On Time in Quantum Physics

Abstract

First, I briefly review the different conceptions of time held by three rival interpretations of quantum theory: the collapse of the wave-packet, the pilotwave interpretation, and the Everett interpretation (Section 2).Then I turn to a much less controversial task: to expound the recent understanding of the time-energy uncertainty principle, and indeed of uncertainty principles in general, that has been established by such authors as Busch, Hilgevoord and Uffink.Although this may at first seem a narrow topic, I point out connections to other conceptual topics about time in quantum theory: for example, the question under what circumstances there is a time operator (Section 4.3).

The Pauli Problem for Gaussian Quantum States: Geometric Interpretation

“…Our discussion of polar duality suggests that a quantum system localized in the position representation in a set X cannot be localized in the momentum representation in a set smaller than that of its polar dual X h. The notion of polar duality thus appears informally as a generalization of the uncertainty principle of quantum mechanics, as expressed in terms of variances and covariances (see [23]). The idea of such generalizations is not new, and can already be found in the work of Uffink and Hilgevoord [25,26]; see Butterfield's discussion in [27]. It would certainly be interesting to explore the connection between convex geometry and quantum mechanics, but very little work has been conducted so far.…”

Possibility and Time in Quantum Mechanics

“…Since then, debates about the meaning of the time-energy uncertainty relation became ubiquitous in the quantum foundations literature, with no general agreement (for a thorough discussion, see [ 41 , 42 ]; see also [ 43 ]).…”

Self-adjoint time operator of a quantum field

“…`External time' t 0 is measured by clocks that are not coupled to the system under investigation. [31][32][33][34] These clocks are located far away at spatial in¯nity such that the e®ects from our system are negligible. We will use the external time t 0 as a reference to measure the vibrations of time in the system.…”