1210.7659 (David Ellerman)

The Objective Indefiniteness Interpretation of Quantum Mechanics    [PDF]

David Ellerman

The common-sense view of reality is expressed logically in Boolean subset logic (each element is either definitely in or not in a subset, i.e., either definitely has or does not have a property). But quantum mechanics does not agree with this "properties all the way down" picture of micro-reality. Are there other coherent alternative views of reality? A logic of partitions, dual to the Boolean logic of subsets (partitions are dual to subsets), was recently developed, and it immediately yields a logical version of information theory. In view of the subset-partition duality, partition logic is the alternative logic that abstractly describes an alternative view of micro-reality. When this mathematics of partitions is "lifted" to vector spaces, then it yields the mathematics of quantum mechanics. Thus the vision of micro-reality suggested by partition logic seems to match that described by quantum mechanics. The key concept explicated by partition logic is the old idea of "objective indefiniteness" (emphasized by Shimony). Thus partition logic, logical information theory, and the lifting program provide the "back story" so that the old idea then yields the objective indefiniteness interpretation of quantum mechanics.

View original: http://arxiv.org/abs/1210.7659