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Generalized Uncertainty Relations: Theory, Examples, and Lorentz Invariance
Braunstein, S. L., Caves, C. M. and Milburn, G. J. (1995-07-01) Generalized Uncertainty Relations: Theory, Examples, and Lorentz Invariance.
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milburn1995.pdf
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milburn1995.pdf |
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| Title |
Generalized Uncertainty Relations: Theory, Examples, and Lorentz Invariance
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| Abstract/Summary |
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 Poincare group.
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| Keyword(s) |
Indeterminancy
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| Date |
1995-07-01
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| Subjects |
240201 Theoretical Physics
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| Author(s) |
Braunstein, S. L.
Caves, C. M.
Milburn, G. J.
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