:40
  Speaker 1: a single spike at that frequency, and there's very little
• 34:43
  Speaker 1: uncertainty in the frequency. Right you hear the sound, you
• 34:45
  Speaker 1: know the frequency. There's only one frequency to the sound.
• 34:48
  Speaker 1: Now think about the corresponding quantity, the shape. If she
• 34:52
  Speaker 1: hits the high sea, then where is that sindwave? That
• 34:55
  Speaker 1: sinwave is everywhere in the room. It goes up and down.
• 34:58
  Speaker 1: It doesn't really have a shape. It's a sine wave everywhere.
• 35:01
  Speaker 1: It fills the room or the opera house or whatever
• 35:03
  Speaker 1: it is. So you know a lot about the frequency
• 35:06
  Speaker 1: of her note. The spectrograph is a spike, but the
• 35:09
  Speaker 1: soundwave itself is very spread out in position. It's filled
• 35:12
  Speaker 1: the whole room. It's everywhere. Well, what if we wanted
• 35:15
  Speaker 1: our opera singer to create a sound that you could
• 35:18
  Speaker 1: only hear in part of the room. And you know
• 35:20
  Speaker 1: that you can get different sounds in different parts of
• 35:22
  Speaker 1: the room if you take advantage of how they can interfere.
• 35:24
  Speaker 1: That's why they very carefully designed acoustics in opera houses,
• 35:28
  Speaker 1: et cetera. But we can get our singer to make
• 35:30
  Speaker 1: a sound that you can only hear in one part
• 35:33
  Speaker 1: of the room, like in only one spot can you
• 35:35
  Speaker 1: hear it, and the other spots it'll be totally silent.
• 35:37
  Speaker 1: She can do this if she adds more frequencies, right,
• 35:40
  Speaker 1: So if she has just one frequency, just the high
• 35:42
  Speaker 1: seats everywhere, Now add another singer singing a different frequency,
• 35:47
  Speaker 1: and those two sine waves have different frequencies, and so
• 35:50
  Speaker 1: they'll cancel out in some places of the room and
• 35:52
  Speaker 1: add up in others. That's constructive and destructive interference at
• 35:55
  Speaker 1: a third singer with another frequency, and you can shape
• 35:59
  Speaker 1: the total effect further. The more frequencies you add, the
• 36:02
  Speaker 1: more you can shape that sound. And if you add
• 36:05
  Speaker 1: an infinite number of singers crowded onto that stage, you
• 36:08
  Speaker 1: can make any sound shape you want. In the room,
• 36:11
  Speaker 1: including a very very narrow spike, so that the sound
• 36:14
  Speaker 1: can only be heard at one spot in the room.
• 36:17
  Speaker 1: So in this scenario, the sound has a huge spread
• 36:20
  Speaker 1: of frequencies but a single very well determined location. All
• 36:24
  Speaker 1: the sound is in one place. So maybe now you
• 36:27
  Speaker 1: see the tradeoff. Either you can have a single frequency
• 36:31
  Speaker 1: the one high scene note, but the position is very
• 36:34
  Speaker 1: broad it's anywhere in the room. Or you can have
• 36:37
  Speaker 1: a broad range of frequencies lots of singers on the stage,
• 36:40
  Speaker 1: but the position is now very very narrow. So because
• 36:43
  Speaker 1: of the wavelike nature of sound, you can't have narrowness
• 36:48
  Speaker 1: in both frequency and in location. Those two things are
• 36:51
  Speaker 1: inherently linked by the nature of the physical process of sound.
