This essay is about two properties that some theories of physics have — determinism and locality — and the gaps that can exist between how they are understood as properties of physical reality, how they are understood as properties of mathematical theories, and how they are formally defined as properties of mathematical theories. I will point out one such gap that seems to have gone widely unremarked, and that could admit an interesting class of physical theories. On the other hand, for readers already well acquainted with Bell's Theorem, it may be helpful to know up front that, ultimately, I will identify a particular class of mathematical theories that have a sort of locality —mathematical locality, but not apparently physical locality— but that do not satisfy the assumptions of the Theorem and therefore are not constrained by Bell's Inequality (and no, this is not related to Joy Christian's work; I'm going to take an orthodox view of Bell's Theorem).
Review of Modern Physics 1986 The interpretational problems of quantum mechanics are considered. The way in which the standard Copenhagen Interpretation (CI) of quantum mechanics deals with these problems is reviewed. A new interpretation of the formalism of quantum mechanics, the Transactional Interpretation (TI), is presented. The basic element of TI is the transaction describing a quantum event as an exchange of advanced and retarded waves, as implied by the work of Wheeler and Feynman, Dirac, and others. The TI is explicitly nonlocal and thereby consistent with recent tests of the Bell Inequality, yet is relativistically invariant and fully causal. A detailed comparison of the TI and CI is made in the context of well known quantum mechanical gedanken experiments and "paradoxes". The TI permits quantum mechanical wave functions to be interpreted as real waves physically present in space rather than as "mathematical representations of knowledge" as in the CI.