Sobre uma fundamentação não reflexiva da mecânica quântica

Abstract

This is an expository article in which we discuss a cluster of topics related to the foundations of quantum physics, mainly regarding the concepts of identity and of individuality of the basic entities dealt with by the theory (or group of theories). We propose that, if one wants to ground the formal counterpart of a possible view of quantum entities as objects devoid of individuality, there are basically two possible alternatives: (a) to maintain classical logic and standard mathematics, say by using a set theory such as the Zermelo-Fraenkel system - in this case we can either assume certain symmetry conditions that enable us to speak about the non-individuality of the quantum entities, or restrict ourselves to certain classes in which only a weaker relation of indistinguishability is defined; (b) to elaborate a new mathematical theory, in which the non-individuality of certain objects is assumed ab initio. After discussing the first alternative by presenting "inner models" of ZFU and of ZFC set theories, in which identity is restricted in some way, we comment on its advantages and disadvantages. Then, motivated by the second hypothesis, we sketch the main aspects of what could be taken as a quantum mechanics grounded on a possible set theory, quasi-set theory, that departs from the standard systems. Since the underlying logic of quasi-set theory is a non-reflexive logic, we call the corresponding mechanics non-reflexive quantum mechanics.