Abstract
The notion of time reversal has caused some recent controversy in philosophy of physics. The debate has mainly put the focus on how the concept of time reversal should be formally implemented across different physical theories and models, as if time reversal were a single, unified concept that physical theories should capture. In this paper, I shift the focus of the debate and defend that the concept of time reversal involves at least three facets, where each of them gives rise to opposing views. In particular, I submit that any account of time reversal presupposes (explicitly or implicitly) modal, metaphysical, and heuristic facets. The comprehension of this multi-faceted nature of time reversal, I conclude, shows that time reversal can be coherently said in many ways, suggesting a disunified concept.
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See for instance the debate about whether time reversal is implemented by an anti-unitary or unitary operator in quantum theories (Callender, 2000; Lopez, 2019; Roberts, 2017); or about whether it should change the sign of magnetic field in classical electromagnetism (Albert, 2000; Arntzenius & Greaves, 2009),
Though I will here refer simply to empirical or structural equivalence, I acknowledge that a purely formal relation does not exhaust the meaning of a symmetry and it needs to be given with further constraints. However, which such constraints are has been matter of some controversy (see Belot, 2013; Dasgupta, 2016).
I even think that this is not excusive of time-reversal invariance either, but a feature of any spatial–temporal symmetry. I will not develop this point further here, but I believe that the same point can be made for spatial symmetries (i.e., space reflection) as well.
Under this more liberal reading of necessity/contingency and its relation to a priori/a posteriori, necessity and a priori seems to come along as well as contingency and a posteriori. Under a stricter reading, there would be two further relations I left out: between a priori and contingency, on the one hand, and between a posteriori and necessity, on the other. For this particular case, I do not see that any of these combinations yields a conceptually fruitful notion of time reversal. However, in general, Saul Kripke (1980) has persuasively argued for the existence of genuine cases. A proposition like “the length of stick S at time \(t_0\) is one meter” would be a priori and contingent (where “the length of S” is a non-rigid designator and “one meter” is so, being hence contingent; but it is obvious that the claim is knowable a priori at least for those users that stipulates the reference of “one meter”). A proposition like “gold is the element with atomic number 79” would be a posteriori and necessary (under the assumption that elements have essences and it is a science’s task to discover them).
It is worth noticing how these approaches somehow relate to the modal facet. A by-stipulation approach will claim that general laws must be time-reversal invariant, but it allows some of their models to be time-reversal asymmetric. In this case, the general laws are those that are necessarily and a priori symmetric, not their models, which could be contingently asymmetric. Contrarily, conforming to the by-discover approach general laws might turn out non-time-reversal invariant, which is equivalent to claim that their solutions are either compatible with −t or +t, but not both.
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Acknowledgments
I thank Olimpia Lombardi, Michael Esfeld, Karim Thébault, Carl Hoefer, María José Ferreira, Frida Trotter, Alexandre Guay, Mathieu Berteloot, Kevin Chálas, Andrea Oldofredi, Federico Benitez and Dustin Lazarovici for so many discussions, comments, revisions and advices that significantly improved early ideas and arguments developed in more detail in this paper. I would also like to acknowledge the helpful feedback from the audience at EPSA 2019 in Geneva and from two anonymous reviewers of the manuscript. This work was supported by an FRS-FNRS (Fonds de la Recherche Scientifique) Postdoctoral Fellowship and made possible through the support of the grant n° 61785 from the John Templeton Foundation. The opinions expressed in this publication are those of the author and do not necessarily reflect the views of the John Templeton Foundation.
Funding
This work was supported by an FRS-FNRS (Fonds de la Recherche Scientifique) Postdoctoral Fellowship and made possible through the support of the grant n° 61785 from the John Templeton Foundation. The opinions expressed in this publication are those of the author and do not necessarily reflect the views of the John Templeton Foundation.
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Lopez, C. Three facets of time-reversal symmetry. Euro Jnl Phil Sci 11, 51 (2021). https://doi.org/10.1007/s13194-021-00355-8
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DOI: https://doi.org/10.1007/s13194-021-00355-8