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

Elliptic Interpretation of the Fine Structure Constant

Authors: Dwight Boddorf
Comments: 2 Pages.

Paper presents fine structure constant as geometric ratio.
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

Quantum State Analysis of the Riemann Zeta Function: Bridging Number Theory and Quantum Mechanics

Authors: Ojong Kwon
Comments: 31 Pages.

The Riemann Hypothesis is an important mathematical problem re- lated to the distribution of prime numbers. This paper explores an ap- proach to proving the Riemann Hypothesis by presenting a new model that combines quantum superposition and the Hurwitz zeta function. By ana- lyzing the effect of the combination of the Hurwitz zeta function ζF (s, q) and the quantum superposition state |ψ⟩ on the transition probabilities of the quantum state, we investigate the zeros of the Riemann zeta func- tion. Using the connection between Euler’s formula and the Riemann zeta function, we simplify the quantum state for the cases where the Riemann zeta function is zero. Numerical simulations are performed to concretely analyze the correlation between the phase changes of the Riemann zeta function and the quantum state, confirming that the zeros of the Rie- mann zeta function are concentrated on the critical line σ = 1/2. This study proposes a new method of understanding the Riemann Hypothe- sis by combining the zeros of the Riemann zeta function and the phase changes of the quantum state.
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

Primes of the Middle [: 137 & 13]

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

Article details the unique position of 137 & 13 relative to their nearest perfect squares.
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

Topological Theory of Hopf Bundle and Mass

Authors: Gary Goodwin
Comments: 8 Pages.

Why a particle has the specific rest mass it does is an open question. An alternative theory of mass is put forward. Mass is the intersection of a Hopf bundle and 3-space. The masses of six lighter hyperons and electron are derived as functions of the proton and neutron masses. Nine free parameters are thereby reduced to two. The most significant outcome is the derivation of the electron mass.
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 the Interpretation of Metric Signature of Temporal Dimensions

Authors: Thomas Emilio Villa
Comments: 3 Pages.

Is time a spectrum, that is, a negative dimension? We suggest in this work a modest yet quite speculative idea: what if the negative sign in front of time-like dimensions is not just a mathematical tool after all? What if the minus sign follows a natural behaviour of time flowing? In this work we are suggesting an unorthodox philosophical interpretation and an explaination of the way that causality is conserved in equations, using the negative sign in front of temporal dimensions. To do so, we use non-conventional approaches like inductive dimension, Lebesgue covering dimension and Minkowski-Bouligand dimension to better understand the nature of time.
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

On the Disnct Aspect of Eleven

Authors: Dwight Boddorf
Comments: 4 Pages. (Converted to pdf by viXra admin - Please only submist article in pdf format)

A distinct aspect of eleven is defined. Aspect is utilized to index one hundred thirty-seven. Index is used to generate a plausible value for the fine structure constant.
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

Electrostatic Fields

Authors: Baran Tuna
Comments: 48 Pages.

Electrostatic fields, cornerstone elements in understanding electrical phenomena, serve as key components in diverse scientific and engineering fields. This paper elucidates the concept of electrostatic fields, explores their properties, and outlines their broad applications. We start from the basics of electric charges and their interactions, leading us to the core principles of electrostatics. A deep dive into Coulomb's law is presented to scrutinize the behavior of electrostatic fields, along with the concept of electric potential and its relationship with the electric field. We underline the instrumental role of electrostatic field analysis in practical applications like electrical power systems, electronics, and telecommunications. Furthermore, we introduce techniques to tackle electrostatic field problems and showcase their applications in engineering and technology. By providing a comprehensive review of electrostatic fields, we aim to deepen understanding and propel further research into this vital domain of electromagnetism.
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

On the Frequency of Light in Vacuum Space

Authors: Larry Huang, Lynn Huang
Comments: 18 Pages.

Based on the fact that the frequency of light is reduced at the same rate (redshift) across a far distance, and the fact that the speed of light is constant, we can yield a mathematical law of light’s frequency loss. This law states for light traveling through vacuum space, its frequency must reduce an amount equal to Hu2092= H/MPC = 2.26*10^(-18) Hertz for every cycle (or every 1 wavelength of travel) of the light wave, where H is Hubble Constant and MPC = Megaparsecs = 30,856,775,814,913,673,000 km or Δf/f = -Hu2092t. This frequency is reducing exponentially against time (f(t) = fu2092e-Hu2092t). In Mathematics, some properties of Digamma function ψ(x) is used to deliver the law. By carefully comparing space’s expansion and this law of frequency loss, we conclude the expansion of space cannot be the reason of light’s frequency reduction, since they contradict one another. Instead, light traveling in space will lose a very small and constant amount of energy for every of its wavelengths that it travels. Finally an experiment is proposed to prove the theory and to find the Hubble Constant without needing to look at galaxies millions of light years away.
Category: Mathematical Physics

