Positive Wigner functions, local hidden variables, and violation ofBell's inequality

A non-negative Wigner function of the EPR state allows violation of Bell's inequality for correlations of spin-like operators. We study this in view of the often stated association of the Wigner function with a distribution function in phase space, i.e., with a probability distribution of local hidden variables. We discuss the limitation to this interpretation of the Wigner function through its relation to the dynamical variables considered. We conclude that Bell's inequality hinges on the assumption that the dynamical variables of the theory have definite values, whether they can or cannot be measured simultaneously.