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What is Quantum Tunneling? · Daniel and Kelly’s Extraordinary Universe

0:00
Speaker 1: Yeah, okay, are you any good at bowling? By any chance?
0:10
Speaker 1: I am either the world's best or worst bull? All right?
0:14
Speaker 1: But when you go bowling, do you ever get any
0:15
Speaker 1: like gutter balls? I can't deny that I get gutter balls,
0:19
Speaker 1: all right? But are you so off the mark that
0:22
Speaker 1: sometimes your bowling ball ends up like in the next lane.
0:25
Speaker 1: I also can't deny that that's ever happened to me.
0:27
Speaker 1: Oh man, Well, in that case, you might have a
0:30
Speaker 1: special physics distinction. Oh how's that? You might be the
0:33
Speaker 1: world's first quantum bowler? Is that another TV show? Like
0:37
Speaker 1: Quantum Leap, but about quantum bowling? That's right, it's the
0:43
Speaker 1: Big Lebowski meets Quantum Leap. It's my new pitch. Hi.
1:03
Speaker 1: I'm Jorge. I'm a cartoonists and the creator of PhD Comments.
1:06
Speaker 1: And I'm Daniel. I'm a particle physicist, a terrible bowler,
1:10
Speaker 1: and the co author of a book with Jorge called
1:13
Speaker 1: We Have No Idea About All the Mysteries of the Universe.
1:16
Speaker 1: So welcome to our podcast Daniel and Jorge Explain the Universe,
1:19
Speaker 1: a production of I Heart Radio. That's Right, in which
1:22
Speaker 1: we take things around us in the universe that we
1:24
Speaker 1: find amazing or crazy, or wet and sticky, or just
1:28
Speaker 1: weird and interesting, and we try to explain them to you. Right,
1:31
Speaker 1: all the strikes, all the gutter balls, and all those
1:34
Speaker 1: spars out there in the universe, that's right, even the splits,
1:38
Speaker 1: We'll roll it right down the middle for you and
1:40
Speaker 1: into your brain. Right. Sometimes there's even quantum spin on
1:44
Speaker 1: the ball. Right. I have no idea how to do
1:46
Speaker 1: spin on the ball. I see people do that. I've
1:48
Speaker 1: tried to do that. It's failed miserably. I'm all about
1:51
Speaker 1: the straight and Grandma rule. It's been actually helped you.
1:54
Speaker 1: Do you think, as a particle physicist would be all
1:56
Speaker 1: pro spinning balls and all that stuff. But I found
1:59
Speaker 1: an impossible My wistomost breaks every time I try to
2:02
Speaker 1: do it well. On the program, we usually talk about
2:05
Speaker 1: topics that people have questions about or people are really
2:07
Speaker 1: curious about about the universe. But physics about how the
2:10
Speaker 1: world and the how reality really works. And so today
2:14
Speaker 1: we're tackling a pretty interesting topic, right, Daniel, that's right.
2:17
Speaker 1: This is a topic people wrote in and asked us
2:19
Speaker 1: to explain. And I think it's because they here talked
2:22
Speaker 1: about in physics podcasts, and you read about it in
2:25
Speaker 1: physics books. There's a bunch of online videos talking about it,
2:28
Speaker 1: but frankly, there are very few actually satisfying explanations, and
2:32
Speaker 1: I think people wanted us to dig into it and
2:34
Speaker 1: see if you can explain to them what's going on.
2:37
Speaker 1: It's definitely one of those topics that sound cool for sure,
2:40
Speaker 1: Like just those two words put together, Well, anything after
2:43
Speaker 1: quantum sounds cool, right, Quantum banana, quantum bowling, even that
2:48
Speaker 1: sounds interesting. An evening of quantum bowling with Daniel and Jorge.
2:52
Speaker 1: That sounds like an event you pay twenty bucks to
2:54
Speaker 1: go to. Right. Well, Today, on the program, we'll be
2:56
Speaker 1: tackling a subject that is almost seems like maybe and
3:00
Speaker 1: that a lot of people associate with perhaps teleportation, the
3:05
Speaker 1: idea that maybe you can move from one spot to
3:07
Speaker 1: another spot kind of instantly or through a wall or
3:11
Speaker 1: something like that, so they On the podcast, we'll be
3:13
Speaker 1: talking about quantum tunneling. Quantum tunneling is one of my
3:21
Speaker 1: favorite topics because it's one of those really weird effects
3:24
Speaker 1: you see in quantum mechanics. You know, when you zoom
3:27
Speaker 1: in on the world and you discover it's microscopic nature.
3:30
Speaker 1: You try to understand it in terms of things we
3:33
Speaker 1: know and understand, and your brain is trying to use
3:35
Speaker 1: particles and waves and all this stuff. This is one
3:37
Speaker 1: of those effects that really just stumps us when it
3:40
Speaker 1: when we try to explain it in terms of macroscopic things.
3:43
Speaker 1: We try to get intuitive handle on it, and so
3:46
Speaker 1: it just shows us that the world is so different
3:48
Speaker 1: from the world that we actually understand. I guess my
3:50
Speaker 1: question annially, is am I going to spend this episode
3:52
Speaker 1: complaining about the naming of this effect? Like is this
3:55
Speaker 1: really like a tunnel like every other episode, like every
3:59
Speaker 1: other episode out of this podcast? Um? Probably? Yes, Probably, UM,
4:04
Speaker 1: spend most of the time you complenty with the name
4:07
Speaker 1: and me trying to argue that the physics version is
4:09
Speaker 1: different from the cultural version or whatever, and that there's
4:12
Speaker 1: poetry in physics. There is some poetry and physics there's
4:16
Speaker 1: also plenty of clumsiness. Now, this is a fascinating topic
4:19
Speaker 1: because it's the kind of thing that's really impossible to
4:22
Speaker 1: explain in terms of classical analogs. You know, things that
4:26
Speaker 1: you have intuition for particles and waves and bowling balls.
4:29
Speaker 1: It's just something that those things can't do, and so
4:32
Speaker 1: it opens the door in our minds. It says the
4:35
Speaker 1: universe is weirder than you will ever understand, right, And
4:39
Speaker 1: that's the kind of thing that got me into physics,
4:41
Speaker 1: you know, the revealing that the universe operates under rules,
4:45
Speaker 1: but rules that are weird and in some ways alien
4:48
Speaker 1: to the to the world that we know. So, yeah,
4:50
Speaker 1: it's got two cool words, quantum and tunneling, and so
4:53
Speaker 1: I don't know, that makes me think of like a
4:55
Speaker 1: something that drills deep down into the quantum realm or
4:59
Speaker 1: you know, something that um lets me like travel to
5:03
Speaker 1: the quantum realm or something. What is the what is
5:06
Speaker 1: the quantum realm? Where is it? How do you get there?
