An Intuitive Logic for Modeling Non-Local Hidden Variable Problems

Abstract We present a notion of an un-measurable state, which we call an Anti-state and derive a simple and intuitive logic for Anti-states. Anti-states are then used to generate structures, which we call Anti-Structures. Theorems 3.25 and 4.2 yield that Anti-Structures are able to model the context changes (and inconsistencies of measured values), occurring in quantum mechanics, where Kochen and Specker in [5] showed these were un-modellable with local hidden variables. In our Examples 3.28, 4.3, and 4.7 , we show that, respectively, the orthohelium experiment (outlined in Kochen, Specker [5]), wave functions, and entanglement all have Anti-Structure models. Our results give a good contrast to the results of Kochen and Specker [5], and establish a limitation on self reference for partial Boolean algebras. This limitation is not held by Anti-Structures in general, and also does not seem to be a limitation that should be put on our physics. The theorems and examples of this paper lead to a series of questions regarding the expressiveness and a measure of contrivance for models of quantum mechanics.