Ο κύριος σκοπός της παρούσας εργασίας είναι να συγκεντρωθούν συγκεκριμένες θεωρήσεις που χρησιμοποιούν τον φορμαλισμό των συνεπών ιστοριών σε βασικά προβλήματα της κβαντικής θεωρίας και κβαντικής κοσμολογίας. Ο φορμαλισμός αυτός είναι πολλά υποσχόμενος για τον τομέα της κανονικής κβαντικής βαρύτητας. Ο λόγος που θα κάνουμε αυτή την ανασκόπηση είναι για να δώσουμε μία ενοποιημένη εικόνα στα ζητήματα αυτά και να μπορέσουμε να τα συγκρίνουμε. Συγκεκριμένα, το πρώτο μέρος αφορά δύο διαφορετικές προσεγγίσεις για το πρόβλημα του χρόνου άφιξης στην κβαντομηχανική, εκ των οποίων και οι δύο χρησιμοποιούν φορμαλισμό ιστοριών. Η πρώτη έγινε από τους Halliwell και Yearsly (2009) και η δεύτερη από τους Anastopoulo και Saviddou (2012). Από την σύγκριση αυτών καταλήγουμε στο συμπέρασμα ότι και οι δύο δίνουν μία αδρομερή μορφή της εξίσωσης του Kijowski. Το δεύτερο μέρος αφορά την κβαντική κοσμολογία. Σε αυτό αρχικά παρουσιάζεται μία προσέγγιση με συνεπείς ιστορίες για την πυκνότητα πιθανότητας στην κβαντική κοσμολογία η οποία έγινε από τον Halliwell (2009). Στην συνέχεια παρουσιάζεται μία προσέγγιση με ιστορίες για μοντέλα μίνι-υπερχώρου από τους Anastopoulo and Savidou (2005). Σε αυτή κατασκευάζονται μοντέλα μίνι-υπερχώρου με όρους προβολικών τελεστών ιστοριών (HPO). Η σπουδαιότητα αυτού του φορμαλισμού έγκειται στο γεγονός ότι η γενική σχετικότητα σε αυτή την μορφή ικανοποιεί και τους χωροχρονικούς διαφορομορφισμούς και την άλγεβρα Dirac, με αποτέλεσμα να είναι εύκολα κβαντίσιμη. / 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.

A measurement-independent formulation of quantum mechanics called ‘regular histories’ (RH) is presented, able to reproduce the predictions of the standard formalism without the need to for a quantum-classical divide or the presence of an observer. It applies to closed systems and features no wave-function collapse. Weights are assigned only to histories satisfying a criterion called ‘regularity’. As the set of regular histories is not closed under the Boolean operations this requires a new con- cept of weight, called ‘likelihood’. Remarkably, this single change is enough to overcome many of the well-known obstacles to a sensible interpretation of quantum mechanics. For example, Bell’s theorem, which makes essential use of probabilities, places no constraints on the locality properties of a theory based on likelihoods. Indeed, RH is both counter- factually definite and free from action-at-a-distance. Moreover, in RH the meaningful histories are exactly those that can be witnessed at least in principle. Since it is especially difficult to make sense of the concept of probability for histories whose occurrence is intrinsically indeterminable, this makes likelihoods easier to justify than probabilities. Interaction with the environment causes the kinds of histories relevant at the macroscopic scale of human experience to be witnessable and indeed to generate Boolean algebras of witnessable histories, on which likelihoods reduce to ordinary probabilities. Further- more, a formal notion of inference defined on regular histories satisfies, when restricted to such Boolean algebras, the classical axioms of implication, explaining our perception of a largely classical world. Even in the context of general quantum histories the rules of reasoning in RH are remark- ably intuitive. Classical logic must only be amended to reflect the fundamental premise that one cannot meaningfully talk about the occurrence of unwitnessable histories. Crucially, different histories with the same ‘physical content’ can be interpreted in the same way and independently of the family in which they are expressed. RH thereby rectifies a critical flaw of its inspiration, the consistent histories (CH) approach, which requires either an as yet unknown set selection rule or a paradigm shift towards an un- conventional picture of reality whose elements are histories-with-respect-to-a-framework. It can be argued that RH compares favourably with other proposed interpretations of quantum mechanics in that it resolves the measurement problem while retaining an essentially classical worldview without parallel universes, a framework-dependent reality or action-at-a-distance.