Mathematical Physics

2605 Submissions

[2] viXra:2605.0034 [pdf] submitted on 2026-05-09 05:58:16

Hilbert’s 6th Problem New re-Interpretation

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

The Classical Electromagnetic Standing Wave Model of the Electron: Energy Self-Consistency and Implications for the Mass—Energy Relation

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