The Indivisible Aspects Theory with Redefined Zeros (IATRZ)

Authors: David C. Salles Jr
Comments: 26 Pages. (Corrections made by viXra Admin to conform with scholarly norm)

The Indivisible Aspects Theory with Redefined Zeros (IATRZ) is a proposed new framework attempting to integrate principles from mathematics, philosophy, and physics. It tries to offers a fresh perspective on zero, infinitesimals, and infinity, plausibly reshaping our understanding of the numerical system. In this new perspective, zero, infinitesimals, and infinity are intricately interconnected, forming a unity. Zero plays a vital role in the emergence of infinitesimals, which, in turn, contribute to the boundless expanse of infinity. The IATRZ system redefines zero as an indivisible component of every value, enabling a holistic comprehension of numerical values. Absolute zero becomes the neutral reference point, allowing for the evaluation and comparison of values. Infinitesimals bridge the gap between zero and finite values, revealing the continuous nature of numerical progression. Infinity represents the limitless potential and vastness of the numerical landscape, allowing us to explore the finest granularity possible. This proposed framework challenges traditional interpretations and invites us to explore the interconnectedness of numerical values.
Category: Mathematical Physics

Constantes Fundamentales: Uniendo Gravedad Y la Expansión Acelerada Del Universo Por Medio Del Bosón de Higgs

Authors: Mohamed Makraini
Comments: 19 Pages. In Spanish

En este artículo, se plantea una nueva reinterpretación de la geometría curva del espacio-tiempo, donde de considera que el espacio-tiempo experimenta una contracción longitudinal. Este efecto, se manifiesta en cambios de la métrica del espacio-tiempo que determinan como se miden las distancias y los intervalos temporales en esa región. Es decir, una variación de dimensión en la escala, tamaño o longitud aparente del espacio-tiempo. Esta reinterpretación es compatible con las ecuaciones de campo de Einstein y Maxwell. La constante gravitacional universal GNewton, la constante de Hubble para la expansión acelerada del universo H(0) y la constante cosmológica asociada con la hipotética energía oscura Λ, se pueden obtener y aproximar mediante este nuevo enfoque, donde la masa del bosón de Higgs con sus privilegiadas y únicas características, juega un papel trascendental para dar respuesta a una multitud de preguntas abiertas en física y en la actualidad cosmológica moderna. La reinterpretación de la geometría curva por la contracción espacio-temporal, proporciona un nuevo marco para entender mucho mejor la gravedad. Al obtener valores muy aproximados de la constante de gravitación universal, es posible determinar la fuerza inversa a la gravedad responsable de la expansión acelerada del universo. Esto es posible gracias a la teoría de divergencia de Gauss, donde la distribución de carga determinada por la constante de Coulomb en el marco de la expansión multipolar definida por el electromagnetismo, constituye una analogía bastante sólida, siendo de forma inversamente proporcional a la gravedad, mediante la cuál es posible obtener y calcular con mucha precisión, el valor de la constante H(0) de Hubble. La constante cosmológica Λ, considerada como una posible energía oscura que impulsa la expansión acelerada del universo, también puede ser obtenida y explicada a través de este nuevo enfoque. La reinterpretación de la geometría curva de la gravedad, como una contracción espacio-temporal, afectaría a las propiedades de la expansión del espacio-tiempo, donde la interpretación de contracción del universo, que describe la Relatividad General, debe ser reinterpretada, comprendida y aceptada, como la gravedad misma a cualquier escala.
Category: Mathematical Physics

Fundamental Constants: Uniting Gravity and the Accelerated Expansion of the Universe Through the Higgs Boson

Authors: Mohamed Makraini
Comments: 19 Pages.

