The 3-sphere Instead of Hilbert Space: A Recent Study - Alexander Soiguine (Research Highlights in Mathematics and Computer Science Vol. 6, 2023)
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 \(S\)3 is transformed into a playground for torsion kind states that do not require abstract Hilbert space vectors. The points \(S\)3 evolve, governed by updated Schrodinger equation, and act in measurements on observable as operators.