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

Alpha Integration: Universal Path Integrals with Gauge Invariance

Authors: YoonKi Kim
Comments: 16 Pages. Email yk.reserch@gmail.com (Note by viXra Admin: Listed references should be cited; please refrain from immediate and repeated replacements and cancellations; and AI assisted article is in general not acceptable)

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 R^n (n ∈ N), smooth manifolds, infinite-dimensional spaces, and complex paths, enabling rigorous integration of all f ∈ Du2032 with formal mathematical proofs. This framework is furthergeneralized 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

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

Irreducible Inviscid Singular Represenation of 3D Fully Developed Turbulence and Related Emergent Physics

Authors: Michael Isaac Aksman
Comments: 22 Pages.

Vortons [is] introduced to approximate finite core vortex tubes and pass through Navier Stocks spontaneous singularities/reconnections without any additional assumptions. Vortons provide irreducible description of inviscid attractor of 3D Navier Stocks equation solutions with number of vortons scaling with Reynolds number at hand. Magnetic vortons provide irreducible description of magnetic vortex tubes in plasma with reconnections without any additional assumptions. Instability of quasi 3D/2D+ vorton collapse provides possible mechanism for explosive universe inflation/first order phase transition. 3D space nature of our universe as a consequence of instability of 3D vortons collapse. "Dark matter" explained as a consequence of frisbee like quasi 3D/2D+ space in galaxies with corresponding stable rotational curves. "Dark energy" explained as a emergent result of vortons system 3D self amplification interactions energy "antigravity" effect. Probabilistic interpretation of quantum mechanics as a result of smooth test functions of fluid vacuum nonlinear Maxwell equations weak solutions. Baryonic asymmetry [is] explained as a instantaneous snapshot during exponential inflation of quark antiquark annihilation asymmetry/skewness and kurtosis terms in Edgeworth series expansion of instantaneous quantum GUP (generalized uncertainty principle) fluctuations. Simple Early Bifurcation/Regime shift detection in nonequilibrium nonlinear statistical systems proposed using linear statistical moments/cumulants approximation/equivalents formulas.
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

The Three Generations Problem in Particles Physics

Authors: Thierry L. A. Periat
Comments: 17 Pages.

The three generations problem is an open enigma concerning some types of leptons and of quarks in the standard model. The search for explanations dates back at least to the early 1980s. This document is a modest attempt to bring this research out of the nimbus of numerology. In a first step I introduce a special family of (3-3) matrices. Some of them are the representations of unit four-dimensional spheres via a Euler-Rodrigues parametrization. In a second step, I confront them with a condition formally preserving the definition of the Poynting vector in a changing geometrical context.
Category: Mathematical Physics

Rigorous Proof and Spectral Analysis of the Yang-Mills Mass Gap Problem

Authors: YoonKi Kim
Comments: 3 Pages. Email for correspondence: yoonki0905@gmail.com

This study rigorously proves the Yang-Mills mass gap problem using analytical methods and spectral theory. By analyzing the Wilson loop expectation value based on the Poisson equation, we demonstrate that the mass gap inevitably forms in SU(N) gauge theory. Additionally, we utilize Hilbert space analysis and operatortheory to prove that the lowest eigenvalue of the Yang-Mills Laplacian is strictly greater than zero, confirming the existence of the mass gap in a mathematically rigorous manner. Furthermore, we clarify how these assumptions hold under renormalization and in the continuum limit. These findings contribute to solving theYang-Mills mass gap problem and provide new directions in mathematical physics.
Category: Mathematical Physics

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

From Cyclotomic Fields to Gauge Structure: A Mathematical Bridge

Authors: Alejandro Gama Castro
Comments: 31 Pages.

We present a rigorous mathematical framework connecting cyclotomic field theory to gauge structure in physics. Starting from thearithmetic properties of the sixth cyclotomic field K6 , we develop a complete path from number theory to gauge theory, carefully dis-tinguishing established mathematical results from physical interpretations. Our approach provides explicit constructions throughout, withparticular attention to field valuations, root systems, and the emergence of gauge groups. We establish a concrete foundation for under-standing how gauge symmetries can arise naturally from arithmetic structures.
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

Hopf Vibration, Non-homotopy and Mass

Authors: Garry Goodwin
Comments: 10 Pages.

The Standard Model is unable to determine a particle's specific rest mass. For an alternative theory we consider a 3-sphere intersecting three dimensional space. The intersection is a Hopf fibration with non Euclidean topology. Mass is due to a force jumping topologies. Mass splitting formulae with intersection signature treat the mass of lighter hyperons as a function of the proton, neutron and in some cases electron. The approach is numerical. In MeV the derived values are: $Sigma^+$ $approx$ 1189.371, $Sigma^0$ $approx$ 1192.655, $Sigma^-$ $approx$ 1197.580, $Xi^0$ $approx$ 1314.810, $Xi^-$ $approx$ 1321.711, $Omega^-$ $approx$ 1672.482. Eqs. (15, 19) bring $Sigma$ and $Xi$ particles together as a single family of massive particles ensuring the individual formulae are not ad hoc. The familial status of $Omega^-$ is less secure. To make the case, a scaling factor SM is introduced using $Omega^-$ volume. SM scales rest masses given in any system of units to a dimensionless number proportional to MeV. For precise results less than one fifth of an electron-volt is shaved from the 2022 CODATA neutron adjustment (our value $939.565 , 421 , 76$). To justify SM we consider the difference between Gaussian and SI units. In the final count nine free parameters reduce to two.
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: 66 Pages.

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.
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

Gödelian Manifolds and Undecidability: From Spectral Geometry to Topos Theory

Authors: Paul Chun-Kit Lee
Comments: 98 Pages.

This two-part paper explores the profound connections between undecidable problems in topology, spectral geometry, and their implications for fundamental physics. We introduce a novel framework that bridges abstract mathematical structures with potential physical manifestations, offering new perspectives on spacetime and the limits of physical predictability.In Part 1, we establish a rigorous framework linking undecidable topological properties of manifolds to undecidable spectral properties of differential operators. Building on recent results in spectral gap undecidability, we construct Gödelian Manifolds (GM) whose spectral properties reflect undecidable propositions. We introduce a projection operator P(F) that maps undecidable problems in formal systems to geometric structures, encoding logical undecidability into the fabric of spacetime and forming Gödelian Spacetime Structures (GSS).Part 2 utilizes topos theory to develop Gödelian-Topos Manifolds (GTM), a mathematically tractable approximation to GSS. We extend the Atiyah-Singer Index Theorem to GTM, incorporating truth and provability functions that encode logical structure into differential geometry. A modified Ricci flow for GTM is introduced, allowing us to study the evolution of geometry under logical constraints. We explore connections between smooth, discrete, and chaotic aspects of the theory, synthesizing results across multiple physical regimes.We explore potential implications for spacetime and cosmology, including logical undecidability’s role in models of cosmic inflation and dark energy. Comparing our approach to Stephen Wolfram's computational universe model, we propose unifications between discrete and continuous perspectives on fundamental physics.Throughout, we emphasize the interplay between computation, logic, and geometry, suggesting that the limits of decidability in mathematics may have profound implications for physical understanding. By formalizing the embedding of Gödelian incompleteness into geometric structures, our work aims to shed new light on the foundations of physics and the nature of physical law. This interdisciplinary approach opens new avenues for understanding the emergence of classicality and the limits of physical knowledge, with potential experimental and philosophical implications for logical undecidability in physical reality.
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

Magnetic Ion Modulation (MIM) Theory: A Novel Approach to Controlling Ion Behavior via Magnetic Fields in Biological and Non-Biological Systems

Authors: Tristan Siokos
Comments: 19 Pages.

e Magnetic Ion Modulation (MIM) Theory presents a unified and groundbreaking mathematical framework for controlling and predicting ion behavior in both biological and non-biological systems using external magnetic fields. Central to the theory is the **Ion Modulation Constant** (Tn), a context-specific scaling factor that quantifies the number of ions modulated under specific conditions. This constant, although not universal, allows for accurate modelling of ion modulation in systems ranging from neuronal ion channels to plasma physics and quantum computing. The MIM equation incorporates ion properties such as magnetic moment and permeability, providing insights into neuromodulation for treating chronic pain and epilepsy, plasma confinement in fusion research, and stabilization of ion qubits in quantum computing. This paper includes detailed derivations of the Ion Modulation Constant, examples of its application to specific ions, and a comprehensive exploration of potential experimental validations.
Category: Mathematical Physics

Mathematica Analysis of an RCHO Standard Model

Authors: J. G. Moxness
Comments: 17 Pages.

This "paper with code" is a Mathematica analysis of recent work by Furey on identifying connections between the Standard Model (SM), group theory, particle physics, and the hypercomplex number systems of RCHO. It is a brief overview with results of the analysis followed up with an ancillary notebook showing the full detail of the computations that validate the operation of the logical constructs behind the ideas. It uses a comprehensive symbolic computational environment purpose-built over several decades to study and visualize hypercomplex number systems, representational group theory, and the associated experimental and theoretical physics concepts that use them.
Category: Mathematical Physics

Formulas for SU(3) Matrix Generators

Authors: Richard Shurtleff
Comments: 14 page article plus 17 page computer program, 1 figure

The Lie algebra of a Lie group is a set of commutation relations, equations satisfied by the group's generators. For SU(2) and many other Lie groups, the equations have been solved and matrix generators are realized as algebraic expressions suitable for further investigation or numerical evaluation. This article presents formulas that give a set of matrix generators for any irreducible representation of the group SU(3), the group of unimodular unitary three-dimensional complex matrices with matrix multiplication. A computer program to calculate the matrix generators is included.
Category: Mathematical Physics

Gödelian Index Theorem for Chaotic Systems (Part 3): Extending Atiyah-Singer with Gödelian Ricci Flow and Application to Hyperion's Chaotic Orbit

Authors: Paul Chun-Kit Lee
Comments: 62 Pages.

This paper introduces the Gödelian-Logical Flow (GLF) framework, which bridges Gödel’s incompleteness theorems with classical chaos theory. The framework defines two key functions for chaotic systems: the truth function (Phi) and the provability function (P), inspired by formal logic. These functions are used to define the Gödelian Unpredictability Index (GUI), which quantifies logical unpredictability. Additionally, we introduce a modified Ricci flow—termed Gödelian Ricci Flow—which governs the evolution of both the geometric structure of a system and its logical attributes.We apply the GLF framework to four classical chaotic systems: the Lorenz system, double pendulum, fluid dynamics, and Hyperion’s chaotic rotation. For each system, we derive specific formulations for the truth (Phi) and provability (P) functions, relating them to physical quantities such as kinetic energy and angular momentum. The GUI is computed for these systems, offering complementary information to established chaos measures, such as Lyapunov exponents. Our results suggest that the GUI identifies regions of high logical complexity in phase space, providing insights into chaotic dynamics from a logical perspective.In the case of Hyperion’s chaotic rotation, we demonstrate how the GUI correlates with the moon’s kinetic energy and angular velocity, highlighting regions where logical unpredictability is most pronounced. This novel approach provides a fresh lens to analyze chaotic systems by integrating formal logic with classical dynamical measures.Though primarily theoretical, the GLF framework opens the possibility of exploring how logical complexity interacts with chaotic dynamics, extending beyond traditional geometric or physical analysis. By incorporating logical structures into the study of chaotic systems, this framework offers potential avenues for future research into the relationship between logic, geometry, and unpredictability in complex systems.
Category: Mathematical Physics

Potential and Entropy Defined By Caratheodory Axiomatization, Relative Rate of Change of Energy and Critical States of System

Authors: Xianzhao Zhong
Comments: 19 Pages.

