Dimensionally Democratic Calculus and Principles of Polydimensional Physics

TL;DR

This paper proposes polydimensional principles using Clifford algebra to unify various physical theories and invariances, extending classical mechanics to include string, membrane, and hypergravity theories.

Contribution

It introduces a new framework based on Clifford calculus and polydimensional invariance principles that generalize classical mechanics and unify multiple advanced physical theories.

Findings

Derived a solution for spinning particles in curved space using extended Clifford calculus.

Proposed invariance of physical laws under local automorphism transformations reshuffling geometry.

Established a generalized basis encompassing string, membrane, and hypergravity theories.

Abstract

A solution to the 50 year old problem of a spinning particle in curved space has been recently derived using an extension of Clifford calculus in which each geometric element has its own coordinate. This leads us to propose that all the laws of physics should obey new polydimensional metaprinciples, for which Clifford algebra is the natural language of expression, just as tensors were for general relativity. Specifically, phenomena and physical laws should be invariant under local automorphism transformations which reshuffle the physical geometry. This leads to a new generalized unified basis for classical mechanics, which includes string theory, membrane theory and the hypergravity formulation of Crawford[J. Math. Phys., {\bf 35}, 2701-2718 (1994)]. Most important is that the broad themes presented can be exploited by nearly everyone in the field as a framework to generalize both the Clifford calculus and multivector physics.