{"title":"PROBING THE STRUCTURE OF QUANTUM MECHANICS","authors":"Diederik Aerts, M. Czachor, T. Durt","doi":"10.1142/9789812778024_0001","DOIUrl":"https://doi.org/10.1142/9789812778024_0001","url":null,"abstract":"We believe that in the decades to come quantum theory will play an increasingly important role for many different fields. One of the reasons is that technology aims at manipulating and controlling information and energy in ever smaller regions of space and windows of time. As a consequence the behavior of the entities to manipulate and control will become more and more quantum. This means not only spectacular advances of new techniques and outlooks on revolutionary applications, but also a constant stress and attention on the theory of quantum mechanics itself. It is well known that quantum mechanics has been scrutinized in all kind of ways during the past decades, but that still a lot of conceptual problems remain. The problems of standard quantum mechanics are however not only of a conceptual nature. Also the formal mathematical structure of quantum mechanics has been investigated with the aim to make the theory more operational and to found the basic concepts in direct correspondence with what happens in the laboratory. Such an operationally founded quantum mechanics may soon become of great value because of the technological","PeriodicalId":424260,"journal":{"name":"Probing the Structure of Quantum Mechanics","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2002-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127479344","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"BEING AND CHANGE: FOUNDATIONS OF A REALISTIC OPERATIONAL FORMALISM","authors":"Diederik Aerts","doi":"10.1142/9789812778024_0004","DOIUrl":"https://doi.org/10.1142/9789812778024_0004","url":null,"abstract":"The aim of this article is to represent the general description of an entity by means of its states, contexts and properties. The entity that we want to describe does not necessarily have to be a physical entity, but can also be an entity of a more abstract nature, for example a concept, or a cultural artifact, or the mind of a person, etc..., which means that we aim at very general description. The effect that a context has on the state of the entity plays a fundamental role, which means that our approach is intrinsically contextual. The approach is inspired by the mathematical formalisms that have been developed in axiomatic quantum mechanics, where a specific type of quantum contextuality is modelled. However, because in general states also influence context -- which is not the case in quantum mechanics -- we need a more general setting than the one used there. Our focus on context as a fundamental concept makes it possible to unify `dynamical change' and `change under influence of measurement', which makes our approach also more general and more powerful than the traditional quantum axiomatic approaches. For this reason an experiment (or measurement) is introduced as a specific kind of context. Mathematically we introduce a state context property system as the structure to describe an entity by means of its states, contexts and properties. We also strive from the start to a categorical setting and derive the morphisms between state context property systems from a merological covariance principle. We introduce the category SCOP with as elements the state context property systems and as morphisms the ones that we derived from this merological covariance principle. We introduce property completeness and state completeness and study the operational foundation of the formalism","PeriodicalId":424260,"journal":{"name":"Probing the Structure of Quantum Mechanics","volume":"10 2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2002-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129374640","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}