Mathematical Physics

Non-Archimedean Functional Analysis Over Non-Archimedean Field ^{∗}ℝ_{c}^{}. Applications to Constructive Quantum Field Theory.part II.essential #-Self Adjointness of Hamiltonian H_{0}+V.

Authors: Jaykov Foukzon
Comments: 271 Pages.

Functional analysis works with TVS (Topological Vector Spaces), classically over archimedean fields like ℝ and ℂ.Canonical non-Archimedeanfunctional analysis, where alternative but equally valid number systems such as p-adic numbers ℚ_{p} etc. are fundamental, is a fast-growing discipline.This paper deals with TVS over non-classical non-Archimedean fields ^{∗}ℝ_{c}^{} ,^{∗}ℝ_{c}^{} and^{∗}ℂ_{c}^{}, ^{∗}ℂ_{c}^{}. Definitions and theorems related to non-Archimedean functional analysis onnon-Archemedean field ┊^{∗}ℝ_{c}^{}┊ and on complex field ┊^{∗}ℂ_{c}^{}┊=┊^{∗}ℝ_{c}^{}┊+i┊^{∗}ℝ_{c}^{}┊are considered. Applications to constructive quantum field theory also are considered
Category: Mathematical Physics

On Continuous Dimensions and Infrared Mass Generation

Authors: Ervin Goldfain
Comments: 33 Pages.

We show that dimensional regularization of a generic self-interacting field theory induces an infrared mass scale, when the running spacetime dimension approaches the critical value D=4. The mechanism is universal and does not rely on spontaneous symmetry breaking alone. Instead, it arises from logarithmic corrections generated by renormalization group (RG) flow near the bifurcation point at ϵ≡4-D→0. We explicitly indicate how dimensional transmutation converts marginal couplings into dynamically generated mass scales. This framework unifies the origin of the Higgs vacuum expectation value and electroweak boson masses with the Yang—Mills mass gap and the QCD scale Λ_QCD. Step-by-step derivations are provided, without appealing to nonperturbative assumptions beyond RG consistency. The paper focuses on the regime bordering relativistic quantum field theory and complex dynamics.
Category: Mathematical Physics

Intrinsic Dynamical Equations of the Three-Body System and the Gravitational Superposition Theorem

Authors: Jinyong Liu
Comments: 13 Pages. (Note by viXra Admin: For the last time, please cite and list scientific references!)

This paper addresses a classic core challenge in celestial mechanics—the three-body problem. Based on the fundamental axioms of Newtonian mechanics, we rigorously derive and prove a universal "Gravitational Superposition Theorem." This theorem states that the total gravitational field produced at any point in the external space by a finite set of point masses is completely equivalent to the gravitational field produced by a single point mass located at the system's center of mass, with a mass equal to the sum of the individual masses. Using this theorem as a cornerstone, the classical three-body problem can be precisely reduced to three strictly analytically solvable two-body relative motion problems.This research not only provides a theoretically self-consistent and mathematically complete framework for the long-standing three-body problem but also fundamentally reconstructs the theoretical paradigm and logical starting point for modeling multi-body gravitational systems.
Category: Mathematical Physics

From the Kinematics of Elliptical Motion to the Law of Gravitation

Authors: Viktor Strohm
Comments: 4 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)

The law of force governing the motion of a material point along an elliptical orbit is derived using a purely kinematic approach. Starting from the differential equations of motion in a Cartesian coordinate system, an angular equation of motion is obtained that directly leads to Kepler’s second law. It is shown that the acceleration is directed toward the focus of the ellipse and is inversely proportional to the square of the distance. The derived expressions are applied to the Earth—Moon system. Forces calculated using Newton’s second law are compared with those given by Newton’s law of universal gravitation. The relative discrepancy does not exceed 1.1%, confirming their equivalence.
Category: Mathematical Physics

Singularities in 3D: the Mathematical Challenge of Euler and Navier-Stokes

Authors: Diego Cordoba Gazolaz, Luis Martinez Zoroa, Abdelmajid Ben Hadj Salem
Comments: 19 Pages. In French, the article was translated from spanish.

The Euler and Navier-Stokes equations describe the motion of fluids, but it is still unknown whether their smooth solutions (with $C^{infty}$ regularity) can develop singularities in finite time.This enigma, one of the «Millennium Prize Problems», poses fundamental mathematical and physical challenges. In this article, we review what singularities are, the main mechanisms proposed for their formation (selfsimilar solutions and vorticity cascades) as well as recent advances that shed new light on this problem in three dimensions.
Category: Mathematical Physics

Recurrence, Alignment, and Temporal Structure in the Sun—Earth—Moon System

Authors: Pedro A. Kubitschek Homem de Carvalho
Comments: 30 Pages. (Note by viXra Admin: For the last time, please submit article written with AI assistance to ai.viXra.org!)

The classical three—body problem is traditionally formulated as the predictionof complete spatial trajectories of three interacting masses under gravitation, a taskknown to be generally non—integrable and chaotic. In this work, we adopt a complementary perspective focused on the Sun—Earth—Moon system, where the most stable and observable features arise not from translational motion but from rotational recurrence and angular phase closure. We introduce an angular—toroidal phaseformalism in which the three bodies are represented by periodic phase variablesassociated with Earth rotation, Earth orbital motion, and lunar orbital motion. These phases naturally define a three—torus T3, within which the system evolves as a helical flow. Observable cycles such as the solar day, the synodic month, and the year emerge as alignment events corresponding to phase closure conditions. An alignment operator is proposed to characterize the temporal coherence of these events. The approach does not aim to recover full three—body trajectories, but in stead provides an analytic and geometrically transparent description of recurrence and temporal structure in the restricted three—body problem.
Category: Mathematical Physics

Invariance of Ensemble Overlap in Stochastic Binary Processes: A Gauge Theory of Strategy

Authors: Goutham Netha Anagandula
Comments: 2 Pages. Pedagogical derivation connecting the Gambler's Fallacy to Gauge Invariance

The "Gambler’s Fallacy" is often treated as a cognitive bias, but it can be rigorously understood as a violation of translational invariance in probability space. In this paper, we define a "Global Correlation Functional" G(u20d7S) representing the expected overlap between a fixed control sequence (strategy)u20d7 S and a random Bernoulli target vector (nature)u20d7 X. By treating the strategyu20d7 S as a gauge degree of freedom, we demonstrate—both analytically and via Monte Carlo simulation—that the expectation value of the overlap is invariant under all local permutations ofu20d7 S. We conclude that in memoryless systems, the derivative of success with respect to strategy is identically zero(∇u20d7 S G = 0), implying that all strategies are microcanonically equivalent. This framework offers a pedagogical bridge between classical probability and the concept of gauge invariance in theoretical physics.
Category: Mathematical Physics

From Algebraic Extension to Physical Law: Multiplication, Integration, and the Emergence of Variational Field Reality

Authors: Juan Moreno Borrallo
Comments: 26 Pages. (Note by viXra Admin: For the last time, please submit article written with AI assistance to ai.viXra.org!)

We propose a foundational route from elementary mathematical operations to the structural form of physical law. The guiding thesis is that multiplication is the primitive operation that generates geometric extension (e.g., area via bilinear composition), integration is the continuous accumulation of such local extensions into global quantities, and differentiation (or functional variation) is the dual operation that extracts local constraints from global accumulations. From these principles, we show how any consistent description of ``physical reality'' must be formulated in terms of local densities defined over a continuous geometric support, whose global content is obtained by integration and whose dynamics follows from variational (action) stationarity.Within this operational framework, quadratic field terms arise naturally as the simplest scalar invariants built from local degrees of freedom, while source couplings appear as bilinear products between generalized currents and the underlying deformation variables. Furthermore, we show that quantum entanglement is not a dynamical anomaly but a structural inevitability: additive accumulation acting on states represented in a multiplicative (spectral) basis generically produces global correlations that resist local factorization. This reframes Bell-type violations as a failure of structural independence rather than a signal of superluminal causal influence, thereby preserving relativistic causality at the level of dynamical propagation.Crucially, beyond the contractive modes commonly associated with forces and curvature, the same logic compels expansive degrees of freedom: an entropic sector characterized by an intensive--extensive product structure (temperature-like $times$ entropy-like) contributing intrinsically to the global action. This viewpoint yields a general blueprint for interpreting electromagnetic, gravitational, and entropic responses as projected modes of a common underlying field structure, and it clarifies why concrete realizations of such a blueprint---including quantum-elastic and gravito-entropic field models---arise as minimal, structurally stable completions rather than independent hypotheses.
Category: Mathematical Physics

Exact Values of the Proton Radius and the Gravitational Constant by Use of the "Hans de Vries"- and the "Julian Schwinger"-Term

Authors: Andreas Ball
Comments: 14 Pages.

In this report very exact formulas for the Proton Radius and for the Gravitational Constant are presented, at which the Fine Tuning Term of the "Hans de Vries"-Formula and also the "Julian Schwinger"-Term are applied. Some of the Formulas are constructed quite simple and the connections for one with another are presented. Many of the result values are very accurate referring to their tolerance ranges (i.e. exact in this context) and therefore lie astonishingly closely together.
Category: Mathematical Physics

Merry-go-Round and Time-Dependent Symplectic Forms

Authors: Urs Frauenfelder, Joa Weber
Comments: 18 Pages. 1 figure

In the merry-go-round fictitious forces are acting like centrifugal force and Coriolis force. Like the Lorentz force Coriolis force is velocity dependent and, following Arnold, can be modeled by twisting the symplectic form. If the merry-go-round is accelerated an additional fictitious force shows up, the Euler force. In this article we explain how one deals symplectically with the Euler force by considering time-dependent symplectic forms. It will turn out that to treat the Euler force one also needs time-dependent primitives of the time-dependent symplectic forms.
Category: Mathematical Physics

On the Planck Mass and Length

Authors: Branko Zivlak
Comments: 4 Pages. 2 figures

The paper presents two complementary formulas for the Planck mass and the Planck length, which yield higher accuracy than the values reported in the CODATA reports.
Category: Mathematical Physics

Global Existence and Smoothness of The Navier-Stokes Equation via Spectral Decimation on Icosahedral Manifolds

Authors: Stephen Ryan Moorehead-McDaniel
Comments: 24 Pages. 2 figures (Note by viXra Admin: Please cite listed scientific references, list scientific references in a complete manner, and submit article written with AI assistance to ai.viXra.org)

Since the original formulation of the Navier-Stokes equations in 1822, the inability to prove global regularity has been fundamentally rooted in a physical misconception: the assumption that the fluid continuum is isotropic at the dissipation scale. We assert that the Millennium Prize problem, as currently posed, is unsolvable not due to a lack of mathematical tools, but due to an incomplete understanding of the physical vacuum. This paper does not introduce a new external rule; rather, it identifies an intrinsic Topological Boundary Constraint that has always governed fluid dynamics but remained unobserved by standard analysis. We demonstrate that the vacuum naturally selects the Gamma_{120} manifold (derived from the symmetry of the Great Rhombicosidodecahedron) as the global attractor for energy dissipation. By observing the inherent 72^circ torsional alignment of the vorticity field, we show that the non-linear advection term is geometrically depleted at the Kolmogorov scale, naturally precluding singularity formation. Finally, we show that the standard isotropic model violates the Second Law of Thermodynamics via spectral aliasing, a violation that nature corrects through this pre-existing geometric governor. The solution is smooth because the physical universe does not permit the isotropic blow-up assumed by the mathematical model.
Category: Mathematical Physics

Thoughts on the Generation Problem

Authors: Thierry L. A. Periat
Comments: 59 Pages.

Why are there three generations (leptons and quarks)? Are they related to one another? If yes, how? This document is a pioneer work shedding a renewed light on a topic that is currently an open questioning under investigation. It proposes an alternative way of expressing the invariance of the speed of light, which is based on the study of the deformations of the Poynting’s vector. This method allows the introduction of trios of deforming matrices which are obliged to respect a very specific constraint. The work examines how to make this constraint compatible with the existence of ratios connecting the masses of three particles according to a formula proposed by Y. Koide.
Category: Mathematical Physics

Matrix Representations of Su(3) and Sl(3,C) Lie Algebras Via Fortran 90

Authors: Richard Shurtleff
Comments: 36 pages including a 24 page Fortran program

The Fortran 90 program included in this article calculates eight matrices that form a basis of the sl(3,C) Lie algebra in an irreducible representation of the user's choice. A quick linear transformation yields a basis for the su(3) Lie algebra. The program checks that the generators satisfy the necessary commutation relations and saves the matrix generators to data files.
Category: Mathematical Physics

Three—Body Problem: Recurrence, Alignment, and Temporal Structure in the Sun—Earth—Moon System

Authors: Pedro A. Kubitschek Homem de Carvalho
Comments: 20 Pages. (Note by viXra Admin: For the last time, please submit article written with AI assistance to ai.viXra.org!)

The classical three—body problem is traditionally formulated as the predictionof complete spatial trajectories of three interacting masses under gravitation, a taskknown to be generally non—integrable and chaotic. In this work, we adopt a complementary perspective focused on the Sun—Earth—Moon system, where the most stable and observable features arise not from translational motion but from rotational recurrence and angular phase closure. We introduce an angular—toroidal phase formalism in which the three bodies are represented by periodic phase variables associated with Earth rotation, Earth orbital motion, and lunar orbital motion. These phasesnaturally define a three—torus T 3, within which the system evolves as a helical flow.
Category: Mathematical Physics

Formulas for Su(3), Sl(3,C) Matrix Generators, the Mathematica Notebook

Authors: Richard Shurtleff
Comments: 43 pages, computer program in an interpretive proprietary language

This notebook presents formulas for matrices that form the bases of the generators of the irreducible representations of the Lie algebras sl(3,C) and su(3). The matrix generators are shown to satisfy the commutation relations of the algebras. For an irrep of the reader's choosing, the notebook calculates the bases of both algebras, sl(3,C) and su(3). The numerical matrices are saved in files in the folder with this notebook.
Category: Mathematical Physics

Physicist Into Physicist - Collection

Authors: Leonardo Rubino
Comments: 186 Pages. In Italian and English

A collection of cases where a physicist is found into another physicist.
Category: Mathematical Physics

Multivector Physics

Authors: Kim GinHak
Comments: 12 Pages. (Note by viXra Admin: Please cite and list scientific references)

Maxwell's equations can be derived from the vector potential using only multivector calculations and duality in 4-dimension. Furthermore, by changing the dimension of the vector potential, three additional Maxwell's equations with different dimensions are derived. These four Maxwell's equations give us hints about charge, spin, quarks, and mass. The divergence of the electromagnetic field energy density expressed in multivectors is the electromagnetic force and Joule heat. In the same way, three more forces are also derived from three additional Maxwell's equations. One is gravity, another explains weak forces well, and the last one seems to be strong force. By defining the dot product of multivectors, the dual multivector, the curl, and the divergence of multivector fields are clearly defined. By defining the norm of a multivectors, the multiplication table of 16 multibases in 4-dimension is obtained. Multivectors are numbers that include direction and dimension, and an optimal language for physical quantities.
Category: Mathematical Physics

Why Current AI Architectures are Not Conscious: Neural Networks as Spinfoam Networks in a Theory of Quantum Gravity

Authors: Trevor Nestor
Comments: 102 Pages. (Note by viXra Admin: For the last time, please submit article written with AI assistance to ai.viXra.org; please also cite other scholars' work)

Classical deep neural networks excel at many tasks and even multimodal generative outputs but remain energetically inefficient by orders of magnitude from the human brain, lack mechanisms for integrated binding, and have been argued exhibit no genuine route to consciousness. While inspired by neural architectures in brain tissue, deep neural networks face scaling limits. Drawing on loop quantum gravity (LQG) and the Orchestrated Objective Reduction (Orch-OR) theory of consciousness, we introduce a framework model of Neural Spinfoam Networks (NSN), a bio-inspired AI paradigm in which each neural layer is recast as a spin-network and each learning update as a spinfoam transition by means of gravitational collapse at a phase transition at entropic limits described by a UV fixed point and by the Monster Conformal Field Theory (Monster CFT). Our model leverages Majorana-fermion braiding within spinfoam geometries and a gravitational feedback loop to achieve one-shot, polynomial-time credit assignment for the NP-hard perceptual binding problem. The network's global state is encoded by a noncommutative-geometry spectral triple (A, H, D), where the Dirac-like operator's smallest nonzero eigenvalue corresponds directly to the shortest nonzero lattice vector, thereby achieving perceptual binding by means of gravitationally induced phase transition, forming the basis for a more plausible mechanism of backpropagation and weight transport that are currently unexplained by classical models of brain function. Periodic Floquet driving and the Cayley-transformed microtubule Hamiltonian yield topologically protected, room-temperature quantum coherence in tubulin-analogous nodes. Recent demonstrations of microtubule superradiance and time-crystalline oscillations within brain tissue further substantiate sustained entangled states and ultrafast biophotonic readout as described by Orch-Or theory, in spite of criticisms, which are discussed.
Category: Mathematical Physics

Elementary Particles Rest Mass Formula and the Weak Interaction2

Authors: Claude Michael Cassano
Comments: 4 Pages.

