The Language for the Theory of Everything

The problem of reconciling the two pillars of theoretical physics, quantum mechanics and general relativity, remains unsolved. Among their many differences are their completely different mathematical bases. Not only does this hinder cross-disciplinary interactions, but also creative insights to unify different branches of physics. In this essay a new, powerful Geometric Algebra is introduced that unifies the mathematical foundations. To do this the inner and outer product are introduced. The former is an extension of the dot product, the latter allows the extension of vectors to higher-dimensional objects. Unifying the inner and outer product produces the powerful geometric product which is used for the rest of the essay. Along the way towards incorporating quantum mechanics, we learn that Geometric Algebra has been hiding behind many mathematical objects ordinarily used in physics: Pseudovectors, complex numbers, spinors but also the infamous Pauli and Dirac matrices. Incorporations of special and general relativity are briefly mentioned as well. Both quantum mechanics and general relativity thus find a place in Geometric Algebra, achieving the wanted unification of mathematics. Many new valuable insights and potential research opportunities have arisen within our discussion as well. With such an abundance of unification and insight, perhaps, we truly can announce that we have found the language for the Theory of Everything.