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A Bell Inequality Analog in Quantum Measure Theory
One obtains Bell's inequalities if one posits a hypothetical joint
probability distribution, or {\it measure}, whose marginals yield the
probabilities produced by the spin measurements in question. The existence of a
joint measure is in turn equivalent to a certain causality condition known as
``screening off''. We show that if one assumes, more generally, a joint {\it
quantal measure}, or ``decoherence functional'', one obtains instead an
analogous inequality weaker by a factor of . The proof of this
``Tsirel'son inequality'' is geometrical and rests on the possibility of
associating a Hilbert space to any strongly positive quantal measure. These
results lead both to a {\it question}: ``Does a joint measure follow from some
quantal analog of `screening off'?'', and to the {\it observation} that
non-contextual hidden variables are viable in histories-based quantum
mechanics, even if they are excluded classically.Comment: 38 pages, TeX. Several changes and added comments to bring out the
meaning more clearly. Minor rewording and extra acknowledgements, now closer
to published versio