Speaker 1: Hey, Daniel, can you pass through walls? No? Keep trying
Speaker 1: and just keep getting more bumps on my head? How
Speaker 1: about can you bean too pleased at the same time?
Speaker 1: Sometimes it feels like I'm supposed to be but I've
Speaker 1: never actually managed it. So I guess you're not a
Speaker 1: quantum object. No. Actually, I'm quite classical. But you're a
Speaker 1: particle physicists. Aren't you made of particles? And aren't those
Speaker 1: particles quantum mechanical? I study particles and I'm made of particles,
Speaker 1: but I follow the rules of classical physics. Classic. I
Speaker 1: mean you're classic, Daniel. I'm not new Coke Daniel. I
Speaker 1: am more hammad cartoonists and the creator of PhD comics.
Speaker 1: I'm Daniel. I'm a particle physicist, but I'm quite classical
Speaker 1: in my tastes. Are you a fan of classical music
Speaker 1: and it's better than quantum music? Let me tell you
Speaker 1: that's a new genre to mak a new category at
Speaker 1: the Grammy. Oh I wish it was a new genre,
Speaker 1: but I'm sure if we type it into Google we
Speaker 1: will find something for quantum music. I feel like that's
Speaker 1: all music these days. It's both good and bad. It's
Speaker 1: kind of incoherent. It's both original and stale. Welcome to
Speaker 1: our podcast, Daniel and Jorge Explain the Universe, a production
Speaker 1: of My Heart Radio in which we explore everything in
Speaker 1: the universe and try to make sense of it. We
Speaker 1: try to understand how things move in our world and
Speaker 1: how tiny particles move. We try to understand the rules
Speaker 1: of the universe, whether they govern supernovas and black holes
Speaker 1: or tiny little electrons, and we try to make sure
Speaker 1: that you understand them. Yeah, because we try to make
Speaker 1: this podcast a super position of both fun and real science,
Speaker 1: physics and banana jokes. You often think those two can't
Speaker 1: be in the same place. Said the same time, what
Speaker 1: makes you say that you haven't met any fun physicists.
Speaker 1: You mean the physicists is fun, or they know how
Speaker 1: to have fun, or just doing physics is fun. Why
Speaker 1: doesn't everybody see that? Come on, I think that's the
Speaker 1: problems and that's the problem. But yeah, it's a weird
Speaker 1: and strange universe out there, and so we like to
Speaker 1: talk about all of the things and make it weird
Speaker 1: and strange. It's pretty unintuitive the universe it is, and
Speaker 1: physics has done a great job of building this edifice
Speaker 1: to help us understand the way the universe really is,
Speaker 1: not the way we think the universe should be or
Speaker 1: might be, or the way that makes sense to us
Speaker 1: based on our limited experience, but actually revealing to us
Speaker 1: the true nature of reality. But sometimes what we learn
Speaker 1: is pretty hard to swallow. Yeah, and specifically quantum mechanics.
Speaker 1: I feel like that really trips people up. It trips
Speaker 1: me up, for sure, And it's kind of hard to
Speaker 1: wrap your head around all of the weird, kind of
Speaker 1: unintuitive phenomenon that happens at the quantum level. Yeah, it
Speaker 1: is pretty weird because quantum particles seem to be following
Speaker 1: different rules. They seem to be able to break rules
Speaker 1: that are hard and fast for things like baseballs and
Speaker 1: basketballs and scoops of ice cream. And that's a hard
Speaker 1: thing to understand because it's weird and it's new. It's
Speaker 1: also hard to understand, like why are there different rules?
Speaker 1: And you know, what's the difference between an electron and
Speaker 1: a baseball? You know, where is the sort of threshold
Speaker 1: between those two where the quantum rules take over or
Speaker 1: the classical rules take over. Yeah, it is kind of
Speaker 1: weird that, you know, things are so weird at that level,
Speaker 1: at the microscopic level, but then once you scale up,
Speaker 1: things feel more gosh normal, more solid, less uncertain, or
Speaker 1: at least more familiar. Right. Science is all about delving
Speaker 1: into the unknown, and typically we try to explain the
Speaker 1: unknown in terms of the known, but that fails if
Speaker 1: the unknown is something really new, something different, something that's
Speaker 1: fundamentally can't be described by what we already know. We've
Speaker 1: often talked about how physics is like exploring the universe,
Speaker 1: but it's just been studying the tail of the elephant,
Speaker 1: and when you look at the rest of the elephant,
Speaker 1: it's not always true that what you learn from the
Speaker 1: tail can help you understand the rest of the elephant.
Speaker 1: Sometimes you really do discover something weird and different. Yeah,
Speaker 1: but is that elephant quantum mechanical, Daniel, Is it really
Speaker 1: there or not there? It's a theoretical thought experiment elephant.
Speaker 1: So it's just totally not there. That's classically non existent.
Speaker 1: Al Right. Well, that connection between the quantum world and
Speaker 1: our regular, everyday world is what we'll be exploring today
Speaker 1: on this episode to be on the podcast. We'll be
Speaker 1: asking the question what is quantum decoherence? That's hopefully a
Speaker 1: coherent question, yes, and quantum decoherence is the key concept
Speaker 1: to understanding the answer to this question. Why do big
Speaker 1: objects not seem to follow quantum rules? What is the
Speaker 1: difference between quantum objects and big objects? Where is the threshold?
Speaker 1: Why do we seem to have two sets of rules
Speaker 1: or is it just that one set of rules sort
Speaker 1: of morpse into the other. Right, it's an important concept,
Speaker 1: and it seems to be sort of related to this
Speaker 1: idea of quantum measurements. I think maybe that's something that
Speaker 1: if you've heard of quantum mechanics or have talked about
Speaker 1: it or seen any videos about it or read about it,
Speaker 1: it's something that seems to be important that you know
Speaker 1: things are quantum, but then when you poke at them
Speaker 1: or measure them or try to look at them, things
Speaker 1: collapse for some reason. Yeah, this is a big and
Speaker 1: still totally unsolved problem in quantum mechanics. Quantum mechanical things
Speaker 1: can have like multiple possibilities, but we don't observe multiple possibilities.
