From: jlg@cochiti.lanl.gov (Jim Giles)
Newsgroups: sci.physics
Subject: Re: Defining local, causal etc., was: Hidden variable theories
Date: 2 Oct 92 19:18:19 GMT
Article-I.D.: newshost.1992Oct2.191819.29150
Organization: Los Alamos National Laboratory

In article <1992Oct1.224027.8421@lmpsbbs.comm.mot.com>, bhv@areaplg2.corp.mot.com (Bronis Vidugiris) writes:
|> [...]
|> Anyway, if you set up an experiment with a pair of photons in the 'singlet'
|> state (i.e. opposite spins) and measure the spin of  both photons along
|> an arbitrary axis with an angle from the vertical of theta1 (for detector1)
|> and theta2 (for detector2)
|> 
|> detector 1     <======     source           =======>    detector 2
|> 
|> 
|> you get the following result from QM
|> 
|> p(theta1,theta2) = p1(delta) = cos^2(theta2-theta1)

This is actually:

   p(theta1,theta2) = p1(delta) = cos^2(theta2-theta1)/2
                                                      ^^

Otherwise, just by lining up the two detectors, *all* the photons
must start being detected!  And we know that each observer actually
only sees *half* the photons on average.

Note also that the above predicts a probability *distribution*.  It
does not predict specific events.  There is no reason to expect that
the photons are each - individually - reifications of the function
at all.

|> [...]
|> However, Bell has shown that any local realistic theory must follow
|> the relationship.
|> 
|> 1-p2(2*delta) <= 1 - 2*p2(delta)

Yes, you can rule out theories that have certain formal properties.
That doesn't mean that you must resort to reification of mathematical
abstractions!  It means that certain theories have been falsified.
If this leaves us *without* any complete theory, the correct thing
to say is that we don't know!  As it happens, we have a perfectly
good *descriptive* theory or the behavior of QM systems' statistics:
which (in some ways) has been the most thoroughly validated ever.  
The EPR "paradox" (assuming that whatever questions about detector 
efficiency are resolved) rules out certain *explanatory* theories - 
and suggests *no* testable alternatives.

|> [...]
|> Anyway, there *is* a way to distinguish between the two condtions I
|> was describing.  Local Realistic theories predict that you will have a
|> constraint on p1(delta).  A simple 'speed-of-light-collapse' theory predicts
|> that p1(delta) *will* change its value when the spins are measured in a
|> 'timelike' manner (i.e within a lightcone) vs a 'spacelike' manner.

This is like being able to distinguish between "leprechauns 
have red  hair" and "leprechauns have green hair" without first 
demonstrating that leprechauns exist at all!  (You might put a 
very sensitive camera in a field, tuned to detect even the 
slightest hint of red in the image - you don't seen any, so 
any leprechauns in there must have been camouflaged against 
the leaves in the field.)  While this may have some value as 
a logical or mathematical exercise, it doesn't really have any 
scientific value.  The problem is that neither "theory" is really 
a theory at all - it is a speculation, an interpretation, a thought 
experiment involving events whose very existance can't be demonstrated.

-- 
J. Giles