Conformal Invariance and the Metrication of the Fundamental Forces

Abstract

We revisit Weyl's metrication (geometrization) of electromagnetism. We show that by making Weyl's proposed geometric connection be pure imaginary, not only are we able to metricate electromagnetism, an underlying local conformal invariance makes the geometry be strictly Riemannian and prevents observational gravity from being complex. Via torsion we achieve an analogous metrication for axial-vector fields. We generalize our procedure to Yang-Mills theories, and achieve a metrication of all the fundamental forces. Only in the gravity sector does our approach differ from the standard picture of fundamental forces, with our approach requiring that standard Einstein gravity be replaced by conformal gravity. We show that quantum conformal gravity is a consistent and unitary quantum gravitational theory, one that, unlike string theory, only requires four spacetime dimensions.

revtex4, 7 pages. Essay written for the Gravity Research Foundation 2016 Awards for Essays on Gravitation

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Cited by in corpus (6)

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• A New Property of the Electromagnetic/Yang-Mills-Conformal Gravity System in Spherical Symmetry
• Disentangling the Cosmic/Comoving Duality: The Cognitive Stability and Typicality Tests