Speaker 1: When you poke an electron, as you say, it picks
Speaker 1: one of them, and we don't really understand how that happens,
Speaker 1: how one of them gets picked, and actually when that
Speaker 1: picking happens, you know, Does it happen when your finger
Speaker 1: touches the electron? Does it happen when you look at
Speaker 1: the results? That happens somewhere in between. That's a really
Speaker 1: interesting and hard problem, and it's related to quantum decoherence,
Speaker 1: but they're not quite the same thing. To today, we'll
Speaker 1: try to explain what quantum decoherence is, how it helps
Speaker 1: us understand the difference between quantum and classical objects. But
Speaker 1: it's important to understand that it doesn't actually solve this
Speaker 1: problem of the quantum measurement. Is that what happens when
Speaker 1: you pull on the tail of the elephant, things get
Speaker 1: real real quick. You get quantum stomped. It makes quantum
Speaker 1: music out of you. All right, Well, this is an
Speaker 1: interesting question what is quantum decoherence? And so as usual
Speaker 1: we were wondering how many people out there in the
Speaker 1: real world know what it means. So as usual, Daniel
Speaker 1: went other into the wilds of the internet to ask
Speaker 1: what is quantum decoherence? So thank you very much to
Speaker 1: everybody who will volunteered your speculation for the podcast. If
Speaker 1: you would like to volunteer for a future podcast, please
Speaker 1: write to us. Two questions at Daniel and Jorge dot com.
Speaker 1: Think about it for a second, soone ask you what
Speaker 1: quantum decoherence is. What would you say it is, or
Speaker 1: at least guess it is. Here's what people had to say.
Speaker 1: I'm not sure if I recognized this right, but I
Speaker 1: think decoherence is about how the quantum and the normal
Speaker 1: little few collide, so how we can map quantum effects
Speaker 1: into all reality. Since coherent means to make sense, I'm
Speaker 1: thinking quantum decoherence is when quantum particles can't logically follow
Speaker 1: the rules of the universe, of the constants of the universe,
Speaker 1: or something of the nature. I'm not sure what quantum
Speaker 1: decoherence is, but I think it might be wave function collapse,
Speaker 1: which is how the wave function of a quantity and
Speaker 1: a quantum system collapses when you measure that quantity. I
Speaker 1: don't know what quantum decoherence is, but my guess would
Speaker 1: be that it is the occurrence of something totally inconsistent
Speaker 1: that disrupts the quantum realm. It's got me thinking of
Speaker 1: something to do with quantum entanglement. All right, Some pre
Speaker 1: coherent answers for the most part, or at least coherent
Speaker 1: in there not knowing what it is. Nobody actually quite
Speaker 1: nailed it. But you know, people are in the vicinity,
Speaker 1: and they seem to understand that there's a concept of coherence,
Speaker 1: at least in quantum mechanics. Somebody said that it is
Speaker 1: sort of where the real world and the normal world collide.
Speaker 1: I guess they do, maybe think it has something to
Speaker 1: do with the connection between the quantum world and our
Speaker 1: everyday experience. Yeah, and that one is the closest I
Speaker 1: think to the right answer, to the right way of
Speaker 1: thinking about it. Quantum to coherence, in brief is the
Speaker 1: idea that explains how quantum objects look like classical objects
Speaker 1: when they get really big and messy. All right, well,
Speaker 1: let's jump into a Daniel and I guess let's start
Speaker 1: with just a quick recap of quantum of a small
Speaker 1: subject called quantum physics. You know, what is it that
Speaker 1: we actually call quantum and how can we kind of
Speaker 1: describe those effects? So the thing to understand is that
Speaker 1: when you look at really small objects, things like electrons
Speaker 1: or photons or individuals tiny particles, they seem to be
Speaker 1: following rules that don't apply to bigger objects like baseballs
Speaker 1: and Basketball's right, and the key concept to understand when
Speaker 1: thinking about these tiny particles is that they're not just particles.
Speaker 1: They're not like tiny versions of a baseball. They're not
Speaker 1: just like miniaturize little blobs of stuff flying through space.
Speaker 1: Right when people were first thinking about the atom, for example,
Speaker 1: they were thinking about the electron like orbiting the nucleus
Speaker 1: like a tiny planet around the star. But we pretty
Speaker 1: quickly figured out that was impossible because if an electron
Speaker 1: orbits and nucleus, then it's going to give off radiation
Speaker 1: because it's accelerating, it's giving off radiation. And they did
Speaker 1: the calculation and discovered, well, that would collapse in like
Speaker 1: a hundred billions of a second because they would lose
Speaker 1: all of his energy. And so instead they had to
Speaker 1: have a new idea for what controls and electron, what
Speaker 1: defines what an electron does and how it interacts, and
Speaker 1: so instead they try to use like wave like properties
Speaker 1: to describe it. So you've probably heard this phrase called
Speaker 1: the wave function. The wave function is just a mathematical
Speaker 1: tool that helps us under and what an electron is
Speaker 1: likely to do. And the key concept is that the
Speaker 1: wave function tells you where a particle is likely to
Speaker 1: be and where it's not likely to be. Sean Carroll
Speaker 1: says that the wave function is the dope ist name
Speaker 1: in the world for one of the most profound things
Speaker 1: in the universe, which really made me laugh. Well, dope
Speaker 1: and profound go hand in hand. I think like physics
Speaker 1: and fun, right, Yeah, well, yeah, I think that is
Speaker 1: maybe the hardest thing to grasp about quantum mechanics and physics.
Speaker 1: You know, I think everyone sort of grows up at
Speaker 1: Leaston's early in school and definitely in popular culture. You know,
Speaker 1: the depiction, like pictures of an atom always look like
Speaker 1: little planetary systems, you know, like a bunch of little
Speaker 1: balls in the middle cluster together, and then other little
Speaker 1: balls kind of swinging around in large orbits and rings
Speaker 1: around that. And that's the picture that we have about
Speaker 1: the atom. But you're saying, at some point we figured
Speaker 1: out that's not possible, like that that doesn't make sense. Yeah, exactly.
