The impossibility of experimental testing of the hidden variables theory

Shasanka Mohan Roy, Virendra Singh

Gijs Leegwater

S. J. Freedman, Richard A. Holt, Costas D. Papaliolios

Yasuo Yoshihuku

It is investigated whether different kinds of hidden variables can be consistently included in a theory in the experimental situation where two correlated photons undergo Compton scattering or are subjected to linear polarizers. We show that it is impossible to make a theory of hidden variables which predetermine simultaneously the linear polarization of one of the photons and the direction into which the other photon will ultimately be scattered.

Stanley Gudder

Robert Golub, S. K. Lamoreaux

This article reviews the history of J. von Neumann’s analysis of hidden variables in quantum mechanics and the subsequent analysis by others. In his book The Mathematical Foundations of Quantum Mechanics, published in 1932, von Neumann performed an analysis of the consequences of introducing hidden parameters (hidden variables) into quantum mechanics. He arrived at two principal conclusions: first, hidden variables cannot be incorporated into the existing theory of quantum mechanics without major modifications, and second, if they did exist, the theory would have already failed in situations where it has been successfully applied. This analysis has been taken as an “incorrect proof” against the existence of hidden variables, possibly due to a mistranslation of the German word prufen. von Neumann’s so-called proof isn’t even wrong as such a proof does not exist, but it is an examination of the limitations imposed by internal consistency of the Hilbert space formulation of the theory. One of the earliest attempts to eliminate uncertainty, by D. Bohm, requires a major modification of quantum mechanics (observables are not represented by Hermitian operators), which supports von Neumann’s first principal conclusion. However, testing the Bohm theory requires constructing a physically impossible initial state. As such, the theory has no experimental consequences, so W. Pauli referred to it as an “uncashable check”. As there are no observable consequences, the Bohm theory is possibly a counterexample to von Neumann’s second conclusion that hidden variables in particular would have already led to a failure of the theory.