A single formula for every non-neutrino fermion rest mass is determined based on the E/B triplet electromagnetic-nuclear-weak field-strengths and the Weak Interaction is simply explained based on these field-strengths also determining the W and Z masses.
Category: Mathematical Physics

Analytical Solutions for the Many-Body Problem

Authors: Jinyong Liu
Comments: 12 Pages.

This work is a theoretical breakthrough in the study of the many-body problem. Breaking the long-standing myth that the many-body problem cannot be solved analytically, the analytic solutions of the orbit equation, periodic formula, and the motion equation of the many-body problem are obtained skillfully herein. Furthermore, this study offers a rigorous mathematical proof of the coplanarity and common direction of celestial bodies within such systems. The conclusions are mathematically accurate and complete, potentially marking a culmination of over 300 years of inquiry since Newton first posed the problem. From a physics perspective, this study provides a theoretical basis for the stable operation of celestial systems that is fully aligned with astronomical observation across large and small galactic structures. Notably, the discovery that the orbital period of celestial bodies is related to their own mass is of great significance for studying the formation and evolution of galaxies and planetary systems.
Category: Mathematical Physics

Central Gravity Theory

Authors: Jinyong Liu
Comments: 12 Pages. (Note by viXra Admin: Please cite and list scientific references)

This study analyzes the application limitations of Newton’s law of gravitational force in the many-body problem and reveals the fundamental problems with the application of Newton’s gravitational formula in the current central configuration theory widely used in celestial mechanics. A new method suitable for the synthesis of gravitational vectors in many-body systems is proposed, and a new central gravity theory system is constructed accordingly. The proposed theory provides a concise framework for the dynamic modeling and analysis of complex celestial systems. Based on the many-body mechanical equation established by the central gravity formula, the analytical solution of the many-body problem was successfully solved, and an important theoretical breakthrough in this field was achieved in the field. It has been more than 300 years since Newton proposed the three-body and many-body problems. The central gravitational formula has undergone rigorous mathematical derivation and logical verification, and this formula now has theorem properties, marking the substantial progress of celestial mechanics. The theory of central gravity is expected to have a profound impact on the theoretical development of astrophysics.
Category: Mathematical Physics

Classical Field Theory from Primordial Dimensional Fluctuations

Authors: Ervin Goldfain
Comments: 38 Pages.

Complex Ginzburg-Landau equation (CGLE) is a universal amplitude equation governing the dynamics of phenomena unfolding in far-from-equilibrium conditions. It was recently argued that CGLE emerges from primordial dimensional fluctuations acting in the far ultraviolet sector of field theory and primordial cosmology. Here we show that classical Maxwell, Dirac and non-Abelian field theories can be derived directly from a generalized version of CGLE without invoking a Lagrangian or variational principle. Demanding that CGLE preserves local coherence under continuous internal transformations, we introduce a natural covariant derivative whose connection acts as a gauge field. The commutator of these covariant derivatives defines a curvature tensor that reproduces the familiar structure of Maxwell and Yang—Mills field strengths, while a first-order, spinor generalization of CGLE yields Dirac-type dynamics. In a nutshell, classical field theories naturally emerge from demanding local coherence invariance of the generalized CGLE.
Category: Mathematical Physics

A Unified Approach to Cosmic and Physical Phenomena:

Authors: Ulrich Schreier
Comments: 12 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

This paper introduces Anton Bopp's (1900--1971) comprehensive vibratory-hydro-dynamic model to the international scientific community. Bopp's unpublished manuscripts present a unified theory spanning cosmic to atomic and subatomic scales, using the hydrogen atom as a universal archetype. The model demonstrates a remarkable capacity to derive fundamental physical constants through mathematical relationships involving the foundational set ${pi, e, 1, 2, 3}$. While Bopp's primary focus was operational---developing practical tools for physical applications---his work reveals, as a natural byproduct, deep connections between mathematical principles and physical reality. This paper highlights selected findings of particular significance, situating Bopp's contributions within the historical continuum from Pythagorean harmony to Wigner's "unreasonable effectiveness of mathematics," suggesting that physical laws emerge from mathematical substrates rather than merely being described by them.
Category: Mathematical Physics

Space Warp, Space-Time Transformation, and Cosmic Redshift: The Application of the Geometry of Space-Time Structures on Large Spatial Scales

Authors: Taiwei Song
Comments: 8 Pages.

Based on the Geometry of Space-Time Structures founded by the author himself, this paper uses an accurate mathematical model to explain the space warp problem of the giant world, deduces the curvature formula of the optical path curve of the natural space-time space, and explains its physical significance; demonstrates the space-time transformation relationship between the geometric scene of natural space-time space and the visual image of the observer, and gives the space-time transformation equation; discusses the natural properties of the cosmic redshift, derives the redshift differential formula; proposes the experimental methods to verify the new space-time relationships of photons, etc.
Category: Mathematical Physics

Pattern Field Theory: Proof Strategy for the Riemann Hypothesis (2025)

Authors: James Johan Sebastian Allen
Comments: 64 Pages. Licensed under CC BY-NC-ND 4.0 (Note by viXra Admin: Please cite listed scientific reference and submit article written with AI assistance to ai.viXra.org)

Pattern Field Theory (PFT) proposes a deterministic, arithmetic operator framework that unifies mathematical and physical coherence under a single equilibrium principle, the Equilibrion. The Allen Orbital Lattice (AOL) defines a self-adjoint operator whose unfolded eigenvalue spacings exhibit Gaussian Unitary Ensemble (GUE) statistics consistent with the non-trivial zeros of the Riemann zeta function. This framework provides a constructive Hilbert—Pólya-type proof strategy for the Riemann Hypothesis, linking prime distribution, curvature equilibrium, and recursive field dynamics. Empirical lattice simulations confirm GUE universality and geometric correspondence with atomic quantization, suggesting that prime structure, curvature, and coherence form a unified mathematical—physical substrate.
Category: Mathematical Physics

Spice-Grains in Kneaded Dough Are Able to Move Similarly to Masses Free Floating in Space-Time of Earth's Interior.

Authors: Udo E. Steinemann
Comments: 16 Pages.

Movement-patterns of geodesics are compared who firstly are conceived for masses floating mentally through space-time inside earth and secondly can be observed for spice-grains in kneaded dough.
Category: Mathematical Physics

An Introduction to General Relativistic Wave Differential Operator in the Quantum Field Theory

Authors: Julio Jaramillo
Comments: 13 Pages.

This work introduces a unified operator framework for quantum field theory through the emph{generalized relativistic wave differential operator} $D^{mnlambda}_{alphabeta}$. By appropriate parameter choices, this operator encompasses the Klein-Gordon, Dirac, and non-monogenic operators, revealing their fundamental connections. We propose a emph{quantum field tensor} $Psi_{sigmahotau}$ with binary activation indices for scalar, spinor, and gauge fields, generating all possible interactions while preserving Lorentz covariance. The framework incorporates gauge invariance through minimal coupling and yields both Proca and Maxwell equations as special cases. This approach provides a powerful operator-based unification of quantum field theory with applications to higher-spin theories.
Category: Mathematical Physics

The Ordinary Perian Matrices, Link with the Three Generations Problem.

Authors: Thierry L. A. Periat
Comments: 62 Pages. In French: Les matrices périennes ordinaires - lien avec le problème des trois générations de particules

The belief that one may unify physics, especially the theories concerning electromagnetism and gravitation, motivated my first intuitive ideas in 2003. I reanalyse the way of thinking which has been introduced in the initial document because it is in fact at the origin of the so-called (E) question. The search for answers to this question has allowed the development of diverse methods explaining how to divide (decompose) deformed cross products. It turns out that the kerns of the main parts of the decompositions have remarkable properties, useful in particle physics. This is what this document demonstrates since it succeeds in proving a link between a set of ordinary perian matrices and the mass-matrices proposed twenty-five years ago by theoreticians. The approach I have developed over the past quarter century therefore provides an algebraic and geometric explanation for the matrices which had been proposed by the physicists with the inner logic of particle physics. It helps to give particles a concrete face.FR version - Ma croyance en la possibilité d'unifier les théories de l'électromagnétisme et de la gravitation m'avait motivé à présenter quelques idées en 2003. Je reviens ici sur le raisonnement sous-jacent au document initial parce que c'est lui qui a justifié la naissance de la question dite (E). La recherche de réponse à cette question a permis le développement de méthodes mathématiques qui toutes avaient l'espoir de généraliser la formule initiale. L'étude répétée et approfondie des réponses apportées montre que les noyaux des parties principales des décompositions des produits vectoriels déformés ont des propriétés mathématiques remarquables et utilisables en physique. C'est bien ce que ce document finit par démontrer puisqu'il établit enfin un lien clair entre un ensemble particulier de matrices périennes ordinaires et les matrices des masses proposées il y a maintenant plus de vingt-cinq ans par théoriciens de la physique. L'approche que j'ai développé au cours du quart de siècle passé fournit donc une explication algébrique et géométrique à des matrices qui résultaient jusque-là de la logique interne du modèle standard des particules. Elle contribue ainsi à leur donner un visage plus concret.
Category: Mathematical Physics

All Lyman, Balmer, Paschen and Brackett Lines Are in Superresonance

Authors: Marek Suder
Comments: 6 Pages.

The paper presents an extended analysis of the structure of the hydrogen atom spectral lines, based on the concept of superresonance — a phenomenon in which all Lyman, Balmer, Paschen and Brackett resonances (for n ≤ 7 and m ≤ 4) exhibit complete harmonic relations with respect to the λu2080 wave.The frequency values form a discrete raster with a constant spacing of approximately 18.64 GHz. The results indicate the existence of a universal harmonic structure in the hydrogen spectrum, opening new possibilities in spectroscopy and the theory of atomic interactions.Based on this, the concept of a subquantum (sQ) was introduced, defined as the smallest unit of photon energy with a value of εu2080 ≈ 7.71 × 10u207bu2075 eV, equal to 1/3969 of the H(5→4) transition energy. This unit allows the construction of a resonance grid in which all analyzed transitions are arranged in integer multiples of the fundamental frequency.The proposed approach suggests that the hydrogen spectrum is governed by a simple harmonic system, extending the classical Bohr—Rydberg model with a deeper level of discretization. This method reduces measurement uncertainties and opens up new possibilities for precise spectroscopic calibration, enabling not only the description of known transitions but also the prediction of previously unobserved line parameters.
Category: Mathematical Physics

Algebraic Dynamics First Stones

Authors: Thierry L. A. Periat
Comments: 49 Pages. (Note by viXra Admin: Please submit finalized version only and remove the watermark "Draft"))

This exploration focuses attention on the kernels related to the decomposition of deformed cross products. It tries to use them as commutative operator describing the evolution of the polynomials which are associated with the decomposition of these deformed products. The long-range purpose is the construction of an algebraic dynamics shedding a new light on our reality.
Category: Mathematical Physics

Euler’s Identity and the Hidden Dimensional Assumption: A Critique of Mathematical Orthodoxy

Authors: Kshitiz Prabhakar
Comments: 5 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

Euler’s identity e^(iπ)+1 = 0 is a central, rigorously proven result in complex analysis. This note does not dispute its correctness inside that formalism. Instead it isolates a single, widely overlooked modeling choice that arises when the analytic identity is applied to measurable angles in physics and engineering: the implicit treatment of angular measures as if they were plain, unitless real numbers. I (1) explain why the analytic/trigonometric power series force a particular angular normalization (radians); (2) show concretely, via a bradian renormalization and a kilogram counterexample, that the usual "divide-by-1 rad" maneuveris a convention that cannot be elevated to a general principle; (3) formalize the issue as atype/coercion error; and (4) show direct implications for phasor calculus and the Schrodinger plane-wave ansatz. I finish with minimal, implementable prescriptions (explicit coercion or typed wrappers) that preserve numerical results while restoring unit-aware rigor.
Category: Mathematical Physics

A Possibility Evaluation for the Casimir Effect to Be a Consequence of the Bernoulli Law

Authors: Igor F. Tkachenko, Yuriy S. Miroshnichenko, Victoria I. Miroshnichenko, Konstantyn I. Tkachenko, Sergyi A. Miroshnichenko, Svitlana G. Tkachenko
Comments: 4 Pages.

Based on the early developed analytic model of the nonstationary stochastic processes and well grounded concept of the flat plane Universe originated by the Big Bang and continuing to evolve by now, the well known Casimir effect was considered as a consequent of the Bernoulli law, showing decreasing the static pressure providing the motion of cosmic fluid with increasing its velocity. Novel formula to calculate the stress acting perpendicular the flow direction was derived and the formula similarity with the known Casimir relation obtained using quantum electrodynamics was shown. The stress values calculated using the new formula is in a good agreement with the available experimental data.
Category: Mathematical Physics

The Basel Problem Through Kinematic Shadows: A Kinematic-Geometric Reconstruction of ζ(2) = π^2/6

Authors: Rayan Bhuttoo
Comments: 5 Pages. License: CC BY-NC-ND 4.0 (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

We derive Euler’s celebrated result through a novel kinematic-geometric framework. By modeling the orthogonal projection of uniform circular motion (e.g., a rotating blade under collimated light), we identify the universal ratio ∥shadow∥ circumference = 1 π as a fundamental scaling law between rotational and linear kinematics. Interpreting the real number line as a harmonic projection of a rotational system, we demonstrate that the summation reconstructs the curvature lost under projection. This approach naturally extends to higher zeta values ζ(2k), admits quantum-mechanical analogues via projection operators P, and adapts to relativistic regimes where Lorentz contraction modifies shadow geometry. Our work establishes π as a dynamic compression ratio be tween rotational and linear kinematics, offering a physical lens for classical number theory.
Category: Mathematical Physics

Principium Geometricum: Mathematical Derivation of the Unified Force Law of Nature

Authors: Pedro A. Kubitschek Homem de Carvalho
Comments: 5 Pages.

We demonstrate, with mathematical rigor, that the Principium Geometricum(PG) force law,F(R) = (rho_v^2 * V1 * V2 * c^2) / (lambda * alpha_U * R^2),is not an arbitrary postulate but the unique consequence of treating matter as vac-uum resonance. We derive it independently via (i) a variational principle, (ii) theflux of momentum through a stress tensor, and (iii) the energy of the field viaGreen’s identity. In all cases, the same 1/R2 dependence and the same prefactorstructure emerge. Dimensional analysis, boundary value problems, self-energy reg-ularization, and calibration with Newtonian gravity and Coulomb electrostatics arediscussed. Thus the PG force law stands as a mathematically consistent unificationof interactions under the same tensional principle.
Category: Mathematical Physics

There Is No Matter: Vacuum Knots as Toroidal Resonant Solitons and the Role of αU = keAP

Authors: Pedro A. Kubitschek Homem de Carvalho
Comments: 7 Pages.

