Modality and the Dual Notion of Time in Quantum Mechanics

M. PASQUALINI; S. FORTIN; O. LOMBARDI

Córdoba

Congreso; XI Conference on Quantum Foundations: Contextuality, coherence and quantumness; 2022

Universidad Nacional de Córdoba

It is common to use modal vocabulary in the field of physics. The notion of "possibility" in which the modal categories are analyzable admits two interpretations. The actualist interpretation considers that every possibility is actual or is not at all. The possibilistic interpretation distinguishes between the realm of the actual and the realm of the merely possible. The question of the interpretation of the notion of possibility acquires a particular urgency when we enter the quantum domain since modality seems to be attached to an intrinsic feature of the reality represented by quantum theory. The first objective of this presentation is to account for the different philosophical interpretations of the notion of possibility and to analyze how an actualist or possibilistic conception underlies some current interpretations of quantum mechanics.In the quantum domain the notion of time is dual. We have, on the one hand, the first notion of time as a parameter linked to the dynamics of quantum probabilities. On the other hand, the theory does not contain any theoretical representation that accounts for the time in which quantum events occur, i. e. the time in which the observables acquire definite values. Precisely, the diversity of interpretations comes to supply in one way or another that lack of definition. The second objective of this presentation is to draw attention to the link that we believe exists between (i) the parameter-time and the domain of the possible and (ii) the event-time and the domain of the actual (as accounted in Lombardi, Fortin and Pasqualini 2022).Finally, efforts are known, motivated by the search for a solution to the problem of time formulated in the context of the program of a quantum theory of gravity, to reduce the so-called parameter-time to internal correlations between quantum observables from a closed system perspective (e.g. Page and Wooters 1983). However, there are not many attempts to construe the event-time of events relationally (as an exception: Fortin, Lombardi and Pasqualini 2022). The third objective of this presentation is then to propose a relational construction of the event-time that can be a suitable complement to the relational program applied to the parameter-time. To do this, we assume the interpretive postulates of the Modal-Hamiltonian interpretation, and propose a model based on the consecutive measurements model.