5:08
Speaker 1: That's a whole other podcast episode. It's on the Admin
5:11
Speaker 1: Movies obviously. All right, well, we'll have to have Paul
5:13
Speaker 1: Rudd on as a guest, and uh and Michael Douglas
5:16
Speaker 1: since he's professor PIM. I mean, they can explain to
5:18
Speaker 1: us all about the PM particles in the quantum realm.
5:21
Speaker 1: But you're at quantum tunneling does have a really cool
5:23
Speaker 1: sound to it, and so, as usual, I was wondering, like,
5:27
Speaker 1: what do people know about quantum tunneling to people. Does
5:29
Speaker 1: everybody already understand this and we don't need to explain it?
5:32
Speaker 1: Or is it a huge mystery to people have misconceptions?
5:35
Speaker 1: And so I walked around campus a you see Irvine,
5:38
Speaker 1: and it costed friendly strangers to ask them. So before
5:41
Speaker 1: you listen to these answers, think about it for a second.
5:43
Speaker 1: If somebody asked you randomly on the street and didn't
5:46
Speaker 1: give you the option of googling it, would you know
5:49
Speaker 1: what quantum tunneling is? That's right, no googling allowed. Here's
5:53
Speaker 1: what people had to say. Do you know what quantum
5:55
Speaker 1: tunneling is? Um? I don't know what makes me think
5:59
Speaker 1: of like the mountain since Wwitzerland and how they have
6:01
Speaker 1: to like build tunnels underneath them and then that's where
6:03
Speaker 1: certain is. So there's probably some quantum tunneling down there.
6:06
Speaker 1: I have Can you explain it? No? I have not?
6:10
Speaker 1: No um not really probably not. Well, I've heard, I've
6:15
Speaker 1: heard of it, but I'm not sure what the concept is.
6:17
Speaker 1: I don't know what's that mean? No, I have not,
6:20
Speaker 1: I do not. I have not heard of that. I
6:22
Speaker 1: have not. Something has to do with light and like hell,
6:24
Speaker 1: the transflor on something like that alright, not a popular
6:28
Speaker 1: or familiar topic, but half the people had never heard
6:31
Speaker 1: of it. That's right. Um, people were pretty clueless, though
6:34
Speaker 1: some people were pretty creative. I love the answer about
6:38
Speaker 1: tunnels near certain that was very creative. Yeah, they said
6:42
Speaker 1: that made them think of the tunnels underneath the mountains
6:46
Speaker 1: of Switzerland, because Switzerland has tunnels and they do physics experiments.
6:50
Speaker 1: So therefore two and two together. Obviously that's what a
6:53
Speaker 1: quantum tunnel is. It's not a terrible answer, like, you know,
6:57
Speaker 1: what kind of tunnel do you need to build a
6:59
Speaker 1: large age uncle it? You know, hey, a quantum tunnel, right,
7:02
Speaker 1: a tunnel in which you do quantum experiments. That's not
7:04
Speaker 1: a terrible answer. Maybe that's more of a quantum ingunnel.
7:08
Speaker 1: And the truth is the Swiss are awesome in building tunnels,
7:10
Speaker 1: and they could sort of have to be because they're
7:12
Speaker 1: surrounded by mountains, but they really are world class in
7:15
Speaker 1: building these tunneling machines. And so it's still surprised that
7:18
Speaker 1: the large Hadron collider is in Switzerland because that really
7:21
Speaker 1: is the best place to build tunnels for your quantum experiments. Yea,
7:24
Speaker 1: they have to dig all those tunnels to burial, that
7:26
Speaker 1: money that they keep for rich people. Oh, that illicitly
7:30
Speaker 1: elicitly gotten gold. You know, hey, what do you mean
7:32
Speaker 1: I have a Swiss bank account in my dream? Well,
7:36
Speaker 1: you know, true story. I discovered, um by opening her mail,
7:39
Speaker 1: that my wife has a Swiss bank account. She has
7:44
Speaker 1: a retirement plan in Switzerland. All right, what what other
7:47
Speaker 1: secrets have you covered by opening her mail? The best
7:52
Speaker 1: part of the story is that she didn't know she
7:54
Speaker 1: had a Swiss bank account until I told her. Feels
7:56
Speaker 1: like a Born movie here. No, it has actually pretty
8:00
Speaker 1: mundate explanation. When we were in Switzerland so I could
8:03
Speaker 1: work on the large age on collider, she had a
8:05
Speaker 1: job working in research in Switzerland, and unbeknownst to her,
8:09
Speaker 1: they opened an account in her name and deposited some
8:11
Speaker 1: retirement funds there and uh, and then we discovered it
8:15
Speaker 1: later and like, oh my gosh, look, Katrina has a
8:17
Speaker 1: Swiss Bank acount with money in it. That's how banking
8:19
Speaker 1: work in Switzerland. They just give it away. Yeah exactly. So, um, yeah,
8:22
Speaker 1: she has a Swiss Bank account, but I don't. Well anyway,
8:25
Speaker 1: so people were not very familiar with quantum tunneling, which
8:28
Speaker 1: means that hey, we can. We can talk about it
8:30
Speaker 1: on the podcast. That's right, It's an awesome topic to demystify.
8:34
Speaker 1: First we'll explain what it is, and then we'll explain
8:36
Speaker 1: how it works and how it's not teleportation. Right, That's
8:39
Speaker 1: my big question is is it like teleportation? Is it
8:42
Speaker 1: associated with teleportation? Can we teleport with quantum tunneling? All right?
8:46
Speaker 1: Start us off, Daniel, What how would you describe what
8:49
Speaker 1: quantum tunneling is? So I think the best place to
8:51
Speaker 1: start is to sort of warm up our intuition, Like,
8:54
Speaker 1: let's think about this problem using things were familiar with,
8:58
Speaker 1: and then we can make the analogy to the quantum
9:01
Speaker 1: version and we can understand where that breaks down, like
9:03
Speaker 1: where our intuition goes wrong. So let's start with our
9:06
Speaker 1: intuition and the sort of the problem. The kind of
9:08
Speaker 1: problem we're trying to describe is sort of like playing
9:11
Speaker 1: with a bowling ball inside an empty swimming pool. This
9:15
Speaker 1: is still for the bowling ball and swimming pool. Yeah,
9:19
Speaker 1: I mean, isn't that a familiar thing when you see
9:21
Speaker 1: a swimming, empty swimming pool and you think, I wonder
9:23
Speaker 1: what would happen if I threw a bowling ball in there? Well,
9:25
Speaker 1: let's give our listeners just a quick idea of what
9:28
Speaker 1: we're talking about. So, quantum tunneling is kind of this
9:31
Speaker 1: idea that a particle or or in the usual case
9:35
Speaker 1: it's an electron, it consider be on one side of
9:38
Speaker 1: a barrier in one moment and then the next moment
9:41
Speaker 1: it's on the other side of the barrier. Right. The
9:43
Speaker 1: generally they have quantum tunneling is that it's really hard
9:46
Speaker 1: to keep electrons in a little trap or in a
9:48
Speaker 1: little hole. That they really they're hard to pin down.
