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Roads to the past: how to go and not to go backward in time in quantum theories

  • Paper in Philosophy of the Natural Sciences
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Abstract

In this article I shall defend, against the conventional understanding of the matter, that two coherent and tenable approaches to time reversal can be suitably introduced in standard quantum mechanics: an “orthodox” approach that demands time reversal to be represented in terms of an anti-unitary and anti-linear time-reversal operator, and a “heterodox” approach that represents time reversal in terms of a unitary, linear time-reversal operator. The rationale shall be that the orthodox approach in quantum theories assumes a relationalist metaphysics of time, according to which time reversal is nothing but motion reversal. But, when one shifts gears and turn to a substantivalist metaphysics of time the heterodox approach to time reversal in quantum mechanics comes up in a more natural way.

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Notes

  1. Despite this theory-dependency, some attempt to coarsely characterize time reversal in a theory-independent way. Steven Savitt (1996: 12-14) has inventoried three kinds of time transformations that might be fairly called ‘time reversal’; some of them boil down to a proper characterization within a physical theory, but others intend to be broader. Recently, Daniel Peterson (2015) argued that some accounts of time reversal (which he calls ‘intuitives’) start out by characterizing a time-reversal operator from a theory-independent perspective.

  2. I will completely circumscribe myself to Schrödinger’s equation. Some interpretation-dependent dynamical equations can also be considered as part of the formal apparatus of quantum mechanics, for instance in GRW or Bohmian Mechanics.

  3. To be clear: ‘being T-invariant under TA’ means ‘being TA-invariant’ as TA specifies the form of the T-operator.

  4. To be clear: ‘being non-T-invariant under T_U’ means ‘being non-T_U-invariant’ as T_U specifies the form of the T-operator

  5. The predicates “positive” or “negative” for the energy spectrum, or “unbounded from below/from above” for Hamiltonians are actually matter of convention. So, the argument could not hinge on which predicate one adopts to describe the system properly. The real problem is not whether or not the Hamiltonian is unbounded from below. The problem is if one starts with a Hamiltonian unbounded from above (but bounded from below) and one ends up with a Hamiltonian unbounded from below (but bounded from above) after a transformation. In some sense, the problem is if there is in general a bound at all. More precisely, a specific Hamiltonian must be bounded (from above or from below), and the problem would come up if one adopts a transformation that turns a Hamiltonian unbounded from above (bounded from below) into a Hamiltonian unbounded from below (bounded from above), so that Hamiltonians (in general) could adopt either of the bounds.

  6. Certainly, I would be naïve to infer from these theoretical considerations that one must engage a susbtantivalist metaphysics of space-time: the structure may be otiose and, from a ‘more parsimonious’ stance in respect of ontology, eliminable. However, it is also true that standard formulations of those physical theories do countenance a substantivalist-like viewpoint.

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Acknowledgements

Funding for this work was provided by grants 57919 from the John Templeton Foundation and Olimpia Lombardi BID PICT 2014-2812 from Agencia Nacional de Promoción Científica y Tecnológica (AGENCIA, Argentina). This work was supported by a fellowship from Consejo Nacional de Invesigación Científica y Tecnologica (CONICET, Argentina)

Many thanks to María José Ferreira, Olimpia Lombardi, Michael Esfeld, Bryan Robertson, Karim Thébault and the Group of Philosophy of Science at Faculty of Natural Sciences and Mathematics of the University of Buenos Aires (particularly Sebastián Fortín and Federico Holik) for helpful discussion of the arguments contained within the paper and for their highly valuable comments on previous versions draft. I am also grateful for the fruitful feedback from EPSA 2017 attendants and for the comments and corrections made by two anonymous reviewers of this manuscript.

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Authors and Affiliations

  1. Institute of Philosophy ‘Alejandro Korn’, University of Buenos Aires, Ciudad Autónoma de Buenos Aires, Argentina

    Cristian López

  2. National Scientific and Technical Research Council (CONICET), Ciudad Autónoma de Buenos Aires, Argentina

    Cristian López

  3. Faculty of Humanities, University of Lausanne, Lausanne, Switzerland

    Cristian López

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Correspondence to Cristian López.

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This article belongs to the Topical Collection: EPSA17: Selected papers from the biannual conference in Exeter

Guest Editors: Thomas Reydon, David Teira, Adam Toon

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López, C. Roads to the past: how to go and not to go backward in time in quantum theories. Euro Jnl Phil Sci 9, 27 (2019). https://doi.org/10.1007/s13194-019-0250-z

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