Author(s)

Alexander Soiguine

SOiGUINE Quantum Computing, Aliso Viejo, USA.

The Geometric Algebra formalism opens the door to developing a theory replacing conventional quantum mechanics. Generalizations, stemming from changing of complex numbers by geometrically feasible objects in three dimensions, followed by unambiguous definition of states, observables, measurements, bring into reality clear explanations of weird quantum mechanical features, for example primitively considering atoms as a kind of solar system. The three-sphere S³ becomes the playground of the torsion kind states eliminating abstract Hilbert space vectors. The S³ points evolve, governed by updated Schrodinger equation, and act in measurements on observable as operators.

Geometric Algebra, States, Observables, Measurements

Soiguine, A. (2022) The 3-Sphere Instead of Hilbert Space. Journal of Applied Mathematics and Physics, 10, 2733-2742. doi: 10.4236/jamp.2022.109183.