This article presents a new reinterpretation of the curved geometry of spacetime, where it is considered that spacetime undergoes longitudinal contraction. This effect is manifested in changes in the spacetime metric that determine how distances and temporal intervals are measured in that region. In other words, a variation in the scale, size, or apparent length of spacetime. This reinterpretation is compatible with Einstein's field equations and Maxwell's equations. The universal gravitational constant of Newton, G, the Hubble constant for the accelerated expansion of the universe, H(0), and the cosmological constant associated with hypothetical dark energy, Λ, can be obtained and approximated using this new approach, where the mass of the Higgs boson with its unique and privileged characteristics plays a crucial role in addressing numerous open questions in physics and modern cosmology. The reinterpretation of curved geometry through spacetime contraction provides a new framework for better understanding gravity. By obtaining very close values of the universal gravitational constant, it is possible to determine the inverse force to gravity responsible for the accelerated expansion of the universe. This is achievable through Gauss's divergence theorem, where the charge distribution determined by the Coulomb constant within the framework of multipolar expansion defined by electromagnetism constitutes a quite solid analogy, being inversely proportional to gravity. This allows for the precise calculation of the value of the Hubble constant, H(0). The cosmological constant Λ, considered as a potential dark energy driving the accelerated expansion of the universe, can also be obtained and explained through this new approach. The reinterpretation of the curved geometry of gravity as spacetime contraction would affect the properties of spacetime expansion, where the interpretation of the universe's contraction described by General Relativity must be reinterpreted, understood, and accepted as gravity itself at any scale.
Category: Mathematical Physics

Knot in Weak-Field Geometrical Optics

Authors: Miftachul Hadi
Comments: 4 Pages. 1 figure.

We construct the geometric optical knot in 3-dimensional Euclidean (vacuum or weak-field) space using the Abelian Chern-Simons integral and the variables (the Clebsch variables) of the complex scalar field, i.e. the function of amplitude and the phase related to the refractive index. The result of numerical simulation shows that in vacuum or weak-field space, there exists such a knot.
Category: Mathematical Physics

Navier-Stokes Equation and Euler Equation

Authors: Wan-Chung Hu
Comments: 7 Pages. In Chinese

The existence of Navier-Stokes equation is still a puzzle. Here, I provide solutions to the compressible or non-compressible fluids of the Navier-Stokes equation. In addition, the smoothness of Navier-Stokes equation is proved. In the above conditions, Navier-Stokes equation can be reduced to Laplace equation or Poisson equation to obtain the solutions and to prove the existence and smoothness of the Navier-Stokes equation.
Category: Mathematical Physics

Space-Time as Spinors

Authors: Julian Simon Brown
Comments: 6 Pages.

We uncover an implicit volume-preserving mapping from the C^4 space of a bispinor onto the past cone belonging to an arbitrary spacetime point in R^{3,1}$. The quotient group SO(3,1) is shown to be given by SO(8)/U(1) x U(1) x SO(3) and a simple geometrical interpretation is presented. We conclude by showing that the novel mapping allows the reformulation of many equations of motion of boson and fermion fields as integral equations over null cones that are devoid of field derivatives.
Category: Mathematical Physics

Can You Paint a Painting Without Any Canvas?

Authors: D. Chakalov
Comments: 3 Pages. (Correction made by viXra Admin - Please conform!)

The mathematical blueprint of the arrow of Time [is discussed] in a nutshell.
Category: Mathematical Physics

Significance of the Number Space and Coordinate System in Physics for Elementary Particles and the Planetary System

Authors: Helmut Christian Schmidt
Comments: 21 Pages.

The universe can be understood as a set of rational numbers Q. This is to be distinguished from how we see the world, a 3-dimensional space with time. Observations from the past is the subset Q⁺ for physics. A system of 3 objects, each with 3 spatial coordinates on the surface and time, is sufficient for physics. For the microcosm, the energy results from the 10 independent parameters as a polynomial P(2). For an observer, the local coordinates are the normalization for the metric. Our idea of a space with revolutions of 2π gives the coordinates in the macrocosm in epicycles. For the observer this means a transformation of the energies into polynomials P(2π). c can be calculated from the units meter and day.π/2 c m day = ^{r_Earth2This formula provides the equatorial radius of the earth with an accuracy of 489 m. Orbits can be calculated using polynomials P(2π) and orbital times in the planetary system with P(8). A common constant can be derived from h, G and c with the consequence for H0: h G c5s8 /m10 ( π4- π2- π-1 - π-3) 1/2 H0_theory= π1/23 h G c3 s5/m8A photon consists of 2 entangled electrons e- and e+m_neutron / m_e=(2π)4 +(2π)3+(2π)2-(2π)1-(2π)0-(2π)-1+2(2π)-2+2(2π)-4-2(2π)-6 +6(2π)-8 = 1838.6836611 Theory: 1838.6836611 m_e measured: 1838.68366173(89) m_eFor each charge there is an energy C = -π+2π-1- π-3+2π-5-π-7+π-9- π-12Together with the neutron mass, the result for the proton is: m_proton=m_neutron + C m_e= 1836.15267363 m_eFine-structure constant: 1/α = π4+ π3+ π2 - 1 - π-1 + π-2 - π-3 + π-7 - π-9 - 2π-10 - 2π-11 - 2π-12 = 137.035999107The muon and tauon mass as well as inner planetary system calculations are also given
Category: Mathematical Physics}

On the Calculation of the Corner Frequency in Bode Plots

Authors: Aloys J. Sipers, Joh. J. Sauren
Comments: 7 Pages.