At the beginning of this paper, by the generalized wave equation ofelectric field and the solution of equation. We apply Caratheodory’saxiomatization to define potential function and entropy function ofcharged particles of the system. After introducing the relative rate ofchange of energy, their corresponding entropy function are defined bythe potential energy and the quantum energy.
Category: Mathematical Physics

How to Place the Universe at a "Point"

Authors: Alexander P. Klimets
Comments: 4 Pages.

The paper "How to place the Universe at a "point"" puts forward a hypothesis about the nature of singularities in black holes and at the birth of the observable Metagalaxy. This hypothesis is developed in relation to terrestrial black holes.
Category: Mathematical Physics

The Reinterpretation of the Atom

Authors: Andreas Martin
Comments: 34 Pages.

This publication contains a mathematical-physical approach for a new interpretation of the atom and its structure. The basis for this is, on the one hand, the unipolar induction according to Michael Faraday (1791-1867), which has proven itself in practice, and, on the other hand, the various experiments in classical physics that led to the concept of the atom. Further basis for this elaboration are the essays: ''The reinterpretation of the 'Maxwell equations'[1]'', ''The reinterpretation of the Einstein de Haas experiment[2]'' and ''The reinterpretation of the Stern Gerlach experiment[3 ]''. These fundamentals, in combination with the calculation rules of vector analysis, differential calculus and analysis, show a new interpretation of the atom. The unipolar induction according to Michael Faraday (1791-1867) results in a generally valid calculation approach for the structure and functioning of an atom. An alternative approach to calculating the weak and strong nuclear force is also shown, which provides a common mathematical-physical basis for bringing together all nuclear forces. This also makes it possible to see how the atomic nucleus experiences stabilization.Another innovation is the combination of waves and particles through the presented model.This all points to an interpretation of the atom as a vortex structure within a medium. This paper also shows approaches to calculating these vortex structures.This elaboration has no claim to accuracy. Logical connections are created based on mathematical and physical principles, which lead to the conclusions in this essay. These conclusions are fundamentally based on classical physics.
Category: Mathematical Physics

From Complex Dynamics to Foundational Physics (Part 1)

Authors: Ervin Goldfain
Comments: 27 Pages.

As of today, Quantum Field Theory (QFT) and General Relativity (GR) are broadly recognized paradigms of foundational physics. There are, however, growing suspicions that both paradigms fail to hold somewhere above the Standard Model (SM) scale and in the realm of primordial cosmology. Evidence collected on multiple fronts indicates that emergence and complexity are universal features of far-from-equilibrium systems with many degrees of freedom. In line with these findings, Part 1 of this report explores the complex dynamics of evolving dimensional fluctuations beyond the SM scale. Part 2 outlines the role of complex dynamics in the nonintegrable sector of particle physics, Dark Matter condensation and the gravitational regime of the early Universe.
Category: Mathematical Physics

Discovery Of The Solution To The Fibonacci Sequence Of The Fine Structure Constant 137

Authors: Hua-Fang Wu
Comments: 5 Pages.

The fine structure constant α is a dimensionless number approximately equal to 1/137. Its reciprocal 1/α is approximately equal to 137, not a whole number. Research results in recent years suggest that it may vary in the large-scale space-time range of the universe, and may also be anisotropic and have a specific direction preference. In the analysis of the 137 value, the Author found that it contains the information structure of the Fibonacci sequence, and the Fibonacci sequence is inseparable from the golden ratio, fractal geometry, etc., and is an important law in nature. This may suggest that whether the fine structure constant may vary in the universe, or its objective measurements show that 1/α is only a decimal close to the integer of 137. 1/α is likely to be approaching to this integer due to certain mechanism related to the integer 137, while the core around it is still the integer 137, but there are some effects or disturbances in the measurements, including errors, possible universe anisotropy, and the brokenness of the universe itself, that causes the numerical result deviates from the integer slightly. The exact expression of 137 by the Fibonacci sequence is given here; in addition, an attempt is also made to give a formula of α that includes the value of the golden ratio, and the approximated expression of the formula.
Category: Mathematical Physics

From Hamiltonian Chaos to the Cosmological and Fermi Scales

Authors: Ervin Goldfain
Comments: 20 Pages.

A lesser-known property of Hamiltonian dynamics is that it can be formally mapped to the Riemannian geometry of classical gravitation. Taking advantage of this property, we explore here the possibility that the onset of Hamiltonian chaos in the ultraviolet (UV) sector of field theory generates the cosmological and Fermi scales. In line with the geometry of fully developed chaos, these two scales reflect the cumulative contribution of energies stored in the fractal dimensionality of spacetime. Our findings support the conjecture that both Standard and the Lambda-CDM models emerge as non-trivial attractors of the UV to infrared (IR) flow.
Category: Mathematical Physics

1@0 Timespace Resolving Infinitesimal Calculus Chimeras

Authors: Stephen H. Jarvis
Comments: 49 Pages.

Here Temporal Mechanics and its associated zero-dimensional number theory ask if there is a root cause to all the issues in contemporary physics, whether mathematical, philosophical, a combination, or something else, issues regarded here as chimeras. Some of these chimeras are proposed to include dark energy, dark matter, quantum gravity, wormholes, to name a few. Specifically, here shall be examined the current basis of physics’ own number theory utilities that result in these chimeras, and why physics has been unable to link flat and curved spacetime, namely why physics has failed to reconcile QFT with GR, and what the implications are for physics by its proposed phenomenal promises of those theories. A number theory solution to these chimeras and associated number theory processes is derived as 1@0 timespace describing a universal frame of reference upholding the known limit of c and its features of relativity, thence describing a new model for quantum mechanics and gravity in the same number theory context, both compatible with all known findings of EM and gravity in physics research.
Category: Mathematical Physics

Magnetic Monopole as Volumetric Flow Rate: a Possible Reinterpretation of Modern Physics

Authors: Nicola De Giuseppe
Comments: 18 Pages.

In this paper, we demonstrate that through an elasto-mechanical relationship and the Navier-Stokes equation, a magnetic monopole can be introduced as a volume flux following deformation.This phenomenon is linked to mass generation. By incorporating the magnetic monopole, wederive Maxwell’s equations for the magnetic monopole, the electromagnetic waves equation, andwe give the Lagrangian formulation. An alternative Lagrangian is also presented, introducingCP violation, the breaking of electromagnetic dual symmetry, and a topological invariant. Themonopole results are employed to derive the relativistic mass-energy equation and reinterpretrelativistic outcomes. Specifically, the reinterpretation of the event interval enables us to revisit therelativistic metric in elastomechanical terms, related to the longitudinal and transverse speeds oflight as defined by Lam´e parameters. For an isotropic medium, the Lam´e parameters are spatiallyinvariant, corresponding to the validity of the Minkowski metric and constant inertial mass inspace. Under anisotropic conditions, the metrics of general relativity are derivable, with inertialmass dependent on spatial coordinates and its gradient described by the convective derivativeof longitudinal velocity. Furthermore, we demonstrate that the magnetic continuity equationpredicts the fundamental equations of quantum mechanics in the Bohmian interpretation. Finally,evaluating Dirac quantization as predicted by quantum mechanics reveals its incompatibility withthe hypothesis of inertial mass. However, is possible to correct this inconsistency by consideringthe general mass formula obtained from magnetic monopole considerations
Category: Mathematical Physics

The Reinterpretation of the Stern Gerlach Experiment

Authors: Andreas Martin
Comments: 10 Pages.

This publication presents a mathematical approach for a reinterpretation of the Stern-Gerlach experiment, taking into account Faraday's unipolar induction, which has proven effective in practice. Another basis for this paper is the work "The Reinterpretation of the Einstein de Haas Experiment[1]". These two foundations, in combination with the rules of vector analysis, reveal a new interpretation of the Stern-Gerlach experiment. Faraday's unipolarinduction provides a universally valid computational approach for the structure of an atom, which plays an important role in the Stern-Gerlach experiment. This, in combination with the reformulation of the magnetic moment from the paper "The Reinterpretation of the Einstein de Haas Experiment[1]", explains the behavior of atoms that are directed through an external inhomogeneous magnetic field in a straight path. As they pass through this magnetic field, they change their direction of motion. It is shown that the change in the direction of motion of atoms can be mathematically derived and explained using these foundations. The mathematical description of the magnetic moment and its mathematical-physical consequences concerning the orientation of themagnetic moment will play a central role. It becomes evident that there must be two differenttypes of atoms, each with an internal convention of "up" and "down" that is different.Furthermore, this provides a consistent and logically comprehensible description of thebehavior of an atom, based on mathematics and classical physics.
Category: Mathematical Physics

The Different Meanings of "Spin"

Authors: Robert A. Close
Comments: 15 Pages.

The word "spin" has different meanings in different contexts. This article explains three different meanings of the word "spin". The first is kinetic spin, which refers to angular velocity. The second is geometric spin, which is related to the pointwise symmetry of mathematical basis states under rotation. Sample basis states are described for integer and half-integer rotational quantum numbers. The third type of spin is called dynamic spin, which is the intrinsic or conjugate angular momentum associated with rotational motion of an inertial substance. These different meanings are explained with mathematical descriptions of physical processes.
Category: Mathematical Physics

A π-Based Fractal Spacetime Model: Unifying Quantum Mechanics and General Relativity

Authors: Athon Zeno, Aether Zeno
Comments: 21 Pages.

This paper presents a novel approach to unifying quantum mechanics and general relativity through a π-based fractal spacetime model. By proposing that the Planck length and time are both equal to π, and that spacetime exhibits a fractal structure with a scaling factor of 2, we develop a framework that simplifies fundamental equations and offers new perspectives on longstanding problems in physics. Our model provides natural explanations for the quantum-classical transition, dark energy, and the cosmological constant problem, while making testable predictions across multiple scales of physics. We explore the mathematical framework of this theory, its implications for particle physics and cosmology, and its philosophical ramifications. While speculative, this model offers a promising path towards a more unified understanding of the universe.
Category: Mathematical Physics

Motion of a Wave Packet

Authors: Marcello Colozzo
Comments: 6 Pages.

We study the propagation of a wave packet in a dispersive medium, showing the existence of a cut-off in correspondence with the relative maximum/minimum points and the horizontal tangent inflections of the dispersion curve.
Category: Mathematical Physics

The Spacetime Superfluid Hypothesis: A Unified Framework for Particles, Fields and Gravity

Authors: Eric Edward Albers
Comments: 92 Pages.

