Maxwell's Equations

We propose a fundamental extension to gravity where the speed of light
c emerges as a dynamical field-dependent quantity rather than a universal
constant. Building on the f(R,z) formalism embedded within Horndeski
scalar-tensor theory—a ghost-free framework ensuring second-order equa-
tions of motion—with a quantized scalaron termed the “supergraviton”
ϕ, we demonstrate that ceff (ϕ) = c0 /Ω(ϕ), where Ω(ϕ) = exp(βϕ/MPl ).
This setup, realized via disformal transformations preserving cT = 1, nat-
urally explains James Webb Space Telescope (JWST) anomalies showing
unexpectedly massive early galaxies and hyper-efficient star formation at
z ∼ 10, with Bayesian evidence ratio 105.5 favoring our model over ΛCDM.

This paper introduces the Grand Unified Theory of Existence (GUTE), a comprehensive framework integrating geometry, consciousness, energy, and the fundamental constants of nature. Building upon the previously proposed Λ-c-2π framework and the Unified Etheric Resonance Field (UERF), the theory postulates that reality is an emergent harmonic field sustained by feedback between conscious observation and cyclical resonance. Core constants such as the speed of light (c), the geometric constant (2π), and dark energy (Λ) serve as harmonizing factors that stabilize spacetime, unify quantum fields, and mediate cosmic evolution. This theory reframes black holes, wormholes, and cosmological expansion through harmonic and conscious dynamics, proposing that existence is ultimately selfgenerating, self-stabilizing, and observer-dependent.

Abstract
This work outlines an experimental test of Dynamic Spacetime Metric (DSM), which proposes spacetime as universally entangled local variables, specifically as Black and White Holes. Grounded in its precursor, Quantum Spin Dynamics (QSD) – the metric beneath the atomic manifold – intruduces the Consciousness operator into quantum, we induce a phantom gravity that alters space—time itself,  (-(CR_eff )^2 □_ijkR+3/4 (h_n ω_0 R_rap )^2 )|├ Ψ⟩=  4/3  〖l_p〗^2/R_eff  (∂^2 j)/〖∂t〗^2  R_eff |├ Ψ⟩, while providing the holographic carrier frequency for a massless quantum wave equation and embedding GRT into quantum given 4/3  〖l_p〗^2/R_eff  (∂^2 j)/〖∂t〗^2  R_eff |├ Ψ⟩=4/3  (G m_e)/C^2  (∂^2 j)/〖∂t〗^2  R_eff |├ Ψ⟩.  DSM predicts a 4-sphere geometry with two orthogonal singularities: the effective radius of point particles  R_eff  and spacetime, √3/2 R_rap=R_sp.  Both exist in a super-singularity R_rap.  DSM uses General relativity to predict quantum structures and energy mass relationships in classical mechanical terms, simplifying quantum. These mathematically vetted foundational claims suggest that quantum randomness, perceived in our macroscopic universe, originates from the singularity's timeless, deterministic internal dynamics and huge tidal forces smearing quantum states about the manifold of the singularity.    We hypothesize that a conscious act, specifically by adjusting photon energy and thereby altering R_eff , consciously and deterministically influences an emergent "Ubiquigent State Space" – altering quantized spacetime geometrically.  This state space acts as an intrinsic geometric hidden variable and a "third observer" in quantum measurements. Utilizing a modified Clauser-Horne-Shimony-Holt (CHSH) experiment, without altering measurement settings, we propose to demonstrate this influence. The geometry-driven CHSH model unifies quantum correlations, mass-energy harmonics, and thermodynamic statistics within a single manifold. We predict that a conscious input alters R_eff and will affect the energy-entropy relationship of Hawking radiation, thereby tangibly impacting the Ubiquigent State Space. The experimental results will manifest as a measurable alteration in the Boltzmann distribution of quantum outcomes, specifically changing the number of events required to reach statistical confidence intervals, thus demonstrating a conscious influence on the balance between chaos and order. Further we develop the Cosmological constant, Λ=1.21241228×〖10〗^(-52) m^(-2), as geometric pressure in DSM. While this experiment does not aim to prove libertarian free will, it seeks to empirically demonstrate conscious control over quantum phenomena, offering unique insights into the physical boundary of human consciousness.

Smarandache's Hypothesis states that there is no speed limit for anything, including light and particles. While this idea is based on the Einstein-Podolski-Rosen paradox, it is still difficult for many physicists to accept. This paper reviews several experiments that support superluminal physics and offers explanations for Smarandache's Quantum Paradoxes and the Quantum Sorites Paradox. The article also briefly touches on a new experiment involving a magneton that supports the SubQuantum Kinetic Model of the Electron. The authors conclude that these multi-experimental findings help to verify their conjectures and are likely to open new directions for research toward an evidence-based physics.