• 36:56
  Speaker 1: You can't use a single frequency to create a narrow spike,
• 37:00
  Speaker 1: a sound that exists only one location in space. It's
• 37:03
  Speaker 1: either narrow frequency in broad position or broad frequency range
• 37:08
  Speaker 1: and narrow position. Frequency and position are conjugate variables, they're
• 37:13
  Speaker 1: linked in that very special way, and that also applies
• 37:16
  Speaker 1: to quantum waves. For a particle in a box, the
• 37:19
  Speaker 1: frequency of the wave function tells you its momentum. So
• 37:22
  Speaker 1: if you want your particle to have little uncertainty, in position,
• 37:26
  Speaker 1: you have to use lots of frequencies, lots of possible
• 37:29
  Speaker 1: momenta which add up to give you that spike. And
• 37:31
  Speaker 1: because you have lots of possible momentum now in your
• 37:34
  Speaker 1: wave function, that means a large momentum uncertainty, So small
• 37:38
  Speaker 1: uncertainty position requires a large momentum uncertainty. And in the
• 37:42
  Speaker 1: other direction, if you want your particle to have little
• 37:45
  Speaker 1: uncertainty in momentum, then you can only use a narrow
• 37:49
  Speaker 1: range of frequencies, which means you'll get a very broad
• 37:52
  Speaker 1: blob in position. You can't build a quantum wave function
• 37:56
  Speaker 1: out of just a few frequencies that also localize in position,
• 38:00
  Speaker 1: for the same reason that the opera singer can't sing
• 38:03
  Speaker 1: a single note and have it be localized in the room.
• 38:06
  Speaker 2: Yeah, I think that maybe a way that I've seen
• 38:08
  Speaker 2: it explain is a little bit talking about like the
• 38:11
  Speaker 2: with of things are you saying they can be described
• 38:14
  Speaker 2: by wave functions? Right, Like something that has like a
• 38:17
  Speaker 2: really wide wave means that it's it's really fuzzy and
• 38:21
  Speaker 2: you don't know where quite where it is, whereas something
• 38:23
  Speaker 2: that is really narrow you can sort of know its position,
• 38:27
  Speaker 2: but it's also going really fast.
• 38:29
  Speaker 1: Maybe exactly for something you know really really well, and
• 38:32
  Speaker 1: it's wave function is going to be super duper narrow,
• 38:34
  Speaker 1: like a spike. But to build a spike in terms
• 38:37
  Speaker 1: of frequencies, in terms of like various possible momenta requires
• 38:40
  Speaker 1: a very large number of them. You need like lots
• 38:42
  Speaker 1: of them to add up and cancel out in just
• 38:44
  Speaker 1: the right way to give you that spike. Whereas you
• 38:46
  Speaker 1: want something really big and fat as a blob, then
• 38:49
  Speaker 1: you need fewer different frequencies to add up to give
• 38:52
  Speaker 1: you that big, fat blob. Something that's very uncertain. So
• 38:55
  Speaker 1: a wave function that's really narrow needs lots of different
• 38:57
  Speaker 1: frequencies to add up, which means different possible momentum because
• 39:01
  Speaker 1: frequency and momentum are the same for a particle, which
• 39:03
  Speaker 1: means a lot of uncertainty in its momentum, Whereas if
• 39:06
  Speaker 1: you have a lot of uncertainty in its position, you
• 39:09
  Speaker 1: only need a few frequencies, which means less uncertainty in
• 39:12
  Speaker 1: its momentum. That gives you a little bit of the
• 39:14
  Speaker 1: flavor of why position and momentum have this special relationship.
• 39:18
  Speaker 1: Quantum manternity is all about very specific pairs of things
• 39:21
  Speaker 1: you can measure that have this relationships, not just like
• 39:23
  Speaker 1: any two things that you measure, right, And so.
• 39:26
  Speaker 2: Maybe it might help to get into some of these
• 39:28
  Speaker 2: other things. So you're saying that position of momentum are
• 39:31
  Speaker 2: linked together in this quantum uncertainty because of its wave nature. Right.
• 39:35
  Speaker 2: For example, if you take to measure the velocity of
• 39:37
  Speaker 2: a wave, somehow it's related also to its frequency, which
• 39:40
  Speaker 2: that's where the fuzziness maybe it comes from. So maybe
• 39:43
  Speaker 2: talk about some of these other variables in quantum mechanics
• 39:46
  Speaker 2: that are also linked together by uncertainty.
