NetNews Usenet Archive 1993 #3/NN_1993_3.iso/spool/sci/physics/23410

Text File | 1993-01-25 | 3.3 KB | 72 lines

Newsgroups: sci.physics
Path: sparky!uunet!wupost!cs.uiuc.edu!vela!wsu-cs!igor.physics.wayne.edu!atems
From: [e-mail] (Dale Atems)
Subject: Re: hidden variables
Message-ID: <[e-mail]>
Sender: [e-mail] (Usenet News)
Organization: Wayne State University, Detroit, MI
References: <[e-mail]> <[e-mail]> <[e-mail]>
Date: Mon, 25 Jan 1993 05:51:32 GMT
Lines: 60

In article <[e-mail]> [e-mail] (Paul Budnik) writes:
>In article <[e-mail]>, [e-mail]
(Dale Atems) writes:
>> [...]
>> Please explain to me what you find wrong with this picture, and/or
>> why it can't be applied to singlet state photons in an Aspect-
>> type experiment.
>>
>There is nothing wrong with the description you provided for a single
>photon. The reason it does not apply to the singlet state case is that
>all the changes you described can be modeled by the Schrodinger equation.
>They do not represent a change in state of the photon but only describe
>how the wave function evolves in time and space. Because the
>evolution of the wave function as governed by the Schrodinger
>equation is local you cannot use it to model what happens in the
>singlet state case. If you could the relativistic Schrodinger equation
>would not be Lorentz invariant. You would have distant changes in
>polarizer angles instantaneously changing the structure of the physically
>distant wave function.

Well, here is a rather half-baked proposal based on what I said
earlier. Let the left and right kets in the singlet state vector
be in the internal spaces of *distant* wavefronts. I have in mind
wavefronts corresponding to distinct photons; thus they are emitted
simultaneously in opposite directions. As each wavefront encounters
a polarizer, expand its kets in a basis aligned with that polarizer.
The encounters need not be simultaneous, but the result is that the
relative angle @ in the formula

      |psi> = 2^(-1/2) (cos@ |x>|x'> + sin@ |x>|y'>
                       -sin@ |y>|x'> + cos@ |y>|y'>)

is the angle between the polarizers at the time the two encounters
occur in a reference frame in which they are simultaneous. In the
simplest case the polarizers and detectors are symmetrically placed
relative to the source and the encounters are simultaneous in the
lab frame; let's consider that case.

Now each wavefront interacts only with the *local* polarizer,
transforming the state vector into

      |psi> = 2^(-1/2) (cos@ |x,0>|x',0> + sin@ |x,0>|y',+>
                       -sin@ |y,+>|x',0> + cos@ |y,+>|y',+>)

using the notation in my last post. The first term emerges from
both polarizers, the second term emerges from the left polarizer
but not the right, etc. No nonlocal interactions, and the joint
detection probability and timing are well-defined.

I have no idea if this can be made mathematically rigorous in
the wave equation formalism. I think it is in the spirit of the
QM description and shows that, at least on the conceptual level,
one need not invoke collapse or nonlocal interactions to obtain
the expected probabilities and timing.

------
Dale Atems
Wayne State University, Detroit, MI
Department of Physics and Astronomy
[e-mail]