保存先:
| 第一著者: | |
|---|---|
| フォーマット: | Recurso digital |
| 言語: | |
| 出版事項: |
Zenodo
2026
|
| 主題: | |
| オンライン･アクセス: | https://doi.org/10.5281/zenodo.19064227 |
| タグ: |
タグ追加
タグなし, このレコードへの初めてのタグを付けませんか!
|
目次:
- <p>We present a non-circular definition of time within Discrete Topological Torsion Theory (DTTT), in which spacetime is a Cosserat micropolar elastic medium and particles are topological solitons. The standard formulation—"time is the phase of soliton oscillation"—is circular because oscillation presupposes time. We resolve this by constructing time from five levels of purely non-temporal concepts: (1) state, (2) successor, (3) orbit, (4) cycle, and (5) time (accumulated cycle count). Time dilation is derived, not postulated, from Axiom A (the Cosserat vacuum with duality condition) and Axiom B (topological solitons requiring strong coupling). The derivation proceeds via three established results: (i) the duality condition produces a single-speed wave equation whose symmetry group is the Lorentz group (Bateman-Cunningham theorem); (ii) the discrete dynamics is a symplectic Störmer-Verlet integrator (Marsden-West theorem); (iii) the strong-coupling constraint required for soliton existence reduces the system to a single field with Lorentz symmetry, yielding the exact Pythagorean velocity budget <span><span><span><span><span><span>β</span><span><span><span><span><span><span><span>2</span></span></span></span></span></span></span></span><span>+</span></span><span><span><span>ω</span><span><span><span><span><span><span><span>2</span></span></span></span></span></span></span></span><span>=</span></span><span><span>1</span></span></span></span></span>, from which the Lorentz factor follows algebraically. The existence of periodic soliton cycles is derived via the Weinstein-Moser theorem: topological protection guarantees a non-degenerate energy minimum; the theorem then guarantees periodic orbits in the full nonlinear system. The continuous wave equation is the leading term in a Symanzik effective expansion in the orbit index <span><span><span><span><span>n</span><span>∈</span></span><span><span>N</span></span></span></span></span>, yielding a falsifiable prediction: a quadratic, CPT-even, non-birefringent modified dispersion relation at <span><span><span><span><span><span>E</span><span><span><span><span><span><span><span><span>QG</span><span>,</span>2</span></span></span></span><span></span></span></span></span></span><span>=</span></span><span><span><span><span><span><span><span>12</span></span><span><span></span></span></span><span></span></span></span></span><span><span>E</span><span><span><span><span><span><span><span><span>Pl</span></span></span></span></span><span></span></span></span></span></span></span></span></span></span> currently <span><span><span><span><span>5.8</span><span>×</span></span><span><span>1</span><span>0<span><span><span><span><span><span><span>8</span></span></span></span></span></span></span></span></span></span></span></span> above the tightest observational bound (LHAASO, 2024). The QFT vacuum catastrophe does not arise because Einstein-Cartan torsion is algebraic and non-propagating; the cosmological constant is estimated within one-two orders of magnitude via the Poplawski torsion condensate mechanism.</p>