The Statistical Interpretation of Quantum Mechanics

1970/10/01 by L. E. Ballentine · 1 voice · 13 citations
Arts and Humanities · Chemistry · Mathematics · Physics and Astronomy · #Computer science #Consistent histories #EPR paradox #Hidden variable theory #History and advancements in chemistry #Interpretation (philosophy) #Interpretations of quantum mechanics #Mathematical economics #Mathematics #Minority interpretations of quantum mechanics #Outcome (game theory) #Philosophy and History of Science #Physics #Quantum #Quantum Mechanics and Applications #Quantum dynamics #Quantum entanglement #Quantum mechanics #Quantum probability #Quantum process #Quantum statistical mechanics #Relational quantum mechanics #Statistical physics #Stochastic interpretation #Theoretical physics

paper · doi:10.1103/revmodphys.42.358

openalex publication_date 1970/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The Statistical Interpretation of quantum theory is formulated for the purpose of providing a sound interpretation using a minimum of assumptions. Several arguments are advanced in favor of considering the quantum state description to apply only to an ensemble of similarily prepared systems, rather than supposing, as is often done, that it exhaustively represents an individual physical system. Most of the problems associated with the quantum theory of measurement are artifacts of the attempt to maintain the latter interpretation. The introduction of hidden variables to determine the outcome of individual events is fully compatible with the statistical predictions of quantum theory. However, a theorem due to Bell seems to require that any such hidden-variable theory which reproduces all of quantum mechanics exactly (i.e., not merely in some limiting case) must possess a rather pathological character with respect to correlated, but spacially separated, systems.

Citations

• Generalized Phase-Space Distribution Functions
• Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?
• Zur Quantenmechanik der Sto�vorg�nge
• The Uncertainty Principle
• On the Problem of Hidden Variables in Quantum Mechanics
• Die gegenw�rtige Situation in der Quantenmechanik
• �ber den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik
• Albert Einstein—Philosopher-Scientist
• On the Formation of Quantum-Mechanical Operators
• Quantum mechanics as a statistical theory
• A Suggested Interpretation of the Quantum Theory in Terms of "Hidden" Variables. I
• Can Quantum-Mechanical Description of Physical Reality be Considered Complete?
• On the Quantum Correction For Thermodynamic Equilibrium

Cited by

• Facts, Values and Quanta
• Probabilistic analysis of three-player symmetric quantum games played using the Einstein–Podolsky–Rosen–Bohm setting
• Quantitative probing of the quantum–classical transition for the arrival time distribution
• Classical interventions in quantum systems. I. The measuring process
• Chronogenesis, Cosmogenesis and Collapse
• Bifurcation and chaos in nonlinear Lindblad equations
• The transactional interpretation of quantum mechanics
• Equilibrium stationary coherence in the multilevel spin-boson model
• Do we really understand quantum mechanics? Strange correlations, paradoxes, and theorems
• Quantum information and relativity theory
• Measurement, Interpretation and Information
• Copenhagen interpretation [wikipedia]
• Quantum mechanics [wikipedia]

Discussions

• This could sound an elementary question, but the more I think about it, more convinced I am that there could be a different perspective. I seriously doubt about what is called "wave particle duality" [stackexchange, -1 points]