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Bell's Theorem and Locally-Mediated Reformulations of Quantum Mechanics
Bell's Theorem rules out many potential reformulations of quantum mechanics,
but within a generalized framework, it does not exclude all "locally-mediated"
models. Such models describe the correlations between entangled particles as
mediated by intermediate parameters which track the particle world-lines and
respect Lorentz covariance. These locally-mediated models require the
relaxation of an arrow-of-time assumption which is typically taken for granted.
Specifically, some of the mediating parameters in these models must
functionally depend on measurement settings in their future, i.e., on input
parameters associated with later times. This option (often called
"retrocausal") has been repeatedly pointed out in the literature, but the
exploration of explicit locally-mediated toy-models capable of describing
specific entanglement phenomena has begun only in the past decade. A brief
survey of such models is included here. These models provide a continuous and
consistent description of events associated with spacetime locations, with
aspects that are solved "all-at-once" rather than unfolding from the past to
the future. The tension between quantum mechanics and relativity which is
usually associated with Bell's Theorem does not occur here. Unlike conventional
quantum models, the number of parameters needed to specify the state of a
system does not grow exponentially with the number of entangled particles. The
promise of generalizing such models to account for all quantum phenomena is
identified as a grand challenge.Comment: 61 pages, 2 figures; accepted for publication by Rev. Mod. Phy
New Slant on the EPR-Bell Experiment
The best case for thinking that quantum mechanics is nonlocal rests on Bell's
Theorem, and later results of the same kind. However, the correlations
characteristic of EPR-Bell (EPRB) experiments also arise in familiar cases
elsewhere in QM, where the two measurements involved are timelike rather than
spacelike separated; and in which the correlations are usually assumed to have
a local causal explanation, requiring no action-at-a-distance. It is
interesting to ask how this is possible, in the light of Bell's Theorem. We
investigate this question, and present two options. Either (i) the new cases
are nonlocal, too, in which case action-at-a-distance is more widespread in QM
than has previously been appreciated (and does not depend on entanglement, as
usually construed); or (ii) the means of avoiding action-at-a-distance in the
new cases extends in a natural way to EPRB, removing action-at-a-distance in
these cases, too. There is a third option, viz., that the new cases are
strongly disanalogous to EPRB. But this option requires an argument, so far
missing, that the physical world breaks the symmetries which otherwise support
the analogy. In the absence of such an argument, the orthodox combination of
views -- action-at-a-distance in EPRB, but local causality in its timelike
analogue -- is less well established than it is usually assumed to be.Comment: 26 pages, 7 figures; extensively revised for resubmissio
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