Speaker 1: It's not like the electron has a trajectory, has a
Speaker 1: path and we just don't know it. It doesn't actually
Speaker 1: have a path that doesn't have like a position at
Speaker 1: every moment in time. Instead, what it has is this
Speaker 1: quantum wave that the quantum wave behaves all sorts of
Speaker 1: normal wave like rules. But what it does is tell
Speaker 1: us where the electron is likely to be, and so
Speaker 1: the electron is likely to be here and it's likely
Speaker 1: to be there now. Sometimes people say that means that
Speaker 1: the electron is in two places at once, but that's
Speaker 1: not actually correct. It means it has the probability to
Speaker 1: be here or there, and those in both probabilities can
Speaker 1: exist at the same time. It doesn't mean it's actually
Speaker 1: in both places at once. If you ask the electron
Speaker 1: where are you, then it collapses as we talked about earlier,
Speaker 1: It picks one place or the other. But the wave
Speaker 1: function describes what's likely to happen. Well, I guess you
Speaker 1: mentioned before that it has a dopey name. Why do
Speaker 1: you think it's a bad name, And what would you
Speaker 1: have called it if not the wave function? And why
Speaker 1: is it called the wave fund? Well, wave, I suppose
Speaker 1: because it follows a wave equation. Shorting's equation is very
Speaker 1: much like equations for other waves that we've seen before,
Speaker 1: that electromagnetism, and it just waves in water. Right, there's
Speaker 1: a certain differential equation which just looks like a wave equation,
Speaker 1: like a wiggle like a like a like a rippling wiggle. Yeah,
Speaker 1: it's like a rippling wiggle, but you know, it's not
Speaker 1: a rippling wiggle in anything physical, right, Like sound waves
Speaker 1: are a wiggle in air, like air pressure. Right yeah,
Speaker 1: light waves are a wiggle in the electromagnetic field, which,
Speaker 1: even if it's hard to imagine, is a physical thing.
Speaker 1: The wave function is complex. It's imaginary values. It's like
Speaker 1: you know, one plus three I and so it's not
Speaker 1: a wiggle in a physical thing itself. So it's it's
Speaker 1: hard to understand because it's like this sort of abstract
Speaker 1: literally complex things in the sense that it exists in
Speaker 1: the imaginary plane, but it controls something real. So I
Speaker 1: wouldn't have called it the wave function, you know, I
Speaker 1: like the word wave, but function to me is sort
Speaker 1: of confusing. Which you have called it the imaginary function? Well,
Speaker 1: I feel like alluding to the imaginary complex plane that
Speaker 1: is not helping me here, I guess, And you just
Speaker 1: brought up maybe a source of confusion, which is that
Speaker 1: you know, you just said the light or a photon
Speaker 1: is like a ripple in the electromagnetic field, right, It's
Speaker 1: a ripple like kind of like a sound waving that
Speaker 1: it's like, it's more intense here in this intense here
Speaker 1: are you saying that? There's also like a photon would
Speaker 1: also have another kind of waving, nous, which is imaginary. Absolutely,
Speaker 1: the photon also has a wave function, right, and that
Speaker 1: wave function determines where the photon is likely to go,
Speaker 1: like which parts of the electromagnetic field are likely to ripple,
Speaker 1: you know, for example, you know, the classical situation is,
Speaker 1: imagine you shoot a photon at two slits in a screen.
Speaker 1: You know which one is it going to go through.
Speaker 1: It has a probability to go through one and a
Speaker 1: probability to go through the other. The wave function controls
Speaker 1: what those probabilities are, right, And if it collapses and
Speaker 1: picks the one on the left, then you get an
Speaker 1: electro magnetic wave through the one on the left. So
Speaker 1: the probability wave and the electromagnetic wave are sort of
Speaker 1: two different things to keep in your mind, and they
Speaker 1: both spread differently. Like why did they call them waves
Speaker 1: in the first place, Like do these like probabilities ripple
Speaker 1: out into space also, or or do they just look
Speaker 1: like a ripple that moves around. They do ripple, and
Speaker 1: they do follow wave mechanics, and that's why they call
Speaker 1: it a wave, and that's why they can do really
Speaker 1: amazing and fascinating things. Because the location of electron is
Speaker 1: controlled by something which is fundamentally a wave, it can
Speaker 1: do things that waves can do. Like it can interfere, Right,
Speaker 1: you can have probabilities interfering with themselves, probably being here
Speaker 1: and there, can interfere with each other and create probabilities
Speaker 1: in other places, just like actual waves can. Right, you
Speaker 1: put two hands in a lake or in a bathtub
Speaker 1: and you make two sources of waves. Those waves can
Speaker 1: interfere with each other, meaning just that they can add
Speaker 1: up or cancel out. So, for example, if I have
Speaker 1: like an electron here, it has like a ripple of
Speaker 1: probability kind of emanating from it, or is that kind
Speaker 1: of static if the electron is static. Well, electrons can't
Speaker 1: actually be totally static, right, because their quantum objects. So
Speaker 1: you can't just like say, electron is here and it's
Speaker 1: not moving. That would violate the Heisenberger in certainty principle,
Speaker 1: would effectively be an electron at absolute zero. But if
Speaker 1: you have an electron, you shoot it out of like
Speaker 1: an electron gun or something, and you want to describe
Speaker 1: what's it likely to do, where is it likely to go?
Speaker 1: Then you have a probability for all those various outcomes, right,
Speaker 1: And the key thing to understand is like, there's not
Speaker 1: a real history that's happening between when you shoot the
Speaker 1: electron and when it hits the wall, and you're just
Speaker 1: learning about it. It's uncertain, right. It has both possibilities
Speaker 1: existing simultaneously until you measure it. And that's the key
Speaker 1: thing that's hard to understand about quantum mechanics is like
Speaker 1: how this measurement changes it from like having two possibilities
Speaker 1: to actually existing in one place, but doesn't exist between
Speaker 1: the places you measure. It only exists where you measure
Speaker 1: in between. They're just probabilities, all right. So you're saying
Speaker 1: that maybe, like an electron is like a little tiny baseball,
Speaker 1: but we just don't know where it is, and where
Speaker 1: it is is determined by this ripple in probability. Yeah,
Speaker 1: I'm saying an electron is like a little tiny baseball,
Speaker 1: but it doesn't have a place where it is. It's
Speaker 1: not like it is someplace and we don't know its
Speaker 1: place is not determined the probability of it being in
Speaker 1: one place or another is determined by the way functions
Speaker 1: like probably to be there seventy one probability be here
Speaker 1: or whatever, so they add up to one. But the
Speaker 1: probabilities are determined by the way function but doesn't actually
Speaker 1: have a location. It just has those probabilities again until
Speaker 1: you measure it, which is the weird bit, and then
Speaker 1: when you measure it then it then it feels like
Speaker 1: you're hit by a baseball. It certainly does. And that's
Speaker 1: why we see these weird quantum effects because these particles
Speaker 1: like electrons can do things that waves can do, like
Speaker 1: if you have two sources of them, you get these
Speaker 1: interference effects, or they can like tunnel through walls. These
Speaker 1: are things that waves can do. Probability waves can do,
Speaker 1: and you get effects because you have these wave like
Speaker 1: properties of the electrons wave function. These probabilities can go
Speaker 1: through walls like the wall doesn't affect it, like it
Speaker 1: just goes through them. The wall does affect that. We
Speaker 1: have a whole fun podcast on quantum tunneling. And it's
Speaker 1: possible to go through walls right because you can have
Speaker 1: a probability to be on one side of the wall
Speaker 1: and then a probability to be on the other side
Speaker 1: of the wall, and you can do that without going
Speaker 1: through the wall. The probability can leak through the wall,
Speaker 1: giving you a chance to be on the other side
Speaker 1: of the wall, even if you're never actually in the wall,
Speaker 1: all right, And so that means that the baseball would
Speaker 1: just appear on the other side, or that that it's
Speaker 1: found a way through the wall. It just appears on
Speaker 1: the other side. Remember that quantum particles don't have to
Speaker 1: have paths between where you've seen them. You see it
Speaker 1: at A and you see it at B doesn't mean
Speaker 1: it went from A to B. Doesn't have like a
Speaker 1: secret history how it got from A to B. It
Speaker 1: was a A and then it was at B. Remember
Speaker 1: they follow fundamentally different rules. It was A, then it
Speaker 1: had lots of probabilities from maybe how it got to
Speaker 1: be not like one of them is true and we
Speaker 1: just don't know it. There are those probabilities. It's undetermined.
