Time in Quantum Measurements

Our formalism for describing quantum measurements is generalized to the multitime case and used to derive rigorous time-energy uncertainty relations. For a free particle, we find that $T\delta H\ge \frac{1}{2}$, where $\delta H$ is the dispersion in energy and $T$ is the measurement duration as given by an external clock of arbitrarily high accuracy. Moreover, any system used as a clock obeys $\delta t\delta H\ge \frac{1}{2}$, where $\delta t$ is the dispersion in the values of time as measured by the system.