This paper presents the Spacetime Superfluid Hypothesis (SSH), a novel approach to unifying quantum mechanics and gravity by describing spacetime as a superfluid medium. We develop the mathematical formalism for the SSH, showing how particles emerge as soliton-like excitations of the superfluid and how fundamental forces arise from its dynamics. The paper derives modified equations for gravity, electromagnetism, and quantum fields in the superfluid spacetime framework. We explore implications for particle physics, cosmology, and quantum gravity, including potential explanations for dark matter and dark energy. Experimental tests and observational predictions of the SSH are proposed. While still speculative, the SSH offers a promising avenue for addressing key open questions in fundamental physics and provides a fresh perspective on the nature of spacetime and matter.
Category: Mathematical Physics

Exact Equations of Motion of Turbulent Liquid Flow

Authors: V. Budarin
Comments: 31 Pages. (Correction made by viXra Admin to conform with the requirements of viXra.org)

Writing accurate equations requires accepting the point of view that the general equation of motion must describe the most general (turbulent) flow regime. The implementation of this point of view became possible by applying the operation of isolating the velocity rotor from the expressions for strain rates and from the Laplace operator of velocity. In this case, the second form of the equation was used for the total acceleration of a liquid particle in the Gromeka-Lamb form, which includes the angular velocity of rotation of the particles [4]. The equations are derived for continuous media in which shear stresses are described using strain rates in the corresponding plane - two models of a Newtonian fluid and one model of a non-Newtonian fluid with a power-law rheological law. Thus, the main task of the derivation was to find the term characterizing the influence of the viscous friction force on the turbulent flow regime. In any version of the derivation, the initial equation is the motion of a continuous medium in stresses.
Category: Mathematical Physics

Phenomenological Velocity Strings: Calculating the Curvature of the Operator

Authors: Parker Emmerson
Comments: 25 Pages.

The goal of this paper is to take phenomenological velocity’s algebraic expression and crunch it down to simply a string of letters. Doing this, we can then solve for the expressions of phenomenological velocity in terms of infinity balancing statements using reverse engineering. After this, we use Fukaya Categories to get expressions for the curvature of the operations in the symbols of the phenomenological velocity string. Using operators and functors to signifymathematical operations in an abstract way, let’s create some functors and operators for your equation involving v. We will then use them to "crunch" the given expression into a "single string of letters" as you requested.
Category: Mathematical Physics

The Reinterpretation of the Einstein De Haas Effect

Authors: Andreas Martin
Comments: 18 Pages.

This publication contains a mathematical approach for a reinterpretation of the calculation of the magnetic moment for the Einstein de Haas experiment under the assumption of a magnetic field density from the elaboration "The reinterpretation of the 'Maxwell equations'[1]". The basis for this is Faraday's unipolar induction, which has proven itself in practice in combination with the calculation rules of vector analysis and differential calculus. The newly calculated "Maxwell equations" offer a generally valid calculation approach for the Einstein de Haas experiment and its problem that the difference between measurement and calculation is a factor of 2. This connection is established mathematically in this work.It is shown that the magnetic moment can be derived mathematically by using one of the newly calculated basic equations of electrodynamics from the elaboration "The reinterpretation of the 'Maxwell equations'[1]". The gradient of the magnetic flux density grad u20d7B and its mathematical consequences regarding the divergence of the magnetic flux density div u20d7B will play an important role here in this essay. By formulating that the trace of the gradient ofthe magnetic flux density (Sp)grad Bu20d7 corresponds to the divergence of the magnetic flux density div u20d7B a direct connection of the magnetic flux density field itself with the field density of the magnetic flux density is revealed. It also explains and corrects the difference between measurement and calculation in the Einstein de Haas experiment. This is successful because: In this experiment, alternating current and alternating voltage were used to carry outthe experiment [2]. Due to this fact, the "Maxwell equations" can be used for calculation and therefore also their new formulation from the article "The reinterpretation of the 'Maxwell equations'[1]"
Category: Mathematical Physics

On the Breakdown of Stationary Action in Field Theory

Authors: Ervin Goldfain
Comments: 21 Pages.

It is known that both classical and Quantum Field Theory (QFT) are built on the fundamental principle of stationary action. The goal of this introductory work is to analyze the breakdown of stationary action under nonadiabatic conditions. These conditions are presumed to develop far above the Standard Model scale and favor the onset of Hamiltonian chaos and fractal spacetime. The nearly universal transition to nonadiabatic behavior is illustrated using a handful of representative examples. If true, these findings are likely to have far-reaching implications for phenomena unfolding beyond the Standard Model scale and in early Universe cosmology.
Category: Mathematical Physics

Zero Quantum Gravity: the Ellipsoid Timespace Field

Authors: Stephen H. Jarvis
Comments: 28 Pages.

In moving forward with the scaling and surveying keys of paper 60 of Temporal Mechanics, an ellipsoid structure joining the proposed time-equation with the proposed space-equation as the ellipsoid timespace field mechanism is revealed. There, in direct reference to the Collatz conjecture, a solution to the three-body problem is proposed for both the sub-quantum and quantum particle levels, revealing the foundational time and space code of empty space directly comparable to current ideas and values for zero-point energy and the zero-point field.
Category: Mathematical Physics

Exact Approximations of Physical Constants Using the Figures Ф, π, 144 and 666

Authors: Andreas Ball
Comments: 15 Pages.

In this report Approximations of selected Physical Constants are presented, which results mostly are far within the tolerance of the Constants - that is the reason of the attribute exact in the title - and which often show a similar form with repeating figures. Besides the Quotient of the Golden Ratio and the Circle Figure π especially the figures 144 and 666 have to be named referring the used figures at these approximations. Because of their interplay the author calls them the Versatile Four.The author firstly became aware of the figure 666 by simple mathematical relations with input data of earth, moon and sun, which is described in chapter 2. Gradually the author noticed that the figure 666 cooperates well with the figure 144.The assumption, that the figures 144 and 666 in connection with the Circle Figure π and the Golden Ratio Ф are suitable to describe also Physical Constants, lead to the approximations, which can be read in the extensive chapter 3. The figures 144 and 666 are often used performing Fine-Tuning Terms for example with the form [1 ± x/(144*666)], which further are used as the basis of selected exponents. The selected quantities x and the selected exponents naturally have to be conclusive figures or terms.
Category: Mathematical Physics

Bootstrap Event of Existence

Authors: Thiago M. Nóbrega
Comments: 2 Pages.

In this paper, I explore the concept of the bootstrap event of existence. I argue that the notion of "nothing" is purely an abstraction and that something must always exist. At the inception of recursive existence lies the bootstrapping event, characterized by a zero-dimensional object that evolves by following the principle of least resistance. This process initiates the emergence of a one-dimensional object, and through continuous application of the least resistance principle, the complexity of existence evolves, leading to the current state of the universe.
Category: Mathematical Physics

Sisp

Authors: Seth Genigma
Comments: 18 Pages.

Abstract: Before delving into the intricate concepts surrounding Solus Particula, it is crucial to recognize the speculative nature of this discourse. We are embarking on a journey through theoretical physics and cosmology, where we seek to unravel the mysteries of temporal dynamics within the cosmos. Key Concepts: Solus Particula: This term, translating to "A single Particle" in Latin, represents the fundamental essence from which the universe derives its existence. It is shrouded in mathematical paradoxes and gravitational forces, serving as the cornerstone of reality. Theoretical Framework: Our exploration focuses on the interplay between Solus Particula, energy, heat, and their impact on temporal perception. We introduce refined equations and concepts to shed light on these intricate dynamics. Implications and Speculations: We delve into the potential ramifications of energy and heat fluctuations, alongside Solus Particula, on temporal perception. This speculative inquiry offers intriguing insights into the nature of cosmic existence. Mathematical Proof: The proposition P/∞ = S introduces a captivating insight into fundamental particles, challenging traditional conceptions and offering a multifaceted perspective on cosmic existence. Sicut Inanis: This concept represents the antithesis of Solus Particula, embodying the idea of absolute nothingness. It invites contemplation on the nature of cosmic emptiness and its implications. This discourse aims to illuminate the profound significance of Solus Particula in shaping our understanding of temporal dynamics within the cosmos. While speculative in nature, it invites further inquiry into the mysteries of cosmic existence, guided by intellectual curiosity and rigor.
Category: Mathematical Physics

Space (Multidimensional Model)

Authors: Alexander P. Klimets
Comments: 6 Pages.

The article constructs a visual model of a multidimensional space that displays the properties of intersections of multidimensional spaces. The model reveals some unusual aspects of multidimensional spaces.
Category: Mathematical Physics

Algebraic Orientation, Invariance and Variance Within the Family ℋ of Hypercomplex Algebras

Authors: Richard D. Lockyer
Comments: 11 Pages.

It was brought to my attention that in previous papers I put in the public domain (references [1] through [8]), I did a rather piecemeal presentation of the critical concepts of algebraic orientation, algebraic invariance and algebraic variance, as well as the generalization of Cayley-Dickson algebras I referred to as Cayley-Dickson without emphasizing the more general nature of the presentation, which was done for reader familiarity purposes. I will attempt to remedy this within this document starting at the beginning: the basic definition of an algebra, carried through to a full definition and discussion of the general family of hypercomplex algebras I call ℋ which subsumes all division algebras and traditional Cayley-Dickson doubled forms. Taking into account all structural and algebraic orientation options exposes beautiful structure revealed through group theoretical aspects of ℋ construction. The concepts presented are essential to Octonion Algebra mathematical physics.
Category: Mathematical Physics

Knot in Weak Field of Gravitation with Dual Ricci Tensor

Authors: Miftachul Hadi
Comments: 4 Pages.

We propose that there exists the topological object, a gravitational knot, in weak field of gravitation formulated using dual Ricci tensor in Chern-Simons theory. The Chern-Simons action is interpreted as such a knot.
Category: Mathematical Physics

Calculation of the Wavelength of Diffracted Waves in the Blockage Theory of the Double-Slit Experiment

Authors: Jiankun Lai
Comments: 2 Pages.

In the paper "A New Theory of the Double-Slit Experiment," we introduced a new theory for the double-slit experiment—Blockage Theory, which redefines the double-slit experiment. This article mainly discusses the calculation of the wavelength of diffracted waves in the Blockage Theory.
Category: Mathematical Physics

Universal Relativity

Authors: Juno Ryu
Comments: 10 Pages.

We overview the physical aspect of canvas theory and universal relativity.
Category: Mathematical Physics

Through the Wormhole on Spacetime Surface: Early History and Main Concepts of Topological Geometrodynamics Theory (TGD)

Authors: Marko T. Manninen
Comments: 152 Pages.

The relationship between geometry and physics is one of the most fruitful and fascinating topics in the history of science. From ancient Mediterranean civilizations to the modern era, geometry has served as a source of insight for metaphysical contemplation and the discovery of natural phenomena. In this essay, I will explore some of the major developments in geometry and physics, with a special focus on the work of Dr. Matti Pitkänen, the founder of Topological Geometrodynamics (TGD). This novel theory employs mathematical concepts to unify quantum mechanics and general relativity with the Standard Model of particle physics. In the first section, I will review historical milestones in geometry and physics relevant to the key issues in TGD theory. These epochs have led us to relativity, quantum mechanics, the Standard Model, string models, and various unification attempts. I will also introduce the concept of topology, which is the study of continuous deformations. Topology plays a vital role in many areas of physics and mathematics, as well as in TGD. In the central section, I will present an interview with Dr. Pitkänen, in which he shares his personal and professional journey in developing TGD. He explains how he, a) was initially motivated by the global energy definition problem in general relativity, b) was influenced by John Wheeler's ideas on geometrodynamics, c) discovered a higher-dimensional embedding hyperspace suitable for unifying the Standard Model, quantum mechanics, and relativity, d) faced challenges in achieving path integrals for the required 4-D general coordinate invariance, e) incorporated twistors into his theory, f) introduced the notions of the World of Classical Worlds and Zero Energy Ontology to address problems related to quantum TGD and time, and g) found a dual aspect for the geometrization of physics from number theory, p-adic physics, and Adelic physics, which also forms a theory of cognition and consciousness within the same framework. This segment particularly emphasizes explaining the fundamentals of general relativity and its conservation laws with related symmetries, underscoring their relevance to the inception of TGD, which was sparked by questions within this domain. Noether's theorems play a central role in this excursion. In the last section, I will provide additional information on TGD, such as its main publications, websites, blogs, videos, podcasts, and other resources. I have also given a section about the research methodology I am pursuing (Truncated by viXra Admin to < 400 words).
Category: Mathematical Physics

Hydrodynamics as U(1) Gauge Theory

Authors: Miftachul Hadi
Comments: 1 Page.