Speaker 1: It's not unknown, it's undetermined, and then later it's aid B.
Speaker 1: So it doesn't have to go from A to B
Speaker 1: in order to be at A and then be at B.
Speaker 1: And this is highlighted by the quantum tunneling experiment because
Speaker 1: you can't go from A to B. There's a barrier there.
Speaker 1: All right, Well, let's get into quantum coherence and how
Speaker 1: that relates or how that ties this uncertainty and this
Speaker 1: way function to real things like baseball. But first let's
Speaker 1: take a quick break. All right, we're talking about quantum decoherence,
Speaker 1: and hopefully Daniel will we're not. We're not breaking down
Speaker 1: into de coherence, talking about is. But okay, So particles
Speaker 1: have a way function which tells you it's like a
Speaker 1: ripple in the imaginary space, that tells you the probability
Speaker 1: where that little tiny baseball where you will find it.
Speaker 1: Maybe you weren't to poke in, Yes, exactly right. So
Speaker 1: then what does coherence and decoherence means? So quantum coherence
Speaker 1: is when you have two possible outcomes for what's going
Speaker 1: to happen to your particle, and those possibilities sort of
Speaker 1: line up like the wave functions for those two possibilities
Speaker 1: line up. Now, any solution to the wave equation, any
Speaker 1: like quantum state, you can take it and added to
Speaker 1: another quantum state to get a third quantum state, which
Speaker 1: is a mixture of the two. So you can mix
Speaker 1: two possible wave functions like if you have when it
Speaker 1: says the electron is gonna arrive at point A, and
Speaker 1: you have another one that says the electron's gonna arrive
Speaker 1: at point B. You can have a mixture that like
Speaker 1: mixes A and B with fifty fifty odds. So that's
Speaker 1: a coherent combination. It just says you have two possibilities
Speaker 1: and you've added them together, and they're coherent because their
Speaker 1: wave functions are sort of syncd up. They start in
Speaker 1: the same place and they sort of wiggle in time
Speaker 1: aim together, right, but they don't end up in the
Speaker 1: same place. Isn't there some kind of cancelation or some
Speaker 1: kind of or are you saying coherence is when they
Speaker 1: don't cancel. They can cancel, right. The fact that they
Speaker 1: can cancel is because they are coherent. You only get
Speaker 1: interference effects from coherence sources of waves. Like go back
Speaker 1: to the example of like bathtubs. Right, so you put
Speaker 1: your hand in the water and you slap it, You
Speaker 1: make a rhythm, and you get waves in the water.
Speaker 1: You do the same thing with your other hand if
Speaker 1: you're doing it in the same way, right, if you're
Speaker 1: like slapping the water in time, then you get these
Speaker 1: waves which either add up or cancel out coherently. If
Speaker 1: your second hand instead it's just like a random just
Speaker 1: like randomly slapping it, then they're not going to add
Speaker 1: up nicely. It's just going to be a big emotion.
Speaker 1: It's going to spread out to nothing. So you only
Speaker 1: get these interference effects when the quantum waves are in sync.
Speaker 1: That's quantum coherence, and that's what allows quantum things to
Speaker 1: be sort of quantumy, meaning that they're in sync in time.
Speaker 1: So what you're saying or in time and space, Yeah,
Speaker 1: they're in sync in time, and so at every point
Speaker 1: in space they can interfere. At one point in space,
Speaker 1: you might get cancelation because they're waving in opposite directions,
Speaker 1: and at another point in space they might support each
Speaker 1: other because they're waving in the same direction. But they
Speaker 1: can only do that consistently if they're in sync in time.
Speaker 1: So it sounds like, you know, particles have these wave
Speaker 1: functions and they someone have to sync up in order
Speaker 1: for them to interact with each other, because if they
Speaker 1: don't sink up, then then what happens They just cancel
Speaker 1: each other out or they can interact, or what happens
Speaker 1: if they don't sink up. If they don't sink up,
Speaker 1: then you don't get any of these interference effects. It's
Speaker 1: like if your noise cancelation headphones, right, if those were
Speaker 1: sort of just like randomly putting out sounds instead of
Speaker 1: like sinking up to the sounds that are coming at
Speaker 1: your ear and producing exactly the opposite sound to cancel
Speaker 1: them out. Right, your noise canceling headphones only work because
Speaker 1: they produce a coherent noise which cancels out the ambient noise. Otherwise,
Speaker 1: if they put out just random, arbitrary noise, they wouldn't
Speaker 1: cancel each other out, and you just get sort of
Speaker 1: normal stuff you can have like A and B. You
Speaker 1: wouldn't have like weird interference effects between the incoming noise
Speaker 1: and the noise produced by the headphones, and all the
Speaker 1: weird quantumness comes from those like interference effects, these effects
Speaker 1: of the probability wave. And if you don't have coherence,
Speaker 1: then you don't get those effects. Okay, so you need
Speaker 1: coherence in order to have interference, just a little maybe
Speaker 1: counter in Twitter. But it's not a frequency thing, right,
Speaker 1: It's not like they have to be the same frequency
Speaker 1: or fit the same number of wavelengths within the same space.
