Possibility and Time in Quantum Mechanics.

Olimpia Lombardi,Matías Pasqualini,Sebastian Fortin

doi:10.3390/e24020249

Abstract

In the discourse of quantum mechanics it is usual to say that non-commuting observables cannot have definite values at the same time, or that they cannot be simultaneously measured. But, what does the term ‘cannot’ mean in this context? Does it stand for impossible? Should Heisenberg’s principle be read in terms of uncertainty or of indeterminacy? On the other hand, whereas the debates about the nature of time in classical and relativistic mechanics have been many and varied, the question about the nature of time in quantum mechanics has not received the same attention, especially when compared to the large amount of literature on interpretive issues. The purpose of this paper is to show that, under a realist interpretation of quantum mechanics, these two matters, possibility and time, are strongly related. The final aim is to argue that, when possibility and actuality are conceived as irreducible modes of being, they are correlated to two different notions of time that can be distinguished in the quantum realm: parameter-time and event-time.

Highlights

In the discourse of quantum mechanics it is usual to say that non-commuting observables cannot have definite values at the same time, or that they cannot be simultaneously measured
Perhaps the fact that the symmetry group of quantum mechanics is the same as that of classical mechanics led many to think that any question about time in non-relativistic quantum mechanics is automatically settled by the same discussion in pre-relativistic classical mechanics
The final aim is to argue that, when possibility and actuality are conceived as irreducible modes of being, they are correlated to two different notions of time that can be distinguished in the quantum realm

Summary

Introduction

In the discourse of quantum mechanics it is usual to say that non-commuting observables cannot have definite values at the same time, or that they cannot be simultaneously measured. Its rejection of metaphysics in favor of logic led most philosophers of Entropy 2022, 24, 249 science belonging to the analytic tradition to avoid ontological discussions by translating them into linguistic and logical questions It is not surprising, that this general position showed a deep skepticism towards any appeal to objective modality, manifested by the de re use of modal concepts. An example of the rejection of metaphysics in favor of logic is the case of Richard Montague [7], who attempts to elucidate the concept of physical necessity in logical terms According to this author, p is physically necessary iff p is deducible from a certain class of physical laws L. When this task focuses on modality, the need of recovering an objective meaning of modality comes to the fore

Actualism Versus Possibilism

Parameter-Time and Event-Time

Actuality and Event-Time

Final Remarks