Time reversal, the arrow of time and ontological commitments

CRISTIAN LÓPEZ

Utrecht

Congreso; The 19th UK and European Meeting on the Foundations of Physics; 2018

Even though there seems not to be a single, all-embracing concept of time reversal in physics, there is a widely-held agreement about how the notion must be specifically characterized in quantum mechanics. According to such view, time reversal must be formally represented by an anti-unitary operator that not only transforms the direction of time (t→-t), but also performs a complex conjugation over the wave function (ψ→ψ^*). Such view has received the support of the overwhelming majority of physicists and philosophers of physics, both in its formal justifications (Wigner 1931, Gibson and Pollard 1978) as well as its conceptual bases (Sachs 1987, Roberts 2017). When applied to Schrödinger?s equation, for instance, such conventional wisdom leads to the result that the dynamical equation is time-reversal invariant, that is, it does not distinguishing between the past-to-future direction from the future-to-past one. This claim has steered philosophers and physicists to hold that quantum mechanics does not pick up a privileged direction of time at its fundamental level: any temporal asymmetry must therefore come from interactions, involve some kind of force, or be interpretation-dependent.In this article, I shall give two arguments that cast some doubts on such widely-held view about time reversal in quantum mechanics and its relation to the arrow of time debate. The argument involves premises that are outwardly philosophical in nature. In the first place, I shall argue that such view assumes uncritically that time reversal is nothing but motion reversal: the formal way to represent time reversal in the literature aims at reversing the direction of motion (yielding a representation of a backward-moving physical evolution), and this is considered as equivalent to reversing the direction of time. However, the relationalism - substantialism debate about the nature of time offer some grounds to challenging such overlooked assumption. In particular, I shall show that the standard procedure to formally define time reversal in quantum mechanics is tacitly committed to a relationalist-like stance on time, and that one might come to represent time reversal differently from a substantialist-like viewpoint. Notably, both ways to represent time reversal could even diverge with respect to whether or not is Schrödinger?s equation time-reversal invariant and, thereby, whether quantum mechanics picks up a privileged direction of time.My second argument is directed towards the relation between time reversal and the philosophical problem of the arrow of time. I shall argue that the standard way to define time reversal in quantum mechanics conflicts with the principal motivation of philosophers of time in addressing the problem of whether is time directed. In particular, I shall show that such standard view, as aims at representing a moving backward evolution, demands the time-reversal transformation to leave Schrödinger?s equation invariant in the absence of all forces or interactions. Indeed, it is first assumed that the dynamical equation meets time-reversal symmetry, and then the question is what formal representation manages to keep it time-reversal invariant. However, this procedure is at odds with the usual way in which philosophers of time introduce the problem of the arrow of time: one wants to know if the world is time asymmetric at its fundamental level, beyond forces and interactions. Therefore, when tackling the problem of the arrow of time, one cannot by any means assume that the theory is time symmetric beforehand. I shall claim that the standard view of time reversal in quantum mechanics might run the risk of circularity when invoked to address this philosophical problem.