Towards the Unification of Gravity and other Interactions: What has been Missed?

TL;DR

This paper proposes a new multidimensional framework for unifying gravity with other fundamental interactions by extending the basic space to a matter-configuration associated space, incorporating Clifford algebra for fermion description.

Contribution

It introduces a novel paradigm where physics is based on a multidimensional space linked to matter configurations, unifying interactions within a Clifford algebra structure.

Findings

General relativity extended to a multidimensional configuration space.

A 16-dimensional manifold describing extended objects with Clifford algebra.

Potential for unification of interactions and fermion description.

Abstract

Faced with the persisting problem of the unification of gravity with other fundamental interactions we investigate the possibility of a new paradigm, according to which the basic space of physics is a multidimensional space ${\cal C}$ associated with matter configurations. We consider general relativity in ${\cal C}$. In spacetime, which is a 4-dimensional subspace of ${\cal C}$, we have not only the 4-dimensional gravity, but also other interactions, just as in Kaluza-Klein theories. We then consider a finite dimensional description of extended objects in terms of the center of mass, area, and volume degrees of freedom, which altogether form a 16-dimensional manifold whose tangent space at any point is Clifford algebra Cl(1,3). The latter algebra is very promising for the unification, and it provides description of fermions.