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Journal of Applied Science and Innovation Studies

Entanglement Reconsidered

Published Feb 1, 2026• 0 citations
Publisher

Abstract

Geometric algebra formalism, along with unambiguous definition of states, opens the door to developing a feasible mathematical structure to replace conventional quantum mechanics.The three-sphere 𝕊 3 becomes the playground of the states as torsion kind ones, eliminating abstract Hilbert space vectors.The 𝕊 3 points act in measurements on observable as operators.

DOI
10.71002/jasis.v3n1p5

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Geometric algebra formalism, along with unambiguous definition of states, opens the door to developing a feasible mathematical structure to replace conventional quantum mechanics.The three-sphere 𝕊 3 becomes the playground of the states as torsion kind ones, eliminating abstract Hilbert space vectors.The 𝕊 3 points act in measurements on observable as operators.
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.
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\mathbb{S}S3 is transformed into a playground for torsion kind states that do not require abstract Hilbert space vectors. The points S\mathbb{S}S3 evolve, governed by updated Schrodinger equation, and act in measurements on observable as operators.
The Geometric Algebra formalism opens the door to developing a theory replacing conventional quantum mechanics. Generalizations, stemming from implementation of complex numbers as geometrically feasible objects in three dimensions, followed by unambiguous definition of states, observables, measurements, bring into reality clear explanations of some weird quantum mechanical features, particularly, the results of double-slit experiments where particles create diffraction patterns inherent to a wave, or modeling atoms as a kind of solar system.
The Geometric Algebra formalism opens the door to developing a theory deeper than conventional quantum mechanics. Generalizations, stemming from implementation of complex numbers as geometrically feasible objects in three dimensions, unambiguous definition of states, observables, measurements, Maxwell equations solution in that terms, bring into reality a kind of physical fields, states in the suggested theory, spreading through the whole three-dimensional space and values of the time parameter. The fields can be modified instantly in all points of space and time values, thus eliminating the concept of cause and effect and perceiving of one-directional time.
The Geometric Algebra formalism opens the door to developing a theory upgrading conventional quantum mechanics. Generalizations, stemming from implementation of complex numbers as geometrically feasible objects in three dimensions; unambiguous definition of states, observables, measurements bring into reality clear explanations of conventional weird quantum mechanical features, particularly the results of double split experiments where particles create diffraction patterns inherent to wave diffraction. This weirdness of the double split experiment is milestone of all further difficulties in interpretation of quantum mechanics.
Even though it has been almost a century since quantum mechanics planted roots, the field has its share of unresolved problems. Could this be the result of a wrong mathematical structure providing inadequate understanding of the quantum phenomena [1]? Part of the problem is that the terms “state”, “observable”, “measurement” require a clear unambiguous definition that will make them universally acceptable in both classical and quantum mechanics. This concrete definition will help to further develop a feasible formalism for the challenging area of quantum computing [2].