The 3-sphere Instead of Hilbert Space: A Recent Study

Abstract

The Geometric Algebra formalism allows for the development of a theory to replace conventional quantum mechanics. Generalizations resulting from the replacement of complex numbers with geometrically feasible three-dimensional objects, followed by unambiguous definitions of states, observables, and measurements, bring into reality clear explanations of strange quantum mechanical features, such as primitively considering atoms as a type of solar system. The three-sphere \(\mathbb{S}\)³ is transformed into a playground for torsion kind states that do not require abstract Hilbert space vectors.  The  points \(\mathbb{S}\)³ evolve, governed by updated Schrodinger equation, and act in measurements on observable as operators.