Time in quantum measurements

The nonidealized statistical-mechanics description of quantum measurements developed by Blankenbecler and Partovi (1985) on the basis of a maximum-uncertainty principle is generalized to treat measurements at more than one time. Uncertainty relations between momentum and time and between energy and time are derived analytically as consequences of the canonical commutation relations and discussed. A lower limit of 1/2 is determined for the product of the measurement duration (as determined by an external clock of arbitrary precision) and the energy dispersion of a free particle, and also for the product of the energy and time dispersions of any system used as a clock. (T.K.)