Hidden Variables: Rehabilitation of von Neumann's Analysis, and Pauli's Uncashable Check
arxiv(2024)
Abstract
In his book The Mathematical Foundations of Quantum Mechanics,
published in 1932, J. von Neumann performed an analysis of the consequences of
introducing hidden parameters (hidden variables) into quantum mechanics. He
showed that hidden variables cannot be incorporated into the existing theory of
quantum mechanics without major modifications, and concluded that if they did
exist, the theory would have already failed in situations where it has been
successfully applied. von Neumann left open the possibility that the theory is
not complete, and his analysis for internal consistency is the best that can be
done for a self-referenced logical system (Gödel's theorem). This analysis
had been taken as an “incorrect proof" against the existence of hidden
variables. von Neumann's so-called proof isn't even wrong as such a proof does
not exist. One of the earliest attempts at a hidden variable theory was by D.
Bohm, and because there were no experimental consequences, W. Pauli referred to
it as an “uncashable check." To our knowledge, a successful hidden variable
extension to quantum mechanics with testable consequences has not yet been
produced, suggesting that von Neumann's analysis is worthy of rehabilitation,
which we attempt to provide in a straightforward manner.
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