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All right, welcome to Arts and Ideas in the Air, Under the Tent and Around Baltimore's
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Wondrous Wednesday.
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So I'm trying to finish up the physics stuff of Wondrous Wednesday for now.
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I think maybe I could say something interesting about quantum field theory, it's always cool,
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next time and then maybe that'll be it.
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Today I wanted to talk about quantum mechanics from a Bohmian perspective, in particular
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this thing called spin, which I talked about last time in the context of showing that there
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is non-locality in the world, meaning that in some sense there is a now, which contradicts
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relativity which says there's no now, and that's sort of like the heart of the tension
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in modern physics that for some reason few people are focused on and is absolutely essential
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in making sense of what people really talk about.
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Now there are a number of quantum mechanical theories that one can talk about and make
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sense of and the one that I like is called Bohmian mechanics.
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The idea is the world is made up of particles moving around and their motion is dictated
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by this wave function.
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Now the most extreme version of this theory is that particles are just simply things with
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positions, they have no sort of weight, mass we like to talk about in physics, no electric
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charge, no nothing, it's just dots moving around and all of those properties, the weight
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and electricity and electric charge and whatever, is all embedded in the wave function itself.
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This is going to be a pretty important idea and what I'm about to explain.
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So last time I talked about spin being think of like a ball on a stick and you're spinning
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it and you can either kind of spin it to the left or you can spin it to the right and you
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can change how the stick points.
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So that's sort of the one sort of supposed to have in mind when one talks about the spin
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of an electron, it spins and this way or that and you know when you subject it to an electromagnetic
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field it always seems as if it's pointing in sort of a definite state, it just kind
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of chooses one and so it goes up or down based on that.
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So the idea is that when you're choosing different directions for spin, it could be anything
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but for some reason when you measure it, it always comes out as if it was pointing in
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the direction that you're caring about measuring and it goes up or down.
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So that's the thing to keep in mind.
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It doesn't make sense classically, classically it could be pointing in any direction and
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then its trajectory would be different based on that.
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So it's weird, right?
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We have this like quantum mechanical thing, like say an electron, very small little thing
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and it's moving in a way that kind of suggests it's a spinning little ball on a stick except
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it doesn't really quite make sense with the classical picture because it was always, no
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matter how you measure it, the axis is always such that it lines up with the measuring device
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in a certain way and it shouldn't.
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And what quantum mechanics says is what is the probability of it being like up or down.
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Now there are other different types of particles with different types of spin results in terms
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of kind of how many ups and downs there might be, you know, there's different states, but
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whatever.
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Electrons are what are called spin one half and they just have the two states, so that's
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nice.
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We'll just focus on them.
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Now Bohmian mechanics says, okay, so standard quantum mechanics says all we can do is talk
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about these probabilities based on the state of the wave function, whatever that means.
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There's these things called operators, they have these things called eigenvectors and
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eigenvalues and it's all this complicated mumbo jumbo that sounds really abstract.
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One can actually, it's actually in some ways with spin, very simple mathematics, relatively
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speaking and, but it doesn't make any sense, there's no intuition about it.
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More importantly, the standard statements is just that these things happen when you
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measure and that's about it.
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No discussion of what a measurement really is, how that comes about, how is a measurement
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something part of a fundamental theory.
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Like the world isn't just a set of measurements, it's us living in our world and so how does
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all these things come about?
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All right, so now Bohmian mechanics says, okay, we've got this wave function evolving
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just according to the usual quantum mechanical sort of nice evolutions, ignoring this kind
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of like discrete kind of like jumping up or down or whatever.
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And instead you have a particle, many, well, all the particles being guided by this one
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wave function.
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And so the idea is that, that basically as this wave function evolves according to all
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the dynamics, the particle's position as it travels will kind of select that part of the
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wave function that's relevant to the future stuff.
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And that's why it all kind of like collapses into something definite because of that particle
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position.
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All right, so that's Bohmian mechanics very briefly, talked about it number of weeks ago.
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But now for spin, what happens is, so let's just focus with one particle.
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One particle is flowing along and the wave function splits into two pieces because of
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this measurement apparatus for detecting spin.
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And it's all just playing around with the values of this wave function, they're complicated
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things, they're little, they're actually like kind of little arrows you might say.
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And it, you know, there's a dynamics associated with it and you have the split and then the
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particle goes with it.
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And so if the particle happens to be in the bit that goes up, then the particle goes up.
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If it happens to be in the bit that goes down, then it goes down.
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It's just following along with the wave function.
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Now there is actually no spinning, nothing's spinning.
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That electron is not actually spinning, it's just a dot moving along with the wave function.
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And from a Bohmian perspective, the interesting thing that is about these experiments is that
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if you analyze it in the framework of Bohmian mechanics, you can set up a scenario where
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basically a particle in the upper half, kind of this wave function always goes up and the
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one in the lower part always goes down.
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And that's just how it works.
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And it actually, if you flip the electromagnetic field, the thing still goes up if it went
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up before and still goes down if it went down before.
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But now because of that switch, one interprets the up and down in the opposite direction.
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And so, you know, instead of spinning the ball left, say, you're spinning it right.
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That would be the classical interpretation of that result.
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And that's just not, like, nothing changed about the particle itself in this theory.
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You can just rewind it and replay it, except you just now are playing a different measurement
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and you're interpreting that measurement in a different way.
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And that's all fine.
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But so it's in this sense that spin is not real.
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And spin not being real is, well, kind of shocking to many people who study quantum
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mechanics because they're always talking about spin.
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It's almost like, you know, the canonical examples and so forth.
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And then there you have it.
