Constrained event space and properties of the physical time observable

¹ Institute of Physics, University of Belgrade - P.O. Box 68, 11000 Belgrade, Serbia
² Vinca Institute of nuclear sciences - P.O. Box 522, 11001 Belgrade, Serbia

^a buric@ipb.ac.rs

Received: 6 May 2011
Accepted: 12 December 2011

Abstract

It is demonstrated that the important common property of operators representing various observable times in quantum mechanics, namely the fact that such an operator is always given by a nonorthogonal resolution of unity, can be obtained from a constraint on the possible physical events, i.e. on the extended space of the Hamiltonian formulation of the parametric dynamics. Operators which could generate meaningful probability distributions for various time measurements are suggested.