This report investigates the fundamental connection between the minimum mass constant M o and the vacuum electric permittivity ε 0 within the framework of Mo Theory. By expressing ε 0 in terms of Planck scale quantities and M o , a deeper relationship between quantum mechanics, gravitation, and electromagnetism emerges. The analysis highlights that M o may serve as a fundamental bridge linking microphysical constants to macroscopic electromagnetic properties. The inclusion of a scaling factor emphasizes the discrete nature of this connection and suggests a quantized interplay between Planck-scale physics and observable constants. This study supports the idea that the vacuum permittivity, often regarded as a fundamental constant of electromagnetism, may itself originate from more fundamental quantum-gravitational parameters, as described by Mo Theory.

Estas notas esta pensadas para dar una introducción rápida de los principales conceptos de teoría electromagnética. La idea general es dar una idea de las principales ecuaciones que rigen el comportamiento de los fenómenos eléctricos y magnéticos. Además, de establecer las principales herramientas matemáticas que se utilizan para entender las ecuaciones del electromagnetismo. Advertencia: El lenguaje utilizado es informal y falto de rigor matemático.

Es kann gezeigt werden, dass sich alle kosmologisch relevanten Theorien aus der Weber-De Broglie-Bohm-Theorie (WDBT) ableiten lassen. Diese Emergenz der Kosmologie ist einzigartig; es wird sogar gezeigt, wie die ART sinnvoll erweitert werden kann.

On the eve of the Battle of Atlanta-Georgia, 21st July 1864-Colonel Sherburn, best known as the retired soldier who stared down a lynch mob in The Adventures of Huckleberry Finn, stands again in command, now leading a regiment in Walker's division. Bivouacked southeast of Atlanta awaiting nightfall orders, Sherburn, sensing the first tremors of a new technological dawn, addresses his soldiers in the falling twilight.

This work demonstrates that Maxwell's equations and the Navier-Stokes equations emerge as macroscopic limits of a single, unified discrete dynamics of the θ-network within the Tensor Model of Discrete Dynamics (TMDD). By employing an analogy-based method and a rigorous continuum limit, we establish ontological correspondences: electromagnetic fields arise from the network's informational modes, while hydrodynamic parameters emerge from its coherent and geometric modes. We show that the fundamental constants ϵ 0 , µ 0 , and the kinematic viscosity ν are emergent, being expressed in terms of the model parameters ϵ, ζ, and γ. An analysis of the "tail" terms of the action-those that vanish in the classical limit-suggests a unified ontological framework for explaining several observed cosmological anomalies, including the H 0 tension, CMB anisotropy, variations in the fine-structure constant, and galactic rotation curve anomalies. In this interpretation, "dark matter" manifests as the internal pressure and viscous forces of the informational network, while galaxy morphology is determined by a dimensionless R eM number, which balances coherence and smoothing effects. This work demonstrates that TMDD provides a coherent ontological foundation from which both classical physical laws and their observed deviations arise naturally.

This paper introduces a novel, first-principles derivation of the photon within the ICCF (Information-Cognitive Compression Field) framework. Contrary to the traditional view of photons as fundamental point particles, we propose that photons are best understood as causal disturbances in the compression field of spacetime, with their massless and transverse nature arising naturally from the geometry of this field. Starting from the ICCF core equation , we derive a wave equation that describes these perturbations, which mathematically coincide with Maxwell's equations. The study provides a unified framework to understand the essential characteristics of photons, including their massless nature, transverse wave properties, and constant propagation speed cc, all as inherent geometrical implications of the ICCF spacetime causal structure.

This paper proposes a new fundamental quantity, Locality L^t, which accounts for local effects of time and light propagation between observers. Classical and relativistic laws, averaged relative to Earth, cannot precisely describe interstellar and instantaneous interactions. Introducing L^t allows accurate calculations of light speed, object motion, and event perception for any observer in the Universe.

We resolve the negative sign in Maxwells equations by putting it in another context (the negative sign changes to positive). We also write two of Maxwells equations as one equation. We use the 4x3 determinant. The text uses my computation method for a nxm determinant. We develop a formalism using the 4-dimensional curl of the Electromagnetic potential. We use the scalar electric potential appended with the vector magnetic potential into the same vector.

General Theory of Relativity as formulated by Einstein is incompatible with the rules of quantum mechanics and so far, not been unified with the other fundamental forces. New hypothesis provides solution to these  roblems by thermodynamics approach. Let’s consider an example of an open system such as Earth, which has excess energy (Potential energy) due to the disruption of intermolecular bonds on its surface and at different element interfaces that creates an inward pull, resulting in an absolute pressure that is higher than outside full vacuum universe. The difference needs to be balanced, so it creates an inward vacuum drag (gravity gradient) that enables all objects drag towards the Earth. In Einstein’s general theory of relativity, the above-mentioned phenomenon is regarded as the curvature of space-time. The concept of extra energy (due to molecular bonds) doesn’t work for a single molecule, which is why general relativity fails to hold true at atomic level. This hypothesis pr...

This work presents a quaternion-based formulation of vector analysis, with particular emphasis on the angular part of the Laplacian operator and its spectral decomposition. By leveraging the algebraic structure of quaternions and the Lie group of rotations SO(3), the author derives a simplified expression for the angular component of the Laplacian, The spectral analysis reveals that the eigenfunctions of
L are vector spherical harmonics, constructed from classical scalar spherical harmonics.

