The Arrow of Time and Time Symmetry in non-Relativistic Quantum Mechanics : On why we have sound reasons to believe in a quantum arrow of time

This thesis deals with the problem of the arrow of time in non-relativistic quantum mechanics, that is, whether time has the property of being objectively directed within the theoiy. Three major arguments are put forth along the thesis: (a) two différent concerns around the problem of the arrow of time can be distinguished; (b) the notion of time reversai is not philosophically neutral, thereby, whether quantum mechanics is time-reversal invariant depends on previously-assumed philosophical commitments; (c) alternative interprétations of the theory display différent tools and means to introduce an arrow of time within the theoiy. The thesis is structured in three parts and nine chapters. The first part seeks to shed some light what the problem of the arrow of time is, fïrst from a broad viewpoint and then within physics. By "shed some light" I mainly mean not only to elucidate many of the involved concepts, but also to disentangle and to sort out some subsidiary problems. That's why I mean this part as "unpacking". The content is organized in two chapters. The first one (Chapter I) deals with the problem of the arrow of time from a metaphysical, broad viewpoint and then introduces the relevant physical concepts to approach it from physics. The second chapter (Chapter II) asserts that there are, at least, two versions of the problem. This distinction has been largely overlooked in the literature, and the two versions of the distinction renders conflated. Furthermore, it will point to the relationship between both versions. The second part focuses on standard non-relativistic quantum mechanics. The guiding question here is whether, and in which sense, non-relativistic quantum mechanics treats time as having an objectively privileged direction. By "standard" non-relativistic quantum mechanics I mean the partially- interpreted formalism free of any so-called interprétation. In such so-fenced-in terrain, the relevant question will thereby have to do with the Schrodinger équation and the notion of time-reversal invariance, managing without any interpretational matter for the time being. The part contains three chapters. The first (Chapter III) introduces, conceptually and formally, the standard non-relativistic quantum mechanics and its symmetry group -Galilean Group. The second chapter (Chapter IV) involves the notions of time reversai and time-reversal invariance in standard non-relativistic quantum mechanics and directly addresses the question of whether The Schrodinger équation is left unaltered under flipping the direction of time. The next chapter (Chapter V) assesses previous results in the light of the arrow of time discussion. The third and last part complexes the scénario to the extent that interprétations of standard non- relativistic quantum mechanics corne into play. Its primary focus will be those interprétations that add further elements to the standard theory and how they deal with the problem of the arrow of time (in either of its versions). Four chapters organize this last part. The first (Chapter VI) overviews how various interprétations come up and in which way their emergence intervenes on the problem of the arrow of time in quantum mechanics. The next chapter (Chapter VII) focuses on the so-called Orthodox Quantum Mechanics. Here the Collapse Postulate is analyzed as a candidate for a quantum arrow of time. The third chapter (Chapter VIII) analyzes spontaneous collapse theories (like GRW-type theories) and to what extent they offer some grounds for a fundamental (structural) arrow of time. The last chapter (Chapter IX) directs its attention at Bohmian Mechanics, the problem of the arrow of time in a Bohmian framework and the rôle that time reversai plays within the theory