On space and time in quantum cosmology

Abstract

The paper considers the properties of space and time in quantum cosmology. It presented the basic ideas of the substantial and relational conceptions of space and time, as well the basic ideas of the continuity and discreteness of space and time. The basics of standard quantum cosmology, i.e. quantum cosmology formulated over the field of real numbers R, have also been presented. Quantum cosmology is the application of the quantum theory to the universe as a whole in the early phases of its evolution, when the universe was very small so that all the four interactions were practically unified. In order to obtain the maximum possible information from quantum cosmology it is necessary that it be "complete". The concept "complete" refers here to the formulation of the theory over the field of real numbers and the field of p-adic numbers Qp. Since p-adic numbers are generally not well-known, the idea of their introduction has carefully been considered. Within the p-adic quantum cosmology representing quantum cosmology over the field of p-adic numbers Qp, the main results concerning the de Sitter model have been presented. The consequence of this (complete) formulation of the de Sitter model is the radius discreteness of the universe.