• 39:48
  Speaker 1: Yeah, And a tiny little quibble there is that it
• 39:52
  Speaker 1: can be explained in terms of like shirting or wave mechanics,
• 39:55
  Speaker 1: but Heisenberg can also explain it without any waves at all.
• 39:58
  Speaker 1: He has a completely different formulation quant mechanics that uses matrices.
• 40:02
  Speaker 1: And for those of you who like know matrix mechanics,
• 40:04
  Speaker 1: you know, like multiplication of matrices doesn't commute that you like,
• 40:08
  Speaker 1: it matters what you order you multiply things by with
• 40:11
  Speaker 1: your matrices, So like it comes out of quantum mechanics.
• 40:13
  Speaker 1: No matter what mathematical formulation you use, matrices or waves
• 40:17
  Speaker 1: or whatever. It's like really deep in there. But you're right,
• 40:20
  Speaker 1: it's not just position and momentum that this affects. There's
• 40:23
  Speaker 1: lots of other things that are paired. Another famous example
• 40:26
  Speaker 1: is energy and time of what like of a particle. So,
• 40:30
  Speaker 1: for example, a particle might have a specific mass, and
• 40:33
  Speaker 1: that affects how long it lasts. So, for example, an
• 40:36
  Speaker 1: electron which lasts forever has a very specific mass. Every
• 40:40
  Speaker 1: electron out there has the same mass exactly, because electrons
• 40:44
  Speaker 1: live for an infinite number of years. But if you
• 40:46
  Speaker 1: have particles whose lifetime is shorter and there's a quant
• 40:49
  Speaker 1: mechanical uncertainty to how long they're going to live, then
• 40:52
  Speaker 1: their mass is more uncertain. So for example, a top quark,
• 40:56
  Speaker 1: it might be one hundred and seventy three GV might
• 40:58
  Speaker 1: be one hundred and sixty five one hundred and eighty one.
• 41:01
  Speaker 1: There's a huge variation there in the possible masses a
• 41:04
  Speaker 1: top quark would have because it doesn't live for very long.
• 41:08
  Speaker 2: So when you say like it lasts, meaning like it
• 41:10
  Speaker 2: it might at any point break down into other things, right,
• 41:14
  Speaker 2: lower energy things, and so it has a lifespan and
• 41:16
  Speaker 2: you're saying, like, how long we expect it to be around?
• 41:19
  Speaker 2: Hole is tied to its mass exactly.
• 41:22
  Speaker 1: Electrons, we think their lifetime is basically infinity. You could
• 41:25
  Speaker 1: wait infinite number of years the electron just sitting out
• 41:27
  Speaker 1: there in space would still be an electron. Top quark
• 41:30
  Speaker 1: lasts for like ten to the minus twenty three seconds,
• 41:33
  Speaker 1: So there's a lot less uncertainty about how long a
• 41:35
  Speaker 1: top quark is going to be in the universe just
• 41:37
  Speaker 1: because its lifetime is shorter, which means there's more uncertainty
• 41:41
  Speaker 1: about its energy, and that comes down to uncertainty about
• 41:43
  Speaker 1: its mass. So there's like a whole distribution of possible
• 41:46
  Speaker 1: masses you could measure for a top quark of masses
• 41:49
  Speaker 1: that it actually has. It's like a fundamental uncertainty and
• 41:52
  Speaker 1: like how much energy there is in this thing, because
• 41:55
  Speaker 1: there's very little uncertainty about how long it's going to last.
• 41:58
  Speaker 1: It's not going to last very long at all.
• 42:00
  Speaker 2: It's not just like uncertainty about where it is and
• 42:02
  Speaker 2: where it's going. It's like concertainty about it's actual like
• 42:05
  Speaker 2: being right, like what it is, how much of it.
