Mathematical Physics

2601 Submissions

[7] ai.viXra.org:2601.0110 [pdf] submitted on 2026-01-26 21:14:03

The Stiffness-Inertia Isomorphism Theory of Physical Laws: A Unified Response Framework from Classical Wave Speed to Quantum Gravity

Authors: Xiao Peng Zhang
Comments: 6 Pages. (Note by ai.viXra.org Admin: Please cite and list scientific references)

This paper proposes and systematically elaborates a framework for the isomorphism of physical laws based on the "stiffness-inertia duality." Research reveals that numerous core formulas—from classical mechanics to quantum field theory, from condensed matter physics to cosmology, and even including string theory and loop quantum gravity—can be expressed as a functional relationship between a "stiffness term" (driving/restoring factor) and an "inertia term" (response/storage factor). The most fundamental form is ( v = sqrt{x/y} ), where ( x ) is the generalized stiffness and ( y ) is the generalized inertia.Taking the elastic wave speed formula ( v_s = sqrt{G/ho} ) as a prototype, we demonstrate how to construct a self-consistent logical network based on it, connecting the six fundamental dimensions of physics (length, mass, time, force, velocity, density) and extending to other physical quantities such as temperature, charge, and entropy. The framework successfully incorporates the core formulas of quantum mechanics, special and general relativity, the Standard Model, quantum electrodynamics, condensed matter physics, and further extends to string theory and loop quantum gravity, revealing deep mathematical isomorphisms among these seemingly disparate quantum gravity theories.We propose a unified stiffness-inertia Lagrangian formalism and derive several novel relations for strongly correlated condensed matter systems. The study suggests that "stiffness-inertia balance" may reveal a universal mathematical structure underlying physical laws, providing a new explanatory perspective and methodological tool for cross-scale, cross-disciplinary unification of physics, and offering a possible framework for the integration of quantum gravity with established physics.
Category: Mathematical Physics

[6] ai.viXra.org:2601.0073 [pdf] submitted on 2026-01-18 15:38:52

Dynamical Generation of Spacetime Torsion from Quantum Geometric Charge: A Testable Extension of Einstein-Cartan Gravity

Authors: Kazik Hubert
Comments: 6 Pages.

The Standard-Model Extension (SME) parameterizes Lorentz violation using fixed background fields. We propose a dynamical alternative where the antisymmetric SME background $(k_G)_{muu}$ emerges as a propagating spacetime torsion field in Einstein-Cartan theory. Its source is the ``Berry curvature'' of composite particles, which acts as a textit{Quantum Geometric Charge}. The coupling is mediated by a species-dependent textit{Geometric Susceptibility} $eta_a$, a calculable property of nuclear and atomic states. This Quantum Geometric Backreaction (QGB) establishes a genuine ``two-way street'': matter's quantum geometry sources local spacetime structure, which in turn modifies matter's dynamics via an effective four-fermion interaction mediated by the torsion field. The dynamical origin yields unique, falsifiable signatures absent in static background models: (i) a linear scaling of interferometric phases with source matter density, (ii) quadratic $eta_a^2$ self-energy corrections revealed in atomic spectroscopy via a textit{Torsional King Plot}, and (iii) the potential for generating detectable fields using macroscopic topological materials with broken time-reversal symmetry. We address theoretical consistency and provide first heuristic estimates of $eta_a$ for $^{85,87}text{Rb}$. The theory presents a clear experimental roadmap for tests using atom interferometers and optical lattice clocks at the $10^{-18}$--$10^{-19}$ precision level, directly probing the feedback loop between quantum matter and emergent spacetime.
Category: Mathematical Physics

[5] ai.viXra.org:2601.0057 [pdf] submitted on 2026-01-14 02:20:35

Scale-Invariant Geometric Quantization: Unifying Nuclear Physics, Chemistry, and Biology Through a Universal Topological Lens

Authors: Herman Herstad Nythe
Comments: 10 Pages.

We propose evidence for universal energy quantization spanning nuclear to biological scales through the fundamental unit EG = Ry/2π = 208.93 kJ/mol, derived from the Rydberg constant. Most significantly, we derive an exact, mass-independent ratio between the particle physics mass scale (MG) and the chemical energy scale (EG) given by MG/EG = 4π2/α3 ≈ 1.016 × 108. This geometric relationship suggests that chemistry represents a holographic projection of nuclear physics governed by vacuum topology and the fine structure constant, offering an alternative to traditional unification theories requiring Planck-scale energies. Analysis of 53 independent measurements reveals systematic correlations with EG achieving 0.02%—8% precision. Key findings include the C-C bond at (5/3)EG (0.05% deviation), the Ge band gap at EG/2φ (0.13%), water electrolysis at EG/√π (0.67%), and Neon ionization at 10EG (0.41%). Preliminary validation through a histogram analysis of 47 bonds from the NIST database reveals a highly significant deviation from uniform distribution (p = 8.3 × 10-6) with strong clustering near predicted harmonics. Furthermore, the framework identifies a biological "temperature lock" where the ratio of activation energy to thermal noise (Ea/RT) equals exactly 20 at mammalian body temperature (310 K), linking thermodynamic stability to icosahedral geometry. Combined statistical analysis yields P < 10-23 against chance. This work suggests a fundamental advance in understanding energy quantization through geometric principles (scaling by π, φ, and α) rather than solely energetic ones.
Category: Mathematical Physics

