Quantum Physics |
Authors: Rüdiger Giesel
We propose a framework in which quantum superposition emerges from the nonassociative structure of the octonion algebra. A dynamical octonion-valued field is introduced whose self-interaction is governed by the octonionic associator. The imaginary octonions define a natural G2 three-form which determines a metric structure, providing a geometric link between algebra and spacetime. The resulting field dynamics are summarized by a single master equation containing propagation, curvature coupling, and nonassociative interaction terms. Because octonion multiplication admitsdistinct ordering channels, the dynamics naturally generate independent algebraic evolution paths whose linear combination reproduces the superposition principle of quantum mechanics. Projection onto quaternionic subalgebras yields complex wavefunctions obeying the Schr¨odinger equation in the nonrelativistic limit. The framework suggests that the Hilbert-space structure of quantum mechanics may originate from the nonassociative nature of the underlying algebraic structure.
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