Quantum mechanics, time and ontology

Against what is commonly accepted in many contexts, it has been recently suggested that both deterministic and indeterministic quantum theories are not time-reversal invariant, and thus time is handed in a quantum world. In this paper, I analyze these arguments and evaluate possible reactions to them. In the context of deterministic theories, first I show that this conclusion depends on the controversial assumption that the wave-function is a physically real scalar field in configuration space. Then I argue that answers which restore invariance by assuming the wave-function is a ray in Hilbert space fall short. Instead, I propose that one should deny that the wave-function represents physical systems, along the lines proposed by the so-called primitive ontology approach. Moreover, in the context of indeterministic theories, I argue that time-reversal invariance can be restored suitably redefining its meaning.