Alguns aspectos do tempo na mecânica quântica

Abstract

This work is the result of an effort towards a better understanding of the nature of time in quantum mechanics. It consists mainly of a study of three distinct subjects: a non-linear quantum theory proposed originally by Weinberg, the study of some quantum mechanical models for closed timelike curves (CTCs) and also the two-state vector formalism of Aharonov and collaborators. The Weinberg theory is interesting because it seems to be sufficiently general, in a sense that it could be thought as a model for any nonlinear quantum mechanical theory. Because of this, when Gisin showed that it implies signalling, many scientists has regarded this result as an evidence of the impossibility of any kind of nonlinearity in quantum theories. However, there are models for quantum mechanical CTCs that introduce nonlinearity in a different manner. Nevertheless, as we have shown, the Deutsch CTC model, which at first seems to present a consistent way to perform time travelling to the past, also leads to signalling. On the other hand, postselected CTCs model, which is also studied in this work, does not seem to lead to signaling, although this is an issue still debated in the literature. As this last topic involves postselection, it is natural to introduce the two-state vector formalism due to Aharonov. This formalism implies the notion of retrocausality in quantum mechanics and has led to important discoveries, such as the concept of weak values and an intriguing theoretical possibility of building a quantum time-translation machine, that we shall also discuss.