On Noncontextual, Non-Kolmogorovian Hidden Variable Theories

Feintzeig, Benjamin H. and Fletcher, Samuel C. (2017): On Noncontextual, Non-Kolmogorovian Hidden Variable Theories. In: Foundations of Physics, Vol. 47, No. 2: pp. 294-315

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 generalize a theorem of Feintzeig (Br J Philos Sci 66(4): 905-927, 2015) 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 experimental possibilities.

• Item Type: Journal article
• Faculties: Philosophy, Philosophy of Science and Religious Science > Munich Center for Mathematical Philosophy (MCMP)
• Subjects: 100 Philosophy and Psychology > 100 Philosophy; 500 Science > 510 Mathematics
• ISSN: 0015-9018
• Language: English