An Indeterminacy Relation for Several Observables and Its Classical Interpretation

1934/11/01 by H. P. Robertson · 7 citations
Physics and Astronomy · Medicine · Mathematics · #Quantum Mechanics and Applications #Biofield Effects and Biophysics #Advanced Thermodynamics and Statistical Mechanics #Observable #Physics #Indeterminacy (philosophy) #Interpretation (philosophy) #Quantum mechanics #Theoretical physics #Mathematical physics #Mathematics #Philosophy

paper · doi:10.1103/physrev.46.794

openalex publication_date 1934/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/04/04

Abstract

An examination of the limitations placed by the conceptual structure of quantum mechanics on the simultaneous measurement of two or more observables leads, for the case of an even number m=2k of observables, to a quantitative estimate, depending only on the mean values of their commutators in the state in question, of the least value which the product of their m uncertanties may assume. This indeterminacy relation is interpreted classically to mean that, by measurement of these observables alone, a point (p, q) in phase space can be determined only to within a certain channel whose normal cross section, as measured by the value of the kth integral invariant taken over it, must be at least of order h^k.

Citations

• The Quantum Postulate and the Recent Development of Atomic Theory1
• �ber den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik

Cited by

• Entanglement verification for quantum-key-distribution systems with an underlying bipartite qubit-mode structure
• Certainty relations between local and nonlocal observables
• Born Reciprocity and the Granularity of Spacetime
• Heisenberg uncertainty relation for three canonical observables
• Generalized-mean Cramér-Rao bounds for multiparameter quantum metrology
• Uncertainty Relation and Inseparability Criterion
• State extended uncertainty relations
• Howard P. Robertson [wikipedia]