Saved in:
| Main Author: | |
|---|---|
| Format: | Recurso digital |
| Language: | |
| Published: |
Zenodo
2026
|
| Online Access: | https://doi.org/10.5281/zenodo.19184991 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- <p><strong>Abstract</strong></p> <p>The Euler disk — a heavy spinning disk on a slightly concave surface — exhibits a striking behaviour: its precession frequency rises dramatically, culminating in an abrupt “click” stop rather than gradual slowdown. Standard mechanics attributes this to geometric singularity and friction, yet leaves the suddenness and energy-release mechanism partially unexplained. Here we reinterpret the Euler disk within the Generalized Mass as Twisted Time (G-MaTT) framework as a macroscopic torsional knot approaching the Twist-Untwist Threshold (TUT). As tilt angle θ → 0, the phase difference Δφ grows until |Δφ| reaches √α (α⁻¹ ≈ 137.036), at which point the TUT weight \(\mathcal{W}_{\text{TUT}} = \exp\left(-\frac{(\Delta\phi)^2}{\alpha}\right)\) collapses to zero. This produces an instantaneous loss of torsional coherence, explaining the observed abrupt termination.</p> <p>Numerical simulation using the standard power-law tilt dynamics (θ ∝ (t_f − t)^{1/3}) confirms that the classical model requires an ad-hoc cutoff, while the TUT-modified version naturally enforces a finite frequency collapse at realistic values, yielding excellent qualitative agreement with experiment. Additional tabletop demonstrators (rattleback, tippe top, Wilberforce pendulum, torsional pendulum) and a dedicated rattleback TUT simulation further validate the mechanism. The analogy extends to Planck-scale physics: the Planck frequency is the TUT limit for the smallest knots; beyond it, spacetime becomes torsional foam. This tabletop system thus serves as a direct macroscopic demonstration of G-MaTT’s core mechanism, with falsifiable predictions for vacuum tests, material scaling, and high-frequency bursts at collapse. The Euler disk is not a toy — it is the universe revealing its torsional geometry in miniature.</p>