Abstract

In this paper a general mathematical model of the World will be constructed. I will show that a number of important theories in Physics are particularizations of the World Theory presented here. In particular, the worlds described by the Classical Mechanics, the Theory of Relativity and the Quantum Mechanics are examples of worlds according to this definition, but also some theories attempting to unify gravity and QM, like String Theory. This mathematical model is not a Unified Theory of Physics, it will not try to be a union of all the results. By contrary, it tries to keep only what is common and general to most of these theories. Special attention will be payed to the space, time, matter, and the physical laws. What do we know about the laws governing the Universe? What are the most general assumptions one can make about the Physical World? Each theory in Physics and each philosophical system came with its own vision trying to describe or explain the World, at least partially. In the following, I will try to keep the essential, and to establish a mathematical context, for all these visions. The purpose of this distillation is to provide a mathematical common background to both physical and metaphysical discussions about the various theories of the World. The mathematical object named World is defined using the locally homogeneous sheaves and sheaf selection which are introduced in the appendices.