[4] ai.viXra.org:2601.0023 [pdf] submitted on 2026-01-08 22:07:05

Finite-Dimensional Davies Interface Lemmas and TFIM Witness Tests for Separation-Dependent Decoherence Rate Envelopes

Authors: Lluis Eriksson
Comments: 14 Pages.

We develop a finite-dimensional technical core relating spatial separation to effective decoherence-rate envelopes in Davies-type open-system dynamics. We use energy pinching and quantify coherence by the relative entropy between a state and its energy-pinched version. As an external input we use a maintenance inequality that lower-bounds incremental power by temperature times the instantaneous coherence-loss rate.On the operator side we prove: (i) an exact Dirichlet-form identity for the zero-Bohr-frequency channel yielding a witness-based lower bound on instantaneous decay envelopes; (ii) a Bohr-block Dirichlet decomposition for a single-channel Davies generator under quantum detailed balance; and (iii) sufficient envelope-suppression lemmas under infrared exclusion and quasi-local spectral tails, including a variant avoiding factors depending on the smallest Gibbs eigenvalue. On the state side we give an asymptotic linearization on Bohr-block perturbations with fixed diagonal, yielding a direction-dependent effective decay rate. We include finite-size transverse-field Ising chain (TFIM) witness diagnostics and fully reproducible scripts producing the figures.
Category: Mathematical Physics

[3] ai.viXra.org:2601.0011 [pdf] submitted on 2026-01-04 08:34:29

Tessellated Temporal Flux: Resolving Kakeya Protrusions Through Gyrobifastigium Multi-Tilings

Authors: Brent Hartshorn
Comments: 11 Pages.

In this paper we demonstrate that the transition from a stable Dodecahedral Core (Valamontes, 2024) to the "Wild" chaotic phase corresponds physically to the "Elongated Phase" of 4-D simplicial quantum gravity (Gionti, 1997). This phase is characterized by the emergence of Besicovitch (Kakeya) needle sets—fractal structures that achieve maximal directional complexity within minimal volumetric measure. We introduce the Gyrobifastigium as the fundamental space-filling unit capable of mediating the geometric friction between the periodic dodecahedral vacuum and the aperiodic Einstein Monotile global structure. Finally, we map this geometric resolution onto a 3D temporal framework ($tau$-space), where the "Big Bang" is redefined as a retrocausal pruning process of a "Nine-Tile" super-compatible state, effectively solving the universal NP-hard tiling problem of the vacuum through informational synchronization.
Category: Mathematical Physics

[2] ai.viXra.org:2601.0009 [pdf] submitted on 2026-01-04 20:45:49

The Truth of Riemann Conjecture Revealed in Three Dimensional Space

Authors: Shanzhong Zou
Comments: 3 Pages.

This article reveals that the Riemann Hypothesis can be attributed to the combined effect of two geometric projections within three-dimensional real space: the projection of the function's non-trivial zeros onto the complex plane, and the projection of the singularity at the point S=1 on the real axis onto the real number plane.
Category: Mathematical Physics

[1] ai.viXra.org:2601.0007 [pdf] submitted on 2026-01-02 13:26:10

Quantitative Recovery Bounds from Vacuum Clustering in Finite-Mode Gaussian States (A Regularized CCR Blueprint Motivated by Split Inclusions)

Authors: Lluis Eriksson
Comments: 21 Pages.

We prove a quantitative clustering—recovery bound for centered quasi-free (Gaussian) states in a finite-mode bosonic CCR (Weyl) setting. Motivated by split inclusions in algebraic quantum field theory, we work in a regularized framework where Gaussian states are parametrized by finite covariance matrices and a recovery map admits an explicit covariance block formula. Using a perturbative Gaussian fidelity input together with explicit coercivity bounds for inverse covariances, we bound the recovery error in terms of a vacuum cross-correlation factor, a cross-correlation perturbation parameter, and a recovery-error matrix norm ||ΔΓ||_HS, with an explicit quadratic+quartic structure. In a distinguished class (Family A, X = X0), this reduces to a bound in terms of the cross-block error ||Δ^(12)||_HS. We include ancillary numerical sanity checks verifying the perturbative regime, a collar-envelope decay model, a dimension sweep n1 = n2 in {1,2,3}, and phase-diagram checks of the perturbative domain.
Category: Mathematical Physics