From: danforth@riacs.edu (Douglas G. Danforth)
Subject: Re: Hidden variable theories
Organization: RIACS, NASA Ames Research Center
Date: Sun, 13 Sep 92 23:15:44 GMT


   
The discussion of "causality" (in whatever its forms) has been triggered
in this news group by the assumption that Bell's inequality is the final
word on objective local theories.  By "local" I mean what Clauser and
Shimmony mean [Clauser, J. and A. Shimony (1978). Bell's theorem:
experimental tests and implications. Rep. Prog. Phys. 41, 1881-1927] that
"a deterministic hidden-variables theory is local if for all a and b and all
v we have:

(A(a)B(b))(v) = A(a,v)B(b,v).

That is, once the state v is specified and the particles have separated,
measurements of A can depend only upon v and a but not b. Likewise
meausrements of B depend only upon v and b."

Since Aspect's 1982 experiment [Aspect, A. (1982). Experimental Realization
of Einstein-Podolsky-Rosen-Bohm Gedankenexperiment: A New Violation of Bell's
Inequalities. Physical Review Letters, Vol 49,No.2,P91] agree's with the
QM predictions and violates Bell's inequality it is assumed that objective
local theories have been ruled out.

This is not true as briefly mentioned by Mermin on pages 167-169 of his
book [Mermin, N. D. (1990), Boojums All the Way Through. Cambridge: Cambridge
University Press]. He says, "detecting the presence of a single photon is not
an easy feat to accomplish, and the detectors do not always fire when a
photon enters. In fact, more often than not, they fail to fire." and ... 
"So if you are stubborn, there is a way to explain the observed data with
instruction sets, one that can only be ruled out (assumming our current ideas
about photons and their detectors are in fact correct) by designing photon
detectors so efficient as to leave no room for such a loophole."

Mermin had just finished explaining how a nondetection state X could be
coupled with red (R=+) and green (G=-) detection states to give the
QM predictions for 3 discrete measurement angles.

It is possible to extend Mermin's analysis (which he attributes to Kenneth
Brownstein) to hold for all measurement angles.  When one does this one
sees that there is no special "conspiracy" needed.  One need only have
an attribute of a photon that is sensitive to the mismatch between the
photon's polarization and the angle of measurement of the detector on
which the photon is impinging.  If the mismatch is too great and the 
photon is in a "sensitive" state then the photon is simply not observed.
The photon knows nothing about what is happening at the other remote
detector.

When a photon is not observed there is a "hole" in the data stream from a
detector. When the data from both detectors is analyzed, a hole in one stream
forces the exclusion of the datum in the other stream. Aspect conditionalizes
his experiment on the JOINT detection of photons. The correlation function is
calculated on the conditionalized data of joint detection. It is this
conditionalization process that increases the correlation between the data
streams to the point that the QM correlation can be realized.

If the number of holes drops to less than 18% of the data then the QM
correlation can not be reproduced using the previously mentioned extension 
of Mermin's analysis (18% is the fraction of misses out of the total number
of impingments on a detector.  Since this is not directly observable one
must use the fraction of joint detections given a single detection.  This
number for the mentioned model is 23% misses).

Until paired photon experiments of sufficient efficiency have been carried
out, it is premature to consider issues of "causality".

Doug Danforth
Newsgroups: sci.physics