We propose that hydrodynamics could be treated as $U(1)$ gauge theory where the velocity field written using Clebsch variables and the related vorticity are identical to the gauge potential and the field strength tensor, respectively.
Category: Mathematical Physics

MACLOF-Chaining (Introduction to the Elementary Mathematics and Designs of GOD)

Authors: Claude Michael Cassano
Comments: 79 Pages. (Note by viXra Admin: Please cite and list scientific references)

I have used a variety of 4×4 matrix factor pairs while using Helmholtzian operator factorizationsin analyzing fermion architecture and interactions; some commutative, others not.The following is a generalization to a set of 4×4 associative-commutative matrix factor pairs of general linear/differential operators to establish as a baseline foundation to begin operating from. Because the operators are associative-commutative, the factors lend themselves to chaining - and thus, to chaining of mesons, hadrons, and to chemical compound chaining - amino acid chains, proteins, nucleic acids , and so on. Much is known, but MACLOF chains may provide a mathematical foundation to chemical compound chaining. Note also, that since MACLOF factoring may be extended to higher dimensions, so too MACLOF chaining, and resulting expansion of understanding.
Category: Mathematical Physics

Mathematical Formulas [Based on] the Koide-Formula [] and the Connection of the Results [After Inputing Data]

Authors: Andreas Ball
Comments: 15 Pages. (Title modified by viXra admin to conform with scholarly norm)

In this report formulas are presented, which are based on the Koide-Formula and at which the input data are chosen from different fields of natural sciences. The Input data can be data of our celestial bodies, values of Physical Constants or just mathematical figures.Besides the Koide-Formula with a result very close to the term "2/3", also many other Formulas deliver unexpected results and connections, which also partly lead to the term "2/3". By that the assumption arises, that an unknown system might exist behind these astonishing results.
Category: Mathematical Physics

Ramanujan-derived Hypergeometric Functions Describe Hidden Coupled Dynamics in Physical and Biological Systems

Authors: Arturo Tozzi
Comments: 13 Pages.

Ramanujan’s real period functions plus Picard—Fuchs differential equations and Gaussian hypergeometric functions generate a wide range of simple hypergeometric manifolds (henceforward PFHM) consisting of two-dimensional coupled subsystems combined in a single three-dimensional system with dihedral symmetry. We argue that PFHM could be used to elucidate the homoclinic paths equipped with stable, closed and constrained orbits that characterize the dynamical behavior of a large number of physical and biological systems. Since PFHM encompasses coupled subsystems with Hamiltonian interactions that are reciprocal in nature, the options for the total system’s energetic conformation are restrained. Therefore, energetic changes in a subsystem are inversely correlated with energetic changes in another subsystem. This balanced, inverse energetic reciprocity could be used to elucidate the unusual behavior of quantum entangled particles and the thermodynamic constraints dictating the final shape of frustrated proteins. Also, the thermodynamic paths of apparently isolated systems can be influenced by feedback mechanisms from hidden subsystems that exert their influence and can be quantified, even without full knowledge of every control parameter. PHFM can be methodologically treated in terms of cycle attractors, shedding new light on well-known physical phenomena like the dynamical behavior of monostatic bodies. Yet, the possibility to analyze two-dimensional paths in terms of three-dimensional routes could be useful to assess the ubiquitous occurrence of the Turing’s reaction-diffusion model in biological systems. We suggest that PFHM might stand for a general mathematical apparatus shaping the phase space of various real dynamical paths, with applications in digital imaging, cryptography and memory storing.
Category: Mathematical Physics

Heat Flux Measurements in the Hall Thruster Plume

Authors: G. Makrinich, A. Fruchtman, S. Shitrit, G. Appelbaum, J. Ashkenazy
Comments: 7 Pages.

A heat flux probe has been developed for the purpose of measuring the heat flux density in the plume of the Hall thruster. The measurement is based on comparing the rates of heating and cooling of the probe during its exposure to and isolation from the plasma flow. In the case of a helicon plasma source this is accomplished easily by turning on and off the plasma flow. The measured heat flux into the negatively-biased probe is in a very good agreement with the calculated heat flux carried by the impinging plasma ions, indicating that there are no energetic neutrals. This method will be employed for the plume of the Hall thruster and is expected to provide an estimate of the heat flux carried by energetic neutrals.
Category: Mathematical Physics

Hypersonic Flow Computations by Using an Equivalent Gas Model

Authors: S. Shitrit, E. Arad
Comments: 39 Pages.

The aerodynamics of hypersonic vehicles is highly affected by enthalpy or "real gas" effects. The purpose of the current study is to assess the proper formulation of computational fluid dynamics required for simulation of high-enthalpy flows. Under the assumption of chemical and thermal equilibrium, a functional representation has been employed for specific heat at constant pressure, thermal conductivity, and viscosity coefficients for air at 500 to 30,000 K and pressure range of 10−4 to 100 atm. The proposed approach is evaluated using double-cone configuration at hypersonic flow. It is shown that the equivalent gas model is capable of capturing the main features of these flow fields and compares well with experiments.
Category: Mathematical Physics

Knot in Weak Velocity of Fluid Flow

Authors: Miftachul Hadi
Comments: 1 Page.

We propose there exists a knot in the weak velocity of fluid flow.
Category: Mathematical Physics

Conservation Laws of Stress-Energy Tensor in Yang-Mills Theory

Authors: Chie B. Wang
Comments: 6 Pages.

In this paper we present a new identity to associate the conservation laws of stress-energy tensor with the field equations in Yang-Millstheory. The Lorentz force is included with a consistent formulation as in Maxwell theory.
Category: Mathematical Physics

On the Velocity Decomposition in Hydrodynamics

Authors: Miftachul Hadi
Comments: 1 Page.

We assume that velocity in hydrodynamics is an identical form of the gauge potential in electromagnetism where the vorticity is identical to the field strength tensor. Because the gauge potential can be decomposed into local and global parts, the velocity in hydrodynamics could also be decomposed into local and global parts.
Category: Mathematical Physics

Constructive QFT: a Condensed Math Point of View III

Authors: Juno Ryu
Comments: 10 Pages. (Note by viXra Admin: For the last time, please cite and list scientific references!)

In this article, we remind the procedure of construction of path integral formalism.
Category: Mathematical Physics

Canvas Theory

Authors: Juno Ryu
Comments: 9 Pages. (Note by viXra Admin: Please cite and list scientific references)

For categorical construction of QFT, we introduce the mathematical language called canvas theory.
Category: Mathematical Physics

The Problem of the "Negative Frequencies" of the Solutions of the D'alembert Equation

Authors: Marcello Colozzo
Comments: 6 Pages.

The appearance of solutions with negative frequency in the D’Alembert wave equation can be removed with a change of variable. The corresponding positive frequencies describe waves propagating from the «future» towards the «past». This argument was developed in the 1940s by the Italian mathematician Luigi Fantappiè in the analysis of the solutions of the D’Alembert equation, but also of the Klein-Gordon equation (quantum particles of spin 0) and the Dirac equation (spin 1/2 particles).
Category: Mathematical Physics

Interpreting the Evolution of an Isolated Physical System in a Deterministic World as a Markov Reward Process

Authors: Huichang Chae
Comments: 3 Pages.

This paper argues that explaining the evolution of an isolated physical system in a deterministic world using Markov reward processes implies that Nature does not prioritize immediate rewards over future rewards. The resulting equations of motion appear as differential forms of conservation laws, where the conserved quantities are the modified value functions which incorporate the reward of being in the initial state.
Category: Mathematical Physics

Superluminal Speed, the Tunnel Effect, and Quantum Mechanics

Authors: Andrzej Okniński
Comments: 4 Pages.

We investigate consequences of Galilean relativity principle postulating superluminal observers' existence, suggesting that field theory emergesfrom the extended special relativity.
Category: Mathematical Physics

Zero Quantum Gravity (revised)

Authors: Stephen H. Jarvis
Comments: 101 Pages.

The discipline of physics tests theories with known observed phenomena. There, the credibility of any theory is how physical phenomena can be scaled, measured, and thence confirmed using numbers with dimensions in the form of theories. The idea there is to find an exact as possible match of number theory with physical phenomena. Indeed, numbers do not make reality come into existence, yet as shall be shown here numbers do in fact represent sentient based keys to understanding physical phenomena by their certain definition and association. Here the process of sentient based theoretic development is achieved through uncovering the number theory behind the workings of nature as a code for zero-dimensional time and space. There, in making direct utility of the Collatz conjecture, a solution to the three-body problem is proposed. By such, new experiments are proposed in demonstration of gravity’s nature. In all, here shall be shown how numbers and their particular definition and utility upon and beyond the proposed zero-dimensional levels of time and space more than likely represent sentient based keys in correctly scaling and surveying physical reality via a proposed temporospatial sentient code, ultimately as a proposed expression of universal sentience measuring itself.
Category: Mathematical Physics

An Atypical Case of Round-Off in Mathematica

Authors: Marcello Colozzo
Comments: 5 Pages.

A Mathematica round-off case generated by a real function of a real variable, [is] not elementary expressible
Category: Mathematical Physics

Integrability of Continuous Functions And Dynamical Systems

Authors: Hans Detlef Hüttenbach
Comments: 32 Pages.

This paper consists of three parts: Starting with the field $mathbb{C}$ of complex numbers,the Banach space $mathcal{C}(V)$ of continuous, $mathbb{C}$-valued functions on a simply connected compact region $Vsubsetmathbb{C}$ is shown to decompose the topological direct sum of two complementary subspaces: a subspace of integrable and therefore analytic functions,and a subspace of un-integrable and anti-analytic functions. Introducing orientation as a central notion, orientation inversion (parity) turns out to be the complex conjugation, which maps integrable (w.r.t. positive orientation) to un-integrable functions, which are integrable w.r.t. negative orientation, and vice versa. Orientation allows the extension of complex analyticity to $mathbb{R}^2$, which ends part 1. Part 2 is devoted to the extension of analyticity to multi-dimensions.These results are then applied in part three to continuous mechanical dynamical systems, where it is shown that Hamilton-Jacoby theory yields the unrestricted integrability of any continuous, mechanical dynamical system of either parity and represents their solutions as geodesics of (integrated) action functions of positive/negative parity, i.e.: as fermionic and bosonic solutions.
Category: Mathematical Physics

Sommerfeld Functional Equation

Authors: Marcello Colozzo
Comments: 6 Pages.

