We consider a number of aspects of the problem of defining time observables in quantum
theory. Time observables are interesting quantities in quantum theory because they often
cannot be associated with self-adjoint operators. Their definition therefore touches on
foundational issues in quantum theory.
Various operational approaches to defining time observables have been proposed in the
past. Two of the most common are those based on pulsed measurements in the form of strings
of projection operators and continuous measurements in the form of complex potentials. One
of the major achievements of this thesis is to prove that these two operational approaches
are equivalent.
However operational approaches are somewhat unsatisfying by themselves. To provide a
definition of time observables which is not linked to a particular measurement scheme we
employ the decoherent, or consistent, histories approach to quantum theory. We focus on the
arrival time, one particular example of a time observable, and we use the relationship between
pulsed and continuous measurements to relate the decoherent histories approach to one based
on complex potentials. This lets us compute the arrival time probability distribution in
decoherent histories and we show that it agrees with semiclassical expectations in the right
limit. We do this both for a free particle and for a particle coupled to an environment.
Finally, we consider how the results discussed in this thesis relate to those derived by
coupling a particle to a model clock. We show that for a general class of clock models the
probabilities thus measured can be simply related to the ideal ones computed via decoherent
histories
