The Theory of Spatial Substance (Formalized Version)
Foundation Report: SC-Substance-Theory-Formalized
Version: 3.0 (Mathematical Foundation)
Abstract
This document presents the final, formalized version of the Theory of Spatial Substance. We demonstrate that the concept of “Spatial Substance” is the physical realization of the hierarchy of division algebras. Its properties, which lead to the emergence of quantum mechanics, are no longer postulates but theorems derived from this fundamental mathematical structure.
From Algebra to Physics
The single physical axiom of the theory is that the substance of reality is an incarnation of the mathematical structure `ℝ→ℂ→ℍ→𝕆`. Theorem 7 demonstrates how this structure generates the principles of quantum physics:
- Quantization: Consequence of the discrete nature of the algebraic hierarchy.
- Spin ½: Consequence of the inherent duality of the algebra `ℂ`.
- Exclusion Principle: Topological consequence of the indistinguishability of excitations in the algebraic space.
Conclusion
Spatial Substance is no longer a philosophical idea, but a well-defined mathematical object whose properties generate physics. The foundation of the theory is now entirely mathematical.