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Wondrous Wednesday 06: Bell's Theorem and Bertlemann's Socks

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Summary

Deep dive into Bell's theorem using Bertlemann's socks paper. Explains Stern-Gerlach measurements, spin correlations, and why pre-existing values cannot explain quantum mechanical results. Quotes from Bohr, Heisenberg, and Jordan.

Transcript

0:00 Welcome to ANI in the air under the tent and around Baltimore. This is wonderous
0:05 Wednesday where I talk about something wonders. So today I'm going to try and
0:14 talk about some more quantum nonlocality. The reference for this is Bertelman's
0:23 socks. That's B-E-R-T-L-M-A-N-N. Socks. It was a paper written, well probably, oh 1981
0:38 it looks like, referencing the work of by the author of a very fundamental finding
0:47 which is really quite an amazing result that gets often ignored. So, well, and
1:00 this paper was written to try and explain to people how things, you know,
1:09 worked with his work. So, and basically it's because the thing that is
1:20 surprising about the result is not at all surprising to most people who would
1:26 just hear it. Makes, you know, reasonable sense. But it, so one has to first
1:35 understand the disbelief that happens with the physics and then understand why
1:42 there's some problem beyond that. So the reference of Bertelman's socks is there
1:47 was this professor, Professor Bertelman, who always wore different colored
1:52 socks. So if, if you saw that he was wearing pink socks on his right foot
2:01 then you knew he was wearing not pink socks on his left foot. That's a
2:06 perfectly reasonable thing to do. Nothing surprising. Oh, I mean, I don't know about
2:11 reasonable but, you know, nothing magical about that, right? He just wore different
2:16 colored socks all the time. Good. So basically the quantum mechanical analog
2:27 was, and I kind of mentioned this last time, you have two particles, so think of
2:33 them as just two little balls, that, you know, are linked to each other in such a
2:39 way that when, when you do a measurement, it's called a Stern-Gerlach measurement,
2:44 if the, so let's call them the left and the right particle. So if the right
2:52 particle goes up, then the left particle goes down. If the right particle goes
2:59 down, the left particle goes up. All right, now it's supposed to be measuring this
3:03 thing called spin. So what is spin? Well, the idea is your particle is spinning
3:11 along an axis, so, you know, like you've got a ball and a stick and you spin it.
3:21 You can spin the ball either, you know, if you're looking at the ball on the
3:26 stick right in front of you, you can spin it to the left or you can spin it to the
3:30 right, okay? And depending on how you spin it and the, how you're holding that stick,
3:38 these particles will travel either up or down in this magnetic field, whatever
3:43 that is, called the Stern-Gerlach magnet is the basic idea. And so, and that's
3:54 perfectly fine and reasonable. So if it's, and the magnetic field is designed so
4:00 that it, you know, if you're, so let's say you're, you're, you're pointing the stick
4:04 in the north direction and then it goes along this field and it goes either up
4:11 or down. Now, you can rotate the, the magnet that's doing this detection and so
4:18 that when you're pointing that stick north, the particle just, all right, sorry,
4:25 let me see, what do I want to rotate? Sorry, I want to rotate the stick magnet,
4:30 leave the magnet alone for now. So the stick was pointing north, it goes up and
4:37 down. Now, if you rotate the stick so it points east and then you send that
4:42 particle through this field, it just goes straight on through classically. So
4:49 that's what's supposed to happen. And if you angle the stick, so it's like
4:54 northeast and you send it through this field, then it will go up but not as far
5:00 up. Now, in quantum mechanics, that's sort of, those middle things don't ever
5:06 happen. It either goes all the way up or all the way down. In reality, a lot of
5:12 it, you don't get any result because experiments are painful. But, so either
5:20 goes up or down. So that, so naively, if you have this picture of spinning balls
5:25 along the stick and the magnetic fields are supposed to behave the way they
5:30 behave in other realms of our existence, you know, you should have had this whole
5:38 spread but you don't, you just have up or down. And so that suggests that the point,
5:43 the stick is always pointing north or if you like pointing south, if it's going
5:48 down, depends on how you want to talk about it. But, you know, if it's rotating the
5:54 other way around the axis, it's, it goes the other direction. And that's it. So you
6:01 just have these two choices. And it's kind of weird because, you know, if you
6:04 have a ball and a stick, right, you can point that stick any way you like. You'd
6:10 think that'd be true for particles. And in particular, you can rotate the magnets
6:14 any way you like. That's the experiment. And you always still see up or down. So
6:20 even, so if it's, it's like, okay, you say, okay, it's pointing north-south, right?