9:51
Speaker 1: And people are probably familiar with that because the Heisenberg
9:53
Speaker 1: and certainty principle, like, you know, you can't really isolate
9:56
Speaker 1: a quantum particle in one little spot in space very long,
10:01
Speaker 1: but you know if you try to do it, then
10:03
Speaker 1: you know eventually it's going to leak out. And and
10:05
Speaker 1: the point of quantum tunneling is that electrons can build
10:08
Speaker 1: these tunnels or burrow through these barriers to to you know,
10:12
Speaker 1: adjacent little holes or adjacent little wells. So that's the
10:14
Speaker 1: idea is that it's like you have a particle, there's
10:17
Speaker 1: a barer in front of it, and at some point
10:20
Speaker 1: it just moves to the other side of the barrier. Yeah, exactly.
10:23
Speaker 1: You can see it on one side of the barrier,
10:25
Speaker 1: and even if it doesn't have enough energy to get
10:27
Speaker 1: over the barrier, sometimes you see it on the other
10:29
Speaker 1: side and you have to ask, like, how did it
10:31
Speaker 1: get here? Right, right, like spontaneously just appears on the
10:34
Speaker 1: other side or what. Yeah, well, sometimes on one side
10:37
Speaker 1: and then it's on the other side, and then it
10:38
Speaker 1: goes back right, And there's a lot of interesting stuff
10:41
Speaker 1: there about like, um, you know, if the particle was
10:43
Speaker 1: here and then later it's there, how did it get
10:46
Speaker 1: from one place from the first place to the next place.
10:49
Speaker 1: Right In your mind, you're used to things. If it's
10:52
Speaker 1: in one spot and then later it's in another spot,
10:54
Speaker 1: you imagine it took a path from one spot to
10:57
Speaker 1: the other spot. Right, That's the way classical things work,
10:59
Speaker 1: based balls, hamsters, whatever. But that's not true for quantum objects.
11:03
Speaker 1: Quantum bologists are here and then later they're there, and
11:06
Speaker 1: there iss not necessarily any path between those places that
11:09
Speaker 1: the particle took. It didn't move, It just was here
11:12
Speaker 1: and then it was there. Yeah, it's frustrating because quantum
11:16
Speaker 1: particles don't have this underlying hidden truth, right, it's not
11:20
Speaker 1: like there is a true story about where the particle
11:24
Speaker 1: was at every moment and we just don't know it.
11:26
Speaker 1: It doesn't have that story. That story doesn't exist. You know,
11:29
Speaker 1: it's it's it's in a location only when you ask
11:32
Speaker 1: where is it? And then it's in a location later
11:34
Speaker 1: when you ask where is it? You're saying it particles
11:37
Speaker 1: don't really have a here or there. It's like they're
11:39
Speaker 1: around here. Well, they have a here, Like at some
11:42
Speaker 1: moment you can say it's here, and another moment you
11:44
Speaker 1: can say it's there. But you can't connect the dots, right,
11:47
Speaker 1: You can't say that there must be a line between
11:50
Speaker 1: those two dots and the particle took that line or there.
11:54
Speaker 1: There doesn't have to necessarily be aligned. It's just here
11:56
Speaker 1: and then later it's there. It's you know, it's like
11:59
Speaker 1: um frames in a movie, but without the intervening um connections.
12:04
Speaker 1: Like if you're watching a movie, you know, the person
12:06
Speaker 1: would be standing here, and then suddenly they'd be standing
12:09
Speaker 1: over there, and then they'll be studying this other part
12:11
Speaker 1: of the frame, right, almost like they were teleporting between spots.
12:18
Speaker 1: I was just going to say that that's not teleportation.
12:20
Speaker 1: Right when you're watching a movie, and you know, and
12:22
Speaker 1: you watch this frame by frame, you don't imagine they're
12:25
Speaker 1: teleporting from frame to frame. Right, you're just saying, well,
12:27
Speaker 1: I know he's here in this frame and he's there
12:29
Speaker 1: at that frame. Right. That's not teleportation. You're saying. A
12:32
Speaker 1: quantum particle doesn't have a path between these two things.
12:35
Speaker 1: It's like, if you ask you where it is, it'll
12:37
Speaker 1: just kind of pop around all over the place. Yeah,
12:39
Speaker 1: you can ask a particle where it is and it
12:41
Speaker 1: will answer, right, and then later you can ask it
12:43
Speaker 1: where it is and it will answer, But you don't
12:46
Speaker 1: necessarily know anything about where it is in the intervening time,
12:49
Speaker 1: and you can't assume that there's some classical path. You know,
12:53
Speaker 1: if you if you ask where's my baseball and what's
12:56
Speaker 1: his velocity? Right, then you can actually predict exactly where
12:58
Speaker 1: it's going to go any moment. And so it has
13:01
Speaker 1: this thing we call the classical path. It's position and
13:04
Speaker 1: velocity at any point in time, and when you're looking
13:07
Speaker 1: at it, you're just sort of sampling that. Right. But
13:09
Speaker 1: for a quantum particle that doesn't exist, you can ask
13:11
Speaker 1: where is it? And you're gonna ask where is it later? Right?
13:14
Speaker 1: But you can't connect the dots between those two and
13:16
Speaker 1: assume that there's a path that it's following. Well, this
13:19
Speaker 1: is a perfect point to take a break, Okay. So
13:35
Speaker 1: then the idea of quantum tunneling is that a particle
13:39
Speaker 1: is on one side of a wall or a barrier,
13:41
Speaker 1: and then the next instant it's in the other side
13:44
Speaker 1: of the barrier. And so that what we want to
13:46
Speaker 1: do here today is sort of explain how that happens
13:49
Speaker 1: and why it's not teleportation. Exactly how does that happened
13:52
Speaker 1: and what does it mean and why it's not teleportation.
