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| viXra.org > Mathematical Physics > 2605 |
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[6] viXra:2605.0113 [pdf] submitted on 2026-05-29 01:02:12
Authors: Taiwei Song
Comments: 6 Pages. 6
This short paper briefly discusses the fundamental concepts, intrinsic rules, and logical relationships of geometry from the most essential perspective, and its relationship with algebra. It also defines natural space-time space and its intrinsic logical relationships and significance. Most of the content in this paper is important achievements of the" Geometry of Space-time Structures " established by the author.
Category: Mathematical Physics
[5] viXra:2605.0112 [pdf] submitted on 2026-05-29 20:37:55
Authors: Urs Frauenfelder, Joa Weber
Comments: 57 pages, 3 figures
In this article we study periodic orbits of an electron attracted by a proton subject to Lorentz, electric, and Euler forces where each of them is allowed to depend periodically on time. This setup is motivated by the elliptic restricted three-body-problem where the Lorentz force corresponds to Coriolis force, the Coulomb force is replaced by the gravitational force, and the electric force of an external source is a combination of centrifugal forces and gravitational forces of other bodies. This is a singular version of a Euler-Hamilton system as discussed in [FW26b]. The singularity is due to collisions of the electron with the proton, respectively of two masses. Due to the possibility of collisions this problem has to be regularized.We show how periodic collisional solutions of this problem can be detected variationally in a non-local Lagrangian setup as well as in a non- local Hamiltonian setup.
Category: Mathematical Physics
[4] viXra:2605.0087 [pdf] submitted on 2026-05-21 23:42:34
Authors: Harsha Kumar Suriyaarachchi
Comments: 11 Pages. (Note by viXra Admin: Please cite listed scientific reference)
This study presents a resolution to the 2500-year-old Zeno’s paradox, restoring the relationship between Space and time to the fundamentals of classical understanding. Further, the calculation shows the instability of the relativistic space-time relationship in resolving the paradox.Zeno’s paradox has four main canonical variants, Dichotomy, Achilles and Tortoise, Arrow Paradox and Moving Rows. A comprehensive analysis is conducted of both classical and contemporary relativistic approaches proposed to resolve the paradox, including standard calculus, the summation of infinite series, models invoking quantised space, quantised time, and various adaptations within relativistic framework. Despite their theoretical sophistication, these approaches are mathematically argued to fall short of providing a satisfactory resolution.Coherent resolution emerges only under the hypothesis that time progresses as an independent, intrinsic and continuous entity, rather than being tied to spatial or kinematic variables. Classical mechanics tends to treat time as an independent parameter, but this feature has not been explicitly utilised in prior attempts to resolve Zeno’s paradox at a fundamental level. The present work proves where previous attempts, including the relativistic framework, fail and re-examines the paradox by explicitly enforcing the independence and the continuity of time as a primary principle, to consistently resolve the paradox.
Category: Mathematical Physics
[3] viXra:2605.0047 [pdf] submitted on 2026-05-13 19:04:41
Authors: Igor Shchitov
Comments: 4 Pages.
The article proves that the solution to the Cauchy problem for the harmonic oscillator equation is not unique, and can have the most unusual properties.
Category: Mathematical Physics
[2] viXra:2605.0034 [pdf] submitted on 2026-05-09 05:58:16
Authors: Payam Danesh, Raoul Bianchetti
Comments: 26 Pages.
The axiomatization of physics, particularly the connection between microscopic dynamics and macroscopic laws, remains a central challenge of Hilbert’s Sixth Problem. A persistent conceptual gap in this program is that probability is typically introduced as a fundamental assumption rather than derived from physical evolution itself. To close this gap, we develop Viscous Time Theory (VTT), an evolutionary framework structured around admissibility, coherence, and recoverability. When paired with an informational action principle, VTT allows probability to emerge naturally as an induced statistical measure over bundles of admissible trajectories. To test this proposed mechanism, we analyze a viscous-time kinetic transport operator, establishing its contraction semigroup structure, spectral gap, and hypocoercive convergence. We then extend the model to nonlinear interaction kernels and evaluate its hydrodynamic scaling limit. The analysis proves that this diffusion-driven operator achieves strict spectral stability, exponential entropy decay, and global nonlinear stability, with the macroscopic scaling limit rigorously yielding nonlinear diffusion dynamics for the coherence density. By providing an analytically tractable layer between microscopic and macroscopic behavior, this work demonstrates how probability, irreversibility, and transport laws can cohesively emerge from informational geometry.
Category: Mathematical Physics
[1] viXra:2605.0031 [pdf] submitted on 2026-05-09 07:44:44
Authors: Chunshu Li
Comments: 5 Pages.
Within the framework of classical electrodynamics, a spherical electromagnetic standing-wave model is constructed. Based on Maxwell equations in vacuum, the lowest-order transverse electric (TE) mode with l=1 in spherical coordinates is adopted, and the half-wave standing-wave condition kru2091=π is imposed as the geometric constraint. Integrating the electromagnetic energy density over the whole domain yields a total field energy exactly equal to the electron rest energy, with the ratio precisely 1.000000. The model gives the fine-structure constant α=ru2091/λc=0.00729735 from geometric relations, consistent with experimental values. No free parameters are introduced; the derivation relies entirely on classical electromagnetic theory. The results show that a self-confined, localized field configuration exists in the solution space of classical electrodynamics, whose numerical characteristics match the known properties of the electron with high fidelity.
Category: Mathematical Physics
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