From: atems@igor.physics.wayne.edu (Dale Atems)
Subject: Re: hidden variables
Organization: Wayne State University, Detroit, MI
Date: Sat, 23 Jan 1993 17:50:12 GMT

In article <508@mtnmath.UUCP> paul@mtnmath.UUCP (Paul Budnik) writes:
>In article <1993Jan21.020948.24425@cs.wayne.edu>, atems@igor.physics.wayne.edu
(Dale Atems) writes:
>>[...]
>> >Just consider the simple case of a photon traversing a reflective
>> >polarizer. The wave function for this experiment exists on both sides of
>> >the polarizer until and unless the photon is detected. If we assume there
>> >is a microscopic event corresponding to the photon traversing the polarizer
>> >then we must assume that the wave function on the other side of the polarize
r
>> >will go to 0 when this event occurs. But we will get the wrong answer if we
>> >do that. [...]
>>
>> The answer to what question? [...]
>
>The answer to the question of what is the probability of observing the
>photon on either side of the polarizer.
 
I was going to drop this whole line of discussion as it seems to me
that you are deliberately distorting what I am saying, but on the
chance that the confusion in this example is genuine, and perhaps
even germane, I will reply.
 
I disagree that the statement that a microscopic event occurs when a
photon traverses a polarizer implies that the photon's wave function
collapses at that point. In the case of polarization by reflection,
the reflected and transmitted waves are in distinct polarization
states. At the Brewster angle, for instance, the reflected wave
is a pure linearly polarized state while the transmitted wave is
a superposition of linearly polarized states. Something has clearly
happened to the photon's wave function on encountering the polarizer
even though that something is not collapse.
 
To return to the case of a photon traversing a linear polarizer,
suppose that the photon is already linearly polarized, say along x,
and the polarizer's transmission axis is along x' making an angle @
with x. One can write the spin part of the photon wave function
on the near side of the polarizer as
 
      |psi> = |x> = cos@ |x'> + sin@ |y'> .
 
Now in the vicinity of the polarizer the exact photon wave function
is undefined as we are dealing with a superposition of correlated
photon-polarizer states. To make this concrete, let |0> refer to
a polarizer that has passed a photon and |+> be a polarizer that
has absorbed it (the '+' meaning that an atom or whatever in the
polarizer has been excited). Then at the polarizer we have
 
      |psi> = cos@ |x',0> + sin@ |y',+> .
 
This is greatly oversimplified, of course, as a passed photon may
really have been absorbed and reemitted, etc, i.e. I am making no
assumptions about the exact nature of the microscopic event. 
 
The point I am trying to make is that while the wave function does
not collapse at the polarizer, only the first term emerges. The
probability that the photon will reach a detector at a distance
L behind the polarizer is (cos@)^2 -- this is essentially Malus's
law.  If we change the polarizer angle at some time, the change in
detection probability will show up L/c later. This is a clear and
unambiguous prediction of wave optics.
 
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.

------
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