In this paper we prove that the relationship ωτ = 1 is a property of logarithmic scale of the horizontal axis in Bode plots. We illustrate the results of our derivations and mathematical conclusions by calculating the point of intersection of the horizontal and the oblique asymptote in a magnitudeplot and the point of symmetry in a phase plot.
Category: Mathematical Physics

Quaternionic Generalization of Telegraph Equations

Authors: Victor L. Mironov, Sergey V. Mironov
Comments: 13 Pages.

Using non-commutative space-time quaternion algebra, we represent the generalization of one-dimensional and three-dimensional telegraph equations, which are widely applied to consider the propagation of an electromagnetic signal in communication lines, as well as to describe particle diffusion and heat transfer. It is shown that the system of telegraph equations can be represented in compact form as a single quaternion equation taking into account the space-time properties of physical quantities. The distinctive features of the one-dimensional and three-dimensional telegraph equations are discussed.
Category: Mathematical Physics

Analytical Models of Plane Turbulent Wall-bounded Flows

Authors: Victor L. Mironov, Sergey V. Mironov
Comments: 21 Pages.

We present the theoretical description of plane turbulent wall-bounded flows based on the previously proposed equations for vortex fluid, which take into account both the longitudinal flow and the vortex tubes rotation. Using the simple model of eddy viscosity we obtain the analytical expressions for mean velocity profiles of steady-state turbulent flows. In particular we consider near-wall boundary layer flow as well as Couette, Poiseuille and combined Couette-Poiseuille flows. In all these cases the calculated velocity profiles are in good agreement with experimental data and results of direct numerical simulations.
Category: Mathematical Physics

Dimensional Regularization and Fractal Spacetime

Authors: Ervin Goldfain
Comments: 20 Pages. (Corrections made by viXra Admin to conform with scholarly norm)

This report expands on the preprint "Dimensional Regularization as Mass Generating Mechanism", posted at the following sites:https://doi.org/10.32388/DW6ZZS , https://www.researchgate.net/publication/370670747
Category: Mathematical Physics

The Most Beautiful Form of the Dirac Equation, and Some Speculations re "123 Mystery"

Authors: Warren D. Smith
Comments: 9 Pages.

Dirac 1928's relativistic electron wave equation had involved 4×4 matrices. We show how to reformulate it using 2×2 matrices only, and also that we can get rid even of them provided we make the wavefunction be biquaternion-valued. The Majorana equation then has quaternion-valued wavefunction. We then speculate that extensions of this idea might be able to solve one or two of the oft-cited "great mysteries" of physics.
Category: Mathematical Physics

Are We Using Bell’s Inequality Wrongly in Polarization of Light Experiments?

Authors: Jayesh Suresh
Comments: 6 Pages.

Bell’s inequality is a widely used theorem to prove that quantum mechanics violates principle of locality. Polarization experiments are used in this regard. This article is an examination to see whether there is any loop hole in our usage of polarization experiments to prove that quantum particles violate Bell’s inequality. In this article, the probability distribution of unpolarised light is examined. On doing so, it is found that the realignment of polarization axis of photon on passing through a polarizer may be the cause of more than expected probabilities
Category: Mathematical Physics

The Velocity-Wavelength Right Triangles Unit Circles Standard Clock and the Twin Paradox

Authors: Claude Michael Cassano
Comments: 6 Pages.

Using energy and momentum definitions: E=(m_0)c²/sqrt(1-v²/c²) and p=(m_0)v/sqrt(1-v²/c²)their frequencies and wavelengths may be shown as reciprocal transformations: f=c/λ_{c} , λ=c/f_{c} yielding the generally referred to: (λ_{c)}(f_{c})=v=v_{g} group velocity ; and λf=(c/f_{c})(c/λ_{c))=c²/((λ_{c)}(f_{c}))=c²/v=v_{p} phase velocity and yields the right triangles: ((((m_0)c)/h)λ_{c})²(v/c)²=1 and [((((m_0)v)/h))λ]²(v/c)²=1 represent wavelength-velocity right triangles with unit hypotenuses (radii of unit circles) As unit circles, the time rate of change of the angle of these wavelength-velocity right triangles may be considered a standard clock of a relativistic reference frame. Analysis may be made for any planets in a solar system; and similarly for binary star/planet/moon system(s) and also for bodies within rotating galaxies. Using this standard relativistic clock the effects of acceleration concerning the twin paradox may be calculated.
Category: Mathematical Physics

Collision Entropy Estimation in a One-Line Formula

Authors: Alessandro Gecchele
Comments: 14 Pages.