6:25 I'll rotate the magnets so north-south doesn't change its direction. And, you
6:29 know, it'll just be up or down if it's pointing in the east direction. And all of a
6:32 sudden it's up and down. And, and then you're, so now you're saying it's in the
6:35 east direction. So this is befuddling to many. And, you know, I mean, naively I
6:45 would just think, well, you got a bad model in your mind. But they didn't go
6:48 that direction. What they went was like, oh, well, you know, the way this happens is
6:56 that as soon as you start measuring in this direction, so I'm measuring as if
7:00 it's going to be north-south, north or south, then that's what it chooses to do.
7:06 It chooses to be aligned along that north-south axis. And then, you know, and
7:15 then it does its behavior. And of course you could think that the magnetic field
7:18 is somehow making it aligned with the north-south in terms of something
7:21 dynamic, in terms of like some kind of like correction thing. There are reasons
7:27 to say that doesn't, that that's not what's going on here. But it is
7:30 definitely the case that the active measurement is making it north-south
7:34 behavior kind of going up or down. Good. Fine. So as I said, this experiment is two
7:41 particles, a right particle and a left particle. And the, and if it goes up, if
7:49 the right particle goes up, then the left particle goes down. Right. And so, so you
7:54 have this conundrum where it's like, okay, it kind of looks like this thing isn't
7:59 the axis of rotation is not defined until you measure what the axis of
8:05 rotation is. And that's fine. I guess it's kind of less of a measurement then, but
8:12 whatever. But instead, you then have this this problem that you can, as soon as you
8:22 make that measurement on the right particle, the reality of the left
8:26 particle is set in stone. So it always happens that if the right particle went
8:32 up, the left particle went down. And of course you could reverse the order. Now
8:36 the problem with this, if the thing didn't exist beforehand, is that you can
8:43 do this measurement far apart. And so what is now comes into play. Right. So as
8:51 soon as you do the measurement on the right particle, the reality of left
8:54 particle is is defined. But when does that happen? When I talked about
9:01 nonlocality, there is no notion of now. Right. I mean, there's a, there's a my
9:08 notion of now. And in my notion of now, that particle stuff always works out
9:13 just fine. But someone else's notion of now would have it be that the left
9:18 particle was measured first. And it went down, and that's why the right particle
9:24 went up. Right. So there's, because it's so far separated, you can have different
9:30 notions of now. And the results are always wherever the results are. And so
9:36 you, so the question then becomes, well, when did that actually choice happen? So
9:41 then you say, well, all right, so maybe it doesn't quite exist in the way we
9:47 understand it, but there's something that's determining this. And so, you know,
9:54 you don't need something faster than light. You know, like, so, you know, the
9:59 fact of Berthelmann's socks, right, one is pink. That means the other one's not pink.
10:04 But that's because there was nothing that happened to his socks when you
10:09 realized the one was pink. They were already pink and not pink. You're just
10:15 observing that this is a perfectly reasonable thing to do. And that's a
10:18 perfectly reasonable hypothesis. So can you assign it so that it's, you know, so
10:25 you can measure the axis, all these different things. You can say, okay, what
10:30 if it's north-south, what if it's east-west, northeast-southwest, whatever.
10:36 It's always going to be definite up or down, and the other one's always going to
10:40 be the opposite. And so can you make that assignment in a way that fits the
10:45 probabilities? That's a question. It's a mathematical question. Can you assign all
10:51 these things so you have the predictions of quantum mechanics that when this
10:54 thing is set up in just such a way, you're going to see, you know, up half the
11:00 time for the north-south, half the time for the, you know, for going down. You
11:09 got some other probabilities. Maybe, you know, if you measure it in the northeast
11:15 direction, you get two-thirds up and one-third down, whatever. I don't know. But
11:21 there are actual facts of the matter about this. Well, predictions at the time
11:26 the paper was written, and then someone actually did the experiments. It took a
11:30 while to get something that was, you could measure faster than the speed of
11:35 light allowed things to talk about. They did it. And, yeah, so they found out that
11:45 quantum mechanics was right, and basically there is no way of assigning values
11:51 beforehand to all the different possibilities that work with the
11:56 probabilities that nature actually has. So that means, basically, that nature's
12:06 now local. Basically, as the particles that the measurement you're doing on
12:15 the one is influencing in some fashion the other particle far away. They could
12:23 be in two different galaxies. They could be on the opposite sides of the universe,
12:27 and this correlation would still hold. As soon as you do that measurement, this
12:31 other thing happens. Like, it's instantaneous. And, again, instantaneous
12:37 doesn't make sense in relativity. You can add it, you know, saying, "Okay,
12:46 this is gonna be the now for everybody." And, you know, you may
12:50 not think it's the now, but it is the now. And go on with that, and that's generally
12:55 fine. General relativity gives it some problems, but whatever. But, you know, we
13:00 don't want that. That's like saying, you know, like, "We have this
13:04 beautiful thing that says there is no now, but we have a problem, so we're just
13:09 gonna say there is a now." And, you know, there's no actual
13:13 contradictions, so we just go like, "Well, whatever." I mean, there are not
13:19 contradictions, but it feels wrong. It feels like the whole point of relativity
13:24 -- well, not the whole point, but the big part of relativity is you have these
13:28 different notions of time and distance based on how fast you're moving, and it
13:35 means that there's no kind of now, and that just is the sensible thing to do.