Speaker 1: It's something a little bit more than that. It's more
Speaker 1: than that they have to be linked up. They have
Speaker 1: to like sync up in time. Otherwise you could have
Speaker 1: like coherence just for a moment, right, but to sink
Speaker 1: up in time to be like consistently giving up these
Speaker 1: probability waves that interfere, then they have to be sort
Speaker 1: of syncd up, which is linked in time that to
Speaker 1: like start at the same place and go down the
Speaker 1: same time or up at the same time. Either way,
Speaker 1: they have to like match each other in phase, right,
Speaker 1: But they can so cancel each other out and be coherent, right,
Speaker 1: Like you can be coherent and destructive at the same time.
Speaker 1: It's different than decoherent, just like noise canceling headphones. Right.
Speaker 1: The cool thing about the quantum wave function is that
Speaker 1: we actually have a lot of intuition for how waves work. Right,
Speaker 1: All these effects, interference and cancelation, these are normal things.
Speaker 1: It's just weird when you apply it to the probability
Speaker 1: for something to happen. So we're very familiar and happy
Speaker 1: to talk about waves and that none of that is weird,
Speaker 1: Like noise canceling headphones are not quantum magic. It's just
Speaker 1: weird when you apply to the probability for an experiment
Speaker 1: to have a certain outcome. Right, And lasers are also coherent, right, Like,
Speaker 1: that's kind of what a laser is, Yes, exactly, a
Speaker 1: laser is a coherent source of light. All the photons
Speaker 1: are like in phase and have the same frequency, so
Speaker 1: they add up together. Right, So it's a very intense
Speaker 1: source of coherent lights. Okay, So that's at the microscopic level,
Speaker 1: like electrons and photons and quirks. They can have this coherence.
Speaker 1: But then something happens when you go up to the
Speaker 1: bigger things, like when we have to worry about coherence
Speaker 1: at the baseball level. Right, Well, we don't have to
Speaker 1: worry about interference of baseballs because they're not coherent quantum objects,
Speaker 1: like all of their particles are not wiggling in phase.
Speaker 1: They're all scrambled and random. It's like a huge choir
Speaker 1: of children all singing different songs at different volumes and
Speaker 1: different speeds. And so what we see is like a
Speaker 1: big average gamush. We don't see any sort of like
Speaker 1: interference effects when two baseballs bounce off each other because
Speaker 1: they don't have coherent quantum waves, their faces are all scrambled.
Speaker 1: All right, Well, let's talk about that scrambling, because I
Speaker 1: think maybe that's the key of what makes things quantumy
Speaker 1: or not, Like maybe step us through, Like, okay, we
Speaker 1: start with one atom, and the particles inside the atom
Speaker 1: do have this wave function, and presimably they're coherent. Like
Speaker 1: are the protons and neutrons and quarks inside of an
Speaker 1: atom coherent together? Or is there already some kind of
Speaker 1: smushing at that level? They can be coherent. Absolutely. There's
Speaker 1: no limit to how large a coherent system can be.
Speaker 1: It just gets harder and harder to do because it
Speaker 1: has to be isolated. The key is that anytime you
Speaker 1: interact with something, then it becomes part of your system,
Speaker 1: and so the system sort of grows and grows and grows,
Speaker 1: so it's easier to start from like like a single particle.
Speaker 1: Take a single electron or a single photon, right, it
Speaker 1: has a certain way of function, and that way function
Speaker 1: is coherent, has like two possibilities for what it can do,
Speaker 1: and those possibilities are coherent, and so you get like
Speaker 1: interesting interference effects. That's why, for example, a single photon
Speaker 1: going through the famous double slid experiment can interfere with itself. Right,
Speaker 1: It's two possibilities are interfering. So single photon with two
Speaker 1: coherent possibilities can interfere with itself. Now things get messy
Speaker 1: once that photon starts to interact with other stuff because
Speaker 1: now the two possibilities for the photon interact differently with
Speaker 1: the environment. You know this interact with the wall or
Speaker 1: interact with the tool whatever you're using to measure it,
Speaker 1: and they change the phases of those two different outcomes,
Speaker 1: and now it's decoherent. So a particle can be coherent.
Speaker 1: You can even have two particles coher but once you
Speaker 1: touch it, once you interact with it, then you can
Speaker 1: break that coherence. Right. But you know we're trying to
Speaker 1: build up from like particles up to a baseball. And
Speaker 1: so like if I assemble you know, three quarts together
Speaker 1: into a proton, are they still coherent together or do
Speaker 1: they start to kind of get out of sink? Once
Speaker 1: I put them together into a proton, they can be
Speaker 1: coherent together. And you can have a single wave function
Speaker 1: that describes just those particles. And if you want to
Speaker 1: have a wave function that describes just those particles, it
Speaker 1: can't be interacting with anything else, because then you'd have
Speaker 1: to include that in the wave function. If you want
Speaker 1: to have a wave function for just your atom, you
Speaker 1: have to keep it isolated, right, And that gets harder
Speaker 1: and harder to do as things get bigger. Like it's
Speaker 1: possible to imagine a photon in an experiment that doesn't
Speaker 1: interact with anything you've built a special trap or whatever.
Speaker 1: It's harder to imagine a baseball that doesn't interact with anything.
Speaker 1: No air, molecules, no photons, know nothing. There's so many
Speaker 1: particles in there, it becomes harder and harder to keep
Speaker 1: it isolated. That's why decoherence appears as soon as things
Speaker 1: get big, because it's really hard to keep larger, realistic
Speaker 1: size things isolated and coherent. Right, I guess I'm trying
Speaker 1: to understand when that comes in. So, like, if I
Speaker 1: build a nucleus side of protons that are all in
Speaker 1: sync inside, then are they all also together in sync?
Speaker 1: Like you know, like carbon has twelve of them in
Speaker 1: the nucleus and they're all content there together, held by
Speaker 1: the strong nuclear force. Are they still coherent or are
Speaker 1: they starting to kind of fuzz out? If you keep
Speaker 1: it isolated, it can stay coherent absolutely. Okay, So then
Speaker 1: I build an atom, I throw in some electrons, and
Speaker 1: that also gets syncd up. And at what point do
Speaker 1: things start to kind of go awry? At the point
Speaker 1: where it becomes impossible to keep it isolated from the
Speaker 1: rest of the universe. But then couldn't I be in
Speaker 1: sync with the rest of the universe Daniel, Yes, exactly.