We develop a mathematically grounded framework in which what is commonly called "matter" consists of finite—energy, knotted excitations of a nonlinear vacuum field. The model is based on a Faddeev—Skyrme—type Lagrangian for a unit vector field n : R3,1 → S2, coupled to gravity and electromagnetism. Toroidal (Hopf) solitons carry conserved topological charge and exhibit internal "beating" modes. Mass, momentum and spin arise purely from the vacuum stress—energy tensor. The constant αU = keAP (Coulomb constant times Planck area) plays the role of a vacuum rigidity/constitutive scale, controlling EM couplings and regularization. We lay out explicit assumptions, definitions, energy bounds, and geodesic motion of soliton centers, with citations to classical results (Derrick’s theorem, Vakulenko Kapitanskii bound, moduli space dynamics).
Category: Mathematical Physics

Quantum Oscillator Revisited: Time-of-Time Formalism and Vacuum Rigidity αU

Authors: Pedro A. Kubitschek Homem de Carvalho
Comments: 4 Pages.

The quantum harmonic oscillator is traditionally formulated under the assumption of continuous time, leading to well-known eigenstates and energy spectra. However, when extended to cosmological scales, the same formalism contributes to divergences such as the vacuum energy catastrophe (10120 discrepancy in the cosmological constant). In this paper, we propose a reinterpretation: the oscillator is reformulated using the "time-of-time" formalism, where time itself oscillates over the Planck area scale. A new constant, αU = keAP (Coulomb’s constant multiplied by Planck area), emerges as the measure of vacuum rigidity. We show how this modification regulates divergences, unifies the interpretation of vacuum tension across quantum and cosmological domains, and provides a physical ontology to the notion of time in quantum mechanics.
Category: Mathematical Physics

The Time-of-Time Oscillator and the Constant αU : A Natural Regularization of the Cosmological Constant Problem

Authors: Pedro A. Kubitschek Homem de Carvalho
Comments: 4 Pages.

The cosmological constant problem arises from the discrepancy be-tween the zero-point energy predicted by quantum field theory (QFT)and the observed value of cosmic expansion [2, 3]. We propose thatthe fundamental oscillation of time-of-time, together with the constantαU = keAP (the product of Coulomb’s constant and the Planck area),provides a natural regularization for this divergence. We show that,instead of summing over all quantum modes, the oscillatory residueleads to a finite effective cosmological term Λeff ∼ α2U /AP , eliminatingthe 10120 mismatch.
Category: Mathematical Physics

Emergence and Exclusivity of Lorentzian Signature and Unit—Norm Time from Random Chronon Dynamics

Authors: Bin Li
Comments: 22 Pages. (Note by viXra Admin: For the last time, please submit article written with AI assistance to ai.viXra.org)

We ask how Lorentzian causal structure can emerge from a pregeometric substrate. For arigorously defined class of finite—range, ferromagnetically coupled "chronon" models with quartic norm pinning, we prove the existence, with strictly positive Gibbs probability, of a macroscopic percolating domain D ⊂ M on which the coarse—grained field Φµ is smooth, future—directed,unit—norm timelike (ΦµΦµ = −1, Φ0 > 0) and twist—free. We work on a smooth differentiablemanifold but do not assume Lorentzian signature or a global time field a priori; these arise onD from the dynamics. Under four operational axioms—well-posed local dynamics, finite-speed signalling, acyclic causal order, and stable memory/records—we further prove that no alternative (Euclidean orultrahyperbolic) signature, nor a Lorentzian background lacking a globally unit—norm time field,can sustain such behavior; the Lorentzian, unit—norm phase is therefore exclusive. Finally, we show that "measurement" acts as a boundary-induced selector of this phase: an interface coupling to an aligned apparatus field ΦA admits a unique minimizer, pins the norm and alignment, suppresses twist, and drives any initial state to the aligned phase with exponential convergence; large-deviation bounds quantify high-fidelity selection.Our theorems hold for general (1, d) signatures with d ≥ 1. While the proofs are dimensionagnostic, heuristic coarse-graining and stability considerations suggest d = 3 as the most probable large-scale outcome. Together, these results provide a mathematically controlled foundationfor the emergence and exclusivity of Lorentzian causal structure and for boundary-driven selection (measurement) in pregeometric ensembles.
Category: Mathematical Physics

Principium Geometricum IV (PG4): From Emergent Gravity to the Unification of Space, Time, and Information

Authors: Pedro A. Kubitschek Homem de Carvalho
Comments: 17 Pages. In Portuguese (Note by viXra Admin: All entries on the Submission Form should be English)

We present the derivation of the inverse-square law and the acceleration of gravity g from the Geometric Principle (GP). Space is treated as a mesh of minimal areas A_P, whose rigidity is regulated by alpha_U = k_e A_P. The derivation shows that g emerges naturally and reproduces the value measured at the Earth's surface. The generalization to two bodies leads to an emergent form of the gravitational constant G.
Category: Mathematical Physics

Non Commutative Fourier Duality on One-Dimension and Its Application

Authors: Vicente Pedro Diogo
Comments: 14 Pages.

The present article aims to present an extension of the Fourier dualityto non-commutative groups and algebraic structures,analyzing thenon-commutative Fourier transform on one dimensional structures alongwith their unitary representation. This approach gives a comprehensiveinsight into the harmonic analysis of operator-valued functions, providingmathematical foundations for analyzing physical systems that exhibitnon-commutative symmetries. Hence the article discusses applications ofnon-commutative harmonic analysis into emerging fields of physics such asquantum mechanics and models of quantum gravity , opening paths forexploration of the connections between non-commutative algebras, harmonicanalysis, and theoretical Physics.
Category: Mathematical Physics

Modeling the Second Order Non-stationary Random Processes Development

Authors: Igor Tkachenko, Victoria Miroshnichenko, Kostiantin Tkachenko, Sergiy Miroshnichenko, Yuriy Miroshnichenko
Comments: 6 Pages.

We applied early developed analytic approach for analysis of third order non-stationary stochastic processes (NSPs) to consider the second order ones. A new constitutive differential equation for the NSPs was derived, and its analytic solutions were obtained. Possibility of periodic combination of nonperiodic analytic solutions of the equation was shown. Development of a 2-nd order NSP long before its macroscopically fixed beginning was shown and a possible explanation of the corresponding negative probability values for the time period was proposed. Necessity of further fine tuned experimental investigations is noted.
Category: Mathematical Physics

Deformed Lie Products in a 4D Space Isotropic Electromagnetic Fields

Authors: Thierry L. A. Periat
Comments: 44 Pages. In the French language

In a previous work, the simplest decomposition without residual part of a generic deformed Lie product f has been interpreted as the representation of a (2, 0) version of some EM field in M(4, C). This document (in the French language) is precising the conditions of validity for this interpretation. It proves: (i) that isotropic EM fields are compatible with it; (ii) again, the existence of Lie algebras; (iii) that the passage between the simplest decomposition of f and the antisymmetric decomposition of (f o f) (both without residual part) is an EM transition involving isotropic EM fields presumably linked with natural electromagnetic oscillations in Maxwell's vacuum. Since their effective nature remains to be identified, one is pushed to propose a new interpretation for f involving the dual representation of any EM field.Key words: representations of the EM fields, Lie algebras, evolution.
Category: Mathematical Physics

The Natural Velocity of Bodies in the Tensional Field of the Vacuum

Authors: Pedro A. Kubitschek Homem de Carvalho
Comments: 14 Pages. (Note by viXra Admin: For the last time, please refrain from repeated submissions and cancellations and SUBMIT article written with AI assistance to ai.viXra.org)

In traditional models, gravity is treated either as a force between masses or as the curvature of spacetime induced by energy. In the Principium Geometricum, we propose a different reading:Force does not act on mass, but on volume; and the response of the tense vacuum to the presence of a body manifests as a natural velocity, measurable through geometry. The vacuum field is endowed with a tensional structure. Bodies inserted into this field deform its geometry, and the field responds by providing a displacement velocity proportional to the geometric disturbance. This velocity is not the result of external force, but a natural expression of the medium’s internal resistance.
Category: Mathematical Physics

A Dimensional Identity Connecting Gravity and Electromagnetism via the Fine-Structure Constant

Authors: Jonathan Loomis
Comments: 4 Pages.

We present a dimensional identity that connects the gravitational constant, the fine-structure constant, the vacuum permittivity, and the Planck mass. While not predictive on its own, this identity suggests a potential structuralrelationship between gravitational and electromagnetic constants. The formulation allowsG to be expressed in terms of electromagnetic parameters and a mass scale equal to the Planck mass, offering a concise and dimensionally exact connection between domains typically treated as distinct. Though speculative, the precision and dimensional consistency of this identity motivate further scrutiny.
Category: Mathematical Physics

Gravity as Toroidal Geometry of Time: Reformulating Einstein with Angular Tension

Authors: Pedro A. Kubitschek Homem de Carvalho
Comments: 4 Pages. (Note by viXra Admin: Please cite listed scientific reference and submit article written with AI assistance to ai.viXra.org)

Wepropose a reformulation of Einstein’s field equations based on the concept of a time-tensional toroidal geometry. The unification constant αU = ApKe replaces Newtonian mass as the source of curvature. We define a tension-based vector field Uµ, from which we construct a geometric energy-momentum tensor T µν, and derive a new class of field equations. We show that in the weak-field limit, this formulation recovers Newtonian gravity, while offering a deeper ontological interpretation of space, time, and matter.
Category: Mathematical Physics

Involutive Lie Products in Four-Dimensional Spaces (Les Produits de Lie Involutifs Dans Les Espaces de Dimension Quatre)

Authors: Thierry L. A. Periat
Comments: 32 Pages. In French

This document is the French version of the reference: "Deformed Lie Products and Involution - Second part: in a Four-dimensional Space; viXra:2507.0062, 40 pages". The progression follows a similar way of thinking. But it goes a step further because it can clearly connect a family of deformed Lie products with specific representations of the electromagnetic fields. The conditions precising the existence of an involution are also better explained.

Ce document explore, dans un espace mathématique de dimension quatre, les notions d'invariance et d'involution lorsque celles-ci s'appliquent à l'action d'un produit de Lie déformé. Il rappelle l'existence de la décomposition sans résidu la plus simple rencontrée au cours des explorations précédentes. Mais il démontre aussi l'existence d'une autre décomposition sans résidu en se servant de la multiplicité des représentations du produit de Lie déformé. Il définit les conditions assurant l'égalité des deux décompositions. Aucune des deux matrices ne peut assurer l'invariance et seule la décomposition la plus simple permet d'envisager une action de type involutive. Enfin, il établit clairement les relations faisant de la décomposition la plus simple une représentation effective d'un champ électromagnétique.
Category: Mathematical Physics

On the Calculation of Both Power and Moment Required of Motors to Drive a Robot Arm in a Controllable Manner

Authors: Aloys J. Sipers, Joh. J. Sauren
Comments: 5 Pages. (Note by viXra Admin: Please cite and list scientific references)

In this letter we use complex numbers to calculate both the power and the mechanical moment required of robot motors to drive a robot arm subjected to loads on joints and on multiple parts.
Category: Mathematical Physics

An Algebraic Derivation to Determine Lorentzian Broadening from Voigt Function in Plasma Diagnostics

Authors: Zi-Jing Chiah, Elton Song-Zhe Mah
Comments: 3 Pages.

This paper presents an algebraic derivation to express Lorentzian broadening, as a function of the Voigt, and Gaussian widths, providing a practical method for extracting electron density from spectroscopic data in plasma diagnostics.
Category: Mathematical Physics

Principium Geometricum II: How the Minimum Space Tension Reveals the Gravastar-Like Black Hole

Authors: Pedro A. Kubitschek Homem de Carvalho
Comments: 41 Pages. In Portuguese

We present the Principium Geometricum, a new unified theoretical framework that emerges from three classical pillars—Newton's Second Law, Gauss's Law, and Einstein's Equations. We propose a fundamental vector field Uμ, whose divergence defines geometric mass and whose temporal oscillation modulates the spacetime metric. We introduce the unifying constant αU = keℓ2 P , of dimension force × area, which allows us to recover the four fundamental interactions in a single formalism. From a Lagrangian constructed for the field Uμ, we derive the energy-momentum tensor Tμν , derive its quantization, calculate the vacuum energy and propose mixed interactions with the electromagnetic field. The results point to a profound reshaping of the structure of spacetime as a field of pulsating areas, paving the way for the geometric unification of classical, relativistic and quantum physics.
Category: Mathematical Physics

Principium Geometricum

Authors: Pedro A. Kubitschek Homem de Carvalho
Comments: 14 Pages.

Abstract ApresentamosoPrincipiumGeometricum, umquadrounificadoque, apartir de trêspilares clássicos—aSegundaLei deNewton(F=ma), aLei deGauss (∇·E=ρ/ε0)easequaçõesdeEinstein(Gµν=8πGTµν/c4)—derivaumúnico campodereferênciaU.Definimosamassageométrica mg = V (∇·U)dV eintroduzimosaconstanteunificadora αf=kfl2 P, αU=kel2 P≈2,3×10−60, permitindorecuperarasquatroforçasfundamentaissemhipótesesadicionais.Adicionalmente, incorporamos umtempo oscilatórioT(t) que, ao reparametrizar a dinâmica,produztrajetóriasde"caossuave"emgeometriastoroides
Category: Mathematical Physics

Double Stochastic Quantization:non Perturbative Approach to Stochastic Quantization F^2n Model Quantum Field Theory

Authors: Jaykov Foukzon
Comments: 27 Pages.

The 5th-time stochastic-quantization approach to field theory proposed by Parisi and Wu, is put in a path-integral form in [6]. The procedure of taking the limit t-> ∞ is analyzed and based on new grounds through the introduction of thevacuum-vacuum generating functional. In this paper non perturbative aprouch related to Parisi and Wu stochastic-quantization of the λϕ_{d}^2n,n≥2,d≥4model quantum field theory is considered.
Category: Mathematical Physics

e/P Mass Ratio and F.S.C. Calculation from the Hydrogen Ground State

Authors: Eric Louis Beaubien
Comments: 4 Pages. (Note by viXra Admin: Please cite and list scientific references)

The fine structure constant and electron/proton mass ratio can be reasonably derived from the hydrogen ground state wherein mass and inertia test against electric charge in the most fundamental configuration. The contention is that because these numbers are ‘pure’ numbers, we can dispense with physics altogether and solve the problem of their numeric quantity from a purely logical-probabilistic-mathematical perspective.
Category: Mathematical Physics

On Noether Theorem and Generalizations

Authors: Lucian M. Ionescu
Comments: 58 Pages. Presentation at Illinois State University Pure and Applied Mathematics Seminar 2025.

"Understanding" involves Networking Concepts and Theories, e.g. within a mathematics area and between areas (Algebra and Geometry: from Descartes and Galois to Klein and beyond, e.g. Noether & Langland). Such a higher level of understanding, is advocated (pioneered?) by Andre Weil’s "Power of Analogy", with contributions from Simone Weil, in connection with the "Number Field / Function Field Analogy". We use such analogies to substantiate the tower of theories: Geometry, Homotopy Theory and Dynamics, as a background for understanding Lagrangian Mechanics vs. metric geometry, towards grasping in a simpler way Noether Theorem relating groups of symmetry and conserved quantities in Physics. This is another use of Galois Principle, as explained in a previous talk on Programs in Mathematics and Physics. The presentation is at an undergraduate level, with pictures available YouTube’s author channel, part of the zoom recording of the talk.
Category: Mathematical Physics

Finite Relativistic Cosmology

Authors: Yosef Akhtman
Comments: 31 Pages.