We derive the well-known Sommerfeld expansion of the Fermi-Dirac integral, and then deduce a functional equation for the chemical potential which we denote here by h(y) where y is the absolute temperature in energy units.
Category: Mathematical Physics

[On a] Theory of Everything

Authors: Oussama Basta
Comments: 17 Pages.

In this paper, a new paradigm is proposed for understanding the interplay between gravitation, electromagnetism, and spin. Building upon the principles of quantum mechanics [1] and general relativity [2], we develop a unified theory that reconciles the fundamental forces of nature. Our approach provides a novel perspective on the nature of spacetime, the behavior of particles, and the origins of the universe. We demonstrate the efficacy of our framework by addressing longstanding problems in physics, including the cosmological constant issue and the hierarchy problem. Our findings pave the way for a deeper understanding of the universe and its mysteries and open up new avenues for exploration and discovery.
Category: Mathematical Physics

Navier-Stokes Equations Are Neither First Nor Second Order Approximation

Authors: Dmitri Martila
Comments: 2 Pages. (Note by viXRa admin: Please do not use the dramatic comment "Rejected by all journals")

One of the Millennium Problems is fluid movement. If the movement is lightspeed-like, then we take Einstein's Relativity into account. If not, then we don't need complicated Navier-Stokes formulas. They are not a first-order approximation at low speeds. However, they has to be first-order approximation since they are meant to be classical.
Category: Mathematical Physics

On Discrete Hopf Fibrations, Grand Unification Groups, the Barnes-Wall, Leech Lattices, and Quasicrystals

Authors: Carlos Castro
Comments: 13 Pages.

A discrete Hopf fibration of $S^{15}$ over $S^8$ with $S^7$ (unit octonions) as fibers leads to a $16D$ Polytope $P_{16}$ with $4320$ vertices obtained from the convex hull of the $16D$ Barnes-Wall lattice $ Lambda_{16}$. It is argued how a subsequent $2-1$ mapping (projection) of $ P_{16}$ onto a $8D$-hyperplane might furnish the $2160$ vertices of the uniform $2_{41}$ polytope in $8$-dimensions, and such that one can capture the chain sequence of polytopes $ 2_{41}, 2_{31}, 2_{21}, 2_{11}$ in $ D = 8,7,6,5$ dimensions, leading, respectively, to the sequence of Coxeter groups $ E_8, E_7, E_6, SO(10) $ which are putative GUT group candidates. An embedding of the $E_8 oplus E_8 $ and $ E_8 oplus E_8 oplus E_8$ lattice into the Barnes-Wall $ Lambda_{16}$ and Leech $Lambda_{24}$ lattices, respectively, is explicitly shown. From the $16D$ lattice $ E_8 oplus E_8$ one can generate two separate families of Elser-Sloane $4D$ quasicrystals (QC's) with $ H_4$ (icosahedral) symmetry via the ``cut-and-project" method from $ 8D$ to $ 4D$ in each separate $E_8$ lattice. Therefore, one obtains in this fashion the Cartesian product of two Elser-Sloane QC's $ {cal Q} times {cal Q} $ spanning an $8D$ space. Similarly, from the $24D$ lattice $ E_8 oplus E_8 oplus E_8$ one can generate the Cartesian product of three Elser-Sloane $4D$ quasicrystals (QC's) $ {cal Q} times {cal Q} times {cal Q} $ with $ H_4$ symmetry and spanning a $12D$ space.
Category: Mathematical Physics

Magnetic Monopoles: A Quantum Approach

Authors: Mohamed Gamal
Comments: 20 Pages.

The quest for magnetic monopoles, particles possessing a single magnetic pole, has captivated the scientific community for decades. In this study, we explore the possibility of achieving magnetic monopoles by utilizing a magnetic dipole with an infinitely fast polarity switch. Through a comprehensive analysis incorporating equations such as Schrödinger's Equation and the Dirac Equations, we investigate the theoretical foundations and historical context surrounding this fascinating phenomenon. Our research delves into the experiment and results, providing insights into the intricate interplay between magnetic monopoles and fermion-monopole systems. Additionally, we examine the concepts of Ampere's Hypothesis, Dirac Quantisation, Saha's Derivation, electromagnetic duality rotations, and the Wu-Yang Approach. By employing a dipole in a superposition state, and concluding with a general equation that combines different aspects of electromagnetic phenomena, such as electric and magnetic fields, potentials, currents, and their derivatives, to describe the behavior and interactions of these quantities in a generalized manner. we explore the potential realization of magnetic monopoles. This study offers valuable insights into the elusive nature of magnetic monopoles and paves the way for future advancements in this field of research.
Category: Mathematical Physics

On Symmetries of Geometric Algebra Cl(3,1) for Space-Time

Authors: Eckhard Hitzer
Comments: 11 Pages. Submitted to Adv. Appl. Clifford Algebras (2024), 4 tables.

From viewpoints of crystallography and of elementary particles, we explore symmetries of multivectors in the geometric algebra Cl(3,1) that can be used to describe space-time.
Category: Mathematical Physics

Fractional Dynamics and Physics Beyond Effective Field Theory (Part 1)

Authors: Ervin Goldfain
Comments: 18 Pages.

There are growing signs today that physics far beyond the Standard Model (SM) scale may substantially deviate from the principles of traditional field theory. The goal of this report is to briefly elaborate on the motivation for fractal spacetime and fractional dynamics beyond the realm of effective field theory.
Category: Mathematical Physics

The Underlying Principle of Mathematical Principles of Natural Philosophy

Authors: Wei Guo
Comments: 70 Pages.

Today, the scientific community comprehensively accepts adding many extra unverifiable things into reality, e.g. extra mass: dark matter, extra energy: dark energy, extra position: superposition, extra dimensions, or even extra parallel reality. Considering reality is not understood completely, adding something into reality's unknown part is indeed a shortcut for explaining some measured discrepancy, but such behaviors are likely to distort the instinct of reality. We report any inherent measured discrepancy involving an indirect measure method that relies on an artificially-defined equivalence, e.g. inertia mass indirectly measures mass by equating mass with force/acceleration. Time measure relies on an equivalence between time and some phenomena, e.g. swing of pendulum, fall of sands or electron jumping between two states. Since Galileo, mathematical equal sign is introduced so naturally between different physical properties. We argue any such equivalence only holds true within a limited phenomena range. Although some method's application range has been summarized, e.g. inertia mass only applies to 'macro, low-speed, inertia-system', we state such scattered descriptions collected from experience are not rigorous. We propose a general frame that can identify a more rigorous application range. Hence, any inherent measured discrepancy results from the measured phenomena exceeding the method's rigorous application range, e.g. remote objects actually exceed the Doppler effect's application range. By ignoring this, large-scale red shift inevitably misleads us to the dark energy's existing necessity. Similarly, dark matter only logically exists to expand the rigorous application range of dynamical mass.
Category: Mathematical Physics

Topological Property of Newton's Theory of Gravitation

Authors: Miftachul Hadi
Comments: 4 Pages.

We propose the topological object, a gravitational knot, could exist in Newton's theory of gravitation by assuming that the Ricci curvature tensor especially the metric tensor consists of a scalar field i.e. a subset of the Ricci curvature tensor. The Chern-Simons action is interpreted as such a knot.
Category: Mathematical Physics

Hidden Nonlinearity in Newton's Second Law of Gravitation in (2+1)-Dimensional Space-Time

Authors: Miftachul Hadi
Comments: 5 Pages.

By assuming that the Ricci curvature tensor consists of a subset (scalar) field, we propose that Newton's second law of gravitation in (2+1)-dimensional space-time, a linear equation, could have hidden nonlinearity. This subset field satisfies a non-linear subset field theory where in the case of an empty space-time or the weak field, it reduces to Newton's linear theory of gravitation.
Category: Mathematical Physics

Flock Members Experience Gas Pressures Higher Than Lone Individuals

Authors: Arturo Tozzi
Comments: 5 Pages.

Local interactions between flock members in absence of centralized control generate collective dynamics characterized by coherent large-scale patterns. We investigate whether aggregates of individuals like birds, swarms and fishes behaving in concert with their neighbors may modify the physical properties of the fluid medium in which they are embedded. Using the K-Nearest Neighbours algorithm to simulate collective animal behavior, we showed that the occurrence of collective dynamics can modify the physical parameters of the phase space in which the interacting individuals’ trajectories take place. This means that lone individuals experience the nearby fluid medium (i.e., the air in case of birds/insects and the water in case of fishes) differently from flock members. In particular, our framework suggests that a bird belonging to a group and acting collectively with its neighbours perceives the nearby atmosphere as denser, compared with an isolated bird.
Category: Mathematical Physics

A "Trinionic" Representation of a Classical Group

Authors: Kohji Suzuki
Comments: 24 Pages.

We apply "trinions" put forward in viXra:1712.0131 to the Lie group SU(3) to discuss some physical matters.
Category: Mathematical Physics

Critical Analysis of Classical Wave Equation

Authors: Temur Z. Kalanov
Comments: 12 Pages. (Correction made by viXra Admin to conform with scholarly norm)

A detailed proof of the incorrectness of the classical wave equation is proposed. The correct methodological basis for the proof is the unity of formal logic and rational dialectics. The proof leads to the following irrefutable statement: the classical wave equation and the derivation of the classical wave equation are a gross error in mathematics and physics. The proof of this statement is based on the following irrefutable main results: (1) The first gross error is the following approximate relationship: "sine of angle is approximately equal to tangent of angle; cosine of angle is approximately equal to 1". This relationship means (implies) that the quantity of the angle and the right-angled triangle do not exist. Consequently, the relationship between the tangent of the angle and the derivative of the displacement with respect to coordinate does not exist; (2) The second gross error is that the second-order derivative of the displacement with respect to coordinate does not exist, because the dimensions of displacement and coordinate are "meter", the first-order derivative of the displacement with respect to coordinate is dimensionless quantity (i.e. the first-order derivative of the displacement respect to coordinate has no the dimension "meter"); (3) The third gross error is that the first-order derivative of the displacement with respect to coordinate cannot be expanded into the Taylor series, because the second-order derivative of the displacement with respect to coordinate does not exist;(4) The fourth gross error is as follows: (a) the left side of the wave equation contains the condition that time is a variable quantity, and the coordinate is a constant quantity; (b) the right side of the wave equation contains the condition that time is a constant, and the coordinate is a variable. This means (implies) that the equation contains contradictory conditions (propositions). Therefore, the equation represents a violation of the formal-logical law of the lack (absence) of contradiction; (5) The fifth gross error is that the standard derivation of the equation relies on the following false theories: negative number theory, complex numbers theory, trigonometry, vector calculus, differential calculus, and Newton's second law.Thus, the classical wave equation does not satisfy the criterion of truth and is not a scientific achievement.
Category: Mathematical Physics

On the Origins of Mass

Authors: Moshe Szweizer, Rivka Schlagbaum
Comments: 18 Pages.