Speaker 1: Some people think that there is a wave function for
Speaker 1: the whole universe, right. The problem is that now we're
Speaker 1: inside the wave function. Now the way function includes us,
Speaker 1: and so it's hard to see these quantum effects now
Speaker 1: because we are part of the experiment. All right, So
Speaker 1: I got an atom and it's coherent and it's syncd up,
Speaker 1: and now I add another atom. Is that a problem
Speaker 1: or does it just get bigger. It's not a problem.
Speaker 1: It gets bigger. It's just harder to keep a coherent
Speaker 1: because you have to keep it isolated from the system.
Speaker 1: Remember one time we talked about building macroscopic like big
Speaker 1: stize stuff that behaves in a quantum mechanical way. This
Speaker 1: has done in a special way using Bose. Einstein condensates
Speaker 1: special form of matter that can be coherent that can
Speaker 1: stay together and you can stay isolated from the rest
Speaker 1: of the system. These things don't last very long. They
Speaker 1: last like, you know, seconds or minutes because it's hard
Speaker 1: to keep them isolated. So it's like real experimental bravado
Speaker 1: if you can put more than a few atoms together
Speaker 1: in a quantum coherent system and keep them coherent, keep
Speaker 1: them from interacting with the rest of the universe and
Speaker 1: getting their way functions sort of muddled up with the
Speaker 1: rest of the universe. Yeah, well, I guess maybe a
Speaker 1: big part of it seems to be this idea of
Speaker 1: an experiment and like who's in on the know and
Speaker 1: who's outside of the experiment, and what does it mean
Speaker 1: for something to be kind of pristine or not pristine?
Speaker 1: So maybe let's get a little bit into that, which
Speaker 1: is I think basically the idea of decoherence. Right, all right,
Speaker 1: let's get into that, but first let's take another quick break.
Speaker 1: All right, we're talking about quantum decoherence, which is kind
Speaker 1: of at the heart of this kind of headache that
Speaker 1: people have about quantum mechanics and trying to understand it
Speaker 1: at an intuitive level. So, you know, small particles can
Speaker 1: have quantum effects and wave functions and weird probability existences.
Speaker 1: But once you start piling them on together, it gets
Speaker 1: harder to kind of keep pristine I guess, right, untouched
Speaker 1: from to an observer from the outside or just to
Speaker 1: the universe into the same because the universe, i imagine,
Speaker 1: doesn't care, right, like the universe if there is a
Speaker 1: quantum way function for the entire universe, like, it doesn't care,
Speaker 1: Like it doesn't know the difference between something that you
Speaker 1: you would think is inquirent or not. Yeah, that's right.
Speaker 1: And the tricky thing here is that we want to
Speaker 1: have a wave function just for our experiment because we
Speaker 1: want to see quantum effects. If we become part of
Speaker 1: the experiment, then we no longer see the quantum effects
Speaker 1: because we only are like on one branch of that history.
Speaker 1: What do you mean we don't see the effects like
Speaker 1: we are also existing in multiple plays at the same
Speaker 1: time to somebody outside of our universe. Somebody outside of
Speaker 1: our universe sees a wave function for the whole universe,
Speaker 1: and they see lots of different possible outcomes, right, and
Speaker 1: those things can exist simultaneously until like if they observe
Speaker 1: the universe. But we're on just sort of one branch
Speaker 1: of that history the way we are existing, and so
Speaker 1: we don't see those other branches necessarily. And so if
Speaker 1: you want to see a quantum effect, you have to
Speaker 1: be like outside of that quantum system and take some
Speaker 1: measurements of it. Right now, as soon as you take
Speaker 1: those measurements of it, you've sort of inserted yourself in
Speaker 1: that quantum system and it becomes much muddier. I think
Speaker 1: you just blew my mind here, because like, if we
Speaker 1: are all part of the quantum function of the universe,
Speaker 1: that means that there are like multiples of me out
Speaker 1: there to some alien observer outside of the universe. Like
Speaker 1: I I only think that I exist as one person
Speaker 1: because what because I am observing myself? I guess. Yeah,
Speaker 1: it's complicated. And this whole question of like who is
Speaker 1: an observer? Who can collapse the wave function? When does
Speaker 1: the wave function get collapsed? It's very complicated. It's a
Speaker 1: whole other philosophical question that it hasn't been resolved. We
Speaker 1: don't know the answer to it. It's like the biggest
Speaker 1: problem in the foundations of quantum mechanics. We're not going
Speaker 1: to figure it out today on the podcast, but it
Speaker 1: is connected to this question of quantum decoherence and quantum
Speaker 1: coherence because we're interested in observing quantum effects, like when
Speaker 1: do things look quantumy and when do the not look quantity,
Speaker 1: and if you are inside the experiment, things don't look quantity.
Speaker 1: Like I've never talked to a photon. I don't know
Speaker 1: what it's like to be a photon in a double
Speaker 1: slit experiment that has experienced one path does it experienced
Speaker 1: some weird combination of multiple paths? But I know what
Speaker 1: it's like to be me, and I don't experience superpositions, right,
Speaker 1: I don't live two lives at the same time. Sometimes
Speaker 1: it feels like it. Yeah, okay, so it kind of
Speaker 1: depends on who you're who you ask whether something feels
Speaker 1: quantity or not. Like, you know, we can have a
Speaker 1: little experiment here in front of us and looks and
Speaker 1: feels quantity, but to the particles inside it doesn't feel quantity,
Speaker 1: or to an observer outside of our universe, we feel
Speaker 1: quantumy to them, oh absolutely, Like there's a very simple
Speaker 1: thought experiment to think about that. Say I set up
Speaker 1: a quantum experiment that can have you know, two outcomes
Speaker 1: A or B, and I run the experiment. Now before
Speaker 1: I read the outcome of the experiment, you could say,
Speaker 1: there's two possibilities A or B. Cool. What if you're
Speaker 1: running experiment and your experiment is me running that experiment.
Speaker 1: So you put me in a box and I do
Speaker 1: the experiment, and I know the outcome, but you don't
Speaker 1: yet know the outcome, right, So I am your experiment.
