On the Separability of Physical Systems
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In the context of Bell-type experiments, two notions of “separability” emerge from the application of some simple considerations from information theory. The first of these applies to physical states construed as probability measures, while the second applies to states construed in terms of “elements of physical reality”. The former is found to be logically equivalent to the “completeness” constraint (a.k.a. “outcome independence” or “factorizabilility”) in Bell-type arguments. Moreover, it is found that there are theories that are separable in the first sense but which are empirically equivalent to no theory that is separable in the second sense. I offer some speculations about the significance of these and a few related results.
Bell's Theorem and the associated empirical tests of the Bell Inequalities are widely considered to reveal some strikingly non-classical features of our world. In the interest of trying to come to a fuller understanding of these features, I wish to propose some suggestions for how we might characterize the “separability” (or lack thereof) of systems in entangled states. For this purpose, I offer the following brief summary of the Bell milieu.1, 2
KeywordsProbability Function Entangle State Physical Reality Bell Inequality Bohmian Mechanic
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