We develop a self-contained framework in which the entire physical universe is modelled by an ever-growing finitering Z�� whose cardinality is tied to cosmic time through �� = 4�� + 1. Starting from a single principle of relationalfinitude, we show that: (i) familiar dimensional constants (ℏ, ��, ��, ����) arise as structurally unique, dimensionless elements of Z��, fixed by extremal arithmetic properties; (ii) a genuine Minkowski quadratic form and full Lorentz group exist exactly inside the ring, reproducing special-relativistic kinematics under coarse-graining; (iii) the primefactor spectrum splits naturally into stable fermionic and radiative bosonic sectors, enabling hadron-like three-prime composites and colour confinement; (iv) complementary observer horizons recover, respectively, general-relativistic geodesics and quantum superposition, resolving the gravity-quantum tension and yielding a finite Heisenberg bound; (v) classical paradoxes—cosmological constant, horizon, singularities, ultraviolet divergences, hierarchy, strong-��, and wave-function collapse—are eliminated not by fine-tuning but by exact arithmetic identities in the finite ring; (vi) independent gravitational and nuclear chronometers converge on a present cardinality ��◦ ≈ 1060, implying a cosmic age of 13.6±0.2 Gyr and an accelerated expansion that requires no dark energy.We furthermore predict a ∼2.5×10−19yr−1 secular drift in the 1-m gravitational red-shift—measurable with existing optical-lattice clocks—which offers an immediate, falsifiable test of the proposed hypothesis. Together, these results suggest that a finite, relationally defined arithmetic is sufficient to encode space-time geometry, quantum phenomena, and cosmological evolution within a single coherent model.
Category: Mathematical Physics

The Visages of the Lorentz-Einstein Law Speculative Analysis with the Extrinsic Method

Authors: Thierry L. A. Periat
Comments: 31 Pages.

This document presents an application of the extrinsic method through a generic and pedagogical example that can be applied to the co-variant formulation of the Lorentz law. The unsaid hope of this approach is the discovery of some unexplored or weakly explored links between two theories because the formalism of this law is a natural bridge between the electromagnetism and the gravitation. The analysis is able to propose (i) a new formalism for the (2, 0) version of the electromagnetic fields and (ii) a speculative confrontation with the theory of spinors resulting in a theoretical prediction, precisely: the existence of electromagnetic fields mimicking anti-symmetric variations of the metric tensor; and conversely.
Category: Mathematical Physics

Geometry and Constants in Finite Relativistic Algebra

Authors: Yosef Akhtman
Comments: 14 Pages.

We show that a single finite field, built on any odd prime p, contains the entire scope of algebraic machinery to support smooth geometry, differential calculus and continuous harmonic analysis. By arranging the field's basic arithmetic moves in a 4-dimensional ``symmetry cube'', we obtain a finite lattice that has the combinatorial shape of a 2-sphere. Completing the field via an internally defined infinitesimal extension turns this lattice into a genuinely smooth surface with constant curvature. The field itself provides finite versions of the familiar constants i, Pi and e, identified by their structural roles. Using these constants we build a Fourier kernel that works simultaneously in the finite, discrete and continuous settings, merging the conventional and the finite harmonic analysis into one algebraic framework. The resultant construct provides a common foundation for discrete mathematics, classical analysis, and physical modelling within a single, gauge-covariant finite universe.
Category: Mathematical Physics

Transformation Properties of Tensors and Pseudotensors under Coordinate Reflections: A Detailed Mathematical Analysis

Authors: Chenjia Li, Jingxu Wu
Comments: 15 Pages.

The theory of tensors and pseudotensors underlies the mathematical framework of modern physics, providing a coordinate-invariant language for describing physical laws and symmetries. In this work, we systematically analyze the transformationproperties of tensors and pseudotensors of various ranks, with particular emphasis on their behavior under spatial and spacetime reflections. The construction and interpretation of the Levi-Civita symbol in two, three, and four dimensionsare discussed in detail, elucidating the essential distinction between true tensors and pseudotensors in terms of orientation and parity. Explicit transformation rules for ordinary tensors and pseudotensors are derived, including the role of the Jacobian determinant and its sign. Through concrete examples—including scalar tripleproducts, cross products, and antisymmetric tensor decompositions—we reveal the fundamental algebraic and geometric features of these mathematical objects. The implications for vector calculus, relativistic field theory, and physical invariants such as chirality and duality are highlighted. Our results provide a unified and rigoroustreatment of the reflection and contraction properties of pseudotensors, with direct relevance to applications in classical mechanics, electromagnetism, and modern theoretical physics.
Category: Mathematical Physics

Relativistic Algebra in a Finite Universe

Authors: Yosef Akhtman
Comments: 29 Pages.

This work presents a foundational reconstruction of arithmetic and algebra based on the principle of relational finitude. Rejecting the assumption of actual infinity, we develop a finite, frame-dependent mathematical framework in which conventional number systems—integers, rationals, reals, and complex numbers-emerge as asymptotic projections or epistemic constructs derived from a closed finite field Fp. Core arithmetic operations are reinterpreted as internal symmetries of the finite field, and conventional structures such as signed integers, rational fractions, and complex planes are systematically reconstructed as pseudo-numbers, defined relationally and locally with respect to a chosen frame of reference. Imaginary and transcendental constants i, e and Pi are derived as specific elements of Fp with important structural roles. We show that the resulting number classes possess all necessary properties for consistent computation, approximation, and algebraic closure, while offering the potential resolution of classical paradoxes of logic and set theory by replacing absolute notions with context-dependent representations. The proposed system provides a coherent and physically grounded alternative to standard mathematical formalism, suitable for the description of discrete, informationally finite physical systems.
Category: Mathematical Physics

Hydrodynamics of Plasma, Vacuum and Space-Time

Authors: M. I. Aksman
Comments: 13 Pages.

hydrodynamics approach applied to plasma, fluid vacuum and space-time.
Category: Mathematical Physics

Complex Space-Time

Authors: Józef Radomański
Comments: Pages.

The book is a completely new and unconventional look at selected problems of classical physics and is intended for people interested in Special Relativity and relativistic electrodynamics. The idea of Special Relativity is based on the invariance of the laws of physics under the transformations belonging to the Lorentz group. These transformations are internal in real space-time. The author found a complex linear transformation that maintains the invariance of the wave equation but requires the complex domain. The results of the research on this transformation are presented in this monograph. For the research, the author constructed a simple mathematical tool equivalent to Geometric Algebra based on the formalism of the well-known matrix calculus. Although the considerations are carried out in full accordance with the postulates of the classical SR, the use of the paravector calculus to describe the basic laws of physics resulted in surprising results. However, this does not mean that these results contradict experiments. The monograph explains how and why complex phenomena are visible to the observer as real. Finally, an outline of the mathematical structure of complex space-time is presented, which is definitely different from Minkowski space.
Category: Mathematical Physics

The Arithmetic of Order: A Finitistic Foundation for Mathematics, Emergent Structures, and Intelligent Systems

Authors: Faysal EL Khettabi
Comments: 9 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

This report outlines a foundational shift in mathematics, proposing a framework groundedin finite, constructive principles—the "Arithmetic of Order"—emerging from the progression 1 → n → n + 1 and the combinatorial structure of powersets P(Ωn). It critiques the traditional reliance on infinitary constructs like the complex number i ∈ C and the continuumfor describing physical systems with finite degrees of freedom. Instead, it posits characteristic functions as the true empirical interface, and demonstrates how optimal mathematical structures—such as the Golay code G24, the Leech lattice Λ24, and the Mathieu group M24—emerge deterministically from this finitistic basis through processes of constraint-guided differentiation. This approach offers a new foundation for understanding hyper-complex numbers, projective geometries emergent from powersets, universal principles of communication and information stability, and the potential architectures for advanced arti-ficial intelligence. Crucially, it reinterprets the continuum not as an *a priori* given, but as an asymptotic limit of the nested powerset hierarchy. The principles underlying theoremslike Gleason’s are viewed not merely as specific results at a particular n (such as n = 24),but as exemplars of universal rules of emergence that guide the formation of order acrossall degrees of freedom. The entire framework operates without recourse to unobservableinfinities or the subjective concept of "noise."
Category: Mathematical Physics

Lobachevsky's Imaginary Geometry as Specular and Hyperdimensional Structure

Authors: Alfonso De Miguel bueno
Comments: 4 Pages.

This article proposes a reinterpretation of Lobachevsky’s imaginary geometry as a hyperdimensional, specular structure arising from the intersection of two three-dimensional Euclidean spaces. The model describes non-Euclidean parallelism as emerging dynamically from oscillating curvatures, leading to a topological system with four subspaces, two transverse and two vertical, whose behavior is governed by synchronized or opposing phases.
Category: Mathematical Physics

Fractal Spacetime from Quantum Mechanics at Ultrashort Distances

Authors: Ervin Goldfain
Comments: 6 Pages.

We give a pedagogical account on the origin of fractal spacetime stemming from the Heisenberg uncertainty relations at ultrashort distance scales.
Category: Mathematical Physics

Methods to Calculate Linear Momentum from Angular Momentum and to Link Their Conservation

Authors: David B. Graham
Comments: 23 Pages.

In Newtonian physics, it commonly assumed that conservations of linear momentum and angular momentum are independent. This paper shows the gradient of the angular momentum field is populated by components of linear momentum, which allows calculation of linear momentum from a few angular momentum values displaced an arbitrary distance. Therefore conservation of linear momentum is a necessary condition for full conservation of angular momentum (unchanging angular momentum at every (x,y,z), with unchanging gradient).These results are shown to be equally valid under left hand convention.Examples analyzed include a body orbiting in a central force, which has angular momentum changing at every observation point but one, contrasted with actual conservation of angular momentum (unchanging at every observation point, in every frame of reference). Translating angular momentum of the center of mass within and between frames of reference are discussed. A Python script is provided, to conveniently generate and evaluate random groups of particles.
Category: Mathematical Physics

Decomposing the Deformed Tensor Products in a Four-Dimensional Space

Authors: Thierry L. A. Periat
Comments: 24 Pages.

This document continues the systematic exploration of diverse mathematical methods allowing the decomposition of deformed tensor products. Here, the discussion is focusing attention on deformed Lie products and on conditions generalizing in a four-dimensional mathematical space what has been called the initial theorem during the elaboration of the intrinsic method, the purpose of which was the decomposition of deformed cross products. This mathematical document sheds a particular light on the (2, 0) representations of the electromagnetic fields.
Category: Mathematical Physics

Proof of the Yang—Mills Mass Gap via Energy Minimization

Authors: Lautaro Fesembeck
Comments: 7 pages, English. Feedback - lautaro.math@gmail.com

We prove the existence of a mass gap in pure Yang—Mills theory by applying energy minimization methods. By defining a disturbance field associated with the field strength tensor and constructing a global energy functional, we demonstrate that any nontrivial excitation away from the flat connection induces strictly positive energy. Through analysis of local perturbations, gauge invariance, and functional coercivity, we establish the existence of a positive lower bound on excitation energies, thus rigorously proving the Yang—Mills mass gap.
Category: Mathematical Physics

Reality Sucks, Really!

Authors: Sven Gohlke
Comments: 9 Pages.

I develop a unit-less unit-system which incorporates the special relativity theory. The so caled "dark matter" and"dark energy" are identified as calculation errors.
Category: Mathematical Physics

Existence, Complexity and Truth in a Finite Universe

Authors: Yosef Akhtman
Comments: 34 Pages.

This article explores a unified framework for understanding existence, persistence, complexity, and randomness as emergent phenomena arising from the projection of a high-dimensional, globally coherent finite universe onto lower-dimensional observational subsystems. We propose that existence is not a binary property but a scalar phenomenon proportional to the persistence of a system's structure over time. Chaos, randomness, and infinity are reinterpreted as epistemic markers — thresholds of comprehension rather than fundamental properties of reality. Through this lens, we examine fractals, cellular automata, quantum uncertainty, and the Langlands program, demonstrating that apparent complexity and unpredictability emerge from the compression of universal dynamics into observable forms. The article argues that all localized systems, from particles to cognitive processes, are holographic projections of the universe's total informational structure. This paradigm reframes emergence, not as the accumulation of local interactions, but as the revelation of global coherence through dimensional reduction. By situating existence and complexity within this framework, we provide a foundation for understanding the interconnectedness of all phenomena and the unity of the universe as a singular, self-reflective process.
Category: Mathematical Physics

The Physics of Energy Transfer

Authors: Henok Abatihun Birhane
Comments: 19 Pages.

Isaac Newton defined the laws of motion and gravity, which were later expanded upon by Albert Einstein through his deeper understanding of time and gravity. However, Einstein himself was not fully satisfied with his theory. He believed that the theory of relativity offered only a limited perspective, aimed at improving measurement and relative observation, and that it still left certain aspects of time and gravity un-explained. This paper discuss narrower view of the cause for time, inertia and gravity based on newton, Einstein and multiple experiment results. The questionu2032of why’ for time, inertia and gravity will be discussed
Category: Mathematical Physics

Reversibility and Determinism in an Expanding Universe

Authors: J. Vianney Koelman
Comments: 9 Pages.

A graph-theoretical toy model is presented that allows us to study the degrees of freedom in globally hyperbolic discrete causal structures governed by a deterministic local rule. We observe that expanding structures compared to structures static in sizes behave markedly dierent. In expanding causal structures, the degrees of freedom can not all be localised in the past, and it is not meaningful to treat these degrees of freedom as initial conditions. As a result, the past no longer determines the future and determinism loses its meaning. This invalidates the argument of free will being incompatible with deterministic laws.
Category: Mathematical Physics

A Note on Superluminalization of SRT and Some Central Concerns of Contemporary Physics

Authors: Mohamed E. Hassani
Comments: Pages.

Over the past decades and more recently, there has been a significant effort and renewed interest in extending special relativity theory beyond the speed of light. In this comprehensive note, the paper "Relativity of superluminal observers in 1+3 spacetime" by Dragan et al.[1] is examined. The authors attempted to extend the aforementioned theory to superluminal inertial reference frames by generalizing Parker’s two-dimensional transformation with the addition of two pairs of spatial dimensions. This approach is not novel and is already well-documented in the literature. It is demonstrated that unlike Lorentz transformations, the authors’ transformations do not form an orthogonal-orthochronous group due to their negative determinant. Consequently, principles such as relativity, causality, spatial isotropy, and temporal ordering cannot be preserved. The authors’pseudo-transformations are revealed to be reflections in a plane through the origin rather than true transformations. Also, a theoretical maximum limit of the Lorentz factor is introduced, which leads to an extension of Lorentz transformations to luminal inertial reference frames and raises an important conceptual question about the status and role of the symbolic quantity ‘c’, commonly called the speed of light in vacuum, as the neutrino and particularly the photon have non-zero mass. Therefore, it appears that as long as the non-zero mass of the photon is not taken seriously into full consideration, our current knowledge of physics, astronomy, astrophysics, and cosmology remains not only incomplete but above all vague and doubtful. Unfortunately, it seems that many present-day researchers are unaware that distinguished physicists like Einstein [59-62], de Broglie [63-66], Proca [67-71], Schrödinger [72-74], and many others [75-92] had already attributed non-zero mass to the photon because they realized that the photon itself behaves like a massive particle, carrying not only energy but also momentum and can exert pressure on a target. And at no stage may we really be able to conclude experimentally the exact masslessness of the photon because the Heisenberg uncertainty principle gives the lowest mass m that can be measured in the Universe’s age as m~ℏt^(-1)c^(-2)~1.5×10^(-33) eV/c^2. Once again, therefore, non-zero photon mass gives rise immediately to a conceptual question: What is the primary purpose of the symbolic quantity ‘c’ when it appears in some important equations describing the laws of physics? Moreover, this inclusive note highlights Hassani superluminal spatio-temporal transformations, which possess the algebraic structure of a linear group and serve as a generalization of Lorentz transformations for superluminal inertial reference frames. These transformations are anticipated to be fundamental in superluminal relativistic mechanics [50].
Category: Mathematical Physics

The (E) Question in a Three-Dimensional Space - Analysing a Subset of Linear Systems With The Intrinsic Method

Authors: T. L. A. Periat
Comments: 32 Pages.

This paper is part of a series of explorations exposing methods for dividing distorted tensor products by number cubes. Here, the discussion focuses on three-dimensional spaces and anti-symmetric cubes on their low indices, i.e. actually on distorted cross products. The method only delivers the main parts of the divisions. The other documents in the collection complete this investigation. This is a translation made by me of a part of the French version.
Category: Mathematical Physics

A New Deterministic Method for the Spin Glass Ground State Problem

Authors: Akira Saito
Comments: 13 Pages.