Speaker 1: Well you know, am I living in the outcomes of
Speaker 1: both experiments until you ask me what's the outcome of
Speaker 1: my experiment? Right? So absolutely, Like the quantumminess depends on
Speaker 1: who's doing the asking and who's doing the observing and
Speaker 1: who has collapsed the wave function. And that's like that
Speaker 1: deep question of quantum mechanics that we don't know the
Speaker 1: answer to, is like when do wave functions get collapsed
Speaker 1: and how did they get collapsed? Right? Like if the
Speaker 1: cat ensured the Inger's box was a physicist, like, the
Speaker 1: cat knows whether or not it's dead or alive, or
Speaker 1: you know, the radioactive particle click or not. But to
Speaker 1: us the cat is dead analyzed, but to the cat
Speaker 1: it's not. That's right. And so that's why I say
Speaker 1: you can observe quantum effects if you're outside the experiment,
Speaker 1: Like you observe a quantum effect on me because I'm
Speaker 1: part of your experiment. I observe a quantum effect on
Speaker 1: the little experiment that I'm running with the cat or whatever, Right,
Speaker 1: I don't experience the quantum effect that you observe in me. Right,
Speaker 1: So then how does that apply to our baseball? Like
Speaker 1: is it? I think kind of like as you pile
Speaker 1: on more particles that are interacting with more things, you're
Speaker 1: sort of opening up those throwed a group boxes. Yeah, exactly.
Speaker 1: There's two ways to think about it, sort of one
Speaker 1: is intuitive and the other is mathematical. The intuitive way
Speaker 1: is that as the baseball starts to interact with more stuff,
Speaker 1: that stuff becomes part of the baseball's quantum wave function, right,
Speaker 1: Like now you have a wave function for the bat
Speaker 1: and the baseball together, and so the bat can no
Speaker 1: longer do like quantum experiments on the baseball because it's
Speaker 1: like entangled with the baseball the same way that like
Speaker 1: I'm inside your experiment, And so the intuitive ways, like,
Speaker 1: as a particle starts to interact with the system around it,
Speaker 1: it gets sort of enmeshed quantum mechanically with the wave
Speaker 1: function of the larger system. So that system is now
Speaker 1: part of that you know, particle or baseball's quantum wave function,
Speaker 1: and it can no longer see the quantum effects of
Speaker 1: those things. That's decoherence. And so the mathematical way to
Speaker 1: think about it is that when a particle interacts with something,
Speaker 1: what happens is that its phase gets shifted a little bit,
Speaker 1: and the phases of the different possibilities get shifted differently
Speaker 1: based on how you're interacting. And so what happens is
Speaker 1: that all the phases of the baseball when it hits
Speaker 1: the bat gets shifted a tiny little bit and they
Speaker 1: all get scrambled. And so now the phases are like
Speaker 1: out of sync and they can't do quantum stuff together
Speaker 1: because they have deco here because they're all like random phases. Wait,
Speaker 1: so you know I was building this baseball from atoms,
Speaker 1: and so it isn't impossible to build a baseball that
Speaker 1: is still coherent, like all of the wave functions inside
Speaker 1: are in sync and happy and quantumy, in which case
Speaker 1: the whole baseball is quantumy. Theoretically possible, practically very very
Speaker 1: difficult because you have to isolate it from the entire
Speaker 1: university nobody could interact with or observe that baseball. Right,
Speaker 1: Let's say I put it inside of a short finger's box.
Speaker 1: It's there, it's not interacting. That baseball is quantumy. That
Speaker 1: baseball is quantumy. Now, like, practically shortening this box is
Speaker 1: impossible because you know, no box is impervious to heat
Speaker 1: and all sorts of other interactions. But let's say theoretically
Speaker 1: you've built some way to isolate the baseball completely. Then yes,
Speaker 1: it is still quantumy. It has not interacted with anything else. Right,
Speaker 1: But I think maybe a key limitation here is that
Speaker 1: it's not that the baseball can be here or in mars.
Speaker 1: The probability of where it is isn't that big, because
Speaker 1: you know, you're just adding tiny little probabilities, right, Like
Speaker 1: it can't be here or a meter away. That quantum
Speaker 1: meanness of the isolated baseball is like it's here or
Speaker 1: it's a few angst from to the right. It could
Speaker 1: actually have quite different possible locations. It depends on how
Speaker 1: you set it up inside the box. It could be
Speaker 1: sensitive to one quantum fluctuation which sends it in one
Speaker 1: direction or the other direction. I think what you're referring
Speaker 1: to though, is more like the classical sense of the
Speaker 1: decohered baseball. Baseball that's like that you're familiar with is
Speaker 1: flying through the air in a normal baseball game. We
Speaker 1: don't see those quantum effects because they all are bridge out,
Speaker 1: because all the quantum effects of all those particles in
Speaker 1: the baseball are not pulling like in the same directions.
Speaker 1: You never see like weird interference effects or weird probability
Speaker 1: distributions because they've all averaged out. They're all decoherent. If
Speaker 1: they were coherent, then yes, the baseball could do quantum
Speaker 1: things the way like Schruninger's cat can do quantum things
Speaker 1: like be dead or alive. Have those possibilities at the
Speaker 1: same time. Okay, so now you're saying that, like, if
Speaker 1: I has this baseball on the box and I open it,
Speaker 1: that's the same thing as hitting it with a bat, Yes,
Speaker 1: because now photons are hitting it and you are seeing
Speaker 1: those photons, and like the bat is connected to a batter,
Speaker 1: and the batter is connected to the ground, and the
Speaker 1: ground is connected to me, and there's air in between,
Speaker 1: and there are photons flying back and forth, meaning like
Speaker 1: like I am kind of inextricably tied to this baseball,
Speaker 1: which means that I am now inside of a larger
Speaker 1: box with the baseball exactly. Then that's why you don't
Speaker 1: see quantum effects on big things, because big things are
Speaker 1: always interacting, you know. Einstein famously asked somebody like, do
Speaker 1: you believe the moon isn't there when you're not looking,
Speaker 1: because he was thinking, like, it's silly to imagine that
Speaker 1: the universe like is uncertain when you're not existing. And
Speaker 1: the answer is like, of course the moon is there
Speaker 1: because photons are hitting it and bouncing off of it,
Speaker 1: and so the universe is always looking because the universe
Speaker 1: is filled with particles and they're always sort of bouncing
Speaker 1: off of things and gravity to right, it's interacting through
Speaker 1: gravity with us. Oh, that's tricky because we don't know
Speaker 1: if gravity is quantum mechanical and if there are gravitons
Speaker 1: bouncing around through space. But in principle yes, and so
Speaker 1: quantum de coherence is just like when an object no
Speaker 1: longer becomes isolated and its wave function is now like
Speaker 1: complicated lee mixed up with the rest of the environment
Speaker 1: so that they don't like add up coherently anymore. Like
Speaker 1: this little bit of the wave function is mixed up
Speaker 1: with that part of the wave function from the bat,
Speaker 1: and that part of the wave function from the ball
Speaker 1: is mixed up with this other bit of the wave
Speaker 1: function from the bat. And if you were outside the
Speaker 1: baseball game, you could view the whole baseball games wave function.
