Time and quantum theory: A history and a prospectus

The historical part of this paper analyzes in detail how ideas and expectations regarding the role of time in quantum theory arose and evolved in the early years of quantum mechanics (from 1925 to 1927). The general theme is that expectations which seemed reasonable from the point of view of matrix mechanics and Dirac׳s q-number formalism became implausible in light of Dirac–Jordan transformation theory, and were dashed by von Neumann׳s Hilbert space formalism which came to replace it. Nonetheless, I will identify two concerns that remain relevant today, and which blunt the force of Hilgevoord׳s (2005) claim that the demand that time feature as an observable arose as the result of a simple conceptual error. First, I advocate the need for event time observables, which provide a temporal probability distribution for the occurrence of a particular event. Second, I claim that Dirac׳s use of the extended phase space to define time and (minus the) energy as conjugates is not subject to ‘Pauli׳s Theorem,’ the result that rules out time observables in von Neumann׳s formalism. I also claim that the need to define these event time observables leads to a novel motivation for considering Dirac׳s extended state space.