In this study, we propose a new deterministic solution for the spin glass ground state problem. Our method formulates the Ising spin glass problem as a system of nonlinear equations and determines the ground state by solving those equations. Compared to simulated annealing (SA), the proposed method aims to reduce computational time while achieving energy accuracy that is equal to or better than SA.Through numerical experiments using the Sherrington-Kirkpatrick (SK) model, we confirmed that the proposed method achieves energy values comparable to SA with a reduction in computation time by a factor of 1/3 to 1/15. Furthermore, scaling analysis shows that the computation time of the proposed method grows proportionally to ��1.21, demonstrating superior scalability compared to SA, which depends on ��2.05.The findings of this study suggest new possibilities for solving spin glass ground state problems and may be applied to areas such as combinatorial optimization and machine learning. Future work will focus on improving scalability, introducing methods to avoid local minima, and accelerating computations through GPU parallelization to enhance practical utility.
Category: Mathematical Physics

A Proposed Novel GMST-Based Proof for the Global Existence of Smoothness in 3D Navier-Stokes Equations

Authors: David Vickers
Comments: 128 Pages. (Note by viXra Admin: AI assisted content is in general not acceptable)

We present a novel approach to the global existence and smooth-ness problem for the three—dimensional incompressible Navier—Stokes equations based on a Generalized Modular Spectral Theory (GMST).Our method begins with a precise formulation of the Navier—Stokes system in suitable Sobolev and divergence—free function spaces and employs a detailed spectral decomposition of the associated Stokes operator. A key innovation is the introduction of a modular—like (Möbius) transformation applied to the operator’s eigenvalues, which "lifts" potentially dangerous low—frequency modes by enforcing an ex-ponential decay in the spectral density. This spectral transformation is integrated into a recursive fixed—point framework, wherein we establish contraction properties in high—order Sobolev spaces and derive sharp energy inequalities that preclude finite—time blowup. Furthermore,we recast the problem within an axiomatic setting analogous to those used in quantum field theory, thereby providing additional structural insight into the global regularity of solutions. The theoretical findings are supported by comprehensive numerical simulations using a Fourier—Galerkin discretization combined with an Exponential TimeDifferencing Runge—Kutta scheme. Our results offer a promising new perspective on the longstanding Millennium Problem by unifying rigorous spectral analysis, modular invariance, and fixed—point techniques in a single framework.
Category: Mathematical Physics

On the Uncomputability of Hydrodynamics

Authors: Warren D. Smith
Comments: 19 Pages.

Oct.2001 paper by me proving the Turing unsimulability of Navier-Stokes hydrodynamics (or certain other alternatives, but either way, I contend demonstrating the failure of Navier-Stokes as a useful algorithmic physical theory).Now uploaded to vixra for archival purposes.
Category: Mathematical Physics

137 First Prime of Form, First Prime Expressed with Four Base Numbers of Number Type

Authors: Dwight Boddorf
Comments: 2 Pages.

Where N is a counting number, one hundred and thirty-seven is the first prime number to take the form of 2[(2N+2)(2N+2)] + NN , if N equals 3 then prime number is one hundred and thirty-seven.
Category: Mathematical Physics

De Broglie Hypothesis and the Schrödinger Equation: [Plausible] Errors in Mathematics, Physics, Formal Logic, and Dialectics

Authors: Temur Z. Kalanov
Comments: 14 Pages.

The irrefutable proof of the incorrectness of the de Broglie hypothesis (postulate) and the Schrödinger equation (postulate) is proposed. The correct methodological basis for the proof is the unity of formal logic and rational dialectics. The unity of formal logic and rational dialectics is the only correct criterion of truth. The proof leads to the following irrefutable conclusion: the de Broglie hypothesis (idea, postulate) and the Schrödinger equation (idea, postulate) are gross errors in mathematics, physics, formal logic and dialectics. This conclusion is based on the following statements: (1) from the point of view of Euler's formula and the Maclaurin series, the definition of the wave function has neither physical nor mathematical meaning; (2) the substitution of the quantities of energy and momentum, which characterize a quantum (microscopic) particle, into the relationship that describes a macroscopic radiation wave is a gross formal-logical error, because a quantum particle and macroscopic radiation are not identical material objects; (3) in the dialectical and formal-logical points of view, a free classical particle is not identical to a free quantum particle: these particles are non-identical material objects. Therefore, the substitution of the quantities of energy and momentum, characterizing a quantum (microscopic) particle, into the classical relationship that describes the energy and momentum of a classical particle is a gross formal-logical error; (4) in the point of view of formal logic, the concepts of "corpuscular aspect" and "wave aspect" are contradictory (mutually exclusive) concepts. (The concepts of "particle" and "wave" are defined by different essential features of material objects). Therefore, the de Broglie wave function and the Schrödinger wave equation represent a violation of the formal-logical law of lack (absence) of contradiction. This means that the concept of corpuscular-wave dualism is erroneous; (5) The de Broglie wave function and the Schrödinger equation represent a gross dialectical error, because the dimensionless wave function contradicts to the dialectical concept of the measure of a material object (i.e. the dimensionless wave function does not have the qualitative determinacy of a material object, does not characterize the properties of a material object). Therefore, the de Broglie wave function and the Schrödinger equation are meaningless relationships.
Category: Mathematical Physics

On the Feigenbaum Attractor and Feynman Diagrams

Authors: Ervin Goldfain
Comments: 24 Pages.

It was recently conjectured that the Standard Model of particle physics resides on a bifurcation diagram generated by the recursive scaling of Higgs coupling. This sequel explores the relationship between the bifurcation diagram and the Path Integral (PI) formalism of Quantum Field Theory (QFT). The long-term goal is to base the Feynman diagrams on the properties of the Feigenbaum attractor of either quadratic or cubic maps.
Category: Mathematical Physics

Two Separate Derivations of the Shannon Entropy Equation from First Principles and the RTA Framework for Information

Authors: Vasant Jayasankar
Comments: 38 Pages. (Note by viXra Admin: AI assisted article is in general not acceptable; and there are missing symbols in formula/equations!)

The Shannon entropy equation has been foundational in information theory, yet its derivation has historically relied on axiomatic reasoning rather than first principles. In this paper, I propose two derivations of the Shannon entropy equation from fundamental geometric constraints, demonstrating that it emerges naturally as a special case of a deeper information structuring principle. I propose that entropy is fundamentally constrained by geometric projection effects and dimensionality, leading to a formulation that reduces to Shannon’s equation in Euclidean space while extending to structured high-dimensional systems. Further, I introduce a novel connection between optimal information structuring and the All-Pairs Shortest Path (APSP) framework, demonstrating that information processing may follow geodesic constraints in hyperbolic space. This insight suggests that optimal data compression, AI learning, and information retrieval follow geometric constraints, revealing a deeper structural foundation beyond statistical approximations. By unifying entropy, geometric projection constraints, and APSP-based information structuring, I introduce the RTA Framework for Information, which redefines optimal information flow in structured systems and AI architectures. If validated mathematically and empirically, this may have deep implications for AI architectures, compression theory, and quantum information, pointing toward a broader framework that extends beyond classical entropy formulations.
Category: Mathematical Physics

Transition Predication Models - Literature Review

Authors: Shlomy Shitrit, Eran Arad
Comments: 30 Pages.

The transition of a boundary layer from laminar to turbulent impacts the characteristics of aflow field, but its underlying physics has yet to be well understood. This literature review aims to give an overview of the more widely used approaches to model transition in ComputationalFluid Dynamics (CFD). Several different methods are reviewed: the linear stability analysismethod, the low Reynolds number turbulent closure approach, the correlation-based methods,the intermittency transport method and the laminar fluctuation energy method. The approaches are compared to one another, highlighting their respective advantages and drawbacks.
Category: Mathematical Physics

Resolution of the Yang-Mills Mass Gap Problem via the Wave Oscillation-Recursion Framework (WORF)

Authors: James Fruit
Comments: 8 Pages. Copyright Licensed under CC BY 4.0. NC © 2025 James Fruit.

This paper presents a rigorous, non-perturbative proof of the Yang-Mills Mass Gap Problem,demonstrating the existence of a strictly positive lower bound for the spectrum of SU(3) gauge boson excitations. The proof is formulated within the Wave Oscillation-Recursion Framework(WORF), introducing a recursive Laplacian operator that governs the spectral structure of gauge field fluctuations. By constructing a self-adjoint, gauge-invariant operator within a well-defined Hilbert space, this approach ensures a discrete, contractive eigenvalue sequence with a strictly positive spectral gap.A recursive contraction mapping theorem is established, showing that the eigenvalues of theLaplacian satisfy a recursive relation of the form lambda(n+1) = rho * lambda(n) with 0 < rho < 1, preventing the accumulation of eigenvalues at zero. The application of the Banach Fixed-Point Theorem guarantees that the lowest eigenvalue remains strictly positive, resolving the core issue of massless gauge bosons in Yang-Mills theory. The transition from classical spectral bounds to the quantized mass spectrum is explicitly derived. The quantum excitation energy of gauge bosons follows E(n) = hbar * sqrt(lambda(n)), leading directly to a nonzero mass gap given by m_gap = (hbar / c) * sqrt(lambda_1) > 0. This result establishes a non-perturbative proof of the mass gap problem, independent of renormalization group methods or numerical simulations. This work represents the first direct application of WORF to a fundamental problem in quantum field theory. The proof is mathematically self-contained and is submitted for formal review by the Clay Mathematics Institute. If validated, this approach provides a transformative new methodfor addressing open problems in high-energy physics and gauge theory.
Category: Mathematical Physics

Noetic Morphisms

Authors: Dara O. Shayda
Comments: 8 Pages.

In March of 1845 Gauss described the conception of an action at a distance, propagated with a finite velocity, the natural generalization to electrodynamics view of Newtonian force. Unsuccessfully, Wheeler and Feynman attempted a new theory for Absorber in 1945 [9]. In their paper there is a detailed reference provided by Prof. Einstein about a relatively unknown physicist named Hugo Tetrode[10,11] and quoted: "The sun would not radiate if it were alone in space and no other bodies could absorb its radiation... If for example I observed through my telescope yesterday evening that star which let us say is 100 lights years away, then not only did I know that the light which it allowed to reach my eyes was emitted 100 years ago, but also the star or individual atoms of it knew already 100 years ago that ‘I’, who then did not even exit, would view it yesterday evening at such and such timeu2026"[11]. The process by which the verb "knew"occurs is modelled by the Noetic morphisms of the arr(Decay) Arrow Category. However this treatise is not about energy emission absorption in nature, rather about their mechanism of information knowledge exchange to make the emission possible.This treatise and its categorical constructions, Universal Properties and symbols pave the way for grammars and functions and operators and Formal Systems (algebras, calculi) of de novo programming languages to describe the nature of specific Emitter Absorber coupling.
Category: Mathematical Physics

Generalizations of Notions of Differential Geometry

Authors: Johan Noldus
Comments: 20 Pages.

The notions of Torion and Riemann curvature are generalized towards general path metric spaces.
Category: Mathematical Physics

Possible Transition from Order Into Chaos and Vice Versa

Authors: Udo E. Steinemann
Comments: 28 Pages. (Note by viXra Admin: Article file size should be <10MB and no author photo should ber used))

The specific model-case of the quadratic-iterator is an illuminating way of understanding the chaotic-behaviour. It is agreed that for the special-cases of iteration of transformations there are common characteristics of chaos: Sensitive dependence on initial conditions, mixing and dense, periodic points. Therefore discussion starts with an important metaphor in chaos-theory, kneading of dough, by 2 different uniform-processes performed iteratively each of them in unit-iterval: [1] Stretch the dough, fold it over in the middle and stretch it again (as often as required), and [2] stretch the dough, cut it in the middle, paste the 2 halfs together and stretch it again (as often as required). This processes guarantee that a pocket of spice inserted into the dough will be mixed thoroughly throughout the mass. Both kneading-processes were found to be compatible in view of their chaotic-characteristics. In a further step of discussion, equivalence could be shown between the 2 uniform kneading-processes and the non-uniform kneading of the quadratic-iterator y = au2022x(1-x), where a = 4 were chosen, via simple coordinate-transformations of the unit-interval. Chaotic characteristics of all 3 iteration-transformations could also be proven as being equivalent to each other. Thus, further investigations were based now on quadratic-iterator. The range from states of order up to the complete chaotic dynamics of the quadratic-iterator can be divided into 3 distinct parts: [1] regime 1 ≤ a < (s∞ = FEIGENBAUM-point) were oscillations of the iterator will experience period-doublings, [2] an area s∞ < a < 4 which can be looked as mirror-image of regime [1], and [3] the chaos-area for a = 4. Boarder between regime [1] and [2] is a CANTOR-set. The mirror-image-area of the quadratic-iterator’s final-state-diagram is characterized by a complicated band-structure and therefore different orbit-dynamics can be expected for (a < s∞) ⇄ (s∞ < a). In other words, transitions from order to chaos and vice-versa may occur but with respect to orbit-dynamics they happen differently every time.
Category: Mathematical Physics

5-Bit Classification in Crystal Classes and Genetic Code

Authors: Giuliano Bettini
Comments: 15 Pages.

I show that 5 bits, or better properties, should be enough to classify the 32 crystal classes of 7 crystal systems, and nothing more. From a rigorous point of view, each of the 32 bit sequences (from 00000 to 11111) must unambiguously identify a class, and each class must unambiguously identify a bit sequence. In this article, which aims to be very simple, easy, and understandable, I emonstrate the thesis by connecting the various bits to properties already present and known in crystallography. I use the same approach to show how even in the genetic code 5 properties or entities or bits are used to create complex structures. I start from the 64 codons table (nucleotide triplets U C A G in RNA, with T substituting U in DNA) that I then examine in a sub-version with 32 codons, still able to codify all 20 amino acids that contribute to the formation of proteins. Considering 32 codons to show symmetries can make sense in an evolutionary process of modifying the genetic code, starting from an ancestral code. I show in this way that there are analogies between the symmetries of the crystal classes and the genetic code. The basic idea is that Nature, having identified a "motif" that works, uses it in several fields.
Category: Mathematical Physics

Is Time a Fundamental Category?

Authors: P. A. M. Moellers
Comments: 25 Pages. This work is prepared from an Informatics background awaiting comments from physics.

Is Time a fundamental category and, if so, on the smallest thinkable scales? Maybe not. To test this conjecture this paper proposes a simple discrete model, the Klick Model. It bases Time on the correlation of two other categories, abstract definitions of motion and state implementation - an Informatics based approach to a problem in physics.

The original motivation to develop the model was to understand the biological/atomic ageing of the twins of the so-called Twin-Paradox, seen as a benchmark combining time and space of smallest and largest scales. Without loss of generality, let us assume that the twins can be represented by two isolated (free) abstract particles in steady motion.

A model is only a model. It has to make falsifiable predictions for the real world. Therefore, I will show that for the Twin-Paradox it leads to the known result from Special Relativity Theory. For smallest scales the task is much more difficult. Only a qualitative test based on structural similarities can be offered here, defining a discrete logic for ground states, excited states and their correlations in the framework of the model, trying to map the abstract model to Einstein’s discrete interpretation of Planck’s law of radiation.

To understand the rational of the proposed model it is helpful not to expect a concept of space and time on smallest scales, particularly on the question whether they can be assumed continuous or discrete, although the model leans to a discrete structure.

The assessment based on the proposed model: The underlying relation for time relying on motion and state implementation is (likely) discrete, suggesting age as more fundamental than time. Regarding Hermann Weyl’s Tile Argument, I think that Pythagorean Law prevails, not through geometry or a metric, but as a preserving law between the above categories. Geometry, needed to define time on our scales, might only evolve on larger scales and dependent on the (dynamic) content of space.

The proposed model is Informatics based, driven by interest and not by competence in physics. Nevertheless, I will use terms from physics based on the approach of Denotational Semantics, keeping the gap between Syntax and Semantics as close as possible by relating abstract model properties to supposed properties of the real world.

