Time reversal invariance and ontology

TL;DR

The paper investigates whether time reversal invariance can be maintained for classical electrodynamics and non-relativistic quantum mechanics under the Albert–Callender notion, which reverses only the temporal order of instantaneous states. It argues that ontological underdetermination allows alternative primitive ontologies in ED and NRQM such that the Albert–Callender TR transformation becomes a symmetry, sometimes aligning with the standard TR, and in other cases yielding a different but consistent transformation (e.g., TC or CPT variants). By examining scalar fields, Wheeler–Feynman theory, and various active/geometric TR notions, the authors show that TR-invariance is not uniquely determined by dynamics but depends on the chosen ontology, thereby challenging the claim that TR-invariance entails a temporal direction in spacetime. The work highlights that while ontological choices can preserve Albert–Callender TR, achieving fully relativistic, field-theoretic invariances remains complex, and the results emphasize the role of ontology in interpreting time-symmetry and its implications for the arrow of time.

Abstract

Albert and Callender have challenged the received view that theories like classical electrodynamics and non-relativistic quantum mechanics are time reversal invariant. They claim that time reversal should correspond to the mere reversal of the temporal order of the instantaneous states, without any accompanying change of the instantaneous state as in the standard view. As such, Albert and Callender claim, these theories are not time reversal invariant. The view of Albert and Callender has been much criticized, with many philosophers arguing that time reversal may correspond to more than the reversal of the temporal order. In this paper, we will not so much engage with that aspect of the debate, but rather deflate the disagreement by exploiting the ontological underdetermination. Namely, it will be argued that with a suitable choice of ontology, these theories are in fact time reversal invariant in the sense of Albert and Callender, in agreement with the standard view.