R 3 ⊕ I 3 : Axioms → Consequences → Tests
Year: 2025
Type: article
Abstract: This two–page brief outlines a coupled spatial framework R3 ⊕ I3, where I3 is pure quaternion imaginary space with a negative volume element (dVI < 0 from ijk = −1).Exchange between sectors occurs only across fixed Planck–area interface patches σ0 = 4 ln 2L^2 P (one bit per patch). Using the Dirac current with the I3 metric yields a negative probability density in I3 , ρI = −Φ†Φ, ensuring PR + PI = 1 without ad hoc conventions. I3 supports evanescent modes with decay length λc = ℏ/(mc) and an imaginary electromagnetic impedance (no propagating radiation). Mode–by–mode vacuum–energy contributions from the two sectors cancel, with a small leakage across σ0 accounting for the observed Λ. Black–hole horizons are quilts of σ0 patches, reproducing SBH = kBA/(4L2P). On–shell scattering in R3 (the S–matrix) remains standard; off–shell structure is geometrized as short R→I →R excursions. Zitterbewegung appears as weak sector exchange at ωZB ≃ 2E/ℏ. We propose near–term tests: π–flip interferometry on an R→I →R loop; Bell–fidelity dephasing under controlled near–field (σ0) coupling; sub–µm near–field tails ∝ e−2d/λc ; and a tiny ZB sideband. The framework preserves Lorentz symmetry and causality in R3 while offering concrete routes to falsification.Keywords: quaternions; negative volume; Planck interface; black–hole entropy; cosmologicalconstant; near–field; Zitterbewegung. “Comments welcome at ; I’ll keep the record updated with revisions.”
Author: Fabriciuss, Ivars
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7081982106
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