• 42:08
  Speaker 1: Is there exactly. And there's a really deep connection between
• 42:11
  Speaker 1: these two variables energy and time, position and momentum. We
• 42:14
  Speaker 1: talked about this philosophical connection in another episode. It all
• 42:17
  Speaker 1: comes out of this theorem No Other's theorem, which tells
• 42:19
  Speaker 1: us like relationships between symmetries and conservation laws. We know
• 42:24
  Speaker 1: the fact that space is the same everywhere in the
• 42:26
  Speaker 1: universe means momentum is conserved. It's another connection there between
• 42:30
  Speaker 1: position and momentum. No Other's law also tells us that
• 42:33
  Speaker 1: energy is conserved if space is the same across time.
• 42:37
  Speaker 1: There's a connection between energy and time. And so you
• 42:40
  Speaker 1: see that there's really a deep connection between these variables.
• 42:43
  Speaker 1: Some of these things are just sort of fundamentally paired physically,
• 42:46
  Speaker 1: position and momentum, energy and time. There's also weird properties
• 42:51
  Speaker 1: of the spins of particles that have these kind of relationships.
• 42:54
  Speaker 2: What do you mean by spin?
• 42:55
  Speaker 1: So particles can have quantum spin right, spin up or
• 42:58
  Speaker 1: spin down depends on how you measure it. Like if
• 43:02
  Speaker 1: you try to measure the spin of a particle, you
• 43:04
  Speaker 1: can do so by putting it in a magnetic field.
• 43:06
  Speaker 1: Then it will align one way or the other way. Well,
• 43:09
  Speaker 1: that's a spin along one axis the axis of that
• 43:11
  Speaker 1: magnetic field. You could also try to measure its spin
• 43:15
  Speaker 1: like at we're using a perpendicular setup. Like take another
• 43:17
  Speaker 1: magnet and rotated ninety degrees. Try to measure it spin
• 43:21
  Speaker 1: in another way, so you like spin in X and
• 43:23
  Speaker 1: spin and y. It turns out these two things are related.
• 43:26
  Speaker 1: You can't know the spin of a particle in two
• 43:28
  Speaker 1: directions simultaneously. Like you measure it spin in X, that
• 43:32
  Speaker 1: will mess up its spin and y. If you measure
• 43:34
  Speaker 1: it spin and why, that will mess up its spin
• 43:36
  Speaker 1: in X. These two things are linked the same way
• 43:38
  Speaker 1: position and momentum are linked. Right.
• 43:41
  Speaker 2: Well, by mess up, you mean like it changes its probability, right,
• 43:45
  Speaker 2: like what it can be.
• 43:45
  Speaker 1: Yeah, there's this famous experiment where they take a bunch
• 43:48
  Speaker 1: of atoms and they put them into a magnetic field
• 43:50
  Speaker 1: so they're either spin up or spin down. Then use
• 43:52
  Speaker 1: a fancy device to filter all them out so they
• 43:54
  Speaker 1: like only take the spin up ones. Then they send
• 43:56
  Speaker 1: this through the experiment again, but rotate it so now
• 43:58
  Speaker 1: they're measuring it like along another axis. And when they
• 44:01
  Speaker 1: send it back through the first device again, they're now
• 44:04
  Speaker 1: both spin up and spin down. So you've taken a
• 44:06
  Speaker 1: beam that are only spin up. You measure it in
• 44:09
  Speaker 1: an orthogonal way, that messes up your original distribution in
• 44:13
  Speaker 1: the first direction. So measuring in one direction messes up
• 44:16
  Speaker 1: the measurement in the other direction. Because these two things
• 44:18
  Speaker 1: are linked fundamentally, you can't know them simultaneously.
• 44:21
  Speaker 2: It kind of feels like maybe these things are paired
• 44:25
  Speaker 2: together by kind of the constraints that measuring those things have.