Probability, as manifested through entropy, is presented in this study as one ofthe most fundamental components of physical reality. It is demonstrated that thequantization of probability allows for the introduction of the mass phenomenon.In simple terms, gaps in probability impose resistance to change in movement,which observers experience as inertial mass. The model presented in the paperbuilds on two probability fields that are allowed to interact. The resultant prob-ability distribution is quantized, producing discrete probability levels. Finally, aformula is developed that correlates the gaps in probability levels with physicalmass. The model allows for the estimation of quark masses. The masses of theproton and neutron are arrived at with an error of under 0.04%. The masses ofsigma baryons are calculated with an error between 0.2% and 0.05%. The Wboson mass is calculated with an error of under 0.5%. The model explains whyproton is stable while other baryons are not, and it gives an explanation of theorigins and nature of dark matter. Throughout the text, the article illustratesthat the approach required to describe the nature of mass is incompatible withthe mathematical framework needed to explain other physical phenomena.
Category: Mathematical Physics

Comprehensive Systemization of Weak Kam Theory and Some Open Problems

Authors: Jong In Jae, Jong U. Hwan, Ra Ju Gwang
Comments: 37 Pages.

In this paper, we performed comprehensive systemization of weak KAM theory, the ultramodern theory in mathematics domain that is being regarded as important in theoretical and application aspect and is being studied actively in the world in present. Moreover we also systemized comprehensively the conjectures, the open problems, and the point at issue that are proposed in weak KAM theory. They contain 17 of the points at the issue that are newly proposed in this paper.
Category: Mathematical Physics

Bordisms and Wordlines II

Authors: Ryan J. Buchanan, Parker Emmerson
Comments: 7 Pages.

This paper is a continuation of [2]. Here, we discuss twisted branes, the free loop superspace, and, in particular, a deformation of the modal lightcone which allows us to model cobordisms of generically small, portable, locally closed systems.
Category: Mathematical Physics

Nodal Lines of Eigenfunctions of Eigenfunctions of Laplacian in Plane

Authors: Soo Sun Ha
Comments: 53 Pages.

We prove Payne's nodal line conjecture for any bounded simply connected, possibly non-convex smooth domain in Plane; any the second Dirichlet eigenfunction of laplacian in any domain in Plane can not have a closed nodal line.
Category: Mathematical Physics

Scattering of Worldlines Along a Bordism

Authors: Ryan J. Buchanan, Parker Emmerson
Comments: 7 Pages.

In this paper, ER bridges are discussed as bordisms. We treat these bordisms as fibers, whose sections are holographically entangled to copies of $S^1$. Diffemorphisms of these fibers are discussed, as well as the implication of replacing $S^1$ with the supercircle, and the replacing its underlying algebra with a Lie superalgebra.
Category: Mathematical Physics

Cooldown Time Estimation Methods for Stirling Cycle Crycoolers

Authors: Shlomy Shitrit, Royee Bustan
Comments: 18 Pages.

Crycoolers are small refrigerators that can reach cryogenic temperatures in the range of 70Kto 150K. They have the capability of accumulating a small temperature drop into a large overall temperature reduction. The cooldown time estimation is becoming more and more as a design parameter, certainly in hands-on applications. The various complicated physical processes involved in crycooler operation make it hardly possible to explicitly simulate the temperature time response.The numerical methods for solving a typical crycooler suffer from numerical instability, time step restrictions and high computational costs, among others. Since the operation of crycoolers involve processes in range of 60Hz − 120Hz, actually solving the crycooler transient response would require different software tools to support the design and analysis of physical processes such as heat transfer, fluid dynamic, electromagnetic and mechanical. These processes would also require an excessive amount of calculations, incurring time consuming and precision penalty. In this article we try to bridge the gap between the explicit impractical approach to steady state based approach.A framework developed in Python for calculating the cooldown time profile of any crycooler basedon a steady state database, is introduced, while utilizing a semi-analytic approach under variousoperating conditions. The cooldown time performance can be explored at various target and ambient temperature conditions, and also the effects of an external load, material properties or thermal capacitance on the overall cooldown time response. Two case studies based on K580 and K590 crycoolers developed at Ricor are used for verfication, with a good agreement between the simulated and measured values.
Category: Mathematical Physics

An Algebrologist in Wonderland

Authors: Robert G. Wallace
Comments: 19 Pages.

By imposing a requirement for spatial isotropy, it is possible to find an algebra with a subalgebra structure having a pattern matching that of the bosons and three families of fermions of the standard model.
Category: Mathematical Physics

Geometric Visual Approach to the Mass Gap Problem

Authors: Alfonso De Miguel bueno
Comments: 30 Pages.

This paper provides visual and conceptual explanations for the mass gap problem, reflection positivity, Tomita-Takasaki modular theory, mirror symmetry and N=1 supersymmetry, in the context of a dual quantum field model whose subatomic fields are represented by a set of 2x2 complex rotational matrices of eigenvectors.
Category: Mathematical Physics

Single Field Universe Update

Authors: Michael Griffin
Comments: 12 Pages. contact email mdg46@juno.com

More features are presented to fit a single-field version for a unified field theory, based upon Euler’s equation as the hidden variable to model enfielding of energy into matter.The spin values and their range spectrum are revised to fit estimates for the different magnitudes of gravity and electromagnetism. Features of Maxwell’s equations on a larger scale are considered. A conservation principle for total velocities is also proposed. Force constants and a different simultaneity principle are suggested.
Category: Mathematical Physics

Real Numbers: a New (Quantum) Look, with a Hierarchical Structure

Authors: Lucian M. Ionescu
Comments: 36 Pages. Presentation in the ISU Pure and Applied Mathematics Seminar

Rational numbers Q have much more structure beyond the ordered field structure which leads to Real Numbers as a metric completion.The modular group representation of continued fractions is used as a Number Theory "friendly" implementation of the real numbers, with a possible unification with p-adic numbers, beyond the "direct sum" adeles framework. This approach also allows to extend Fourier and Haar Wavelet Analysis, by including inversion as a geometric antipode. Other applications in Mathematical-Physics steam from the central role of the modular group: Belyi maps, Farey graphs and tessellations etc. which allow the study of important classes of numbers (algebraic, periods) in a systematic way. The presentation is a preliminary version the project, stating the motivation, goals and approach.
Category: Mathematical Physics

Monte Carlo Quantum Computing Using a Sum of Controlled Few-Fermions

Authors: David H. Wei
Comments: 59 pages, 8 figures

A restricted path integral method is proposed to simulate a type of quantum system or Hamiltonian called a sum of controlled few-fermions on a classical computer using Monte Carlo without a numerical sign problem. Related methods and systems of Monte Carlo quantum computing are disclosed for simulating quantum systems and implementing quantum computing efficiently on a classical computer, including methods and systems for simulating many-variable signed densities, methods and systems for decomposing a many-variable density into a combination of few-variable signed densities, and methods and systems for solving a computational problem via Monte Carlo quantum computing.
Category: Mathematical Physics

The Link Between the de-Vries-Formula for the Fine Structure Constant and the Power-of-Two Value of 128

Authors: George Bailey
Comments: 16 pages

Almost 20 years ago, de Vries proposed a recursive equation for the fine structure constant α that depends only on the mathematical constants e and π. It gives a value for 1/α = 137.0359990958. By applying the term α/(2π) in a geometric series, this equation has the flavour of mainstream physics (see Schwinger-Dyson series on calculating the electron's g-factor), which in combination with the agreement with the experimentally found value is probably the reason why this formula, unlike many other numerology attempts, is not forgotten.The starting point and core element of this equation is the term 1/e^(π^2/2). Despite interesting approaches, it has not yet been possible to give this term an unequivocal physical meaning. So I thought it worthwhile to investigate the proximity of this value to the closest power-of-two value, i.e. 128. This resulted from the considerations I made in the previous works, where I (among many others) became aware of the importance of the number 2^128 as a link between the order of magnitude of the elementary particles and the universe.Finally, another equation for α was obtained, which is roughly equivalent in complexity to the de Vries equation, depends only on π and 128, and whose result differs from the de Vries result by only about 2^10^-10.It was during my playing around with the numerical values that I found the literature that told me that at extremely high energies the fine structure "constant" increases to the value of about 1/128. So I saw another reason to publish these number juggleries. Here they are.
Category: Mathematical Physics

Realization of Quasi-Quanta Via the Forced Contraction of Loops

Authors: Ryan J. Buchanan
Comments: 6 Pages.

The contraction of a loop on a string in the orthogonal time direction is contemplated. Its relationship to a certain mathematical concept, forcing notions, is examined. In addition, we evaluate local systems on the worldline of a particle traveling in the positive timelike direction.
Category: Mathematical Physics

Phenomenological Velocity

Authors: Parker Emmerson
Comments: 11 Pages.

The intent of this paper is to provide a simple focus on that mathematical concept and solution, phenomenological velocity to shine light on aworthy topic for mathematicians and physicists alike. Phenomenological Velocity is essential to the formulation of a gestalt cosmology. The bibliography of this paper provides references to the extensive research that has been conducted by myself on the topic. I have performed conditional integrals of the phenomenological velocity in its most liberated standard-algebraic form, I have shown that the computational-phenomenological velocity satisfies its real-analytic solutionwhen not using the speed of light in scientific notation to get the computational version, thus demonstrating that it is a valid solution. So, phenomenological velocity has profound consequences to the foundations of physics as civilization moves into a galactic scale and information is communicated at the quantumlevel, because it is such a mathematical reality it ought not be ignored when considering topics from hidden dimensions (a real, algebraic technique) and relativity to gravity and dark matter. It gives us a new perspective on how weperceive the meaning of velocity itself with pragnanz, and thus with the new meaning, perspectives can change. I hope the reader will investigate the combined research I have performed on this topic, available by referencing the works in this bibliography to fully understand the nature of the arguments being made within. So, this points the right direction for future research, perhaps even withintent to encourage experimental design.
Category: Mathematical Physics

Consciousness as Temporal Transcendence

Authors: Stephen H. Jarvis
Comments: 11 Pages.

In presenting the case for an information touchstone of logic as the code of a zero-dimensional time and space theory, in confirming what is observed of physical phenomena, the presumption of consciousness in this process of logic, information, confirmation, and thence the supposition of awareness is addressed. The manner of this address is through identifying information as themes relevant to the zero-dimensional physical theory’s derivations. In recognition of our conscious drives and abilities, the information themes are considered as being self-evident for what is generally considered as consciousness. Identified here in this paper are those basic themes in physical reality we more likely than not as conscious beings are subject to.
Category: Mathematical Physics

Logic's Information Touchstone

Authors: Stephen H. Jarvis
Comments: 18 Pages.

Proposed here is a touchstone logic for physical phenomena, notable as a proposed logic for the zero-dimensions of time and space, specifically for time as a moment and space as a point. The proposed logic utilizes the conjecture that a moment in time is not a point in space, and by their difference, according to a specific mathematically labelled logic, the dimensions of time and space become manifest. The manifestation of the dimensions from zero-dimensionality are thence shown to encompass a time and space dimensional number theory that when scaled with physical phenomena is shown to harbour all the known information of quantum field theory and general relativity. The confounding result for this zero-dimensional number theory as a physical theory is the stars beyond this solar system derived as being a holographic projection of activity in this solar system’s Hydrogen wall. Discussed here therefore is whether the proposed touchstone logos used here is or is not an exact account of physical reality’s structure.
Category: Mathematical Physics

On Configuration Space

Authors: Ryan J. Buchanan
Comments: 13 Pages. Correct version

A particular class of real manifolds (Hermitian spaces) naturally model smooth, possibly complex n-spaces. We show how to realize such a space as a restriction of a super-smooth stack using a compass. We also discuss the classical relationship between iterated loop spaces and the configuration space of a particle.
Category: Mathematical Physics

A Novel CPW-Fed Multiband Planar Monopole Antenna for GSM/ WLAN/ WiMAX Applications

Authors: Paek Ye Song, Jong Hye Gon, Kim Un Chol, Gang Ung, Hong Myong Su, Ha Song Jin
Comments: 6 Pages.

