Physics – Quantum Physics
Scientific paper
1995-07-07
Physics
Quantum Physics
39 pages of text plus one figure; text formatted in LaTeX
Scientific paper
10.1006/aphy.1996.0040
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 $N$ 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.
Braunstein Samuel L.
Caves Carlton M.
Milburn Gerald J.
No associations
LandOfFree
Generalized uncertainty relations: Theory, examples, and Lorentz invariance does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Generalized uncertainty relations: Theory, examples, and Lorentz invariance, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Generalized uncertainty relations: Theory, examples, and Lorentz invariance will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-565204