Gravity and electromagnetism on conic sedenions

Abstract

Conic sedenions from C. Musès' hypernumbers program are able to express the Dirac equation in physics through their hyperbolic subalgebra, together with a counterpart on circular geometry that has earlier been proposed for description of gravity. An electromagnetic field will now be added to this formulation and shown to be equivalent to current description in physics. With use of an invariant hypernumber modulus condition, a description of quantum gravity with field will be derived. The resulting geometry reduces in very good approximation to relations expressible through customary tensor algebra. However, deviations are apparent at extreme energy levels, as shortly after the Big Bang, that require genuine conic sedenion arithmetic for their correct description. This is offered as method for exploration into bound quantum states, which are not directly observable in the experiment at this time. Extendibility of the invariant modulus condition to higher hypernumber levels promises mathematical flexibility beyond gravity and electromagnetism. © 2006 Elsevier Inc. All rights reserved.