13:55
Speaker 1: And so you you think a great way to think
13:57
Speaker 1: get into this topic is to think about bowling balls.
13:59
Speaker 1: And yeah, well, I mean, what is a barrier after all? Right,
14:02
Speaker 1: Like I think people think about electrons is tiny little balls.
14:05
Speaker 1: So I was thinking about let's use a bowling ball
14:07
Speaker 1: because that's macroscopic and what is really a barrier? Right,
14:11
Speaker 1: I mean people might be thinking like, what kind of
14:12
Speaker 1: barriers are we talking about? And so let's imagine a
14:15
Speaker 1: macroscopic barrier, like a familiar one. Right, You're the bottom
14:19
Speaker 1: of swimming pool with a bowling ball. By the way,
14:21
Speaker 1: this is amazing video of a guy. This what inspired
14:24
Speaker 1: me is this amazing video online of a guy with
14:26
Speaker 1: the bowling ball in a swimming pool and he can
14:28
Speaker 1: do these hilarious tricks where he puts like the pins
14:31
Speaker 1: behind him and he rolls the bowling ball and it
14:33
Speaker 1: does these crazy moves and he knocks off all the pins. Anyway,
14:37
Speaker 1: so you're the bottom of the swimming pool with the
14:39
Speaker 1: bowling ball, right, and what happens you just put it down.
14:41
Speaker 1: Let's make it clear the pool is empty. I'm not
14:44
Speaker 1: drowning here, I'm not empty swimming pool. I'm not holding
14:49
Speaker 1: onto his heavy ball. And and then sitting at the
14:51
Speaker 1: bar of gear does not make this anymore complicated. Yeah,
14:55
Speaker 1: it's an empty swimming pool with a bowling ball. But
14:58
Speaker 1: let's also make it clear it's one of these swimming
14:59
Speaker 1: pool is that it has a curved floor, right, like
15:02
Speaker 1: a bowl shaped floor, right like if if it's a
15:05
Speaker 1: swimming pool with straight edges at the bottom, this is
15:09
Speaker 1: not going to work, that's right. Also, there's no like
15:11
Speaker 1: chain saws or you know, traps or you know, rabbit
15:15
Speaker 1: hamsters or anything else in the swimming pool. Just you know,
15:18
Speaker 1: to be clear, just just the bowling ball in an
15:20
Speaker 1: empty curved pool, you know, or if it's easier for you,
15:23
Speaker 1: imagine a grape in the bottom of a bowl or whatever.
15:25
Speaker 1: But the point is what happens when you put the
15:27
Speaker 1: bowling ball at the bottom of the swimming pool. It
15:29
Speaker 1: just sits there, right, It doesn't leave. You're never going
15:32
Speaker 1: to find it in your neighbor's empty swimming pool, right,
15:35
Speaker 1: It's always going to be in that pool. And the
15:38
Speaker 1: barrier in this case is the edge of the swimming pool.
15:40
Speaker 1: You mean, like, if you don't touch it, if you
15:42
Speaker 1: don't push it, if the wind doesn't blow, it is
15:44
Speaker 1: just going to stay there. That's right exactly. And you
15:46
Speaker 1: expected to stay there. You don't expect to come by
15:48
Speaker 1: one day and find it in your neighbor's swimming pool. Right.
15:51
Speaker 1: It is that if something does disturb it, like a
15:53
Speaker 1: raccoon comes by and pushes it, it's just going to
15:56
Speaker 1: roll back down to the bottom of the pool again. Right,
15:59
Speaker 1: that's kind of the idea. That's right exactly, because the
16:01
Speaker 1: walls of the pool are the barrier, right, That's where
16:04
Speaker 1: we talk about. It's a potential barrier. And if a
16:06
Speaker 1: raccoon comes and pushes it, you know, and he pushes it,
16:09
Speaker 1: you know, as hard as a raccoon can. Then it's
16:11
Speaker 1: gonna roll up, and then it's gonna roll back down,
16:13
Speaker 1: and it might roll back up the other side, but
16:16
Speaker 1: it's never gonna roll higher than it then it went originally, Right,
16:20
Speaker 1: It's just gonna eventually relax down to the bottom of
16:23
Speaker 1: the swimming pool. And so if you don't give it
16:25
Speaker 1: enough energy to go over the lip, then it's trapped
16:28
Speaker 1: in the pool. Right, It's never going to get out
16:30
Speaker 1: of the pool unless it has enough energy to go
16:33
Speaker 1: up and over the edge of the swimming pool, right,
16:35
Speaker 1: And so that's the barrier, like that's the wall, yeah, exactly,
16:38
Speaker 1: And your intuition says it's trapped, right, if you don't
16:41
Speaker 1: give enough energy, it's never ever, ever, ever, ever, ever
16:45
Speaker 1: ever ever going to end up in your neighbor swimming pool, right,
16:47
Speaker 1: that's where your intuition says, right, unless there are some
16:50
Speaker 1: really strong raccoons. But that's what different. I don't know
16:53
Speaker 1: what kind of neighborhood this is with all these empty
16:54
Speaker 1: swimming pools and like tough gangs of raccoons pushing bowling balls.
16:59
Speaker 1: But we're to get out quite the science fiction dystopia here.
17:02
Speaker 1: But Yeah, you don't expect it to ever be able
17:04
Speaker 1: to get out of the pool by itself. That's right,
17:07
Speaker 1: exactly that barrier you can consider it to be perfect. Right.
17:10
Speaker 1: The only way um to the next swimming pools to
17:13
Speaker 1: go over the barrier. Right, You can never go through
17:16
Speaker 1: the barrier. These raccoons are not tough enough to throw
17:18
Speaker 1: the bowling ball like and crush the ground and get
17:21
Speaker 1: through it. Right. Wait, what are their Swiss raccoons and
17:24
Speaker 1: they dig a tunnel? Yeah, or they're like superhero raccoons
17:31
Speaker 1: like um in one of those Marvel movies system, isn't
17:33
Speaker 1: there some super raccoon or is he just look like
17:35
Speaker 1: a raccoon and he's not actually a raccoon and never
17:37
Speaker 1: actually in genetically modified raccoon aliens that look like human
17:41
Speaker 1: like Earth raccoons And never quite figured that one out.
17:43
Speaker 1: But we digress, we do, we do digress. That's the analogy.
