Ο χρόνος άφιξης στην κβαντομηχανική και το πρόβλημα του χρόνου στην κβαντική κοσμολογία

Abstract

The major purpose of this study is to consecrate specific approaches to some problems of quantum theory and quantum cosmology, in terms of decoherence histories formalism which is a very promising formalism for the canonical quantum gravity theories. The reason is to give a unified picture to these issues in order to be possible to compare them. Specifically, the first part contains two different approaches to the time of arrival in quantum mechanics, both of these use a histories formalism. The first is from Halliwell and Yearsly (2009) and the second from Anastopoulos and Saviddou (2012). By comparing them we deduce that both of them first gives a coarse-grain form of the Kijowski' s probability distribution. The second part concerns quantum cosmology. In this, we presented a decoherent histories approach to quantum cosmological probabilities, in which was used a complex potential, from Halliwell (2009). After that we present a histories approach to minisuperspace models by Anastopoulos and Savidou (2005). In this, minisuperspace models is written in terms of histories projector operator (HPO) formalism. The spectacular of this is that in that form general relativity satisfies both spacetime diffeomorfisms and Dirac algebra, which is very important because it is easier to be quantized.