Mathematical Models of Spacetime in Contemporary Physics and Essential Issues of the Ontology of Spacetime :: Physics Papers

Mathematical Models of Spacetime in Contemporary Physics and Essential Issues of the Ontology of Spacetime ABSTRACT: The general theory of relativity and field theory of matter generate an interesting ontology of space-time and, generally, of nature. It is a monistic, anti-atomistic and geometrized ontology — in which the substance is the metric field — to which all physical events are reducible. Such ontology refers to the Cartesian definition of corporeality and to Plato's ontology of nature presented in the Timaeus. This ontology provides a solution to the dispute between Clark and Leibniz on the issue of the ontological independence of space-time from distribution of events. However, mathematical models of space-time in physics do not solve the problem of the difference between time and space dimensions (invariance of equations with regard to the inversion of time arrow). Recent research on space-time singularities and asymmetrical in time quantum theory of gravitation will perhaps allow for the solution of this problem based on the structure of space-time and not merely on thermodynamics. Since the General Theory of Relativity is a fundamental model of spacetime, most often used as a starting point for a physicists' research, I will begin my analysis with an attempt to formulate the consequences of the GTR for spacetime ontology and, generally, ontology of nature. The preliminary remark, however, has epistemological character. The formulation of the GTR resulted in definite fall of a dogmatic thesis of distinguished value of the 3-dimensional Euclidean geometry, as the only geometrical structure, adequate for a description of nature. This thesis was formulated explicitly by Kant, who considered this structure to be apriori form of inspection, and as such it was to validate the science. Kant's epistemology was created mainly to validate science, whose best developed part was embodied in the classical mechanics. However, the attitude of the authors of the field theory of matter towards Kant's epistemology was not negative at all, which can be proved by the words of Weyl , who, although confessed that in himself a philosopher had been dominated by a mathematician, began his work Space, Time, Matter with philosophical considerations devoted to the question of time and space, considerations comparable to those of Kant. The formulation of the General Theory of Relativity was of major importance for the spacetime ontology, mainly because it ended the famous debate between Clarke and Leibniz concerning the ontological status of spacetime. In this debate Clarke defended the Newton's position in which he emphasized ontological independence of time and space with regard to physical events.