• 44:31
  Speaker 2: It's impossible to measure the spin of a particle in
• 44:34
  Speaker 2: the up and down direction and in the site to
• 44:37
  Speaker 2: side direction at the same time, and therefore those two
• 44:39
  Speaker 2: things are linked.
• 44:40
  Speaker 1: Yeah, those two things are definitely linked. You know, why
• 44:43
  Speaker 1: these two things are linked and not other two things
• 44:46
  Speaker 1: is a really interesting and deep question. I think that's
• 44:48
  Speaker 1: fundamentally a question of the episode, like why is there
• 44:51
  Speaker 1: any quantum uncertainty in classical physics? All these things are
• 44:54
  Speaker 1: totally separate and independent, and quant mechanics has like linked
• 44:57
  Speaker 1: some certain pairs of quantities together and said, is a
• 45:00
  Speaker 1: limited information in these things? And you know, the philosophical
• 45:03
  Speaker 1: answer to that question is a little bit slippery, you know,
• 45:06
  Speaker 1: like we have this mathematical description that we can use
• 45:09
  Speaker 1: to predict all these wonderful quantumic experiments, and those mathematics
• 45:13
  Speaker 1: have this uncertainty built into them inherently, So you can
• 45:16
  Speaker 1: then look at that theory and say like, well, why
• 45:18
  Speaker 1: you know, and no, it's matrix mechanics or here's a
• 45:20
  Speaker 1: frequency analysis of a wave function. Fundamentally, that's not really
• 45:23
  Speaker 1: a satisfying answer because it doesn't tell us like why
• 45:26
  Speaker 1: we don't live in the universe without this uncertainty. Why
• 45:28
  Speaker 1: couldn't you have built a classical universe without them? Why
• 45:31
  Speaker 1: did the designers of the universe, whoever they are, give
• 45:34
  Speaker 1: us the universe with this property instead of other properties?
• 45:37
  Speaker 2: These things are not They're tied to each other, but
• 45:40
  Speaker 2: they're not tied across different categories. Like, for example, you
• 45:43
  Speaker 2: can know the position of a particle and its mass
• 45:46
  Speaker 2: and it's been along the up and down direction right perfectly,
• 45:49
  Speaker 2: those three things.
• 45:50
  Speaker 1: Pick one in each category and you can know it
• 45:51
  Speaker 1: as well as you like.
• 45:52
  Speaker 2: All right, So then it sounds like we haven't answered
• 45:55
  Speaker 2: the question of the episode.
• 45:58
  Speaker 1: The answer to the question of the episode is we
• 46:00
  Speaker 1: don't know, right. It's a feature of our universe the
• 46:02
  Speaker 1: way like the speed of light is a feature of
• 46:04
  Speaker 1: our universe. We observe it, we can build mathematical theories
• 46:07
  Speaker 1: to describe it. We can then scratch our heads and say, hm,
• 46:10
  Speaker 1: does it have to be this way, and we don't
• 46:11
  Speaker 1: have an answer to that. We don't know if it
• 46:13
  Speaker 1: would have been possible to build a universe that was classical.
• 46:17
  Speaker 1: We actually talked about that on a recent episode. Philosophically
• 46:20
  Speaker 1: and fundamentally, theoretically, you might have been able to build
• 46:22
  Speaker 1: a classical universe without any quantum uncertainty, but ours seems
• 46:26
  Speaker 1: to have this feature.
• 46:27
  Speaker 2: But I think, as you said, you know, it's a process, right,
• 46:30
  Speaker 2: We're in the middle of this process, and it might
• 46:32
  Speaker 2: be that in the future we do know why the
• 46:34
  Speaker 2: speed of light had to be a certain velocity, right.
• 46:37
  Speaker 1: Yeah, and in the future and we understand quantum gravity
• 46:39
  Speaker 1: and string theory, there might be a simple reason like, oh,
• 46:42
  Speaker 1: the universe has this property and therefore you have quantum uncertainty,
• 46:46
  Speaker 1: or the universe is this way and therefore the speed
• 46:49
  Speaker 1: of light is what it is. But you know that's
• 46:51
  Speaker 1: just going to generate more questions, right, whatever property that
• 46:54
  Speaker 1: is that gives rise to quantum uncertainty, we're then going
• 46:56
  Speaker 1: to ask, well, why that property?