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Now let's get back to what we were talking about last week where you had two particles
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that were paired in such a way that they fly off.
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If one goes up, the other one goes down, and then vice versa.
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So this is the kind of the setup of the Bell experiments and basically the fact that one
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could go up while the other one goes down was suggesting that there was something predetermined
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about it because these measurements happen so far apart, or that they're communicating
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faster than light.
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And in fact, it's the latter, and Bell's work showed that it had to be the latter, not the
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former.
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But the interesting thing is, of course, Bohmian mechanics actually has something that seems
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to be predetermined, right?
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Particles are at these definite positions.
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Well, so what's going on here?
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Well, basically, the value of the spin is not defined beforehand.
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That's not defined.
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The position of the particle is, but spin doesn't mean anything until you have an experimental
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setup.
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So if you have this experimental setup that you're going to change and they're kind of
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far apart, then as soon as that experiment, you know, does its measurement on the thing,
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it changes the wave function.
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It separates the two pieces that used to be together, the two pieces being, you know,
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one piece that goes up and one piece that goes down, they were living together.
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And now because of the measurement, they're living in separate worlds.
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Why is that?
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Because now there's a kind of an extra dimension, you might say, the environment, the measurement
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results, whatever.
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But there's an extra dimension that kind of separates them, these two pieces, and wherever
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the particle happened to be in one of those two pieces, it'll flow along with that piece.
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And it's instantaneous, and this is the weird thing, but it's instantaneous and so it affects
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the other piece.
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And so the other piece, you know, the wave functions are correlated, I mean, it's the
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same wave function, but I mean, these separate kind of pieces in our physical space are correlated
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so that if on the one side of the piece went up, that the particle was in, then on the
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other side of the other particle would be in a piece that went down.
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And that's just sort of how that works, which comes out of the mathematics and evolution
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and setup of these experiments and whatever.
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So biomechanics has this weird thing where it does say it's kind of predetermined in
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a certain sense, in the sense that there's position, but it's really not because it depends
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on the experimental setup, and that setup is communicated to these distant pieces through
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the wave function.
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This wave function is this universal thing that lives in a now, and it requires knowing
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where everything else in the universe is right now in order to really use it.
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I mean, most of the time it's not that dependent on it, practically speaking, but technically
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it depends on the position of everything in the universe right now.
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And that's kind of like a hard thing to swallow, except it's really just reflecting on the
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fact that there needs to be a now for quantum mechanics.
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But it is the heart of the mystery and the problem.
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Now in a relativistic setup, basically one does need to figure out what this now is.
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You have to put it into the theory to make it sensible, and so one can do it.
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The easiest thing is just to pick one.
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You just pick the slices of now, just say this is what it is, and so you run your evolution
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of the system with that slicing, and it's all good and everything works out and everything's
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fine.
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If you picked a different slicing, you would also have something that worked out just fine,
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but it would be a different kind of working out, that kind of slicing up of space and
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time into kind of things of now does impact the evolution of the particles, but it doesn't
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impact the statistics.
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And so there's no way to detect that now, which is also weird, that now is completely
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hidden from us, even in a theory that relies on the now.
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It all just kind of fits, but it's all sort of like, what?
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That's the mystery.
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That's the wonder.
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Why do you have this fundamental thing that requires a now, and then that now gets hidden?
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Completely hidden, can't be detected.
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So that's the mystery.
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There are ways of defining this now in some ways, such as like, say, kind of the time
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distance to the Big Bang, there's kind of a center of mass kind of frame of reference
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that you can kind of do in relativity.
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There are different ways.
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There's even attempts to define it from the wave function itself.
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So the wave function evolves.
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It doesn't need this slicing.
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That's why the slicing isn't apparent, but you can actually define a slicing from it
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in some ways, and so you can use that, but there's nothing compelling the choice, and
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that's sort of the problem.
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So yeah.
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So that's boy mechanics, somewhat in a nutshell.
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It essentially says there's these definite results because there's definite particles
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moving around.
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They're being guided by the wave function.
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All the weirdness is in the wave function, which also means that in all these different
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interpretations of quantum mechanics, that weirdness is also present.
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All the weirdness is kind of encapsulated in the wave function, and particles are just
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moving around to give us this definite sense of reality.
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Now there are other theories, such as mini worlds, which is kind of like saying, well,
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instead of having this one definite choice, all the choices happen, and one can write
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down a theory that actually makes sense of that in some ways, but it's kind of weird,
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because you don't really know what the probabilities mean, because now everything kind of happens,
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and so it's kind of in the perspective of the universe of this one thing kind of seeing
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the future, and this one, and I don't know, it's not really clear what one gains from
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it, except to say, well, we were using all this thing all the time, and there you go.
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There's also things that actually modify the evolution of the wave function to try to have
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things collapse.
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There's kind of a range of parameters that work for them, and that range has been getting
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narrow and narrow as experiments get better and better.
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Maybe in 20, 30 years, those will all be ruled out.
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I don't know.
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I don't know how good the range is or not, and what we can realistically deal with, but
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so there are other theories.
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I like Bohm mechanics because, well, basically the whole thing started by saying, okay, what
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if we had particles, and so those things should have position, and as soon as you do that,
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you write down Bohm mechanics.
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It's really a pretty easy theory to write down if you know the mathematics, and you
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know some simple facts about quantum mechanics.
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It's not that hard to get.
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So that's in a nutshell Bohm mechanics.
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I might try to talk about quantum field theory next time, particularly in connection with
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Bohm mechanics, and we'll see how those things go, and that's all I have to say.
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All right.
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Have a good day, and see you all later.