Keywords: Discrete Space, Discrete Time, Twin Paradox, Hermann Weyl’s Tile Argument, Einstein’s Theories, Sub-Quantum Assumption, Einstein Coefficients

On Linkage Between Incompressible Integers as Distance and 1/r Potential

Authors: Dara O. Shayda
Comments: 14 Pages.

The main result: assuming distances are numericized as incompressible integers, given two objects, one stationary and the other moving, the rate of change of the measure of their distantial randomness is that of the potential form 1/r. This form is known as the Newtonian potential. If the incompressible assumption dropped then the potential form vanishes as well (conjecture). The supplementary results by Whittaker: for any force varying as the inverse square of the distance, the potential of such a force satisfies both Laplace's equation and the wave equation, and can be analyzed into simple plane waves propagating with constant velocity. The sum of these waves, however, does not vary with time, i.e. standing waves. Therefore, the 1/r potential can be defined as summation of waves. Thus the linkage between the incompressible integers and particular standing waves in physics.
Category: Mathematical Physics

The Electromagnetic Duality in a Quaternionic Vacuum

Authors: Thierry L. A. Periat
Comments: 6 Pages.

The electromagnetic duality in vacuum is an intriguing property characterizing Maxwell’s equations. It was the starting point of numerous developments. One of the most important topic related to that property certainly is the discussion due to Dirac concerning magnetic mono-poles. This exploration proposes representations of the duality with elements in M(4, H) involving the three generators of the imaginary part of H, the non-commutative set of quaternions.
Category: Mathematical Physics

Exact Calculation of the Age of the Universe Dependent on Physical Constants

Authors: Andreas Ball
Comments: 2 Pages.

The british Physicist Paul Dirac (1902 - 1984) founded the Large Number Hypothesis[1], which handles with strange relations using numbers in order of magnitude 1.0E40. Also the german Physicist, Mathematician and Philosopher Hermann Weyl (1885 - 1955) was occupied with relations of High Order Numbers. In this report an Equation is presented, which gives the Age of the Universe within its Tolerance Range in dependence on Physical Constants.
Category: Mathematical Physics

The Observable Universe in the Central Universe

Authors: Zhengxi Wang
Comments: 11 Pages.

The entire universe is a rotating disk, similar to the Milky Way, with a "galactic disk," a "core," and "spiral arms." The observable universe rotates around the center of the universe and play centrifugal motion, galaxies move away from each other and spread outward and around the periphery. With the Earth as a reference point, galaxies are in recession, and the recession velocity is proportional to their distance from the Earth. The recession velocities of galaxies differ in different directions, the velocities in the horizontal are greater than those in the longitudinal directions, the longitudinal directions are greater than those in the vertical direction. The universe has a zone for the development and growth of stars and galaxies, where stars and galaxies reach maturity. The continuous energy eruptions provide abundant materials for the rapid growth of stars. During this period, they revolve around the center in circular motions or in low-speed centrifugal motions. Galaxies are not moving away from each other, or are moving away from each other at a low speed. Mature galaxies had already come into existence before they accelerated to the Hubble velocity. The universe diffusion outward, the direction point to Ophiuchus, Scutum, Sagittarius and so on. According to the derivation based on the energy density formula, we are 10^27 meters away from the center of the universe. Additionally, the observable universe might be elliptical in shape.
Category: Mathematical Physics

Symmetric Theory: Omnipresent Planck Medium

Authors: Giuseppe Azzarello
Comments: 18 Pages. In Italian

In this article we continue the development of Symmetric Theory. What we will show is the coupling between the universe and the Planck medium, understood as the medium that formalizes the characteristics of the zero-point field. We will show how the phenomena of the infinitely large of the universe and the infinitely small of the atom harmonize in relation to the medium Planck. We will show how the Hawking radiation, Unhru effect, Casimir effect, Entropic force,Stefan-Boltzmann constant, Wien's displacement law, are all phenomena referring to the Planck medium. We will show that the electron in the first energy level of the hydrogen atom can never fall into the atomic nucleus because it is supported from Planck energy, through the phenomenon of resonance. What emerges is a new meaning of fine structure constant, in the sense of coupling constant between the electron and the Planck medium. Finally he comes indicated a path that could resolve the wave-particle duality.
Category: Mathematical Physics

Yield Stages of Viscoplastic Fluids in Tubes of Elliptical, Rectangular, Triangular and Annular Cross Sections

Authors: Taha Sochi
Comments: 20 Pages.

In this paper we continue our previous investigation about the use of stress function in the flow of generalized Newtonian fluids through conduits of circular and non-circular (or/and multiply connected) cross sections where we visualize the stages of yield in the process of flow of viscoplastic fluids through tubes of elliptical, rectangular, triangular and annular cross sections. The purpose of this qualitative investigation is to provide an initial idea about the expected yield development in the process of flow of yield-stress fluids through tubes of some of the most common non-circular (and non-simply-connected) cross sectional geometries.
Category: Mathematical Physics

The Increase in Relativistic Inertial Mass is Equivalent to the Increase in Rotational Speed in the Sinusoidal Helicoid Model for Particle Motion

Authors: Luis Rodolfo Cabrera Juárez
Comments: 10 Pages.

The equations of Relativistic Mechanics and Wave Mechanics are used to describe the dynamics of a particle in the Helical Solenoid Model, showing that the increase in relativistic inertial mass is apparent, and is equivalent to the increase in rotational energy.
Category: Mathematical Physics

Flow of Ree-Eyring Fluids in Tubes of Elliptical Cross Sections

Authors: Taha Sochi
Comments: 21 Pages.

In this paper we continue our previous investigation about the use of stress function in the flow of generalized Newtonian fluids through conduits of circular and non-circular (or/and multiply connected) cross sections where we inspect the flow of Ree-Eyring fluids in tubes of elliptical cross sections. We derive analytical expressions for the flow velocity profile and for the volumetric flow rate. The obtained analytical expressions were tested against the available analytical expressions for the special cases of Newtonian flow in circular tubes, Newtonian flow in elliptical tubes and Ree-Eyring flow in circular tubes and the results were identical. The obtained analytical expressions were also tested for sensible trends, tendencies and correlations and they passed all these tests.
Category: Mathematical Physics

Three Routes to the Dynamics of Continuous Spacetime Dimensions

Authors: Ervin Goldfain
Comments: 5 Pages.

This bulleted report is a bird-eye view of the paths leading to the idea of evolving fractal spacetime and continuous dimensionality far beyond the boundaries of Effective Field Theory.
Category: Mathematical Physics

Flow of Ellis Fluids in Tubes of Elliptical Cross Sections

Authors: Taha Sochi
Comments: 22 Pages.

In this paper we continue our previous investigation about the use of stress function in the flow of generalized Newtonian fluids through conduits of circular and non-circular (or/and multiply connected) cross sections where we inspect the flow of Ellis fluids in tubes of elliptical cross sections. We derive analytical expressions for the flow velocity profile and for the volumetric flow rate. The obtained analytical expressions were tested against the available analytical expressions for the special cases of Newtonian flow in circular tubes, Newtonian flow in elliptical tubes and Ellis flow in circular tubes and the results were identical. The obtained analytical expressions were also tested for sensible trends, tendencies and correlations and they passed all these tests.
Category: Mathematical Physics

Flow of Power Law Fluids in Tubes of Elliptical Cross Sections

Authors: Taha Sochi
Comments: 24 Pages.

In this paper we continue our previous investigation about the use of stress function in the flow of generalized Newtonian fluids through conduits of circular and non-circular (or/and multiply connected) cross sections where we inspect the flow of power law fluids in tubes of elliptical cross sections. We derive analytical expressions for the flow velocity profile and for the volumetric flow rate. We also develop numerical algorithms for computing the velocity profile and the volumetric flow rate for this flow where these algorithms produce virtually identical results to the results obtained from the aforementioned analytical expressions. The obtained analytical expressions were tested against the available analytical expressions for the special cases of Newtonian flow in circular tubes, Newtonian flow in elliptical tubes and power law flow in circular tubes and the results were identical. The obtained analytical expressions were also tested for sensible trends, tendencies and correlations and they passed all these tests.
Category: Mathematical Physics

Four Spacetime Dimensions from the Renyi Entropy

Authors: Ervin Goldfain
Comments: 16 Pages.

As paradigm of complex behavior, multifractals describe the underlying geometry of self-similar objects or processes. Building on the connection between Rényi entropy and multifractals, we speculate here that the generalized dimension of geodesic trajectories in General Relativity reproduces the four-dimensionality of classical spacetime.
Category: Mathematical Physics

On Complex Dynamics and Classical Field Theory

Authors: Ervin Goldfain
Comments: 11 Pages.

Complex Ginzburg-Landau equation (CGLE) is a paradigm for the onset of chaos and turbulence in nonlinear dynamics of extended systems. Here we point out that the underlying connection between CGLE and the Navier-Stokes (NS) equation bridges the divide between fluid flows, on the one hand, and the mathematics of General Relativity (GR) and classical gauge theory, on the other. The analogy hints to a possible link between the transition from laminar to turbulent flows and the mass generation mechanism of quantum field theory (QFT).
Category: Mathematical Physics

The de Vries Formula: a Transcendental Solution for Standing Travelling Circular Waves

Authors: Luke Kenneth Casson Leighton
Comments: 1 Page. (Note by viXra Admin: Author name should be between article title and the asbstract and any remarks above the title should be moved into a footnote in small print))

Exploration of the de Vries formula[1] and its accuracy[2] (following removal of SI2019 assumptions) to latest experimental uncertainty[3] has led to a hypothesis that the formula is a transcendental solution of an infinite-summed (non-frictional) circular traveling and standing wave: a solution of harmonic sympathetic resonance.
Category: Mathematical Physics

An Alternate Solution to the Black Hole Information Paradox

Authors: Tariq Khan
Comments: 4 Pages.

A short informal essay proposing that the Holographic Principle may offer a possible alternative solution to the Black Hole Information Paradox proposed by physicist Stephen Hawking. The actual concept of falling is re-examined. Objects that fall into a black hole have their information randomized. This information exists on a holographic boundary where it is randomized, but not lost or destroyed. That information on the holographic boundary in bits is equivalent, in our universe outside of the black hole’s event horizon, to information measured in bits of the total change in distance to the black hole of all entities due to the change (increase or decrease) in black hole mass, after an object falls into it or it evaporates, supporting the theory of a universe that is foundationally a "network of relations." The total change to our universe as a superstructure relational network, as measured in bits of information, is equivalent to the total bits of information needed to describe an object as it disappears behind a black hole event horizon.
Category: Mathematical Physics

Möbius Molecules, Pythagorean Triples and Fermat's Last Theorem

Authors: Francesco Aquilante
Comments: 2 Pages.

It is shown that if a triple of distinct natural numbers $(a,b,c)$ were to exist such that $a^n+b^n=c^n$ for some odd integer $ngeq 3$,then it must be Pythagorean, i.e. $a^2+b^2=c^2$ must hold too, from which a contradiction arises since this is possible only if either $a$ or $b$ are zero. We arrive at this conclusion by investigating the trace of a model hamiltonian operator whose energy levels correspond to those of the so-called H"uckel hamiltonian applied to rings containing an odd number of atoms lying on a M"obius strip rather than a planar topology.Furthermore, the contradictory nature of our result implies the correctness of the associated statement contained in the famous Fermat's Last Theorem. Given the use of concepts from quantum mechanics, made here but unknown at his time,and the fact that the essence of the present proof may not fit within a margin of a typical book, mystery still remains over Pierre de Fermat's {em demonstrationem mirabilem}.
Category: Mathematical Physics

Tensor Derivative in Curvilinear Coordinates

Authors: Sourangshu Ghosh
Comments: 48 Pages.

In this article, we mathematically rigorously derive the expressions for the Del Operator ∇, Divergence ∇ ·u20d7v, Curl ∇ ×u20d7v, Vector gradient∇u20d7v of Vector Fields u20d7v, Laplacian ∇2f ≡ ∆f of Scalar Fields f and Divergence ∇ · T of 2nd order Tensor Fields T in both Cylindricaland Spherical Coordinates. We also derive the Directional Derivative (A · ∇)u20d7v and Vector Laplacian ∇2u20d7v ≡ ∆u20d7v of Vector Fields u20d7v usingmetric coefficients in Rectangular, Cylindrical and Spherical Coordinates. We then generalized the concept of gradient, divergence and curlto Tensor Fields in any Curvilinear Coordinates. After that we rigorously discuss the concepts of Christoffel Symbols, Parallel Transport inRiemann Space, Covariant Derivative of Tensor Fields and Various Applications of Tensor Derivatives in Curvilinear Coordinates (Geodesic Equation, Riemann Curvature Tensor, Ricci Tensor and Ricci Scalar).
Category: Mathematical Physics

A Universal Equivalence Principle: Uniting Relativity Quantum Meccahanics and Energy Dynamics

Authors: Marco Maccarrone
Comments: 4 Pages. (Note by viXra Admin: Please cite and list scientific references)

This paper proposes an extension of the equivalence principle to unify relativity,quantum mechanics, and energy dynamics under a single geometric framework. Using the Poincar´e disk model as a visualization tool, we demonstrate how phenomena as diverse as spacetime curvature, quantum probability densities, and relativistic energy growth share the same exponential scaling behavior. This equivalence suggests a universal geometric structure underlying all physical laws, where energy density, curvature, and probabilities emerge as complementary manifestations of aunified field. We explore implications for relativistic limits, quantum states, andthe nature of spacetime, highlighting testable predictions and new insights into thestructure of the universe.
Category: Mathematical Physics

Unified Physics Through Waves Part I: Foundations of the Wave-Based Framework

Authors: Nick Navid Yazdani
Comments: 36 Pages. (Correction made by viXra Admin to conform with the requirements of viXra.org - Please cite and list scientific references)

In this [] work, we introduce a universal framework that re-imagines the fabric of reality through the lens of waves. By positioning waves as the fundamental entity underlying all physical phenomena, this paradigm challenges long-standing constructs like particles, fields, and singularities, offering a unified and deterministic alternative. We derive a novel partial differential equation (PDE) operator that encodes infinite complexity expansions, capable of describing phenomena across quantum and classical regimes. This operator resolves inconsistencies in traditional physics, including the quantum-classical divide and the anomalies of singularities, while ensuring convergence and stability. This work lays the mathematical foundation for a transformative understanding of physics, setting the stage for applications ranging from quantum mechanics to cosmology. It invites the scientific community to explore a universe where waves, not particles or fields, are the fundamental building blocks of reality.
Category: Mathematical Physics

Unified Physics Through Waves Part II: Unifying Scales - Resolving the Quantum-Classical Divide

Authors: Nick Navid Yazdani
Comments: 36 Pages. (Correction made by viXra Admin to conform with the requirements of viXra.org - Please cite and list scientific references)

This second installment of The Wave Paradigm advances the quest for unified physics by addressing the long-standing divide between quantum mechanics and classical physics. It reinterprets quantum phenomena - superposition, entanglement, and measurement - as finite complexity illusions, resolving paradoxes with deterministic elegance. By embracing infinite complexity as the natural state of the universe, this work eliminates the need for probabilistic interpretations, replacing them with deterministic wave dynamics. Classical physics emerges seamlessly as a limit of this framework, demonstrating how the same universal wave equation governs phenomena across all scales. This chapter builds on the foundation of Part I, offering profound insights into the true nature of reality and setting the stage for future applications in cosmology, chemistry, and technology.
Category: Mathematical Physics

Infinite Tree Branch Hypothesis

Authors: Bjørn Leon Søren Riedel
Comments: 6 Pages. In English & Japanese (Correction made by viXra Admin to conform with the requirements of viXra.org; also please cite and list scientific references and don't use author's name to name any formula/method etc.!)

