Skip to main content
OSTI.GOVU.S. Department of Energy Office of Scientific and Technical Information
U.S. Department of Energy
Office of Scientific and Technical Information
 

A retrospective review of von Neumann’s analysis of hidden variables in quantum mechanics

Journal Article · · Academia quantum
 [1];  [2]
  1. North Carolina State University, Raleigh, NC (United States)
  2. Yale Univ., New Haven, CT (United States)
+ Show Author Affiliations
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.
Research Organization:
North Carolina State University, Raleigh, NC (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Nuclear Physics (NP)
Grant/Contract Number:
FG02-97ER41042
OSTI ID:
3010149
Journal Information:
Academia quantum, Journal Name: Academia quantum Journal Issue: 1 Vol. 1; ISSN 3064-979X
Publisher:
Academia.edu JournalsCopyright Statement
Country of Publication:
United States
Language:
English

References (9)

On the impossible pilot wave journal October 1982
Von Neumann’s ‘No Hidden Variables’ Proof: A Re-Appraisal journal June 2010
von Neumann’s Theorem Revisited journal June 2021
Von Neumann’s impossibility proof: Mathematics in the service of rhetorics journal November 2017
A Suggested Interpretation of the Quantum Theory in Terms of "Hidden" Variables. I journal January 1952
On the Problem of Hidden Variables in Quantum Mechanics journal July 1966
Hidden variables and the two theorems of John Bell journal July 1993
Von Neumann's Hidden-Parameter Proof journal August 1961
Grete Hermann as Neo-Kantian Philosopher of Space and Time Representation journal February 2018

Similar Records

A proof of von Neumann's postulate in Quantum Mechanics
Journal Article · Tue May 04 00:00:00 EDT 2010 · AIP Conference Proceedings · OSTI ID:21367264
INDETERMINATE CHARACTER OF THE REDUCTION OF THE WAVE PACKET IN QUANTUM THEORY
Journal Article · Sat Mar 31 23:00:00 EST 1962 · Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D · OSTI ID:4830908
Context-invariant quasi hidden variable (qHV) modelling of all joint von Neumann measurements for an arbitrary Hilbert space
Journal Article · Sun Mar 15 00:00:00 EDT 2015 · Journal of Mathematical Physics · OSTI ID:22403119

Related Subjects

density matrix
hidden variables
history
quantum statistics