{Integer-order Rényi entropies are synthetic indices useful for the characterization of probability distributions. In recent decades, numerous studies have been conducted to arrive at valid estimates of these indices starting from experimental data, so to derive a suitable classification method for the underlying processes. However, optimal solutions have not been reached yet. A one-line formula limited to the estimation of collision entropy is presented here. The results of some specific Monte Carlo experiments gave evidence of its validity even for the very low densities of the data spread in high-dimensional sample spaces. The strengths of this method are unbiased consistency, generality and minimum computational cost.
Category: Mathematical Physics

A Compact CPW-Fed Triple Band Monopole Antenna with Simple Structure for WLAN/WiMAX Applications

Authors: Baek Ye Song, Kim Nam Chol Kim Un Chol, Kim Ju Il, Song Sung Bom
Comments: 5 Pages.

In this paper, a new compact coplanar waveguide (CPW)-fed triple band monopole antenna with dual circular rings and two L-shaped parasitic strips on the ground plane is presented. The fabricated antenna with new simple structure has a compact size of 26 mm × 34 mm. The proposed antenna has impedance bandwidths of 2.39-2.69 GHz, 3.21- 4.12GHz and 5.08 -5.86GHz with a reflection coefficient of less than -10dB. The measured performances are compared with the simulated results and show good agreement. The proposed triple band monopole antenna also has good omnidirectional radiation patterns and available gain. The simple structure, ease of implementation, compact size and good performances make the proposed antenna an excellent candidate for WLAN and WiMAX applications.
Category: Mathematical Physics

Design and Implementation of a Compact CPW-Fed Planar UWB Antenna with Quadruple Band Notched Characteristics

Authors: Kim Dae Il, Kim Un Chol, Ryu Dong Myong, Choe Jong Yol, Pak Chung Jin
Comments: 9 Pages.

A novel coplanar waveguide ()-fed planar UWB antenna with quadruple band-notched property is presented. The quadruple band rejection is achieved by etching a M-shaped slot on the radiation patch and a U-shaped slot on the feed line, and adding two L-shaped parasitic strips near radiator patch and two split ring resonators (SRRs) on the back surface of the substrate. The voltage standing wave ratio (VSWR) results show that the proposed antenna exhibits good wideband performance over an UWB frequency range from 3 to 11.8 GHz with VSWR less than 2, except for four stop-bands at 3.3~3.75GHz, 5.15~5.85GHz, 7. 2~7.76GHz, 8~8.55GHz respectively. It also demonstrates a nearly omnidirectional radiation pattern and available gain. The fabricated antenna has a tiny size, only 34mm 31mm0.508mm. The simulated results are compared with the measured results and good agreement is obtained. The simple structure, compact size and good characteristics make the antenna an excellent candidate for UWB applications.
Category: Mathematical Physics

Gauge Invariance in Counting and Combinatorics

Authors: Koustubh Kabe
Comments: 7 Pages. This paper explores a new kind of gauge invariance that makes its appearance in counting and combinatorics.

There is perhaps no part of mathematics that is more intimately connected with everyday experiences than probability theory and statistics. The element of chance dominates the physical world. Probability is the heart of physics, in particular — quantum physics. At the probability theory lies combinatorics. We make an observation in the combination of n objects taken r objects at a time. We find a sort of combinatorial gauge invariance hidden there in that the combination of �� objects taken �� at a time or �� − �� at a time is the same. It has been argued that the Pauli Exclusion Principle is not a principle or cause at all; rather it is an effect of the combinatorics which essentially delivers the Fermi Dirac Statistics. We explore the consequent applications in quantum mechanics and field theory with particle statistics.
Category: Mathematical Physics

Grondvesten (Foundations)

Authors: Hans van Leunen
Comments: 360 Pages. In Dutch (Dit is onderdeel van het Hilbert Book Model project)

