PIRSA:16010073

On Noncontextual, Non-Kolmogorovian Hidden Variable Theories

Feintzeig, B. (2016). On Noncontextual, Non-Kolmogorovian Hidden Variable Theories. Perimeter Institute. https://pirsa.org/16010073

Feintzeig, Benjamin. On Noncontextual, Non-Kolmogorovian Hidden Variable Theories. Perimeter Institute, Jan. 21, 2016, https://pirsa.org/16010073 

          @misc{ pirsa_PIRSA:16010073,
            doi = {10.48660/16010073},
            url = {https://pirsa.org/16010073},
            author = {Feintzeig, Benjamin},
            keywords = {Quantum Foundations},
            language = {en},
            title = {On Noncontextual, Non-Kolmogorovian Hidden Variable Theories},
            publisher = {Perimeter Institute},
            year = {2016},
            month = {jan},
            note = {PIRSA:16010073 see, \url{https://pirsa.org}}
          }

Benjamin Feintzeig

University of California, Irvine

Talk number
PIRSA:16010073
Collection
Talk Type
Subject
Abstract

One implication of Bell's theorem is that there cannot in general be hidden variable models for quantum mechanics that both are noncontextual and retain the structure of a classical probability space.  Thus, some hidden variable programs aim to retain noncontextuality at the cost of using a generalization of the Kolmogorov probability axioms.  We present a theorem to show that such programs are committed to the existence of a finite null cover for some quantum mechanical experiments, i.e., a finite collection of probability zero events whose disjunction exhausts the space of possibilities.  This serves as a kind of "no-go" theorem for these alternative, or generalized, probability theories.