From: scerir (scerir@libero.it)
Date: Thu Oct 11 2001 - 01:04:51 MDT
Adrian Tymes wrote:
> The entangled two particles have a property, spin, that is guaranteed
> to be opposite. Whatever the one particle's spin is or becomes, the
> other is immediately the opposite. If all you do is measure it, then
> that's like picking one ball out of a bag that has a white and a black
> ball, then being able to instantly determine from your ball what the
> other ball's color is, no matter how far away it is.
Yes, but you don't need entangled particles. One electron
is enough, as pointed out by L. de Broglie (1959).
de Broglie's paradox.
Consider a box B with *reflecting* walls.
The box B can be divided in two boxes B1, B2
by a double sliding reflecting partition. Initially the
box B contains an electron. Then the box B is divided
into B1 (taken to Paris) and B2 (taken to Tokyo).
The new situation is described by 2 w.f., one defined
in the volume V(B1), the other in the volume V(B2).
The original w.f. was defined in volume V(B).
Let's be P(B1) the probability for finding the
electron in B1 and P(B2) the probability for finding
the electron in B2. Before measurement, for QM, our
electron is in B1 *and* in B2. After measurement
our electron is in B1 *or* in B2. In detail. An observation
is performed in Paris at time T_0 and the electron is
found in B1. For T > T_0 the probability P(B2) of
observing the electron in B2 (in Tokyo) must be zero.
But P(B2) is given by the integral over V(B2) of the
squared modulus of the w.f. in V(B2). Thus the vanishing
of P(B2), at T > T_0, implies the vanishing of the
w.f. in V(B2).
Most physicists would say that the electron observed in Paris
at T_0 was *already* there. And that those 2 w.f. represented
just our *knowledge* prior to that observation.
Note that de Broglie's paradox exists only for physicists
who insist on a realistic philosophy (particles exist
objectively) and not for positivists (it makes no sense
to talk about an un-observed particle).
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