From: atems@igor.physics.wayne.edu (Dale Atems)
Subject: Re: The instantaneous transfer of information in QM calculations
Organization: Wayne State University, Detroit, MI
Date: Mon, 11 Jan 1993 03:11:32 GMT

In article <484@mtnmath.UUCP> paul@mtnmath.UUCP (Paul Budnik) writes:
>In article <1993Jan10.164016.16419@cs.wayne.edu>, atems@igor.physics.wayne.edu (Dale Atems) writes:
>> This is certainly not true of the spin-1/2 analog. I can do that
>> calculation using only the "linear" part of QM, and the prediction is
>> valid as interaction with Stern-Gerlach magnets does not affect the
>> spin part of the wave function. The predicted correlations depend only
>> on the singlet state wave function before detection; what happens to the
>> wave function as a result of detection is not relevant.
>
>Then you will not be able to prove Bell's inequality is violated. It is
>important to understand that tests of Bell's inequality involve more than
>just two detections. They also involve a knob or device for affecting those
>detections. In the photon case it is a polarizer. In the case your describe
>it would be some apparatus that would force the spin to be aligned along
>a certain axis if a detection is made. You will only be able to prove
>the expected correlations violate Bell's inequality if the measurement
>or alignment of the spin of one particle influences the probability of
>detection of the other. Since these two events, the alignment of the spin
>of one particle and the detection of the other are space-like separated,
>the only law of physics that would predict such an influence is some
>version of quantum collapse.

        |
        |\
        | \                                                  |
        |  \                                                 |
        |   \ ---                                    ---     |
        |     -----------------[ ]----------------------     |
        |     ---                                    --- \   |
        |   Magnet 1          Source             Magnet 2 \  |
        |                                                  \ |
        |                                                   \|
        |                                                    |
     Detector 1                                          Detector 2
       Site 1                                              Site 2
 
 
Consider an experimental setup designed to test the version of Bell's
inequality that applies to spin-half particles in the singlet state. The
particles are charged and are deflected by Stern-Gerlach magnets whose
orientation determines which component of spin we are measuring. Let's
say one deflector is oriented to determine the spin along unit vector a,
the other along unit vector b where the directions of a and b are
arbitrary. The place where the particle lands depends on which way it
was deflected and thus determines whether the measured component of
spin was + or -.
 
Bell's inequality for this situation takes the form of a relationship
between correlation functions < (S(1,a) S(2,b) > where S(i,a) is the
component of particle i's spin along a, and similarly for b. To determine
such a correlation function experimentally, *in principle* all you need
to do is repeat the experiment a sufficient number of times, measuring
the spins of both particles and forming the product S(1,a) S(2,b) for
each pair, sum the products and divide by the number of pairs detected.
I don't see where you need to assume anything about what happens to the
wave function of one particle after the other is detected. One simply
measures spin components and computes a statistical average.
 
Of course, a finding that the observed correlations violate Bell's
inequality says nothing about locality if they could have been produced
by an exchange of information. As I understand it, the basic
premise behind Bell's proof is that all components of each particle's
spin are fixed when the singlet state is prepared and do not change
afterward. I believe that the point to making the relevant intervals
space-like is to ensure that the spins cannot be prepared according
to the settings of the magnets by signals sent from the magnets to
the source, and cannot be changed during flight by signals sent
from one particle to the other, or from a magnet or detector to
the distant particle.

------
Dale Atems
Wayne State University, Detroit, MI
Department of Physics and Astronomy
atems@igor.physics.wayne.edu
Newsgroups: sci.physics,alt.sci.physics.new-theories,sci.skeptic,alt.alien.visitors,alt.paranormal