2025/04/23 by C. S. Unnikrishnan · 1 voice
Physics and Astronomy · Arts and Humanities · #Quantum Mechanics and Applications #Philosophy and History of Science #Advanced Thermodynamics and Statistical Mechanics
paper · doi:10.20935/acadquant7657
openalex publication_date 2025/04/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
The impossibility of making quantum mechanics deterministic by adding ‘hidden variables’ was discussed by J. von Neumann in 1932. His proof of the impossibility of dispersion-free ensembles was criticized as being logically circular, by Grete Hermann soon after, and as fundamentally flawed, by John Bell in 1964. Bell’s severe criticism and an explicit counter-example are generally considered as the definitive demonstration that J. von Neumann’s proof is inadequate. I show, without using the formalism of quantum mechanics, that J. von Neumann’s central assumption of the linear additivity of the expectation values, even for incompatible (noncommuting) observables, is a necessary consequence that follows directly from the fundamental conservation laws of physical quantities, applicable universally. With this result, J. von Neumann’s result is fully resurrected. I identify the physical reason why dispersion-free ensembles cannot exist. After discussing the conflict of Bell’s counter-example with the factual mechanics, I highlight the result that the local hidden variable theories, for which the Bell’s inequalities were derived, are grossly incompatible with the fundamental conservation laws. In a scrutiny of the vital difference between the ‘causal incompleteness’ of quantum mechanics, discussed by J. von Neumann, and the ‘representational incompleteness’ discussed by Einstein, Podolsky, and Rosen, I prove the striking demarcating result that a multi-particle system that is considered causally completed can remain EPR-incomplete. I identify the wave nature of the action as the reason behind the irreducible quantum dispersion and the impossibility of dispersion-free ensembles.