In an attempt to demonstrate that local hidden variables are mathematically possible, Pitowsky constructed "spin-[Formula: see text] functions" and later "Kolmogorovian models", which employs a nonstandard notion of probability. We describe Pitowsky's analysis and argue (with the benefit of hindsight) that his notion of hidden variables is in fact just super-determinism (and accordingly physically not relevant). Pitowsky's first construction uses the Continuum Hypothesis. Farah and Magidor took this as an indication that at some stage physics might give arguments for or against adopting specific new axioms of set theory. We would rather argue that it supports the opposing view, i.e., the widespread intuition "if you need a non-measurable function, it is physically irrelevant".In an attempt to demonstrate that local hidden variables are mathematically possible, Pitowsky constructed "spin-[Formula: see text] functions" and later "Kolmogorovian models", which employs a nonstandard notion of probability. We describe Pitowsky's analysis and argue (with the benefit of hindsight) that his notion of hidden variables is in fact just super-determinism (and accordingly physically not relevant). Pitowsky's first construction uses the Continuum Hypothesis. Farah and Magidor took this as an indication that at some stage physics might give arguments for or against adopting specific new axioms of set theory. We would rather argue that it supports the opposing view, i.e., the widespread intuition "if you need a non-measurable function, it is physically irrelevant".

arXiv:1606.06849Foundations of PhysicsNov 21, 20163 citations

Quantum violation of stochastic noncontextual hidden-variable theories

Shasanka Mohan Roy, Virendra Singh

We formulate stochastic noncontextual hidden-variable theories. In such theories the hidden state \ensuremath{\lambda} specifies not definite values, but expectation values A\ifmmode\bar\else\textasciimacron\fi{}(\ensuremath{\lambda}), . . . of observables A, . . . and noncontextuality means that A\ifmmode\bar\else\textasciimacron\fi{}(\ensuremath{\lambda}) is independent of which other commuting observables commuting with A are measured together with A. We show via Bell inequalities that such theories conflict with quantum theory and propose a two-photon experimental test. We also show that for a single particle of spin ( ${2}^{\mathit{n}}$ -1)/2, quantum violation of classical noncontextuality grows exponentially with n.We formulate stochastic noncontextual hidden-variable theories. In such theories the hidden state \ensuremath{\lambda} specifies not definite values, but expectation values A\ifmmode\bar\else\textasciimacron\fi{}(\ensuremath{\lambda}), . . . of observables A, . . . and noncontextuality means that A\ifmmode\bar\else\textasciimacron\fi{}(\ensuremath{\lambda}) is independent of which other commuting observables commuting with A are measured together with A. We show via Bell inequalities that such theories conflict with quantum theory and propose a two-photon experimental test. We also show that for a single particle of spin (${2}^{\mathit{n}}$-1)/2, quantum violation of classical noncontextuality grows exponentially with n.

Physical Review AOct 1, 199321 citations

Context Independence as a Statistical Property of Hidden Variable Theories

Federico Laudisa

International Journal of Theoretical PhysicsJan 1, 19980 citations

{2}^{\mathit{n}}

-1)/2, quantum violation of classical noncontextuality grows exponentially with n.