Generalized uncertainty relations: theory, examples, and Lorentz invariance
From MaRDI portal
Publication:1356916
DOI10.1006/APHY.1996.0040zbMATH Open0881.47046arXivquant-ph/9507004OpenAlexW3105254144WikidataQ57741273 ScholiaQ57741273MaRDI QIDQ1356916
Author name not available (Why is that?)
Publication date: 16 June 1997
Published in: (Search for Journal in Brave)
Abstract: The quantum-mechanical framework in which observables are associated with Hermitian operators is too narrow to discuss measurements of such important physical quantities as elapsed time or harmonic-oscillator phase. We introduce a broader framework that allows us to derive quantum-mechanical limits on the precision to which a parameter---e.g., elapsed time---may be determined via arbitrary data analysis of arbitrary measurements on identically prepared quantum systems. The limits are expressed as generalized Mandelstam-Tamm uncertainty relations, which involve the operator that generates displacements of the parameter---e.g., the Hamiltonian operator in the case of elapsed time. This approach avoids entirely the problem of associating a Hermitian operator with the parameter. We illustrate the general formalism, first, with nonrelativistic uncertainty relations for spatial displacement and momentum, harmonic-oscillator phase and number of quanta, and time and energy and, second, with Lorentz-invariant uncertainty relations involving the displacement and Lorentz-rotation parameters of the Poincar'e group.
Full work available at URL: https://arxiv.org/abs/quant-ph/9507004
No records found.
No records found.
This page was built for publication: Generalized uncertainty relations: theory, examples, and Lorentz invariance
Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q1356916)