17:50
Speaker 1: Right now, Think instead of the bowling ball, think of
17:53
Speaker 1: an electron. And then when we talk about barriers, we're
17:56
Speaker 1: talking about you know, barriers to that electron. So maybe
18:00
Speaker 1: made by other particles, you know, protons or something that
18:03
Speaker 1: would repel it, right, something that would you would build
18:06
Speaker 1: to try to keep the electron localized like a little trap,
18:09
Speaker 1: like a like a little magnetic field. Maybe he is
18:12
Speaker 1: keeping it trapped or something. Yeah, a little magnetic field
18:16
Speaker 1: or electrostatic potential or something anything you can do to
18:19
Speaker 1: trap an electron. And people do this, right, they want
18:21
Speaker 1: to study individual electrons or individual ions. They build atom
18:24
Speaker 1: traps the pretty cool um and so people actually do this.
18:28
Speaker 1: But it's also a good case study for quantum mechanics
18:30
Speaker 1: because it helps us think about how these things work
18:33
Speaker 1: and don't work. So it's a it's a very popular
18:35
Speaker 1: sort of junior level quantum mechanics problem in college. So
18:39
Speaker 1: what happens. You put the electron in this little well, right,
18:42
Speaker 1: and it's like a barry. It's like a swimming pool,
18:44
Speaker 1: and you think, if the electron doesn't have enough energy
18:47
Speaker 1: to go over the edge, then it's trapped, right, just
18:49
Speaker 1: like the bowling ball. If it doesn't have enough energy,
18:52
Speaker 1: how could it ever get into the neighboring swimming pool. Well,
18:54
Speaker 1: the thing you find is that even though it doesn't
18:57
Speaker 1: have enough energy, sometimes it appears is in your neighbor's
19:01
Speaker 1: swimming pool. Like it gets through that barrier. It appears
19:05
Speaker 1: in the adjacent well. Like if you have a series
19:08
Speaker 1: of these um potential wells, you know, these these little
19:11
Speaker 1: traps made for electrons, and you put it in one,
19:14
Speaker 1: you come back the next day and find it in
19:15
Speaker 1: the next one. Even though it didn't have enough energy
19:18
Speaker 1: to go over that barrier, even though it was trapped
19:21
Speaker 1: by a magnetic field, it somehow slipped out, yes, exactly,
19:25
Speaker 1: And so that's the that's what we call quantum tunneling. Right,
19:28
Speaker 1: how did it get through the barrier? In principle, the
19:31
Speaker 1: barrier should be should bar it, right, that's what barriers do.
19:35
Speaker 1: It should borrow it from passing, just the way you're
19:38
Speaker 1: the ground does, the end of the swimming pool does.
19:41
Speaker 1: So the question is why does an electron not get stuck, right,
19:44
Speaker 1: because if it tried to move, the field would push
19:47
Speaker 1: it back into the trap. But somehow it's able to
19:51
Speaker 1: live out or create a tunnel exactly exactly. And your
19:55
Speaker 1: instinct might be to say, well, maybe like momentarily goes
19:58
Speaker 1: over the barrier, like you know, I don't know Heisenberg
20:01
Speaker 1: Uncertainty blog blog. You know, maybe it borrows a little energy,
20:04
Speaker 1: momentarily gets over the barrier. Right. That's tempting because you
20:08
Speaker 1: want to think of the barrier as working, and so
20:11
Speaker 1: do you want to think that if it's going to
20:12
Speaker 1: go to the other well, is somehow has to go over.
20:14
Speaker 1: But it doesn't, right, it can't. It's a conservation of energy,
20:17
Speaker 1: so that that explanation doesn't work. The electron doesn't get
20:20
Speaker 1: more energy momentarily magically, it um it's just on one
20:24
Speaker 1: side of the barrier and then it's on the next.
20:25
Speaker 1: Like zoos didn't come down and touch the bowling ball
20:29
Speaker 1: and push it into the other swimming pool. That's impossible,
20:32
Speaker 1: that's right. We're assuming that there's no other source of energy, right,
20:35
Speaker 1: and and it never has enough energy to go over
20:38
Speaker 1: the edge of the swimming pool and into the next one.
20:40
Speaker 1: So the only way to the other swimming pool is
20:42
Speaker 1: to tunnel, is to go through the barrier. And then
20:45
Speaker 1: once it's out and on the other side of the barrier,
20:49
Speaker 1: does it stay there or does it sometimes pop back
20:52
Speaker 1: in or does it fly off? At that point it
20:54
Speaker 1: pop it pops back in. Yeah, it can pop back
20:56
Speaker 1: in and it can go to the next one. Right.
20:59
Speaker 1: The point it is that you can never really trap
21:01
Speaker 1: an electron. And the reason is not that it goes
21:04
Speaker 1: over the edge, and the reason is not really teleportation, right,
21:09
Speaker 1: And the reason is that these these barriers and a
21:12
Speaker 1: quantum level are just different than the barriers we have
21:15
Speaker 1: here at the macroscopic level, and electrons are different from
21:18
Speaker 1: bowling balls. Right. We like to think of them that
21:20
Speaker 1: way because it's useful, because the way we understand the
21:23
Speaker 1: unknown is to do it in terms of the known.
21:25
Speaker 1: But in the end, these things can do things, These
21:28
Speaker 1: quantum mechanical things can do things that the classical things,
21:32
Speaker 1: the macroscopic things that we're familiar with, just can't do.
21:35
Speaker 1: And one of those things is the electron. It has
21:38
Speaker 1: a chance to just ignore the barrier. It's like every
21:40
Speaker 1: time it goes up against the barrier, a die is
21:43
Speaker 1: rolled and if it comes up you know, all sixes,
21:45
Speaker 1: it's like, haja barrier, I get to ignore you. You
21:48
Speaker 1: said every time it goes up against the barrier, Meaning
21:51
Speaker 1: is it like it's always pushing against the barrier or
21:54
Speaker 1: is it like a continual roll to die or what? No,
21:57
Speaker 1: that's a good point, And the way I was speaking
21:59
Speaker 1: about it, it's wrong because I was talking about it
22:01
Speaker 1: like having a classical path, like it has a position
22:04
Speaker 1: and a velocity at every moment. In reality, it's motion
22:08
Speaker 1: is governed by this wave equation, right, the wave function
22:11
Speaker 1: that we used to describe where it is, and that
22:14
Speaker 1: tells us where it's more likely to be and where
22:16
Speaker 1: it's less likely to be. And we know that for
22:19
Speaker 1: it to get from one side of the barrier to
22:21
Speaker 1: the other, it has to go through the barrier. We
22:23
Speaker 1: know this because it can be inside the barrier. Like
22:27
Speaker 1: in principle that should be impossible, right, like, how do
22:29
Speaker 1: you how can you be inside the barrier? You're not
22:31
Speaker 1: breaking the bearer, The bear is not destroyed, but it
22:34
Speaker 1: can sort of like defy the barrier, can sort of
22:36
Speaker 1: ignore the barrier. It has a probability to just sort
22:39
Speaker 1: of like shrug off the barrier the way a teenager
22:41
Speaker 1: shrugs off a curfew. You know. So the trap, the
22:44
Speaker 1: magnetic field that trap is traveling the electron doesn't affect
22:48
Speaker 1: the probability of where the electron can be, or it
22:52
Speaker 1: does doesn't. It doesn't it like squeeze the probability cloud
22:56
Speaker 1: of the electron or something like that. It totally does.