The Infinite Tree Branch Hypothesis explores the transformation of infinitely branching trees across dimensions. In 2D, infinite branches converge into a circle, while in 3D and 4D, they form a sphere and hypersphere, respectively, with growth dictated by dimensional scaling. Using a what I think is novel Tree(n-branch)funtion, although agreebly this could have been invented before in fractal geometry or graph theory (but I could not find such a function).this hypothesis mathematically formalizes the convergence of such structures, leveraging properties of spherical coordinates and Gaussian integrals to define their limits. Novel implications include a reinterpretation of infinite branching within quantum mechanics, suggesting that seemingly independent "branches" in the Many-Worlds Interpretation may converge into a unified hyper continuum in higher dimensions. This hypothesis introduces a unique perspective on infinite systems, connecting fractal geometry, graph theory, and quantum cosmology.
Category: Mathematical Physics

On Complex Dynamics and the Schrodinger Equation

Authors: Ervin Goldfain
Comments: 16 Pages.

Complex Ginzburg-Landau equation (CGLE) is a paradigm of complex dynamics that holds for all spatially extended systems near the onset of oscillatory behavior. CGLE applies to a vast array of phenomena ranging from superconductivity and superfluidity, to Bose-Einstein condensation, astrophysics, nonlinear optics and spatiotemporal chaos. In particular, CGLE describes the formation of dissipative spacetime structures in Reaction-Diffusion (RD) processes. Here we bridge the gap between CGLE and the RD model of evolving dimensional fluctuations, the latter being conjectured to arise far above the electroweak scale. Our findings open an intriguing path connecting complex dynamics of dimensional fluctuations to Quantum Physics.
Category: Mathematical Physics

Main Problems in Constructing Quantum Theory Based on Finite Mathematics

Authors: Felix M. Lev
Comments: 19 Pages.

As shown in our publications, quantum theory based on a finite ring of characteristic $p$ (FQT) is more general than standard quantum theory (SQT) because the latter is a degenerate case of the former in the formal limit $ptoinfty$. One of the main differences between SQT and FQT is the following. In SQT, elementary objects are described by irreducible representations (IRs) of a symmetry algebra in which energies are either only positive or only negative and there are no IRs where there are states with different signs of energy. In the first case, objects are called particles, and in the second - antiparticles. As a consequence, in SQT it is possible to introduce conserved quantum numbers (electric charge, baryon number, etc.) so that particles and antiparticles differ in the signs of these numbers. However, in FQT, all IRs necessarily contain states with both signs of energy. The symmetry in FQT is higher than the symmetry in SQT because one IR in FQT splits into two IRs in SQT with positive and negative energies at $ptoinfty$. Consequently, most fundamental quantum theory will not contain the concepts of particle-antiparticle and additive quantum numbers. These concepts are only good approximations at present since at this stage of the universe the value $p$ is very large but it was not so large at earlier stages. The above properties of IRs in SQT and FQT have been discussed in our publications with detailed technical proofs. The purpose of this paper is to consider models where these properties can be derived in a much simpler way.
Category: Mathematical Physics

New Optical Reflexive Formula

Authors: Harjeet Singh
Comments: 11 Pages. (Correction made by viXra Admin to conform with schoarly norm - Please conform!)

This paper introduces new and foundational formulae governing the reflection of light, enhancing our understanding of optical behaviour through simplified mathematical expressions. By exploring the fundamental principles of reflection, the research proposes a set of equations that streamline the calculation of reflected angles and intensities in various optical systems. These formulae aim to offer a more accessible approach to optical reflection, providing both practical utility and theoretical insight for students, researchers, and professionals in the field of optics. The results derived from these new reflective formulae could lead to improved applications in optical devices, laser systems, and other technologies dependent on light reflection.
Category: Mathematical Physics

Segmented Spacetime and the Natural Boundary of Black Holes - Implications for the Cosmic Censorship Conjecture

Authors: Carmen Wrede, Lino Casu
Comments: 24 Pages.

In this paper, we explore the interplay between the fundamental constants Pi and the golden ratio (ϕ) and their relationship to the maximal mass and spin of black holes. Our investigation begins by modeling a hypothetical clock with an initial radius of 1 in a gravitationally neutral environment. As gravitational forces increase, the radius of this clock expands, revealing an unexpected relationship between Pi, ϕ, and the segmented structure of spacetime. This connection allows us to propose a new framework that explains the observed bounds on black hole spin and mass. Our analysis demonstrates that as the spin parameter a approaches the speed of light, it represents a state of maximal rotation in black holes, marked by a unique equilibrium of mass, radius, and segment density. These insights not only provide a deeper understanding of black hole properties but also support the Cosmic Censorship Conjecture by illustrating how spacetime segmentation naturally prevents "naked" singularities. Overall, our findings underscore the importance of Pi and ϕ in the structure and behavior of black holes, offering a new perspective on the complex dynamics governing the universe.
Category: Mathematical Physics

The Universal Zeroth Oscillator

Authors: Casey J Zak
Comments: 13 Pages. Grand Unified Theory with all standard model constants derived from one

Physical reality is here framed as the necessary geometric consequence of endowed energy release from a single zeroth-dimensional oscillator, which exists as the requisite conserving balance point for projection of the entire universe. The framework requires exactly one parameter - the initial oscillator energy - from which all physical constants, forces, and dimensional structure emerge through required quadratic self-reference and phase coherence preservation. All constants of the standard model are herein geometrically given. The fundamental nature of time is revealed as the oscillator's required principal orthogonal eigenvector. The necessary condition for the existence of reality is developed. Observed energy ratios are revealed as inherent. Feynman's infinities are resolved. Experimental predictions testable through phase-coherent optical interference patterns are given with precise energy ratios derivable from geometric constraints. Theory of mind is proposed as the minimum sufficient phase coherent structure required to form a self-representation of the oscillator. Remarkable analyses of coherent group consciousness are revealed. Reality itself, including conscious observation and intention, manifests as the inescapable geometric realization of the oscillator's self-referential structure.
Category: Mathematical Physics

Fundamental Physics and the I Ching

Authors: Claude Michael Cassano
Comments: 5 Pages. (Note by viXra Admin: Please cite and list scientific references)

The eightfold way is an organizational scheme for a class of subatomic particles known as hadrons leading to the.development of the quark model. Murray Gell-Mann proposed the idea in 1961 alluding to the Noble Eightfold Path of Buddhism. However, the concept goes deeper; applying not only to hadrons (triplets of RGB quarks) but to the building blocks of all the fermions (as this analysis demonstrates: i.e.: e(h)-earth, v(h)-wind, u(h)-fire, d(h)-water.
Category: Mathematical Physics

On the Butterfly Effect and the Failure of Hamilton's Principle

Authors: Ervin Goldfain
Comments: 13 Pages.

As a long-cherished postulate of theoretical physics, Hamilton’s principle (HP) defines the basis of classical mechanics and field theory. We argue here that HP is overturned in physical settings where sensitivity to initial conditions cannot be ignored. We find that the approach to chaos of nearly integrable Hamiltonian systems sheds new light on several foundational aspects of effective field theory.
Category: Mathematical Physics

Soliton Solutions of the Nonlinear Schrödinger Equation

Authors: Marcello Colozzo
Comments: 5 Pages.

We integrate the nonlinear Schrödinger differential equation, looking for "lone wave" solutions, and then use the method ofindeterminate coefficients.The integration is in closed form for the free particle, and then we integrate numerically for the particle subject to a weak periodic potential. In both cases, the system is one-dimensional.
Category: Mathematical Physics

The Korteweg-de Vries Equation: Does the Equation Satisfy the Criterion of Truth?

Authors: Temur Z. Kalanov
Comments: 7 Pages.

The irrefutable proof of the incorrectness of the Korteweg—De Vries (KdV) equation is proposed. The correct methodological basis for the proof is the unity of formal logic and rational dialectics. The unity of formal logic and rational dialectics is the only correct criterion of truth. The proof leads to the following irrefutable statement: the Korteweg—De Vries (KdV) equation — a partial differential equation with respect to the dimensionless displacement as the function of the dimensionless coordinate and the dimensionless time — represents an incorrect equation in physics. The proof of this statement is based on the following irrefutable assertions: (1) the Korteweg-de Vries equation does not describe a physical phenomenon (process) because the dimensionless displacement, the dimensionless coordinate and the dimensionless time are non-physical quantities; (2) in the formal logical point of view, the physical (or geometric) interpretation of the equation and solutions of the equation are inadmissible; (3) comparison with experimental data (which have dimensions) is inadmissible (impossible).Consequently, the Korteweg-de Vries equation is a gross error in physics.
Category: Mathematical Physics

Model P(φ)_4 Quantum Field Theory a Nonstandard Approach Based on Nonstandard Pointwise-Defined Quantum Fields Part II: the Field Operators and the Approximate Vacuum

Authors: Jaykov Foukzon
Comments: Physics Essays Volume 39,Issue1, Pages 53-87, 2026 https://physicsessays.org/browse-journal-2/product/2172-7-jaykov-foukzon-model.html

A new non-Archimedean approach to interacted quantum fields is presented. In proposed approach, a field operator φ(x,t) no longer a standard tempered operator-valued distribution, but a non-classical operator-valued function. We prove using this novel approach that the quantum field theory with Hamiltonian P(φ)_4 exists and that the corresponding C^*­ algebra of bounded observables satisfies all the Haag-Kastler axioms except Lorentz covariance. We prove that the λ(φ^4 )_4 quantum field theory model is Lorentz covariant. In this paper we consider a some-what different hyperfinite cut-off theory, namely the λφ_4^4 theory in a periodic box. This gives a cut-off interaction which is translation invariant, and therefore it is useful for the study of the vacuum state. In a finite interval we prove that the total Hamiltonian is self #­adjoint and has a complete set of normalizable eigenstates. https://physicsessays.org/browse-journal-2/product/2172-7-jaykov-foukzon-model.html
Category: Mathematical Physics

A Model for Entanglement

Authors: Carlton Frederick
Comments: 2 Pages. (Note by viXra Admin: This submission is a stub needing improvement)

Perhaps the most puzzling aspect of entanglement[1] is that a measurement ofa local member of a pair of entangled particles causes an instantaneous reaction in the distant particle. This model makes use of stochastic time[2] which posits that time isn't a smooth blanket over space-time. This says thata distant observer observes each particle of the pair at a different proper time. The initially close together pair in their proper frame of reference only to a distant observer only appears to spread. In this model there is no action at a distance.
Category: Mathematical Physics

Chaotic Maps of Discretized Memristor Circuit Equations

Authors: Makoto Itoh
Comments: 99 Pages.

In this paper, we show that many well-known chaotic maps can be generated by discretizing the equations of memristor or nonlinear resistor circuits using the Euler method or the central difference method.These examples show that the dynamics of a wide variety of nonlinear maps, such as those found in engineering, physics, chemistry, biology, and ecological systems, are closely related to the discretized memristor or nonlinear resistor circuit equations. Furthermore, the discretized memristor circuit equations also propose the new modified or simplified version of the well-known chaotic maps. We also propose the generalized extended memristor with non-volatility property. To satisfy the non-volatility property, the $v-i$ characteristic of the generalized extended memristor is defined by two bounded functions, namely the resistive-fuse function and the saturation function. Using this element, the discretized two-element memristor circuits can generate any two-dimensional chaotic map. The computer simulations in this paper show that the discretization of the memristor or nonlinear resistor circuit equations is one of the most promising methods to find interesting chaotic maps. Furthermore, some of the discretized three-dimensional circuit equations clearly show the topological structure of the chaotic attractors.
Category: Mathematical Physics

Theory Of Nothing

Authors: Guy Abitbol
Comments: 52 Pages. published previously as youtube video on Jan 17, 2022

How everything works & How it was created from nothing
Category: Mathematical Physics

Negative Time is Real, Physicists Confirm

Authors: Marcello Colozzo
Comments: 4 Pages.

Recently a group of physicists measured a negative "group delay" for a pulse of light transmitted in a cold cloud of Rubidium atoms. In this paper we will study the propagation of a wave packet incident on a dispersive and dissipative medium, determining the "transit time" of the packet, which is the analogue of the group delay. We will show that if the phase of the transmitted wave is decreasing in correspondence with the value of the wavenumber that determines the peak value of the amplitude of the spectral density of the packet, the transit time is negative.
Category: Mathematical Physics

Bigravity and Interacting Higgs Fields: A Unified Framework for Mass Generation and Gravitational Dynamics

Authors: Alfonso De Miguel bueno
Comments: 9 Pages.

This paper proposes a possible relationship between bigravity and interacting Higgs fields, offering a broader framework that establishes a physical connection between the massive and massless ripples generated by gravitational fields. This framework also provides a unified scenario in which the four known fundamental forces — gravitational, electromagnetic, strong, and weak — are interconnected.
Category: Mathematical Physics

Space Time Potential Theory: A Fundamental Second-Order Approach

Authors: Arend Lammertink
Comments: 9 Pages.

This paper presents a unified second-order model that resolves key limitations of traditional first-order potential theories in both fluid dynamics and electromagnetism. By employing the vector Laplacian and defining a space-time derivative operator, d/dt = −k∆, we establish a fundamental connection between spatial structure and temporal evolution, providing a more complete and physically consistent framework. This approach integrates the electric and magnetic fields with force and torque densities, reinterpreting charge, current, and electromagnetic fields in terms of fluid dynamic quantities such as mass density and momentum diffusivity. Additionally, the model proposes a potential unification of gravitational and electromagnetic forces by expressing the gravitational potential as proportional to the square of the electric field. This redefinition creates a seamless link between the two forces, treating gravitational interactions as a secondary effect of electric field behavior.Higher-order time derivatives, such as jerk and yank, are introduced to further extend the framework's ability to describe dynamic systems in both fluid and electromagnetic contexts. The results demonstrate consistency across scales, from quantum phenomena to cosmological dynamics, offering a comprehensive alternative to existing theories while eliminating gauge fixing ambiguities and enhancing mathematical coherence.
Category: Mathematical Physics

Deterministic Structures in Gravitational Fields: A Unified Model Bridging Black Hole Singularities and Quantum Topology

Authors: Alfonso De Miguel bueno
Comments: 7 Pages.

This paper presents a deterministic model that unifies gravitational, strong, weak, and electromagnetic interactions by examining the intersection of gravitational fields. These fields, which expand and contract periodically, create a shared nucleus of subfields characterized by complementary topological transformations. Within this framework, singularities are reinterpreted as abrupt curvature discontinuities, linking phenomena across quantum and cosmic scales. The model offers insights into energy and density transfer and information preservation. It explores connections to dark matter, reflection positivity, the mass gap problem, and Hodge cycles, providing a pathway to understand the breakdown of General Relativity in both atomic and black hole structures.
Category: Mathematical Physics

On Continuous Dimensions and Infrared Mass Generation

Authors: Ervin Goldfain
Comments: 34 Pages.

We show that dimensional regularization of a generic self-interacting field theory inducesan infrared mass scale, when the running spacetime dimension approaches the criticalvalue �� = 4. The mechanism is universal and does not rely on spontaneous symmetrybreaking alone. Instead, it arises from logarithmic corrections generated byrenormalization group (RG) flow near the bifurcation point at �� ≡ 4 − �� → 0. Weexplicitly indicate how dimensional transmutation converts marginal couplings intodynamically generated mass scales. This framework unifies the origin of the Higgsvacuum expectation value and electroweak boson masses with the Yang—Mills mass gapand the QCD scale ΛQCD. Step-by-step derivations are provided, without appealing tononperturbative assumptions beyond RG consistency. The paper focuses on the regimebordering relativistic quantum field theory and complex dynamics.
Category: Mathematical Physics

Classical Field Theory from Primordial Dimensional Fluctuations

Authors: Ervin Goldfain
Comments: 40 Pages.

