Time observables in quantum theory

Thomas Pashby

Quantum mechanics has provided philosophers of science with many counterintuitive insights and interpretive puzzles, but little has been written about the role that time plays in the theory. One reason for this is the celebrated argument of Wolfgang Pauli against the inclusion of time as an observable of the theory, which has been seen as a demonstration that time may only enter the theory as a classical parameter. Against this orthodoxy I argue that there are good reasons to expect certain kinds of 'time observables' to find a representation within quantum theory, including clock operators (which provide the means to measure the passage of time) and event time operators, which provide predictions for the time at which a particular event occurs, such as the appearance of a dot on a luminescent screen. I contend that these time operators deserve full status as observables of the theory, and on reflection provide a uniquely compelling reason to expand the set of observables allowed by the standard formalism of quantum mechanics. In addition, I provide a novel association of event time operators with conditional probabilities, and propose a temporally extended form of quantum theory to better accommodate the time of an event as an observable quantity. This leads to a proposal to interpret quantum theory within an event ontology, inspired by Bertrand Russell's Analysis of Matter. On this basis I mount a defense of Russell's relational theory of time against a recent attack.

H. D. Zeh

Valia Allori

Eugene Terry Tatum

Quantum theory according to the Copenhagen interpretation holds that, when a quantum interaction is observed (i.e., “measured”), the observer’s measuring devices temporarily become a part of the quantum system. Relativity theory holds that the event clock of the absorbed or emitted photon or graviton is frozen in time relative to all clocks outside the observed system. If we harmonize both theories, this would appear to imply that time continuity must be interrupted at each instant of observed photon or graviton interaction with matter. It is as if a segment of space-time is clipped out during each such observed interaction. If so, we must dispense with the notion of an absolutely smooth and continuous space-time and replace it with an observation-dependent, discontinuous, relativistic/quantum space-time. Mathematical physicists should be able to model this hypothesis (call it a “time-jump hypothesis”) and its inherent discontinuous space-time in their further efforts at unification.

Hrvoje Nikolić

In the usual formulation of quantum theory, time is a global classical evolution parameter, not a local quantum observable. On the other hand, both canonical quantum gravity (which lacks fundamental time-evolution parameter) and the principle of spacetime covariance (which insists that time should be treated on an equal footing with space) suggest that quantum theory should be slightly reformulated, in a manner that promotes time to a local observable. Such a reformulated quantum theory is unitary in a more general sense than the usual quantum theory. In particular, this promotes the non-unitary Hawking radiation to a unitary phenomenon, which avoids the black-hole information paradox.

Kimberly R. Chapin