A Kind of Collapse in a Simple Spacetime Model

Abstract

We have studied a kind of collapse that may occur to a spacetime in the framework of a simple model introduced in previous papers. All the concepts of our model are defined in terms of only two primitive concepts, namely those of preparticle and of membership relation of set theory. Preparticles are considered to be the most elementary components of matter. Particles are represented by sets of sets of preparticles. A point of a spacetime is represented by an equivalence class of points of crossing between particles such that all these points of crossing have the same structure. We introduce two postulates. Firstly, that two points of a spacetime appear distinct from each other only because they have different structures. Secondly, that the extension of a spacetime can be defined only with respect to a given collection C of physical systems (in the sense that only those points of a spacetime crossed over by particles belonging to physical systems entering in C are the points which contribute to the extension of this spacetime). We then show that if the extension of a spacetime is defined with respect to only one very large physical system, this extension vanishes.