Szczegóły publikacji
Opis bibliograficzny
Euclidean-Lorentzian dichotomy and algebraic causality in Finite Ring Continuum / Yosef AKHTMAN // Entropy [Dokument elektroniczny]. — Czasopismo elektroniczne ; ISSN 1099-4300 . — 2025 — vol. 27 iss. 11 art. no. 1098, s. 1–9. — Wymagania systemowe: Adobe Reader. — Bibliogr. s. 9, Abstr. — Publikacja dostępna online od: 2025-10-24. — Y. Akhtman - dod. afiliacja: Gamma Earth Sàrl, Morges, Switzerland
Autor
Słowa kluczowe
Dane bibliometryczne
| ID BaDAP | 165400 |
|---|---|
| Data dodania do BaDAP | 2026-01-13 |
| Tekst źródłowy | URL |
| DOI | 10.3390/e27111098 |
| Rok publikacji | 2025 |
| Typ publikacji | artykuł w czasopiśmie |
| Otwarty dostęp |  |
| Creative Commons | |
| Czasopismo/seria | Entropy |
Abstract
We present a concise and self-contained extension of the Finite Ring Continuum (FRC) program, showing that symmetry-complete prime shells 𝔽𝗉 with 𝗉=4𝗍+1 exhibit a fundamental Euclidean-Lorentzian dichotomy. A genuine Lorentzian quadratic form cannot be realized within a single space-like prime shell 𝔽𝗉, since to split time from space one requires a time coefficient 𝑐2 in the nonsquare class of 𝔽×𝗉, but then 𝑐∉𝔽𝗉. An explicit finite-field Lorentz transformation is subsequently derived that preserves the Minkowski form and generates a finite orthogonal group 𝑂(𝑄𝜈,𝔽𝑝2) of split type (Witt index 1). These results demonstrate that the essential algebraic features of special relativity—the invariant interval and Lorentz symmetry—emerge naturally within finite-field arithmetic, thereby establishing an intrinsic relativistic algebra within FRC. Finally, this dichotomy implies the algebraic origin of causality: Euclidean invariants reside within a space-like shell 𝔽𝗉, while Lorentzian structure and causal separation arise in its quadratic spacetime extension 𝔽𝗉2.
