The Trivector Spacetime Carries Quantum Mechanics
Abstract
A real Clifford algebra can host many four-dimensional spacetimes: a spacetime family is a quadruple of mutually anticommuting unit axes with squares (−, +, +, +), and it generates an F-space — a Minkowski span, a copy of Cl(3, 1), and a stable bivector algebra. An exact census filters families by whether the full Lorentz algebra acts on their axes. We show that the first physical F-space produced by these filters, the trivector family of Cl(3, 1), carries a complete quantum mechanics: a complex unit I with I 2 = −1 central in the even subalgebra, a spinor module S = ∼ C4 carrying that complex structure, four canonical pairs [A, B] = cI, and the Dirac dynamics. All algebraic claims are verified in integer arithmetic. The family is the Hodge dual of the vector family, so the result validates trivector frames — a grade-three time axis loses no quantum structure — and leaves open whether the quantum axioms can select among the mixed families.
Related
- Theoretical Analysis of Temporal Anomalies, 5D Spacetime Geometry, and Quantum Eraser Mechanics in Superluminal Metric Engineering
- The Speed of Light as a Spacetime Conversion Rate: The Conflicting Conceptions of Time in Relativity and Quantum Mechanics, and Their Scale Interpretation
- The Hitchhiking Philosopher's Guide to the Universe: A Question-Led Introduction to the Mechanics of Recursive Spacetime
- The Pauli Probability Spectrum Carries the Pure-State Quantum Fisher Metric
- Trivector Traction Suturing Technique in Minimally Invasive Root Coverage Procedures: A Report of Two Cases
BibTeX
@misc{pommier2026trivector,
title = {{The Trivector Spacetime Carries Quantum Mechanics}},
author = {Jean-Patrick Pommier},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23540597},
url = {https://zenodo.org/records/23540597},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The Trivector Spacetime Carries Quantum Mechanics
AU - Jean-Patrick Pommier
PY - 2026
DA - 2026/10/21
PB - Zenodo
DO - 10.5281/zenodo.23540597
UR - https://zenodo.org/records/23540597
AB - A real Clifford algebra can host many four-dimensional spacetimes: a spacetime family is a quadruple of mutually anticommuting unit axes with squares (−, +, +, +), and it generates an F-space — a Minkowski span, a copy of Cl(3, 1), and a stable bivector algebra. An exact census filters families by whether the full Lorentz algebra acts on their axes. We show that the first physical F-space produced by these filters, the trivector family of Cl(3, 1), carries a complete quantum mechanics: a complex unit I with I 2 = −1 central in the even subalgebra, a spinor module S = ∼ C4 carrying that complex structure, four canonical pairs [A, B] = cI, and the Dirac dynamics. All algebraic claims are verified in integer arithmetic. The family is the Hodge dual of the vector family, so the result validates trivector frames — a grade-three time axis loses no quantum structure — and leaves open whether the quantum axioms can select among the mixed families.
ER -