Het Hilbert Book Model project heeft deze publicatie opgeleverd. De zoektocht naar een betrouwbare basis van de fysieke werkelijkheid heeft veel tegenslagen gekend en verloopt traag. Als gevolg hiervan raakte de reguliere natuurkunde op een zijspoor. Kwantumveldentheorie, kwantumelektrodynamica en kwantumchromodynamica gebruiken het minimale actieprincipe als basis. Het Hilbert Book Model laat zien dat continuüms tot de derde fase van een speciale verzameling behoren en niet kunnen werken als basis van de wiskundige fysica. Dit document laat zien hoe de drie fasen van de speciale verzameling leiden tot een vectorruimte en getalsystemen, die van toepassing zijn op een systeem van Hilbertruimten waarin het lokale universum en een parallel multiversum kunnen optreden. Ook laat het document zien dat de wetenschap het Higgs-deeltje of het Higgs-veld niet als onderdeel van het standaardmodel moet beschouwen. In plaats daarvan zou het standaardmodel van de experimentele deeltjesfysici zich moeten beperken tot de elementaire fermionen. De meeste natuurkundigen interpreteren fotonen als excitaties van het elektrische veld. Daarentegen interpreteert het HBM fotonen als ketens van donkere energieobjecten, en de donkere energieobjecten zijn schokfronten die het veld verstoren en zodoende het lokale universum vertegenwoordigen. Hoplandingen van de toestandsvectoren van de fermionen produceren bolvormige schokfronten die met lichtsnelheid wegsnellen van de locatie van deze landing. Dit is in strijd met de ideeën van behoudswetten die in de reguliere natuurkunde spelen. Volgens het HBM heeft een oerknal nooit plaatsgevonden. Het model beschouwt twee gedeelten en aan het begin van het tweede gedeelte begint de tijd samen te lopen met een voortdurende schepping van fermionen.

The Hilbert Book Model project has produced this publication. The search for a reliable basis of physical reality has had many setbacks and is progressing slowly. As a result, mainstream physics got sidetracked. Quantum field theory, quantum electrodynamics and quantum chromodynamics use the minimal action principle as a basis. The Hilbert Book Model shows that continuums belong to the third stage of a special set and cannot function as the basis of mathematical physics. This paper shows how the three phases of the special set lead to a vector space and number systems, applicable to a system of Hilbert spaces in which the local universe and a parallel multiverse can occur. The paper also shows that science should not consider the Higgs boson or the Higgs field part of the Standard Model. Instead, the experimental particle physicists' standard model should be limited to the elementary fermions.Most physicists interpret photons as excitations of the electric field. In contrast, the HBM interprets photons as chains of dark energy objects, and the dark energy objects are shock fronts that distort the field and thus represent the local universe. Hop landings of the fermions' state vectors produce spherical shock fronts that speed away from the location of this landing at the speed of light. This is contrary to the ideas of conservation laws at play in mainstream physics. According to the HBM, a big bang never happened. The model considers two parts, and at the beginning of the second part, time begins to coincide with a continuous creation of fermions.
Category: Mathematical Physics

Model λ(φ^2n )_4,n≥2 Quantum Field Theory: A Nonstandard Approach Based on Nonstandard Pointwise-Defined Quantum Fields

Authors: Jaykov Foukzon
Comments: 30 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^2n )_4,n≥2 quantum field theory models are Lorentz covariant.
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

Topological Theory of Hopf Bundle and Mass

Authors: Garry Goodwin
Comments: 9 Pages.

Why a particle has the specific rest mass it does is an open question. The rudiments of an alternative theory to the Standard Model are put forward to try an answer this question. To perturb an object with Hopf fibration topology, a force in ordinary space jumps topologies. The size of the jump is the object's resistance to the force and the measure of its mass. Various mass splitting formulae carry the signature of a 3-sphere intersecting three dimensional space. The signature points to homotopic non-equivalence. Using this signature the masses of six lighter hyperons and electron are found to be functions of the proton and neutron.
Category: Mathematical Physics

Topological Theory of Hopf Bundle and Mass

Authors: Garry Goodwin
Comments: 7 Pages.

Why a particle has the specific rest mass it does is an open question. An alternative theory of mass is put forward. Rest mass is due to discrepant topologies found at the intersection of a Hopf bundle and 3-space. The rest masses of six lighter hyperons and electron are derived as functions of the proton and neutron, reducing nine free parameters to two. The most significant outcome is the derivation of the electron mass due to baryon mass splitting.
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 the Distinct Aspect of Eleven

Authors: Dwight Boddorf
Comments: 4 Pages.

A distinct aspect of eleven is defined. Aspect is utilized to index one hundred thirty-seven. Index is used to generate a plausible value for the fine structure constant.
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

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

Hilbert and Pólya Conjecture, Dynamical System, Prime Numbers, Black Holes, Quantum Mechanics, and the Riemann Hypothesis

Authors: Mohamed Sghiar
Comments: 13 Pages. In this version I deduce the proof of Hilbert Polya's conjecture

In mathematics, the search for exact formulas giving all the prime numbers, certain families of prime numbers or the n-th prime number has generally proved to be vain, which has led to contenting oneself with approximate formulas [7]. The purpose of this article is to give a simple function to produce the list of all prime numbers.And then I give a generalization of this result and we show a link with the quantum mechanics and the attraction of black Holes. And I give a new proof of lemma 1 which gave a proof of the Riemann hypothesis [4]. Finally another excellent new proof o f the Riemann hypothesisis given and I deduce the proof of Hilbert Polya's conjecture
Category: Mathematical Physics

Space-Time as Spinors

Authors: Julian Simon Brown
Comments: 6 Pages.

