Quantentheorie der Zeitmessung. II

Abstract

The possibility is discussed that the observable time may be described by a hermitian operator, which is maximal but not hypermaximal. The special example considered regards systems having a continuous energy spectrum with a lower bound. It is shown that in this case physical states can be constructed which are elements of the domain of definition of the time operator and which approximate its eigenfunctions with arbitrary accuracy. Hence time is observable within the limits of the precision of real measuring devices. The situation is thus very similar to that of physical quantities which correspond to hypermaximal operators with continuous spectrum. This suggests that v.Neumann's axiom stating that there is a one-to-one connection between observables and the hypermaximal operators of the Hilbert space of states, is too restrictive.