22:59
Speaker 1: It affects it, but it can't trap it completely. It's
23:02
Speaker 1: just impossible to trap it completely unless the barrier is
23:05
Speaker 1: infinitely high, the barrier is infinitely strong, then the electron
23:10
Speaker 1: is totally trapped. But as long as the barrier is
23:13
Speaker 1: not infinite, right, imagine the swimming pool. It's infinitely deep,
23:16
Speaker 1: then the quantum mechanical bowling ball can't get out. But
23:20
Speaker 1: if the if it's even if it's super high, it's
23:22
Speaker 1: a billion miles high, but not infinite, then the quantum
23:25
Speaker 1: mechanical one can get to the other side. It just
23:27
Speaker 1: has a chance. But you're right, it does affect that
23:29
Speaker 1: it squeezes those probabilities. The probabilities are shaped by the barrier.
23:32
Speaker 1: But you're saying there's still a little tiny probability that
23:36
Speaker 1: it's going to jump over, not jump over, but go through, right,
23:40
Speaker 1: And the probability is smaller if as the barrier gets wider,
23:43
Speaker 1: and it's smaller as the barrier gets taller, So that
23:46
Speaker 1: that all makes sense. The thing that's confusing is like,
23:49
Speaker 1: how do you explain what it's doing in the barrier?
23:51
Speaker 1: Is it just like ignoring the barrier and you just
23:53
Speaker 1: have a chance to avoid the barrier. It's it's hard
23:57
Speaker 1: to come up with a sort of like an intuitive
23:59
Speaker 1: under standing of what it's doing there you know, it's
24:02
Speaker 1: like it's in the Noman's land. It's in the place
24:04
Speaker 1: where nothing should be, but there it is, right is it?
24:07
Speaker 1: Because the bowling ball is not really a bowling ball, right,
24:10
Speaker 1: it's more like a cloud, kind of like a like
24:12
Speaker 1: a fog. And you're saying, sometimes the fog can sort
24:16
Speaker 1: of extend and kind of appear on the other side
24:19
Speaker 1: of the swimming pool. If you measure an electron, you say, okay,
24:22
Speaker 1: it's in my trap, and then you ask where is
24:24
Speaker 1: my electron likely to be in one second? Then most
24:27
Speaker 1: likely it's to be it's going to be in the trap.
24:29
Speaker 1: There's a little bit of probability it's going to be
24:31
Speaker 1: in the barrier, and there's a little bit of probability
24:33
Speaker 1: it's going to be in the next one. Right, it's
24:36
Speaker 1: going to be in the next trap. So you know,
24:39
Speaker 1: after you know where electron is, that doesn't tell you
24:41
Speaker 1: where it is necessarily a second later. It's just you
24:44
Speaker 1: have a probability distribution of where you're going to find it,
24:47
Speaker 1: and we can candulate those probabilities using the Shortinger equation.
24:50
Speaker 1: But that's again, that's just a description of what we
24:53
Speaker 1: have observed. Right, the exhorting equation itself is not an explanation.
24:57
Speaker 1: It's just like a mathematical formulation the success He describes
25:00
Speaker 1: what we've observed. Oh, I see, it's a probability of
25:03
Speaker 1: where it's going to be if you measure it. So
25:06
Speaker 1: if you measure it, there's a tiny little probability you're
25:08
Speaker 1: going to measure it in your neighbor's pool. Yes, exactly.
25:12
Speaker 1: And it's tempting to think, oh, well, that's just particles. Right,
25:15
Speaker 1: particles are here, and then particles are their. Right, that's
25:18
Speaker 1: not the property that allows the electron to quantum tunnel. Right.
25:22
Speaker 1: You can have that property in an infinitely deep swimming
25:25
Speaker 1: pool where electrons can't tunnel, right, an infinitely deep potential well, right,
25:31
Speaker 1: the electrons can't get out. That's the only one that
25:34
Speaker 1: can completely hold them. But in now well, electrons can
25:37
Speaker 1: still be here and then later be over there, and
25:39
Speaker 1: then later be over here, as long as you're still
25:41
Speaker 1: within the well. But if the wall is not infinitely high,
25:45
Speaker 1: then there there's a probability that randomly it's gonna ignore
25:51
Speaker 1: or jump over the barrier and be on the other side.
25:53
Speaker 1: If you measure that's right, not jump over, but go through, right,
25:56
Speaker 1: jumping over means why not jump over? Well, jumping over
25:59
Speaker 1: means don't really know, right, you do not like he
26:01
Speaker 1: was hit inside and then it was outside, and you
26:04
Speaker 1: don't know. You don't really know what the path it
26:06
Speaker 1: took to get outside, right. Well, to get over, it
26:09
Speaker 1: would need to have enough energy to go over the barrier, right,
26:11
Speaker 1: and that energy has to come from somewhere, and we
26:14
Speaker 1: have energy conservation in our universe, and so it can't
26:17
Speaker 1: go over the barrier, right. It's like the raccoon pushing
26:20
Speaker 1: the bowling ball. If it doesn't have enough energy to
26:22
Speaker 1: push it over the lip, it's just never going to
26:24
Speaker 1: go over the lip. Um. And the reason this works,
26:28
Speaker 1: we can do the calculations, and the reason it works
26:31
Speaker 1: is because the electron is in the barrier. Like bear,
26:34
Speaker 1: quantum barriers are just different from classical barriers. They're sort
26:36
Speaker 1: of optional. You just always have a chance to ignore them,
26:39
Speaker 1: you know. It's like a speed traps. Sometimes the copsies
26:43
Speaker 1: you and sometimes he doesn't. But if you find it
26:45
Speaker 1: inside the barrier, doesn't it mean it gained a whole
26:48
Speaker 1: bunch of energy. No, it can be inside the barrier,
26:51
Speaker 1: meaning that it doesn't have enough energy to be there.
26:54
Speaker 1: But it's there anyway, where does the probability come from?