We uncover an implicit volume-preserving mapping from the $mathbb{C}^4$ space of a bispinor onto the past cone belonging to an arbitrary spacetime point in $mathbb{R}^{3,1}$. The quotient group $SO(3,1)$ is shown to be given by $SO(8)/U(1) cross U(1) cross SO(3)$ and a simple geometrical interpretation is presented. We conclude by showing that the novel mapping allows the reformulation of many equations of motion of boson and fermion fields as integral equations over null cones that are devoid of field derivatives.
Category: Mathematical Physics

Basic Non-Archimedean Functional Analysis Over Non-Archimedean Field ^{∗}ℝ_{c}^{#}. Application to Constructive Quantum Field Theory

Authors: Jaykov Foukzon
Comments: 298 Pages.

Functional analysis works with TVS (Topological Vector Spaces), classically over archimedean fields like R and C. Canonical non-Archimedeanfunctional analysis, where alternative but equally valid number systems such as p-adic numbers p etc. are fundamental, is a fast-growing discipline. This paper deals with TVS over non-classical non-Archimedean fields (Note: Unintelligible portion of the abstract is removed by viXra Admin)
Category: Mathematical Physics

Basic Non-Archimedean Functional Analysis Over Non-Archimedean Field ^{∗}ℝ_{c}^{#}. Application to Constructive Quantum Field Theory

Authors: Jaykov Foukzon
Comments: 74 Pages.

Main Definitions and theorems related to non-Archimedean functional analysis on non-Archemedean field ┊^{∗}ℝ_{c}^{#}┊ and on complex field ┊^{∗}ℂ_{c}^{#}┊=┊^{∗}ℝ_{c}^{#}┊+i┊^{∗}ℝ_{c}^{#}┊areconsidered
Category: Mathematical Physics

Significance of the Number Space and Coordinate System in Physics for Elementary Particles and the Planetary System

Authors: Helmut Schmidt
Comments: 21 Pages. I am grateful for every comment!

In physics, a single center of gravity is assumed for forces. However, at least 3 fixed points π, π², π³are required as the center, orthograde for the 3 spatial dimensions. With this approach, the universe can be understood as a set of rational numbers Q. This is to be distinguished from how we see the world, a 3-dimensional space with time. Observations from the past is the subset Q⁺ for physics. A system of 3 objects, each with 3 spatial coordinates on the surface and time, is sufficient for physics. For the microcosm, the energy results from the 10 independent parameters as a polynomial P(2). For an observer, the local coordinates are the normalization for the metric. Our idea of a space with revolutions of 2π gives the coordinates in the macrocosm in epicycles. For the observer this means a transformation of the energies into polynomials P(2π). This is used to simulate the energies of a system. c can be calculated from the units meter and day.π/2 c m day = r_Earth²This formula provides the equatorial radius of the earth with an accuracy of 489 m. Orbits can be calculated using polynomials P(2π) and orbital times in the planetary system with P(8). A common constant can be derived from h, G and c with the consequence for H0:h G c⁵s⁸ /m¹⁰ ( π⁴- π²- π^-1 - π^-3) ^1/2 H0_theory= π^1/23 h G c³ s⁵/m⁸A photon consists of 2 entangled electrons e^- and e⁺m_neutron / m_e=(2π)⁴ +(2π)³+(2π)²-(2π)¹-(2π)⁰-(2π)^-1+2(2π)^-2+2(2π)^-4-2(2π)^-6 +6(2π)^-8 = 1838.6836611 Theory: 1838.6836611 m_e measured: 1838.68366173(89) m_eFor each charge there is an energy C = -π+2π^-1- π^-3+2π^-5-π^-7+π^-9- π^-12Together with the neutron mass, the result for the proton is: m_proton=m_neutron + C m_e= 1836.15267363 m_eFine-structure constant:1/α= π⁴+ π³+ π²-1- π^-1 + π^-2- π^-3 + π^-7 - π^-9- 2 π^-10-2 π^-11-2 π^-12 = 137.035999107The muon and tauon masses as well as calculations for the inner planetary system are given.
Category: Mathematical Physics

Dimensional Regularization and Fractal Spacetime

Authors: Ervin Goldfain
Comments: 20 Pages.