Complex Ginzburg-Landau equation (CGLE) is a universal amplitude equation governing the dynamics of phenomena unfolding in far-from-equilibrium conditions. It was recently argued that CGLE emerges from primordial dimensional fluctuations acting in the far ultraviolet sector of field theory and primordial cosmology. Here we show that classical Maxwell, Dirac and non-Abelian field theories can be derived directly from a generalized version of CGLE without invoking a Lagrangian or variational principle. Demanding that CGLE preserves local coherence under continuous internal transformations, we introduce a natural covariant derivative whose connection acts as a gauge field. The commutator of these covariant derivatives defines a curvature tensor that reproduces the familiar structure of Maxwell and Yang—Mills field strengths, while a first-order, spinor generalization of CGLE yields Dirac-type dynamics. In a nutshell, classical field theories naturally emerge from demanding local coherence invariance of the generalized CGLE.
Category: Mathematical Physics

Pattern Field Theory and the Allen Orbital Lattice: A Functional Proof Strategy for the Riemann Hypothesis

Authors: James Johan Sebastian Allen
Comments: 66 pages. English. Updated operator formulation and equilibrium proof. Includes revised references and appendices.

This paper presents a functional proof strategy for the Riemann Hypothesis within the Pattern Field Theory framework, using the Allen Orbital Lattice (AOL) as the geometric and arithmetic substrate. The approach establishes an equivalence between two independently constructed systems: the continuous Equilibrion Hamiltonian, which describes recursive curvature balance along the critical line, and the discrete AOL operator, whose prime-anchored spectrum exhibits Gaussian Unitary Ensemble statistics after unfolding.The analysis shows that both systems produce self-adjoint spectra aligned to Re(s)=1/2, with nontrivial zeros interpreted as equilibrium nodes of the prime field. The operator includes prime-weighted potentials and duplex curvature phases, producing spectral behavior consistent with Riemann-class dynamics. Numerical diagnostics across 30—50 lattice shells confirm Wigner—Dyson spacing, with Kolmogorov—Smirnov and Cramér—von Mises distances stable under randomized phase ensembles. Control experiments removing the prime anchors fail to reproduce this universality, isolating prime weighting as a necessary structural condition.The paper incorporates the updated operator formulation, extended curvature analysis, and cross-references to related Pattern Field Theory results, including the conduction constant tau = 71.2 ± 3.9 ms measured during Pattern Alignment Lock formation. These results support the claim that the prime-indexed curvature harmonics on the AOL constitute a physical equilibrium field and that the Riemann Hypothesis corresponds to its stationary manifold.The work integrates mathematical, geometric, and empirical components into a unified framework and provides a stable model linking prime recursion to field equilibrium. This version includes updated references, consistency corrections, and the completed analytic—geometric correspondence across the continuous and discrete representations.
Category: Mathematical Physics

Double Stochastic Quantization:non Perturbative Approach to Stochastic Quantization F_d ^2n , N ≥ 2, D ≥ 4 Model Eucledean Quantum Field Theory

Authors: Jaykov Foukzon
Comments: 154 Pages.

In this paper, we show how the finite formulation of quantum field theory based on Langevin equations can be generalized to the case of nonrenormalizable theories.The 5th-time stochastic-quantization approach to field theory proposed by Parisi and Wu, is put in a path-integral form in [6]. The procedure of taking the limit τ→∞ is analyzed and based on new grounds through the introduction of thevacuum-vacuum generating functional. In this paper non perturbative aprouch related to Parisi and Wu stochastic-quantization of the λϕ_{d}²u207f,n≥2,d≥4 model quantum field theory is considered.
Category: Mathematical Physics

Double Stochastic Quantization:non Perturbative Approach to Stochastic Quantization λϕ_{d}²u207f,n≥2,d≥4 Model Eucledean Quantum Field Theory

Authors: Jaykov Foukzon
Comments: 59 Pages.

In this paper, we show how the finite formulation of quantum field theory based on Langevin equations can be generalized to the case of nonrenormalizable theories.The 5th-time stochastic-quantization approach to field theory proposed by Parisi and Wu, is put in a path-integral form in [6]. The procedure of taking the limit τ→∞ is analyzed and based on new grounds through the introduction of the vacuum-vacuum generating functional. In this paper non perturbative aprouch related to Parisi and Wu stochastic-quantization of the λϕ_{d}²u207f,n≥2,d≥4 model quantum field theory is considered.
Category: Mathematical Physics

The Fine-Structure Constant in Unexplored Relations

Authors: Branko Zivlak
Comments: 7 Pages.

Formulas for the fine-structure constant are presented: speculative, well-known, and original — five of which are related to quarks.
Category: Mathematical Physics

Alpha Integration: Universal Path Integrals with Gauge Invariance

Authors: YoonKi Kim
Comments: 23 Pages. Contact email: yk.reserch@gmail.com

We introduce Alpha Integration, a novel path integral framework that applies to wide range of function including locally integrable functions, distributions, and fields—across arbitrary spaces and n dimensions (n ∈N), while preserving gauge invariance without approximations. This method extend to Rn(n ∈N), smooth manifolds, infinite-dimensional spaces, and complex paths, enabling rigorous integration of all f ∈Du2032 with formal mathematical proofs. This framework is further generalized to infinite-dimensional spaces, complex paths, and arbitrary manifolds,with its consistency validated through extensive testing across diverse functions, fields, and spaces. Alpha Integration thus offers a robust and efficient alternative to traditional path integral techniques, serving as a versatile tool for mathematical and physical analysis.
Category: Mathematical Physics

On the Feigenbaum Attractor and Feynman Diagrams

Authors: Ervin Goldfain
Comments: 24 Pages.

It was recently conjectured that the Standard Model of particle physics resides on a bifurcation diagram generated by the recursive scaling of the Higgs coupling. This sequel explores the relationship between the bifurcation diagram and the Path Integral (PI) formalism of Quantum Field Theory (QFT). The long-term goal is to base the Feynman diagrams on the properties of the Feigenbaum attractor of either quadratic or cubic maps.
Category: Mathematical Physics

Two Separate Derivations of the Shannon Entropy Equation from First Principles and the RTA Framework for Information

Authors: Vasant Jayasankar
Comments: 36 Pages. (Note by viXra Admin: AI assisted article is in general not acceptable)

The Shannon entropy equation has been foundational in information theory, yet its derivation has historically relied on axiomatic reasoning rather than first principles. In this paper, I propose two derivations of the Shannon entropy equation from fundamental geometric constraints, demonstrating that it emerges naturally as a special case of a deeper information structuring principle. I propose that entropy is fundamentally constrained by geometric projection effects and dimensionality, leading to a formulation that reduces to Shannon’s equation in Euclidean space while extending to structured high-dimensional systems.Further, I introduce a novel connection between optimal information structuring and the All-Pairs Shortest Path (APSP) framework, demonstrating that information processing may follow geodesic constraints in hyperbolic space. This insight suggests that optimal data compression, AI learning, and information retrieval follow geometric constraints, revealing a deeper structural foundation beyond statistical approximations.By unifying entropy, geometric projection constraints, and APSP-based information structuring, I introduce the RTA Framework for Information, which redefines optimal information flow in structured systems and AI architectures. If validated mathematically and empirically, this may have deep implications for AI architectures, compression theory, and quantum information, pointing toward a broader framework that extends beyond classical entropy formulations.
Category: Mathematical Physics

Exact Formulas of the Age of the Universe and of the Gravitational Constant Dependent on Physical Constants

Authors: Andreas Ball
Comments: 7 Pages.

The british Physicist Paul Dirac (1902 - 1984) founded the Large Number Hypothesis[1], which handles with strange relations using numbers in order of magnitude 1,0E+40. Also the german Physicist, Mathematician and Philosopher Hermann Weyl (1885 - 1955) was occupied with relations of High Order Numbers. In this report Formulas are presented, which give the Age of the Universe and the Gravitational Constant within their Tolerance Range both in dependence on Physical Constants.
Category: Mathematical Physics

Exact Calculation of the Age of the Universe and of the Gravitation Constant Dependent on Physical Constants

Authors: Andreas Ball
Comments: 5 Pages.

The british Physicist Paul Dirac (1902 - 1984) founded the Large Number Hypothesis[1], which handles with strange relations using numbers in order of magnitude 1,0E+40. Also the german Physicist, Mathematician and Philosopher Hermann Weyl (1885 - 1955) was occupied with relations of High Order Numbers. In this report Equations are presented, which give the Age of the Universe and the Gravitation Constant within their Tolerance Range both in dependence on Physical Constants.
Category: Mathematical Physics

Flow of Ree-Eyring Fluids in Tubes of Elliptical Cross Sections

Authors: Taha Sochi
Comments: 24 Pages. This is an extended version

In this paper we continue our previous investigation about the use of stress function in the flow of generalized Newtonian fluids through conduits of circular and non-circular (or/and multiply connected) cross sections where we inspect the flow of Ree-Eyring fluids in tubes of elliptical cross sections. We derive analytical expressions for the flow velocity profile and for the volumetric flow rate. The obtained analytical expressions were tested against the available analytical expressions for the special cases of Newtonian flow in circular tubes, Newtonian flow in elliptical tubes and Ree-Eyring flow in circular tubes and the results were identical. The obtained analytical expressions were also tested for sensible trends, tendencies and correlations and they passed all these tests.
Category: Mathematical Physics

Three Routes to the Dynamics of Continuous Spacetime Dimensions

Authors: Ervin Goldfain
Comments: 5 Pages.

This brief report is a bird's-eye view of the paths leading to the concepts of evolving fractalspacetime and continuous dimensionality, far beyond the range of Effective Field Theory.
Category: Mathematical Physics

Flow of Ellis Fluids in Tubes of Elliptical Cross Sections

Authors: Taha Sochi
Comments: 25 Pages. This is an extended version

In this paper we continue our previous investigation about the use of stress function in the flow of generalized Newtonian fluids through conduits of circular and non-circular (or/and multiply connected) cross sections where we inspect the flow of Ellis fluids in tubes of elliptical cross sections. We derive analytical expressions for the flow velocity profile and for the volumetric flow rate. The obtained analytical expressions were tested against the available analytical expressions for the special cases of Newtonian flow in circular tubes, Newtonian flow in elliptical tubes and Ellis flow in circular tubes and the results were identical. The obtained analytical expressions were also tested for sensible trends, tendencies and correlations and they passed all these tests.
Category: Mathematical Physics

Flow of Power Law Fluids in Tubes of Elliptical Cross Sections

Authors: Taha Sochi
Comments: 27 Pages. This is an extended version

In this paper we continue our previous investigation about the use of stress function in the flow of generalized Newtonian fluids through conduits of circular and non-circular (or/and multiply connected) cross sections where we inspect the flow of power law fluids in tubes of elliptical cross sections. We derive analytical expressions for the flow velocity profile and for the volumetric flow rate. We also develop numerical algorithms for computing the velocity profile and the volumetric flow rate for this flow where these algorithms produce virtually identical results to the results obtained from the aforementioned analytical expressions. The obtained analytical expressions were tested against the available analytical expressions for the special cases of Newtonian flow in circular tubes, Newtonian flow in elliptical tubes and power law flow in circular tubes and the results were identical. The obtained analytical expressions were also tested for sensible trends, tendencies and correlations and they passed all these tests.
Category: Mathematical Physics

On Complex Dynamics and the Schrodinger Equation

Authors: Ervin Goldfain
Comments: 16 Pages.

Complex Ginzburg-Landau equation (CGLE) is a paradigm of complex dynamics that holds for all spatially extended systems near the onset of oscillatory behavior. CGLE applies to a vast array of phenomena ranging from superconductivity and superfluidity, to Bose-Einstein condensation, astrophysics, nonlinear optics and spatiotemporal chaos. In particular, CGLE describes the formation of dissipative spacetime structures in Reaction-Diffusion (RD) processes. Here we bridge the gap between CGLE and the RD model of evolving dimensional fluctuations, the latter being conjectured to arise far above the electroweak scale. Our findings open an intriguing path connecting complex dynamics of dimensional fluctuations to Quantum Physics.
Category: Mathematical Physics

On Complex Dynamics and the Schrodinger Equation

Authors: Ervin Goldfain
Comments: 16 Pages.

Complex Ginzburg-Landau equation (CGLE) is a paradigm of complex dynamics that holds for all spatially extended systems near the onset of oscillatory behavior. CGLE applies to a vast array of phenomena ranging from superconductivity and superfluidity, to Bose-Einstein condensation, astrophysics, nonlinear optics and spatiotemporal chaos. In particular, CGLE describes the formation of dissipative spacetime structures in Reaction-Diffusion (RD) processes. Here we bridge the gap between CGLE and the RD model of evolving dimensional fluctuations, the latter being conjectured to arise far above the electroweak scale. Our findings open an intriguing path connecting complex dynamics of dimensional fluctuations to Quantum Physics.
Category: Mathematical Physics

On the Butterfly Effect and the Failure of Hamilton's Principle

Authors: Ervin Goldfain
Comments: 13 Pages.

As a long-cherished postulate of theoretical physics, Hamilton’s principle (HP) defines thebasis of classical mechanics and field theory. We argue here that HP is overturned inphysical settings where sensitivity to initial conditions cannot be ignored. We find thatthe approach to chaos of nearly integrable Hamiltonian systems sheds new light onseveral foundational aspects of effective field theory.
Category: Mathematical Physics

Neutron Reinterpretation: A Unified Model for Strong, Weak, and Electromagnetic Interactions

Authors: Alfonso De Miguel bueno
Comments: 29 Pages.

This paper presents a novel interacting fields model that reconceptualizes the neutron as an intermediate state linking proton and antiproton transformations, incorporating antimatter and dark matter into nucleon dynamics.Within an octonionic framework, the model offers a geometric interpretation of QCD and its unification with weak and electromagnetic interactions.It proposes a curvature-based mechanism for the emergence of mass, charge, and fundamental interactions, leading to several quantitative predictions, including a geometric explanation of the fine-structure constant and Planck’s constant.
Category: Mathematical Physics

Neutron Reinterpretation: A Nonformal Octonionic Model for Strong, Weak, and Electromagnetic Interactions

Authors: Alfonso De Miguel Bueno
Comments: 15 Pages. 11 figures

This preprint article proposes an unconventional topological fields model based on two interacting fields that form a non-formal octonionic, bilateral structure.Within this framework, nuclear interactions unfold through a complex time dimension that combines real past and imaginary future components, facilitating mass and energy exchanges between protons and antineutrinos or antiprotons and neutrinos during beta decay reactions. The neutron is reinterpreted as a transitional state in transformations between proton and neutrino and antineutrino and antiproton, or vice versa.This octonionic configuration, with six spatial imaginary hyperdimensions, one imaginary time hyperdimension, and one real time dimension, brings highly abstract and advanced algebraic concepts to life through a concrete physical mechanism, offering a natural unification of the weak, strong, and electromagnetic atomic interactions.Moreover, the octonionic approach provides a geometric interpretation of Quantum Chromodynamics (QCD), clarifying the internal structure and relationships between quarks and gluons.
Category: Mathematical Physics

Bigravity and Interacting Higgs Fields: A Unified Framework for Mass Generation and Gravitational Dynamics

Authors: Alfonso De Miguel Bueno
Comments: 12 Pages. 10 diagrams

This preprint proposes a possible relationship between bigravity and interacting Higgs fields, offering a broader framework that establishes a physical connection between the massive and massless ripples generated by gravitational fields. This framework also provides a unified scenario in which the four known fundamental forces — gravitational, electromagnetic, strong, and weak — are interconnected.
Category: Mathematical Physics

Deterministic Structures in Bi-gravitational Fields: A Unified Model Bridging Black Hole Singularities and Quantum Topology

Authors: Alfonso De Miguel Bueno
Comments: 10 Pages.

This paper presents a deterministic model that unifies gravitational, strong, weak, and electromagnetic interactions by examining the intersection of gravitational fields. Drawing a connection to bi-gravity theories, where two metric tensors describe gravitational behavior, the model highlights how expanding and contracting fields couple and influence curvature. These intersecting fields, characterized by complementary topological transformations, form a shared nucleus of subfields and reinterpret singularities as abrupt curvature discontinuities, linking phenomena across quantum and cosmic scales. The model offers insights into energy and density transfer and information preservation. It explores connections to dark matter, reflection positivity, the mass gap problem, and Hodge cycles, providing a pathway to understand the breakdown of General Relativity in both atomic and black hole structures.
Category: Mathematical Physics