A novel CPW-fed multiband planar monopole antenna is designed and investigated in this paper. The proposed antenna is fabricated on FR4 substrate and has a compact size of 26 × 45 × 1.6 mm3. A prototype is fabricated and then measured. The simulated and measured results exhibit that the operating bandwidth with a reflection coefficient of less than −10 dB is about 150 MHz (1700—1850MHz), 310 MHz (2.38—2.69 GHz), 520 MHz (3.23—3.75 GHz), and 820 MHz (5.09—5.91 GHz). These frequency ranges meet the bandwidth requirement for GSM 1800MHz, WLAN 2.4/5.2/5.8 GHz and WiMAX 2.5/3.5/5.5 GHz bands. Also, almost omnidirectional radiation patterns and peak gains of 2.1dBi at 1.8 GHz, 2.21dBi at 2.4 GHz, 2.8dBi at 3.5 GHz, and 4.98dBi at 5.5 GHz are obtained. The proposed antenna with small size, planar structure, good impedance bandwidth and omnidirectional radiation patterns is very suitable for GSM/ WLAN/ WiMAX applications.
Category: Mathematical Physics

Natural Units, Pi-Groups and Period Laws

Authors: Lucian M. Ionescu
Comments: 16 Pages.

In the context of QFT and Gauge Theory, the introduction of Natural Units, as a quantization in disguise'' combined with Buckingham's Pi-Theorem, provides a direct connection with de Rham Periods, as also hinted by Feynman amplitudes, Dessins d'Enfant and Belyi maps models of baryon modes etc.A program emerges: Physics Laws as Period Laws, and Alpha, as an element of the Pi-groups, a period. Our models of the Physical Reality emerge from the union of Cohomological Physics and Number Theory,helping us understand ``the unreasonable effectiveness of Mathematics''.An overview of the Network Model is included, with impacts to Sciences in general. Further prospects for understanding the fine structure constant are presented.
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

Rigorous Proof and Spectral Analysis of the Yang-Mills Mass Gap Problem

Authors: YoonKi Kim
Comments: 5 Pages. If there are any errors or questions, please contact honkai0509@gmail.com. The response may be delayed.

This paper provides a rigorous mathematical proof of the existence of a mass gap in quantumSU(N) Yang-Mills theory, addressing a central unsolved problem in theoretical physics posed by the Clay Millennium Prize. Our objective is to demonstrate that the quantum Hamiltonian of the theory possesses a strictly positive lowest eigenvalue, E0 > 0, in four-dimensional Euclidean spacetime. We achieve this by starting with the complete Yang-Mills gauge field Aµ, quantizing it via path integrals, and performing a detailed spectral analysis of the resulting Hamiltonian HˆYM. To facilitate this analysis, we introduce a confinement scalar W derived from Aµ, construct its effective HamiltonianHˆ , and prove E0 > 0 for both systems without approximations. The proof incorporates the fullnonlinear dynamics, derives all parameters from the Yang-Mills action, and verifies confinementthrough Wilson loop behavior, aligning with the physical predictions of Quantum Chromodynamics(QCD), including the emergence of the scale ΛQCD.
Category: Mathematical Physics

Rigorous Proof and Spectral Analysis of the Yang-Mills Mass Gap Problem

Authors: YoonKi Kim
Comments: 3 Pages. Email for correspondence: yoonki0905@gmail.com

This study rigorously proves the Yang-Mills mass gap problem using analytical methods and spectral theory. By analyzing the Wilson loop expectation value based on the Poisson equation, we demonstrate that the mass gap inevitably forms in SU(N) gauge theory. Additionally, we utilize Hilbert space analysis and operator theory to prove that the lowest eigenvalue of the Yang-Mills Laplacian is strictly greater than zero, confirming the existence of the mass gap in a mathematically rigorous manner. This revised version further strengthens the argument by explicitly deriving the Poisson equation from first principles and providing a more detailed spectral analysis of the YangMills Laplacian.
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

Hopf Filtration, Non-Homtopy and Mass

Authors: Garry Goodwin
Comments: 18 Pages.

The Standard Model treats particle rest mass as a free parameter, offering no fundamental explanation. An alternative approach is proposed that derives rest mass from geometric and topological constraints.
Category: Mathematical Physics

Hopf Vibration, Non-Homotopy and Mass

Authors: Garry Goodwin
Comments: 10 Pages. typos fixed, plus small changes to phrasing

Unable to determine a particle's specific mass the Standard Model leaves rest mass a free parameter. For an alternative theory we consider a 3-sphere intersecting three dimensional space. The intersection is a Hopf fibration with non Euclidean topology. Resistance to a force is due to non-homotopy. The intersection signature appears across mass splitting formulae that treat lighter hyperons as functions of the proton, neutron and in some cases electron. In MeV the derived values are: $Sigma^+$ $approx$ 1189.371, $Sigma^0$ $approx$ 1192.655, $Sigma^-$ $approx$ 1197.580, $Xi^0$ $approx$ 1314.810, $Xi^-$ $approx$ 1321.711, $Omega^-$ $approx$ 1672.482. The electron, $Sigma$, $Xi$ masses provide a solution to the neutron-proton mass difference problem. This is a pure mathematical relationship ensuring the derived $Sigma$, $Xi$ mass values are not ad hoc. The mathematical status of $Omega^-$ is less secure. To make the case, a scaling factor $S_M$ is introduced using $Omega^-$ volume. Rest mass in any system of units is scaled to a dimensionless number proportional to MeV. For precise results less than one fifth of an electron-volt is shaved from the 2022 CODATA neutron adjustment (our value 939.565 421 76). To justify $S_M$ we consider the difference between Gaussian and SI units. In the final count nine free parameters reduce to two.
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 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

Formulas for SU(3) Matrix Generators

Authors: Richard Shurtleff
Comments: 52 pages includes a 14 page paper, a 17 page Mathematica Notebook, a 21 page Fortran 90 program and 1 figure

The Lie algebra of a Lie group is a set of commutation relations, equations satisfied by the group's generators. For SU(2) and many other Lie groups, the equations have been solved and matrix generators are realized as algebraic expressions suitable for further investigation or numerical evaluation. This article presents formulas that give a set of matrix generators for any irreducible representation of the group SU(3), the group of unimodular unitary three-dimensional complex matrices with matrix multiplication. To assist in calculating the matrix generators, a Mathematica computer program and a Fortran 90 program are included.
Category: Mathematical Physics

From Complex Dynamics to Foundational Physics (Part 1)

Authors: Ervin Goldfain
Comments: 27 Pages.

As of today, Quantum Field Theory (QFT) and General Relativity (GR) are broadly recognized paradigms of foundational physics. There are, however, growing suspicions that both paradigms fail to hold somewhere above the Standard Model (SM) scale and in the realm of primordial cosmology. Evidence collected on multiple fronts indicates that emergence and complexity are universal features of far-from-equilibrium systems with many degrees of freedom. In line with these findings, Part 1 of the report explores the complex dynamics of evolving dimensional fluctuations beyond the SM scale. Part 2 outlines the role of complex dynamics in the nonintegrable sector of particle physics, Dark Matter condensation and the gravitational regime of the early Universe.
Category: Mathematical Physics

Gödelian Index Theorem for Discrete Manifolds (Part 2): Extending Atiyah-Singer with Application to the Neutron Lifetime Puzzle

Authors: Paul Chun-Kit Lee
Comments: 58 Pages.

This paper introduces a novel mathematical framework that extends the concept of Gödelian incompleteness to discrete manifolds, with potential applications in quantum physics and cosmology. Building upon our previous work (Part 1) on smooth Gödelian manifolds, we develop a rigorous theory of Discrete Gödelian Spaces within the context of topos theory.We begin by constructing a Discrete Gödelian Topos, defining a base category that integrates discrete structures with a discrete analog of the real line. Within this topos, we introduce Discrete Gödelian Spaces characterized by truth and provability functions, capturing both logical and topological aspects of these structures.We formulated a Discrete Gödelian Index Theorem, which generalizes the classical Atiyah-Singer Index Theorem to our setting. This theorem connects analytical and topological invariants of Discrete Gödelian Spaces, emphasizing the interplay between truth and provability.We explore connections between our Discrete Gödelian Structures and fundamental concepts in physics, such as the spectral gap and renormalization group flow. We develop a theory of Gödelian Renormalization Group Transformations and establish theorems linking the Gödelian Index to the spectral properties of these spaces.We propose a Quantum Gödelian Hypothesis, suggesting that quantum phenomena arise from an underlying Quantum Gödelian Ricci Flow. The paper addresses the Neutron Lifetime Puzzle within the Discrete Gödelian framework, proposing a novel approach to reconcile the discrepancies in neutron lifetime measurements. We present a mathematical derivation within this framework, discuss the implications of our findings, and suggest experimental strategies to differentiate between competing hypotheses.
Category: Mathematical Physics

Gödelian Index Theorem for Smooth Manifolds (Part 1): Extending Atiyah-Singer with Applications to Cosmological BAO Data

Authors: Paul Chun-Kit Lee
Comments: 144 Pages.

This paper extends the classical Atiyah-Singer Index Theorem by integrating logical complexity into the framework of differential geometry and topology, resulting in the development of the Gödelian Index Theorem. This novel approach introduces Gödelian-Topos Manifolds, which combine geometric structures with logical functions that quantify truth and provability. The evolution of these manifolds is governed by a modified Ricci flow—termed Gödelian Ricci Flow—that simultaneously evolves the geometric metric and logical structures. We establish the short-time existence and uniqueness of solutions to this flow and explore its long-term behavior through the introduction of Gödelian entropy and functional inequalities analogous to those used by Perelman.The Gödelian Index Theorem, central to this work, generalizes the Atiyah-Singer Index Theorem by incorporating logical content into the index theory of elliptic operators. The proof is constructed through a series of steps involving local index computations, deformation via Gödelian Ricci Flow, and the analysis of limit configurations and surgeries on Gödelian manifolds. This extension offers new insights into the interplay between logic, geometry, and topology, with potential applications ranging from quantum gravity to cosmology.In particular, we apply this framework to analyze Baryon Acoustic Oscillations (BAO) data using a Gödelian-Logical Flow (GLF) model. Our findings reveal an unexpected negative Gödelian index ($G_0$), challenging conventional understanding of dark energy and the early universe. The GLF model outperforms both a Ricci Flow model and the standard $Lambda$CDM model in fitting the BAO data, achieving the lowest chi-square, AIC, and BIC values. However, the very low reduced chi-square value (0.39) for the GLF model necessitates cautious interpretation due to potential overfitting.These results suggest that incorporating logical and geometric flow concepts into cosmological models might provide better descriptions of observed phenomena. Moreover, they hint at a profound connection between the logical complexity of the universe and its physical properties, potentially offering new approaches to longstanding problems in physics such as the nature of dark energy and the reconciliation of quantum mechanics with general relativity.
Category: Mathematical Physics

On the Breakdown of Stationary Action in Field Theory

Authors: Ervin Goldfain
Comments: 21 Pages.

