The physics and the philosophy of time reversal in standard quantum mechanics

Abstract

A widespread view in physics holds that the implementation of time reversal in standard quantum mechanics must be given by an anti-unitary operator. In foundations and philosophy of physics, however, there has been some discussion about the conceptual grounds of this orthodoxy, largely relying on either its obviousness or its mathematicalphysical virtues. My aim in this paper is to substantively change the traditional structure of the debate by highlighting the philosophical commitments underlying the orthodoxy. I argue the persuasive force of the orthodoxy greatly depends on a relationalist metaphysics of time and a by-stipulation view of time-reversal invariance. Only with such philosophical background can the orthodoxy of time reversal in standard quantum mechanics succeed and be properly justified.

The metaphysical underdetermination of time-reversal invariance

“…Almost any quantum-mechanical textbook justifies succinctly why this is the right representation of time reversal (see, for instance, Gasiorowicz, 1966;Messiah, 1966;Ballentine, 1998, among others). More thorough justifications have also been provided in the philosophical literature, even though they differ in the details and emphases (see Sachs, 1987;Roberts, 2017;Lopez, 2021). The reader is referred to the references therein for further details.…”

“…Therefore, if time reversal means change reversal, then the anti-unitary time-reversal transformation is the only adequate one. In Lopez (2021), I claim that this implementation of time reversal is contingent upon a philosophical background that provides the necessary conceptual tools to justify why time reversal must transform certain magnitudes in a specific way.…”

“…There has lately been some interest in the philosophy of physics community around the concept of 'time-reversal invariance'. On the one hand, some discussions centered in which is the right implementation of time reversal in different physical theories, mainly in classical electromagnetism and non-relativistic quantum mechanics (see, for instance, Savitt, 1996;Callender, 2000;Albert, 2000;Earman, 2002;Malament, 2004;North, 2008;Arntzenius & Greaves, 2009;Peterson, 2015;Roberts, 2017;Allori, 2019;Lopez, 2021;Struyve, 2022 among others). On the other, some have disputed, or defended, the philosophical relevance of time-reversal invariance in relation to the problem of the direction of time (Sklar, 1974;Earman, 1974;Horwich, 1987;Callender, 1995;Hutchison, 1993Hutchison, , 1995Savitt, 1996;Arntzenius, 1997;Lopez & Esfeld, 2022).…”

“…From a general perspective, this paper aims to contribute to the rich recent literature on time reversal and its relation to ontology and cases of underdeterminacy (for instance, Allori, 2019;Farr, 2020;Lopez, 2021;Porter Williams, 2022;Struyve, 2022). In some sense, my paper draws on the literature, but it seeks to make a more general, and maybe more radical, point.…”

Spontaneous Collapse Theories and Temporal Primitivism about Time’s Direction

“…Though there has been some discussion about how time reversal must be implemented in standard quantum mechanics (see [9,31,50], the common view has it that time reversal is implemented by an anti-unitary operator T that transforms the time parameter as T ∶ t → −t , that keeps the position T ∶ x → x , and, interestingly, that transforms the wave-function into its complex conjugate T ∶ → * . One of the reasons to implement time reversal in terms of an anti-unitary operator is that it keeps the spectrum of the Hamilonian bounded-from-below, whereas a unitary implementation does not (see [31,50] for further details and discussion). In this way, we can guarantee that any time-reversed Hamiltonian keeps its spectrum invariant.…”