Speaker 1: Then you can say, oh, I still see quantum effects, right,
Speaker 1: because I'm looking at the wave function of the whole
Speaker 1: baseball game. But if you're inside, you are the batter, right,
Speaker 1: then now you're only seeing one slice of it. All right.
Speaker 1: Well it's weird because you know, I feel like the
Speaker 1: word decoherence means that things get out of sink, but
Speaker 1: really it means I got sucked into the box. Yeah,
Speaker 1: you are entangled right and decoherent, right, Yeah, exactly. I
Speaker 1: see how that's confusing. Yeah, it's more like I got
Speaker 1: sucked into the box. But the word decoherence kind of,
Speaker 1: you know, implies like some kind of like noise or
Speaker 1: some kind of like breakdown of things. And I think
Speaker 1: the key there is that, you know, just the ball
Speaker 1: itself has not become decoherent. Are you no longer have
Speaker 1: just a wave function that describes the ball. You have
Speaker 1: to describe the ball and the bat or Jorge and
Speaker 1: the cat. There's no way function by itself that now
Speaker 1: describes the ball because the ball is entangled with the bat,
Speaker 1: and so the balls isolated individual wave function is no
Speaker 1: longer coherent. It's like a part of a larger wave function.
Speaker 1: It can't be isolated. And so that's why you can't
Speaker 1: get quantum effects on the ball anymore, because it's complicatedly
Speaker 1: tied up with the things you want to use to
Speaker 1: measure those quantum effects. Because we are the ball now, Daniel,
Speaker 1: the ball on us are one. That's what decoherence means, right,
Speaker 1: kind of like it. It gets so complicated. I guess
Speaker 1: that's why we use the word decoherence, just because it
Speaker 1: gets complicated beyond our ability to be outside the box.
Speaker 1: It's like we're in the box now and we can't
Speaker 1: make out what these quantumness effects are. Yeah, exactly, it's
Speaker 1: too much for us to calculate, too much for us
Speaker 1: to understand. And so what happens is that quantum mechanics
Speaker 1: doesn't fail, doesn't go away. This is just what quantum
Speaker 1: mechanics looks like at a big scale. Quantum mechanics over
Speaker 1: zillions and zillions of objects. Looks different because you don't
Speaker 1: see those coherent effects anymore. They only exist when you
Speaker 1: have like one or two or three little things that
Speaker 1: you can keep separated, so you can have a wave
Speaker 1: function just for that. When you're part of the wave function,
Speaker 1: quantum mechanics says that things look different. They look more
Speaker 1: smeared and averaged out. So it's not like classical physics
Speaker 1: is in agreement with quantum mechanics. It's what quantum mechanics
Speaker 1: looks like, sort of from a high altitude, right, like,
Speaker 1: to an alien observer outside of our universe, we are
Speaker 1: still all coherent. We are you and I and this
Speaker 1: podcast and that baseball. It still looks like a pristine
Speaker 1: quantum universe. Yeah, and I hope that alien that has
Speaker 1: that deep understanding quantum mechanics has a coherent understanding of
Speaker 1: what we've been talking about today, because it's gotten pretty
Speaker 1: tricky al right. Well, I think hopefully that gives people
Speaker 1: a sense of kind of the issues involved. You know,
Speaker 1: it's kind of about what you consider the box to be,
Speaker 1: what's interacting with what, and how these kind of probabilities
Speaker 1: add up or don't add up, And it's not just
Speaker 1: like an academic question or a philosophical question. It's actually
Speaker 1: really important for quantum computing. If you want to build
Speaker 1: a quantum computer, you need cubits. You need weird particles
Speaker 1: that follow quantum rules so you can have them do
Speaker 1: quantum computations. And to do that, you need to keep
Speaker 1: them isolated. And that's okay to do for one cubit,
Speaker 1: two cubits, three cubits, But imagine having a really big
Speaker 1: quantum computer with thousands and thousands of cubans or millions
Speaker 1: or trillions, right, you gotta keep them all isolated and
Speaker 1: all individually coherent. It becomes really difficult. So this is
Speaker 1: something people are literally working on, is building larger coherent
Speaker 1: quantum systems. Yeah. I can't wait for that quantum phone
Speaker 1: so I can take quantum pictures of my kids playing
Speaker 1: quantum So you can ignore that email and answer it
Speaker 1: at the same time. Yeah, that's right, So I can
Speaker 1: do everything at the same time, exactly. And this is
Speaker 1: really closely connected to deep issues and the philosophy of
Speaker 1: quantum mechanics. You know who's doing the observing, why does
Speaker 1: it matter? When does the wave function collapse? And I
Speaker 1: want to have another episode where we talk about wave
Speaker 1: functional collapse in the measurement problem. But this is sort
Speaker 1: of like a warm up to that because it helps
Speaker 1: you understand, you know why sometimes the probabilities are more
Speaker 1: classical instead of quantum mechanical. Quantum coherence tells you, like,
Speaker 1: you know, it's likely to happen. It doesn't explain why
Speaker 1: it collapses from two possibilities down to one actual thing.
Speaker 1: That's the tricky part. That's one of the tricky parts.
Speaker 1: That's the trickiest part. It's all tricky. But you just
Speaker 1: have to get inside the box and then it's not tricky. Yeah, exactly,
Speaker 1: Then you understand it. You don't understand just like the cat,
Speaker 1: Yeah exactly. If you want quantum mechanics to go away,
Speaker 1: just you know, only work on big, complicated systems where
Speaker 1: those effects don't appear because they're all decoherent. All right, Well,
Speaker 1: we hope you enjoyed dad and got a better sense
Speaker 1: of quantum mechanics. Thanks for joining us, See you next time.
Speaker 1: Thanks for listening, and remember that Daniel and Jorge Explain
Speaker 1: the Universe is a production of I Heart Radio or
Speaker 1: more podcast from my heart Radio. Visit the I heart
Speaker 1: Radio app Apple podcasts or wherever you listen to your
Speaker 1: favorite shows. No.