• 46:58
  Speaker 2: So basically it's a never ending story, I hope.
• 47:03
  Speaker 1: So then I'll keep having a job.
• 47:05
  Speaker 2: Well, assuming people want you to do it, or I
• 47:07
  Speaker 2: guess you could do it you can pay yourself. I
• 47:09
  Speaker 2: guess it's still a job. If you pay yourself yourself,
• 47:12
  Speaker 2: you can be a self employed physicists.
• 47:14
  Speaker 1: Yeah, there's lots of great self employed physicists out there.
• 47:16
  Speaker 2: What if I just say that the answer is forty two?
• 47:19
  Speaker 2: Is there a universe out there where the answer is
• 47:21
  Speaker 2: forty two?
• 47:23
  Speaker 1: The answer to what question?
• 47:24
  Speaker 2: I don't know the answer of why the speed of
• 47:26
  Speaker 2: light is the way it is, it's because the number
• 47:31
  Speaker 2: forty two, I don't know.
• 47:32
  Speaker 1: I'd love to live in a universe where that answer
• 47:34
  Speaker 1: made sense for that question, but I don't think that's
• 47:36
  Speaker 1: this universe.
• 47:37
  Speaker 2: I wonder if them that universe they have the Hitchhiker's
• 47:40
  Speaker 2: Guide to the Galaxy. Or I guess in an infinite
• 47:43
  Speaker 2: multiverse there is a universe for the answer is forty two.
• 47:47
  Speaker 2: And also Douglas.
• 47:48
  Speaker 1: Adams was right, yes, and it all makes sense.
• 47:52
  Speaker 2: Yes, And then that one you'd be out of a job,
• 47:54
  Speaker 2: but not cartoonist, because we can always draw cartoons of
• 47:57
  Speaker 2: the number forty two.
• 47:58
  Speaker 1: That's right, and cartoonists can always be self employed.
• 48:00
  Speaker 2: All right, Well, I hopefully that gives you a sense
• 48:03
  Speaker 2: of how this universe still has a lot that can't
• 48:07
  Speaker 2: be explained. You know, there's these fundamental uncertainties in it
• 48:11
  Speaker 2: and what we can and cannot measure. At the same time,
• 48:15
  Speaker 2: it is sort of a magical table kind of for now,
• 48:17
  Speaker 2: right it is.
• 48:18
  Speaker 1: We can describe it mathematically, and we can give answers
• 48:20
  Speaker 1: to like why the mathematics works this way and why
• 48:23
  Speaker 1: these things bubble up from the mathematics, but we don't
• 48:25
  Speaker 1: fundamentally know why we live in a universe with quantum uncertainty.
• 48:29
  Speaker 2: Yeah, and if you eat out of a magical table,
• 48:32
  Speaker 2: is that a good way to control your diet?
• 48:36
  Speaker 1: If you don't know the lengthen with of your table,
• 48:37
  Speaker 1: it's a good way to make a big mess on
• 48:39
  Speaker 1: the floor.
• 48:40
  Speaker 2: Yeah, there you go. You might be sitting down your
• 48:42
  Speaker 2: food in empty space. All right, Well, we hope you
• 48:45
  Speaker 2: enjoyed that. Thanks for joining us. See you next time.
• 48:53
  Speaker 1: For more science and curiosity, come find us on social
• 48:56
  Speaker 1: media where we answer questions and post videos on Twitter, Discord, Instant,
• 49:01
  Speaker 1: and now TikTok. And remember that Daniel and Jorge Explain
• 49:05
  Speaker 1: the Universe is a production of iHeartRadio. For more podcasts
• 49:09
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• 49:13
  Speaker 1: you listen to your favorite shows,