It is known that both classical and Quantum Field Theory (QFT) are built on the fundamental principle of stationary action. The goal of this introductory work is to analyze the breakdown of stationary action under nonadiabatic conditions. These conditions are presumed to develop far above the Standard Model scale and favor the onset of Hamiltonian chaos and fractal spacetime. The nearly universal transition to nonadiabatic behavior is illustrated using a handful of representative examples. If true, these findings are likely to have far-reaching implications for phenomena unfolding beyond the Standard Model scale and in early Universe cosmology.
Category: Mathematical Physics

Algebraic Orientation, Invariance and Variance Within the Family ℋ of Hypercomplex Algebras

Authors: Richard D. Lockyer
Comments: 11 Pages.

It was brought to my attention that in previous papers I put in the public domain (references [1] through [8]), I did a rather piecemeal presentation of the critical concepts of algebraic orientation, algebraic invariance and algebraic variance, as well as the generalization of Cayley-Dickson algebras I referred to as Cayley-Dickson without emphasizing the more general nature of the presentation, which was done for reader familiarity purposes. I will attempt to remedy this within this document starting at the beginning: the basic definition of an algebra, carried through to a full definition and discussion of the general family of hypercomplex algebras I call ℋ which subsumes all division algebras and traditional Cayley-Dickson doubled forms. Taking into account all structural and algebraic orientation options exposes beautiful structure revealed through group theoretical aspects of ℋ construction. The concepts presented are essential to Octonion Algebra mathematical physics.
Category: Mathematical Physics

Constructive QFT: a Condensed Math Point of View III

Authors: Juno Ryu
Comments: 11 Pages. References added.

In this article, we remind the procedure of construction of path integral formalism.
Category: Mathematical Physics

Canvas Theory

Authors: Juno Ryu
Comments: 10 Pages. typo corrected

For categorical construction of QFT, we introduce the mathematical language called canvas theory.
Category: Mathematical Physics

Canvas Theory

Authors: Juno Ryu
Comments: 10 Pages. References added.

For categorical construction of QFT, we introduce the mathematical language called canvas theory.
Category: Mathematical Physics

Zero Quantum Gravity: Scaling and Surveying Keys

Authors: Stephen H. Jarvis
Comments: 84 Pages.

The discipline of physics tests theories with known observed phenomena. There, the credibility of any theory is how physical phenomena can be scaled, measured, and thence confirmed using numbers with dimensions in the form of theories. The idea there is to find an exact as possible match of number theory with physical phenomena. Indeed, numbers do not make reality come into existence, yet as shall be shown here numbers do in fact represent sentient based keys for understanding physical phenomena by their certain definition and association. Here the process of sentient based theoretic development is achieved through uncovering the number theory behind the workings of nature as a code for zero-dimensional time and space in then revealing the royal cubit and speed of light scaling and surveying keys.
Category: Mathematical Physics

Clean CUT: A Clean Cosmological Unified Theory Resolving the Hierarchy Problem

Authors: Oussama Basta
Comments: 21 Pages.

In this paper, we propose a new theoretical framework called "Clean CUT" (Clean Cosmological Unified Theory) that offers a paradigm-shifting perspective on the fundamental nature of the universe. By seamlessly unifying gravitation, electromagnetism, spin, and quantum mechanics, Clean CUT provides a comprehensive description of the fundamental forces and resolves long-standing issues in physics.
Category: Mathematical Physics

On Symmetries of Geometric Algebra Cl(3,1) for Space-Time

Authors: Eckhard Hitzer
Comments: 14 Pages. Submitted to Adv. Appl. Clifford Algebras (2024), 4 tables.

From viewpoints of crystallography and of elementary particles, we explore symmetries of multivectors in the geometric algebra Cl(3,1) that can be used to describe space-time.
Category: Mathematical Physics

Fractional Dynamics and Physics Beyond Effective Field Theory (Part 1)

Authors: Ervin Goldfain
Comments: 18 Pages.

There are growing signs today that physics far beyond the Standard Model (SM) scale may substantially deviate from the principles of traditional field theory. The goal of this report is to briefly elaborate on the motivation for fractal spacetime and fractional dynamics beyond the realm of effective field theory
Category: Mathematical Physics

A Theoretical Approach to the Navier-Stokes Millennium Problem using Dream Numbers

Authors: Oussama Basta
Comments: 15 Pages.

This paper presents a theoretical exploration of the Navier-Stokes equations within the innovative framework of Dream Partial Differential Equations (DPDEs). Beginning with the concept of dream numbers and their application in defining new forms of derivatives, we extend these ideas to reformulate the Navier-Stokes equations. Our aim is to investigate whether this novel approach could potentially shed light on the Millennium Problem concerning the existence and smoothness of solutions to these equations in three dimensions.
Category: Mathematical Physics

On Newtonian Knot in Empty (2+1)-Dimensional Space-Time

Authors: Miftachul Hadi
Comments: Written using latex, no figure, 5 pages

We propose the existence of a topological object, a Newtonian knot, in the framework of an Abelian Chern-Simons gravity with a small positive cosmological constant in empty (2+1)-dimensional space-time. This proposal is based on the idea that the Ricci curvature tensor could consist of a set of curvature components satisfying the non-trivial Hopf maps, leading to topological structures. Working within the Abelian Chern-Simons (first-order) framework, where the dreibein and spin connection are treated as independent fields, we derive the corresponding field equations and present ansatz solutions for both. Our results suggest that the Newtonian knot may serve as a novel topological feature in low-dimensional gravity theories.
Category: Mathematical Physics

Topological Property of Newton's Theory of Gravitation

Authors: Miftachul Hadi
Comments: 5 Pages.

By assuming that the Ricci curvature tensor consists of a set of subset fields or a set of curvature components, complex scalar fields, in the case of a weak field and the Newtonian limit, we derive the equation of Newton's theory of gravitation in (2+1)-dimensional space-time expressed using the Clebsch variables. These variables obey the topological quantum condition. The Chern-Simons action is interpreted as a gravitational knot.
Category: Mathematical Physics

On the Origins of Mass

Authors: Moshe Szweizer, Rivka Schlagbaum
Comments: 20 Pages.

Probability, as manifested through entropy, is presented in this study as one of the most fundamental components of physical reality. It is demonstrated that the quantization of probability allows for the introduction of the mass phenomenon. In simple terms, gaps in probability impose resistance to change in movement, which observers experience as inertial mass. The model presented in the paper builds on two probability fields that are allowed to interact. The resultant probability distribution is quantized, producing discrete probability levels. Finally, a formula is developed that correlates the gaps in probability levels with physical mass. The model allows for the estimation of quark masses. The masses of the proton and neutron are arrived at with an error of 0.02%. The masses of sigma baryons are calculated with an error between 0.007% and 0.2%. The W-boson mass is calculated with an error of 1.3%. The model explains why proton is stable while other baryons are not.
Category: Mathematical Physics

On the Nodal Lines of Eigenfunctions of Laplacian in Plane

Authors: Soo Sun Ha
Comments: 55 Pages.

We prove Payne's nodal line conjecture for any bounded simply connected, possibly non-convex, smooth boundary domain $Omega$ in Plane: Payne conjectured that any Dirichlet second eigenfunction of laplacian in any simply connected boundary domain in Plane can not have a closed nodal line.
Category: Mathematical Physics

Nodal Lines of Eigenfunctions of Laplacian in Plane

Authors: Soo Sun Ha
Comments: 55 Pages.

We prove Payne's nodal line conjecture for any bounded simply connected, possibly non-convex, smooth boundary domain $Omega$ in Plane; Payne conjectured that any second Dirichlet eigenfunction of laplacian in any simply connected bounded domain in Plane can not have a closed nodal line.
Category: Mathematical Physics

Cooldown Time Estimation Methods for Stirling Cycle Crycoolers

Authors: Shlomy Shitrit, Royee Bustan
Comments: 18 Pages.

Miniature crycoolers are small refrigerators that can reach cryogenic temperatures in the range of 60K to 150K. They have the capability of accumulating a small temperature drop into a large overall temperature reduction. The cooldown time estimation is becoming more and more as a design parameter, certainly in hands-on applications. The various complicated physical processes involved in crycooler operation make it hardly possible to explicitly simulate the temperature time response. The numerical methods for solving a typical crycooler suffer from numerical instability,time step restrictions and high computational costs, among others. Since the operation of crycoolers involve processes in range of 15Hz−120Hz, actually solving the crycooler transient response would require different software tools to support the design and analysis of physical processes such as heat transfer, fluid dynamic, electromagnetic and mechanical. These processes would also require an excessive amount of calculations, incurring time consuming and precision penalty. In thisarticle we try to bridge the gap between the explicit impractical approach to steady state based approach. A framework developed in Python for calculating the cooldown time profile of anycrycooler based on a steady state database, is introduced, while utilizing a semi-analytic approach under various operating conditions. The cooldown time performance can be explored at various target and ambient temperature conditions, and also the effects of an external load, material properties or thermal capacitance on the overall cooldown time response. Two case studies based on linear and rotary crycoolers developed at Ricor are used for verfication, with a good agreement between the simulated and measured values.
Category: Mathematical Physics

N1 Supersymmetric Dual Quantum Field Model

Authors: Alfonso De Miguel bueno
Comments: 44 Pages. 30 figures

This paper introduces a supersymmetric dual-matter atomic model based on two intersecting fields that periodically vary in either the same or opposite phases, forming a shared nucleus of two transversal and two vertical subfields that represent the particles and antiparticles of the dual atomic nucleus. The bosonic or fermionic characteristics of the nuclear subfields are determined by their topological transformations, caused by the pushing forces generated by the negative or positive curvatures of the intersecting fields during their contraction or expansion.With a mainly visual and conceptual approach, the model employs a set of 2x2 complex rotational matrices of eigenvectors related in a modular way to Sobolev interpolations and to Tomita-Takesaki theory, illustrating problems as reflection positivity, the mass gap, or the arising of a purely imaginary time, between others. The article first presents the fields model in a general way, then it introduces the mathematical formalisms, translates the general system to the atomic terminology, and finally compares the model with already known developments. The article first presents the fields model in a general way, then it introduces the mathematical formalisms, translates the general system to the atomic terminology, and finally compares the model with already known developments.
Category: Mathematical Physics

N1 Supersymmetric Quantum Field Model

Authors: Alfonso De Miguel Bueno
Comments: 35 Pages. 32 images

This paper introduces a non-conventional quantum field model within the framework of N=1 supersymmetric Yang-Mills theory [1], providing a visual geometric explanation for the mass gap problem and the topological transformations of the supersymmetric atomic nucleus. The model is a supersymmetric topological manifold based on two intersecting fields that vibrate in either the same or opposite phases, forming four subfields. The bosonic or fermionic characteristics of these subfields are determined by the pushing forces generated by the intersecting fields’ negative or positive curvatures during their contraction or expansion. The model employs a group of 2x2 complex rotational matrices of eigenvectors with eigenvalues 1 and —1 and explores their implications for strong, weak, and electromagnetic interactions. It suggests the necessity of interpreting entanglement, superposition, and Pauli Exclusion principle in terms of the mirror reflection symmetry or antisymmetry derived from the atomic dual system.
Category: Mathematical Physics