26:57
Speaker 1: You know what I mean? Like for it to be probable,
26:59
Speaker 1: He's who have some sort of physical explanation, doesn't it. Yeah,
27:04
Speaker 1: And the explanation is that the bowling ball analogy is
27:07
Speaker 1: wrong because this is not a bowling ball and these
27:10
Speaker 1: are not a swimming pool. It's a weird, lobby, wavy,
27:13
Speaker 1: fuzzy thing that can do this thing that no bowling
27:17
Speaker 1: ball or swimming pool can do. And the barrier also
27:20
Speaker 1: is a little fuzzy, right that you can't build a
27:22
Speaker 1: perfectly strong barrier unless it's infinitely high um. In quantum mechanics,
27:28
Speaker 1: barriers are not the same as swimming pools, right, that
27:30
Speaker 1: they're different. And so the analogy breaks down, and these
27:33
Speaker 1: things can do things that that the things were familiar
27:36
Speaker 1: with can't do, and one of them is that sometimes
27:38
Speaker 1: they sort of ignore each other. With that, let's take
27:42
Speaker 1: a break. We'll be back in just a short minute.
28:02
Speaker 1: But um, and the interesting thing is that it's not
28:05
Speaker 1: just electrons, right, like you're talking about all particles. Oh yeah,
28:09
Speaker 1: electrons are just the simplest case, But any quantum mechanical particle,
28:12
Speaker 1: any particle that's motion is primarily described by like the
28:16
Speaker 1: shortening air equation. So single particles or ions or nuclei,
28:19
Speaker 1: whatever these things can do this also we see it
28:21
Speaker 1: all over the place. It's actually an important part of
28:24
Speaker 1: loss of physical processes that we know and love. Well.
28:27
Speaker 1: I think it's interesting to think about the idea that,
28:29
Speaker 1: you know, these walls in the room that I'm in
28:32
Speaker 1: um are sort of just barriers to right, Like they're like,
28:36
Speaker 1: what's preventing my hand from going through the wall. It's
28:39
Speaker 1: not just my inner peace, but uh, it's it's like
28:43
Speaker 1: the electromagnetic forces between my hand and the wall exactly.
28:47
Speaker 1: And that, as you say, is a quantum mechanical barrier.
28:50
Speaker 1: Like the very tip of your finger. Imagine that's an electron.
28:53
Speaker 1: When it approaches the wall, it meets a barrier, a
28:56
Speaker 1: barrier made by the electrons in the wall, and that's
28:59
Speaker 1: what doing the repulsion. And so you're right, there's a
29:01
Speaker 1: tiny chance so that first electron is just going to
29:04
Speaker 1: go right through the barrier instead of bouncing off of it,
29:07
Speaker 1: and I might lose that one electron from my finger,
29:11
Speaker 1: you might, Or there's an even tinier chance that the
29:14
Speaker 1: next set of particles will will quantum tunnel through, and
29:18
Speaker 1: an even tinier chance that also the next ones will.
29:20
Speaker 1: So there's some non zero chance that you'll put your
29:23
Speaker 1: hand through the wall without breaking the wall. That's crazy.
29:26
Speaker 1: It's it's non zero chance that I can walk through,
29:29
Speaker 1: or do I walk through the wall or appear on
29:31
Speaker 1: the other side or both. I know this would be
29:34
Speaker 1: a horge quantum tunneling through the wall. Yeah, there's totally
29:38
Speaker 1: a non zero chance. Now you could stand there all day,
29:41
Speaker 1: your whole life, walking into walls and not successfully go
29:44
Speaker 1: through it. And I'm pretty sure that would be your
29:46
Speaker 1: experience because the probabilities we're talking about are ridiculously tiny, Like,
29:50
Speaker 1: for these barriers are pretty tall, and there's lots of
29:53
Speaker 1: particles and have to happen for all of them, and
29:55
Speaker 1: so it's basically impossible, but not technically exactly zero. So
30:00
Speaker 1: there is a possibility, Daniel, that you're sitting right there
30:02
Speaker 1: where you are will suddenly find yourself on the other
30:05
Speaker 1: side of the wall that's in front of you, right exactly.
30:08
Speaker 1: There is a possibility I could quantum tunnel into the
30:10
Speaker 1: bathroom or whatever. Let's say it happens right now. Proof
30:14
Speaker 1: would you say you teleported to a battle. I mean,
30:18
Speaker 1: what's what's the difference between that and actually teleporting. Well,
30:22
Speaker 1: we did a whole episode about teleportition, remember, and we
30:26
Speaker 1: decided that teleportition is impossible while this is possible. And
30:30
Speaker 1: you know, it's really tempting to connect this this um
30:33
Speaker 1: idea of tunneling with the concept that part of quantum
30:36
Speaker 1: particles can sort of skip their way through life, right,
30:39
Speaker 1: they don't need to exist at every moment, sort of
30:41
Speaker 1: they're here and then they're there and the other thing.
30:43
Speaker 1: And so if you want to call this telepartition, then
30:45
Speaker 1: every particle is teleporting all the time, right, So that's
30:48
Speaker 1: my problem with it. It's like this is a natural
30:50
Speaker 1: thing that particles are always doing, even without barriers, Like
30:54
Speaker 1: even a particle in an infinite box is doing this
30:56
Speaker 1: sort of skipping thing because it doesn't exist between the
30:59
Speaker 1: moments you're observing it. So if this is teleprotation, then
31:02
Speaker 1: that's teleprotation also, and everything is constantly teleporting. You're saying
31:06
Speaker 1: that you don't want to call it teleprotation, not because
31:09
Speaker 1: it's not teleprotation, which I would argue maybe it is experientially,
31:15
Speaker 1: but it's just that if you call it teleprot teleportation,
31:17
Speaker 1: it would sort of the dilute or or break the
31:21
Speaker 1: definition of teleprotation. Yeah, if this is teleprotation, then we're
31:25
Speaker 1: all teleporting all the time. So if everyone is nice,
31:28
Speaker 1: then nobody's nice. It's kind of right, like it's the
31:32
Speaker 1: teleporters quantum dilemma exactly, all right, So that that that
31:37
Speaker 1: that makes a bit more sense. And quantum tunneling is
31:40
Speaker 1: really important, like it happens in the sun. If you
31:42
Speaker 1: want nuclear fusion to happen, the kind of thing that
31:44
Speaker 1: powers the sun, that generates all that light that you
31:47
Speaker 1: know makes you look so nice and tan and grows
31:50
Speaker 1: all that food that you eat, then you need these
31:52
Speaker 1: particles to be able to quantum tunnel through some of
31:55
Speaker 1: the potential barriers that they face. You know, particles infusion
32:00
Speaker 1: don't like to touch each other, right because nuclei are
32:03
Speaker 1: both positively charged because of all the protons. So to
32:05
Speaker 1: get them to fuse, you have to push them together,
32:08
Speaker 1: and they're repelling each other, and that's a barrier. So
32:11
Speaker 1: you've got to get them sometimes through that barrier in
32:13
Speaker 1: order to do the fusion. And you're saying sometimes they
32:16
Speaker 1: tunnel to that, but mostly do they mostly get pushed
32:19
Speaker 1: together or do they actually tunneled together. I think it's
32:22
Speaker 1: some of both. I mean, the center of the sun
32:24
Speaker 1: is so hot and so dense that these particles can
32:27
Speaker 1: just sort of overcome the cool embarrier like they have
32:29
Speaker 1: enough energy. But definitely, um tunneling is an important part
32:32
Speaker 1: of it, Like fusion wouldn't be the fusion we know
32:34
Speaker 1: and love without quantum tunneling. If everything is fusion, then
32:37
Speaker 1: nothing is fusion. That's what you're saying. That's right, that's
32:41
Speaker 1: the theme today, right, label everything um. And there are
32:44
Speaker 1: other effects, like you know, back to electrons. Electrons don't
32:49
Speaker 1: like to stay in little traps, but if you're building
32:51
Speaker 1: chips for computers, then you'd like your electrons to be
32:54
Speaker 1: in certain places you want to know, like hey, this
32:57
Speaker 1: transistor is all on or this transistor is off or whatever.
