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Hi Mikael,

The ideas behind Bell's Theorem, and the related Einstein-Rosen-Podolsky Paradox (or EPR paradox) are right at the foundations of quantum mechanics. I'm not sure that I myself fully appreciate the depth of Bell's Theorem, nonlocality, many-worlds, and the other weirdnesses of quantum theory. But I'll take a shot at addressing your question. Have a seat, this is sort of lengthy. :)

First let me try to describe quantum theory briefly, in my own words:

"In order to properly describe the behavior of a particle, you have to
figure out *all possible behaviors* of that particle. A real
particle will actually behave as if all of the allowable behaviors were
present, some more likely than others, all interfering with one another,
superimposed or "mixed" with one another, etc.. However, whenever the
particle interacts with something else it *must* choose one and only
one behavior. (If you already know a bit of quantum mechanics, I hope that
this statement makes sense. I just want to make clear what terms I use,
and what aspects of the theory I will talk about below.) Behavior can mean
"position", "speed", "energy" ... for example, in the classic "Young's
double-slit experiment", you observe that single electrons exit in multiple
positions, that they interfere with one another, but when the time comes to
measure them they "choose" a single position-state. Good examples of
Bell's Theorem use "spin direction" as the behavior. The real question
involved is: when I force a mixed state to "choose" one of its available
options, how exactly does the choice occur? Especially if the mixture
extends over a large region of space, and the choice-forcing measurement
only touches a small neighborhood?

Actually, the usual example of the Bell experiment (dealing with
spin-directions) can be sort of confusing. Let me raise some of the same
issues in a simpler context. Suppose I put a very light particle in a big
sealed box, in such a way that I *have no idea where it is*. So the
"behavior" to look at is "position". In quantum mechanics, the true state
of the particle within the box says that *the particle is in a mixture
of all possible values of "position"*. A measurement has a certain
probability of causing a "choice" of any particular position. The mixed
state of the particle extends over the *entire box*, and if we force
the particle to "choose", it will no longer be mixed and will no longer
extend over the whole box. So somehow the particle jumps from a large,
extended state, into a small localized state, when we measure it.

The problem is that the box is very large. If I do a measurement and find
the particle in (say) the upper northeast corner, then a simultaneous
measurement is *certain* not to find the particle in the opposite
corner. But, hang on, we said that the particle's true state was
distributed all over the box - how does the "part of the particle" in the
southwest corner *know* that a choice has been forced up in the
northeast? If there really is some sort of "probability field" on one end
of the box, how does that field know to go away when the particle decides
to emerge on the other end? Even if the two ends are separated by meters,
kilometers, or light-years? It seems as though the choice affects the
whole collection of behaviors at once, no matter how far apart they are or
what the speed of light is.

The natural objection: maybe the particle isn't some mysterious mixture
extending over the whole box, but has actually existed in one state all
along. If the particle actually is in the northeast, of course it can't be
found in the southwest! But this is to deny that the particle was in a
mixed state extending over a large space. This contradicts other aspects
of quantum mechanics - indeed, the whole of quantum mechanics rests on the
idea of mixed-states, and the
idea that they choose particular states at particular times. There
*really is* a difference between a mixed or superposition state and
a "well-defined state that we haven't made note of". A box containing a
particle in the northeast corner is different than a box containing a
particle in a superposition of all possible locations.

In technical terms, the "mixed" state of a particle is described by something called a wavefunction, and the particular states that can be chosen are called "eigenfunctions".

The usual Bell's Theorem example, involving electron spins or photon
polarizations, is important because it *shows* exactly how a mixed
state is different than an unmixed state. It's subtle, but it works. This
is the key to your
question - you *cannot* say that "Of course we observe a single
behavior everywhere at once, since it was behaving that way all along,
whether we looked at it or not." It is *demonstrably not true* that
the system was in a single state all along. It was in a genuinely mixed,
undetermined state. (In the usual Bell example, it's true that the
particles had one spin up and one spin down, but they really don't choose
which one gets which spin, until the measurement! There are two available
configurations (up-down or down-up), and the initial state mixes both of
them!)

Understanding superposition-of-states, understanding the actual experiments with Bell's Theorem, and following the debate - which continues even today - about what quantum states really mean, is a big task. I hope this answer helps a little bit. You'll have to do lots of reading (and, ideally, actual problem-solving) to really get a grip on these things. In particular, understanding how a "mixed state" really behaves (and how it differs from a "well-defined state that nobody has measured yet") is a challenge, but a surmountable one!

- Try a MadSci search on the terms: "Bell Paradox", "EPR", "nonlocality", or "quantum entanglement"
- A great book by an excellent author: "Quantum Reality" by Nick Herbert
- slightly mathematical treatment: click here.
- or a wordier treatment, here.
- The actual Bell thought-experiment is sometimes illustrated with a simple card game.
- Richard Feynman's lecture (you can find it on video or audio) on "The Great Conservation Laws" talks about why locality (i.e., the opposite of nonlocality) is a big deal.
- But of course it's worth learning quantum mechanics the old-fashioned way: from a textbook. I recently noticed an old one by Leonard Schiff which is excellent. But most of them (including whatever you have in Sweden) cover the basics well enough.

-Ben Monreal

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