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