Vol.2, No 4, 2002 pp. 173 - 182
UDC 530.1.140.8
ON SPACE AND TIME IN QUANTUM COSMOLOGY
Ljubiša Nešić1, Stojan Obradović2
1Department of Physics, Faculty of
Sciences and Mathematics,
University of Niš, Serbia and Montenegro
2Section of Serbian Physical Society,
Ratka Pavlovica 20, Prokuplje,
Serbia and Montenegro
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.
O PROSTORU I VREMENU U KVANTNOJ KOSMOLOGIJI
U radu su razmatrane karakteristike prostora i vremena u kvantnoj kosmologiji.
Prezentovane su osnove ideja o supstancijalnoj i relacionoj koncepciji
kao i o neprekidnosti i diskretnosti prostor i vremena. Dati su takodje
elementi standardne kvantne kosmologije, odnosno kvantne kosmologije formulisane
nad poljem realnih brojeva R. Kvantna kosmologija predstavlja primenu kvantne
teorije na vasionu kao celinu u ranim fazama njene evolucije kada je univerzum
bio veoma mali tako da su sve interakcije praktično bile ujedinjene. U
postupuku dobijanja maksimalno moguće informacije na osnovu kvane kosmologije
neophodno je da ona bude "kompletna". Pojam "kompletna" se odnosi na formulisanje
teorije nad poljem realnih brojeva kao i poljem p-adičnih brojeva Qp. Obzirom
da polja p-adičnih brojeva nisu dobro poznata, u radu je prikazana ideja
o njihovom uvođenju u fiziku. U okviru p-adične kvantne kosmologije, koja
predstavlja kvantnu kosmologiju nad poljem p-adičnih brojeva Qp, prezentovani
su glavni rezultati koji se odnose na De Siterov model. Posledica ovakve
(kompletne) formulacije De Siterovog modela je diskretnost radijusa uviverzuma
koji on opisuje.