This report expands on the preprint "Dimensional Regularization as Mass Generating Mechanism", posted at the following sites:https://doi.org/10.32388/DW6ZZS,https://www.researchgate.net/publication/370670747
Category: Mathematical Physics

No Singularities in Schwarzschild Black Hole and Big Bang

Authors: Yongrong Bao
Comments: 5 Pages. (Note by viXra Admin: Author name on the form and in the article in pdf must match!)

We prove no singularities in Schwarzschild black hole (SBH) and Big Bang considering the quantum effect. We find the equation of gravitational energy density inside SBH; derive that the gravitational energy density is proportional to the square effective temperature far from the event horizon in SBH interior, whether the gravitational fields of SBH are Coulomb-like or wave-like; obtain their entropic density is direct proportion with the effective temperature. Then we assume that the center of SBH and Big Bang being in the minimum entropy state, which value is equal to the Boltzmann constant; propose the SBH uncertainty relation (UR) and Big Bang UR by the generalized relational expression (GRE) and prove, which suggest no singularity in them.
Category: Mathematical Physics

Collision Entropy Estimation in a One-Line Formula

Authors: Alessandro Gecchele
Comments: 14 Pages.

We address the unsolved question of how best to estimate the collision entropy, also called quadratic or second order Rényi entropy. Integer-order Rényi entropies are synthetic indices useful for the characterization of probability distributions. In recent decades, numerous studies have been conducted to arrive at their valid estimates starting from experimental data, so to derive suitable classification methods for the underlying processes, but optimal solutions have not been reached yet. Limited to the estimation of collision entropy, a one-line formula is presented here. The results of some specific Monte Carlo experiments give evidence of the validity of this estimator even for the very low densities of the data spread in high-dimensional sample spaces. The method strengths are unbiased consistency, generality and minimum computational cost.
Category: Mathematical Physics

Collision Entropy Estimation in a One-Line Formula

Authors: Alessandro Gecchele
Comments: 15 Pages.

We address the unsolved question of how best to estimate the collision entropy, also called quadratic or second order Rényi entropy. Integer-order Rényi entropies are synthetic indices useful for the characterization of probability distributions. In recent decades, numerous studies have been conducted to arrive at their valid estimates starting from experimental data, so to derive suitable classification methods for the underlying processes, but optimal solutions have not been reached yet. Limited to the estimation of collision entropy, a one-line formula is presented here. The results of some specific Monte Carlo experiments give evidence of the validity of this estimator even for the very low densities of the data spread in high-dimensional sample spaces. The method strengths are unbiased consistency, generality and minimum computational cost.
Category: Mathematical Physics

Collision Entropy Estimation in a One-Line Formula

Authors: Alessandro Gecchele
Comments: 14 Pages. Keywords: Rényi entropies; collision entropy estimation; collision entropy rate estimation

We address the unsolved question of how best to estimate the collision entropy, also called quadratic or second order Rényi entropy. Integer-order Rényi entropies are synthetic indices useful for the characterization of probability distributions. In recent decades, numerous studies have been conducted to arrive at their valid estimates starting from experimental data, so to derive suitable classification methods for the underlying processes, but optimal solutions have not been reached yet. Limited to the estimation of collision entropy, a one-line formula is presented here. The results of some specific Monte Carlo experiments give evidence of the validity of this estimator even for the very low densities of the data spread in high-dimensional sample spaces. The method strengths are unbiased consistency, generality and minimum computational cost.
Category: Mathematical Physics

Collision Entropy Estimation in a One-Line Formula

Authors: Alessandro Gecchele
Comments: 14 Pages.

Integer-order Rényi entropies are synthetic indices useful for the characterization of probability distributions. In recent decades, numerous studies have been conducted to arrive at valid estimates of these indices starting from experimental data, so to derive a suitable classification method for the underlying processes. However, optimal solutions have not been reached yet. A one-line formula limited to the estimation of collision entropy is presented here. The results of some specific Monte Carlo experiments gave evidence of its validity even for the very low densities of the data spread in high-dimensional sample spaces. The strengths of this method are unbiased consistency, generality and minimum computational cost.
Category: Mathematical Physics

Model λ(φ^2n )_4,n≥2 Quantum Field Theory: A Nonstandard Approach Based on Nonstandard Pointwise-Defined Quantum Fields

Authors: Jaykov Foukzon
Comments: 48 Pages. doi:10.1088/1742-6596/2701/1/012113

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^2n )_4,n≥2 quantum field theory models are Lorentz covariantJaykov Foukzon 2024J. Phys.: Conf. Ser. 2701 012113doi:10.1088/1742-6596/2701/1/012113
Category: Mathematical Physics