33:00
Speaker 1: And and it gets harder and harder to make transistors
33:03
Speaker 1: be reliable as they get smaller and smaller, because you
33:06
Speaker 1: get dominated by these quantum effects, and these little traps
33:08
Speaker 1: get smaller and smaller, and electrons like to jump out
33:11
Speaker 1: of them, and you don't want your ones in your
33:13
Speaker 1: computer to suddenly switch into zeros. And so this actually
33:17
Speaker 1: is a big effect in miniaturizing transistors, which is a
33:20
Speaker 1: big effect in speeding up your iPhone. At some point,
33:23
Speaker 1: if you make electronics small enough, the quantum effects are
33:27
Speaker 1: gonna totally miss everything up. Yeah, exactly. Quantum mechanics messes
33:30
Speaker 1: it up again, bummer, Why can't they just be elect
33:35
Speaker 1: strikes out. Quantum mechanics strikes out again. Why can't we
33:40
Speaker 1: just use little bowling balls and tiny little swimming pools
33:42
Speaker 1: instead of electrons? Sorry, and bowling striking is good, so
33:46
Speaker 1: it wins. Yeah, it strikes out, exactly. You brought a
33:51
Speaker 1: full circle. They're very nice, all right. So that's that's
33:53
Speaker 1: pretty much quantum tunneling. It's this idea that particles are
33:57
Speaker 1: all quantum, and as such, they have these weird fuzzy
34:02
Speaker 1: uh location right, They're not in any particular place, and
34:05
Speaker 1: so it's impossible to trap a particle because it's fuzzy
34:09
Speaker 1: and it might slip out. That's right. Quantum barriers are
34:12
Speaker 1: just different from the ones you're familiar with, the work
34:15
Speaker 1: under different rules, and those rules have little random exceptions
34:19
Speaker 1: to them, so sometimes they can just be ignored and
34:21
Speaker 1: it's weird and it's confusing, and your intuition breaks down.
34:24
Speaker 1: But it's also wonderful because it shows you how the
34:27
Speaker 1: world works at a smaller level. Right, it reveals to
34:30
Speaker 1: you where your intuition is wrong, and that that means
34:33
Speaker 1: that it's showing you the truth of the universe. Yeah,
34:35
Speaker 1: and the and the truth is bowling. Exactly. The truth
34:42
Speaker 1: is quantum bowling. This episode brought to you by the
34:44
Speaker 1: American Bowling Association. Yeah, exactly. But so that's what happens
34:50
Speaker 1: at the microscopic level, but on the larger level, we
34:53
Speaker 1: we can't do that because you know, there's a lot
34:55
Speaker 1: of lactrons in my hand, and the chance that all
34:58
Speaker 1: of them are going to quantum tunnel at this time
35:00
Speaker 1: it's just almost zero. Yeah, exactly. Like if there's a
35:03
Speaker 1: chance for you to roll a one million sided die
35:07
Speaker 1: and get zero, you know that's probably can happen. But
35:10
Speaker 1: if you have to do that for a million die
35:12
Speaker 1: all at once um and get the same answer, then
35:15
Speaker 1: it's basically very improbable, almost impossible. So you the macroscopic
35:20
Speaker 1: stuff sort of gets averaged out, but still possible. It's
35:23
Speaker 1: still possible. Absolutely, you could quantum tunnel through the walls
35:27
Speaker 1: and not counted as teleportation. All right, It's just what
35:33
Speaker 1: quantum stuff does Yeah, yeah, drives them physicists crazy. No,
35:39
Speaker 1: it excites us. Is it's wonderful. We're always looking for
35:42
Speaker 1: weird quantum effects that show us how the universe works.
35:45
Speaker 1: It's you know, it's a it's a it's what we
35:47
Speaker 1: what we live for, these little moments. All right, Well,
35:50
Speaker 1: we hope you enjoyed that discussion and hope that answered
35:53
Speaker 1: all of the questions that listeners had about what is
35:56
Speaker 1: quantum tunneling. Thanks for sending in your questions. They're inspiring
35:59
Speaker 1: and if you have of questions about things you'd like
36:01
Speaker 1: to see explained, please send them to us at questions
36:04
Speaker 1: at Daniel and Jorge dot com. We love your messages,
36:08
Speaker 1: that's right. And if you are Swiss one would like
36:10
Speaker 1: to tunnel some money over to us, we are also
36:12
Speaker 1: available at feedback at Daniel and Jorge dot com or
36:16
Speaker 1: just dump it right into Katrina's bank account if that's
36:18
Speaker 1: more convenient you go, all right, thanks for listening. If
36:33
Speaker 1: you still have a question after listening to all these explanations,
36:36
Speaker 1: please drop us a line. We'd love to hear from you.
36:39
Speaker 1: You can find us at Facebook, Twitter, and Instagram at
36:42
Speaker 1: Daniel and Jorge. That's one word or email us at
36:45
Speaker 1: feedback at Daniel and Jorge dot com. Thanks for listening
36:49
Speaker 1: and remember that Daniel and Jorge Explain the Universe is
36:52
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