TITLE:
Logical Difficulty from Combining Counterfactuals in the GHZ-Bell Theorems
AUTHORS:
Louis Sica
KEYWORDS:
HZ-Theorem; Bell-Theorem; Noncommutation; Counterfactual; Hidden Variables; Locality; Nonlocality
JOURNAL NAME:
Applied Mathematics,
Vol.4 No.10C,
October
23,
2013
ABSTRACT: In eliminating the fair sampling assumption, the
Greenberger, Horne, Zeilinger (GHZ) theorem is believed to confirm Bell’s
historic conclusion that local hidden variables are inconsistent with the
results of quantum mechanics. The GHZ theorem depends on predicting the results
of sets of measurements of which only one may be performed. In the present
paper, the noncommutative aspects of these unperformed measurements are
critically examined. Classical examples and the logic of the GHZ construction
are analyzed to demonstrate that combined counterfactual results of
noncommuting operations are in general logically inconsistent with performed
measurement sequences whose results depend on noncommutation. The
Bell theorem is also revisited in the light of this result. It is concluded
that negative conclusions regarding local hidden variables do not follow
from the GHZ and Bell
theorems as historically reasoned.