"Time in Quantum Physics: From an external parameter to an intrinsic observable"
10/21/2013Special guest in our Physics Colloquium: Prof. Dr. Klaus Fredenhagen, (Universität Hamburg, II. Institut für Theoretische Physik)
Abstract:
An old An old problem of quantum physics is the description of time measurements by quantum mechanical observables. In the Schrödinger equation time plays a distinguished role as an external parameter. The Schrödinger equation may be understood as a constraint in an extended system where time is considered as an additional degree of freedom. The difficulty with this concept is that there are no normalizable solutions of the constraint, thus the standard probability interpretation of states is not possible.
We show that one can instead interpret the solutions in terms of conditional probabilities. Two interesting cases are considered: The first one fixes a time interval and determines probabilities of observables under the condition that the time parameter has a certain value. This corresponds to the standard interpretation of solutions of the Schrödinger equation. The second one asks for events which last only a finite time. An example is the stay of a freely moving particle within a finitely extended region. Under the condition that such an event takes place one can compute the probability distribution of the time variable; this is interpreted as the probability distribution of the instances of time at which the selected event takes place. The general concept is illustrated in simple examples.