13:41 Quantum mechanics says, "No. No, it's not."
13:49 So, so this was the work by J.S. Bell, and look at Bell's inequality, Bell's theorem,
14:02 Berthelmann's socks. Berthelmann's socks is a readable paper, mostly. You'll skim
14:09 some parts, but a lot of it is like good text, and he's got some nice, nice quotes
14:13 of some, you know, quantum physics people. Let me just see if I can pull up one,
14:22 because it's kind of cool to hear. Let's see, so Bohr, he was the one that came up
14:31 with the first sort of idea of quantum mechanics having these kind of like jump
14:38 orbits, kind of, so like electron circling the proton, or the nucleus of
14:45 the atom, and can only be in certain orbits for some reason. That was his idea.
14:52 Anyway, so he said, let's see, "Bohr once declared when asked whether the quantum
14:57 mechanical algorithm could be condensed, can be considered as somehow mirroring
15:01 an underlying quantum reality. There is no quantum world. There is only an
15:05 abstract quantum mechanical description. It is wrong to think that the task of
15:09 physics is to find out how nature is. Physics concerns what we can say about
15:12 nature." Heisenberg says, and so like Heisenberg is another big name, came up
15:21 with one of the formulations of quantum mechanics, says, "In the experiments about
15:25 atomic events, we have to do with things and facts with phenomena just as real as
15:29 any phenomenon in daily life, but the atoms of the elementary particles are
15:33 not as real. They form a world of potentialities or possibilities rather
15:36 than one of the things or facts." And then, perhaps even more strongly,
15:42 Jordan, who came up with an important interpretation of quantum mechanics
15:48 involving probabilities, I think that was Jordan, was that born? I don't know. Anyway,
15:56 he's another big name, less of a big name, but, "Jordan declared with emphasis
16:02 that observations not only disturb what has to be measured, they produce it. In a
16:06 measurement of position, for example, as performed with the gamma-ray microscope,
16:09 the electron is forced to a decision. We compel it to assume a definite position.
16:13 Previously, it was, in general, neither here nor there. It has not yet made its
16:17 decision for a definite position. If by another experiment the velocity of the
16:22 electron is being measured, this means the electron is compelled to decide itself.
16:25 For some exactly defined value of the velocity, we ourselves produce the
16:29 results of measurement." So this is their notion that, you know, quantum mechanics
16:35 doesn't have definite values until you do an experiment on it, until you do a
16:39 measurement. Now, this is just kind of nutty to me, just on the face of it. I
16:45 mean, there is a reality. I experience reality, but, you know, to each their own. And, you
16:50 know, the idea that Bell pursued was, you know, so Einstein, Podolsky, and Rosen came
16:58 up with the argument that, hey, this stuff has to be defined beforehand. Here's how
17:02 you do it because of this, you know, otherwise you have this, you need it now.
17:07 You need it now, which isn't in line with relativity. So, instead, you know, what
17:14 Bell discovered was that, actually, that idea doesn't work. And so you're left
17:19 with the fact, okay, you know, you definitely have to have a now. And once you
17:24 have a now, you can say, well, nothing's defined until you measure it. And once you
17:26 measure it, it's now defined for everything that matters. You've got the
17:31 now. So, that's cool. All right, so, can we do better than that? Well, you can. So, I
17:41 think I'll, hopefully next week, conclude with the Bohmian version of what's going
17:48 on with spin. Just to give you a clue here, one of the great catchphrases of my
17:56 collaborators on this is, even spin is not real. All right, hopefully I can
18:05 explain that next time. But, so, to sum up today's point, you have these, you know,
18:13 correlations up down for these particles, and it doesn't matter how you orient the
18:18 measuring devices, you're always going to have an up and down, you're always going to
18:21 have it correlated with the other one. And so, but you can't, they can't all be
18:29 predetermined in advance. Now, I will say that there is one way to avoid the now,
18:38 which is to say that when you do an experiment, you don't actually get a
18:41 result. You only get a result, it only comes into focus when you're able to
18:46 take the results of both kind of sides of the experiments, they come together,
18:50 and they come together in just the right way, and that's when it's all defined.
18:54 That's kind of how the many worlds version of quantum mechanics escapes all
18:59 this stuff. However, to escape the now by saying there actually is nothing actually
19:04 definite and existing right now, well that seems kind of crazy. So, yeah. Anyway,
19:12 next week, Bohmian version of this stuff, and then, I don't know, maybe I'll be done
19:17 with physics. We'll see. All right, I have a good one.