Identifier 160202
TitleA 5D categorical model of the Elementary Process Theory incorporating Special Relativity
Type of publicationpreprint
Author(s)M.J.T.F. Cabbolet
KeywordsElementary Process Theory, Special Relativity, correspondence principle, pseudo-Riemannian geometry, 5-manifold, compact dimension
Publication date2016-07-08
AbstractOne of the two main issues with the Elementary Process Theory (EPT), a first-order scheme with a speculative interpretation as elementary principles, is that there is thus far no proof that it agrees with existing knowledge. The objective of this paper is to show that the EPT agrees with the knowledge obtained from the successful predictions of Special Relativity (SR). For that matter, the notion of a model of the EPT is identified with a category, whose objects are set-theoretic models of the EPT, and whose arrows are isomorphisms between these models: each object is then associated with a model of the universe of the EPT in the reference frame of an observer, and each arrow with a transformation between coordinate systems of different observers. A 5D categorical model of the EPT that incorporates SR is then fully specified: objects in the universe of the EPT are modeled as point-particles, gamma-rays, or time-like strings, all represented by integrable hyperreal functions on a pseudo-Riemannian 5-manifold with a compact fifth dimension. Processes of inertial motion, Bremsstrahlung, and laser cooling are described, and fundamental differences with other 5D theories are discussed. In addition, the intended relevance of the EPT for physics as a grand unifying scheme is precisely defined. The main conclusion is that the EPT has been proven to agree with SR by specifying a categorical model of the EPT, which is a new application of category theory to physics.
CopyrightOpen access