PRINCIPIA GEOMETRICA PHYSICAE

Abstract

We show that quadratic spaces are a fundamental clue to understand the structure of theoretical physics. Classical Physics is embedded within a 5-D flat quadratic space, 3 Space-, one Timeand one Actionlike basis manifolds (Lorentz signature 1,4) faithfully providing a Relativistic Theory (START) describing Newtonian, Maxwell, geometrical optics and General Relativity as particular linear and quadratic forms of this (flat) START space. The 5-D space has a quadratic form which maps into the real quadratic form of a (hyperbolic-complex) 4-D space-time dS = dS • dS† . Otherwise the understanding of a many electron quantum mechanical (QM) system, with all its QM intricacies, is presented considering the QM ”density” as a quadratic form and the QM ”wave function” as its corresponding linear form. Space-Time-Action, General Relativity, Geometric Optics. 83D05, 83Exx, 11E88, 15A66(67). E-mail: keller@servidor.unam.mx and keller@cms.tuwien.ac.at 1 Physics and Quadratic Spaces Physics is understood as the science describing nature as a whole in a useful way. For the Scientific Method (SM) the usefulness requires that two observers will find