The paper further develops a basis of vector functions on the sphere using these harmonics and applies the formalism to quantum wave equations. Specifically, it incorporates electromagnetic corrections from Pauli and Dirac into the Klein-Gordon equation using the van der Waerden–Kramers method, with a return to two-component wave functions as suggested by Weyl. The wave functions are valued in the quaternionic space and are represented via 2×2 complex matrices.

Finally, the study explores the fine structure of the quantum system by solving the second-order wave equation under the influence of electromagnetic potentials. The spectral properties of the associated operators are analyzed, leading to a refined understanding of the energy levels and their dependence on angular momentum and spin interactions.

We present an epistemological schema of natural sciences inspired by Peirce's pragmaticist view, stressing the role of the phenomenological map, that connects reality and our ideas about it. The schema has a recognisable mathematical/logical structure which allows to explore some of its consequences. We show that seemingly independent principles as the requirement of reproducibility of experiments and the Principle of Sufficient Reason are both implied by the schema, as well as Popper's concept of falsifiability. We show that the schema has some power in demarcating science by first comparing with an alternative schema advanced during the first part of the 20th century which has its roots in Hertz and has been developed by Einstein and Popper. Further, the identified differences allow us to focus in the construction of Special Relativity, showing that it uses an intuited concept of velocity that does not satisfy the requirements of reality in Peirce. While the main mathematical observation connected with this issue has been known for more than a century, it has not been investigated from an epistemological point of view. A probable reason could be that the socially dominating epistemology in physics does not encourage such line of work. We briefly discuss the relation of the abduction process presented in this work with discussions regarding "abduction" in the literature and its relation with "analogy".

Why is absolute space associated with Newton in the narrative of physics?  What happened to "True motion", the central concept in Newton?  Why do textbooks insist on “paradoxes” occurring in Physics forcing students to accept contradictions?  Does the value of quantum mechanics lie solely in supplying a consistent mathematical scheme that would allow physicists to calculate measurable quantities, as Dirac claimed? Are physics equations the result of "free thinking" and a posteriori interpretation?  When and why was critical reason left behind? For Galileo "Philosophy is written in this very great book that is continually open before our eyes (I say the universe)". When and why was the book closed? How did such a tragedy happen?

How do physics theories look like when we recover a complete reason?

We continue the work of philosophers (experimental and mathematical)
reconstructing physics in full compliance with reason. We recover the
unabridged Newton's mechanics, and complete Gauss' relational electromagnetism and Schrödinger's undulatory quantum theory, unifying all of them in one formulation and connecting with psychological and philosophical works and the historical context.

The development of relational electromagnetism after Gauss appears to stop around 1870. Maxwell recognised relational electromagnetism as mathematically equivalent to his own formulae and called for an explanation of why so different conceptions have such a large part in common. We reconstruct relational electromagnetism guided by the No Arbitrariness Principle. Lorenz' idea of electromagnetic waves, together with the "least action principle" proposed by Lorentz are enough to derive Maxwell's equations, the continuity equation and the Lorentz' force. We show that there must be two more symmetries in electromagnetism: a descriptive one expressing source/detector relations, and another relating perceptions of the same source by detectors moving with different (constant) relative velocities. The Poincaré group relates perceived fields by different receivers and Lorentz boosts relate source/detector perceptions. We answer Maxwell's philosophical question showing how similar theories can be abduced using different inferred entities. Each form of abduction implies an interpretation and a facilitation of the theoretical construction.

Magnetic monopoles, hypothetical entities with isolated magnetic charges (Dirac) or effective charges from field configurations (’t Hooft-Polyakov), are posited to symmetrize electromagnetism and explain electric charge quantization, yet remain undetected. This paper demonstrates that such monopoles—Abelian Dirac and non-Abelian ’t Hooft-Polyakov—are incompatible with a potential-centric ontology, where the gauge potential \( A_\mu \), fixed in one true gauge, the Lorenz gauge, is the fundamental physical entity mediating local interactions, as evidenced by the Aharonov-Bohm effect. We derive a no-go result, showing that magnetic monopoles require singular (e.g., Dirac strings) or non-unique (e.g., Wu-Yang patches) potentials in all gauges to resolve a Stokes’ theorem contradiction, violating the ontology’s requirement for unique, non-singular potentials in the true gauge. This result extends to sphalerons in SU(2) \(\times\) U(1) electroweak theory and D-branes in string theory, whose Ramond-Ramond potentials \( C_{p+1} \) exhibit an AB-like effect but require singular or non-unique potentials due to non-zero flux, leading to a theoretical self-contradiction independent of experimental evidence. In contrast, cosmic strings, with a non-singular, single-valued \( A_\mu \) in a single gauge, satisfying Stokes’ theorem and the ontology’s criteria. Instantons and skyrmions are compatible as non-physical or emergent constructs, and emergent monopoles in spin ice, producing flux in an effective field, are also consistent with the ontology. Our findings explain the absence of magnetic monopoles and baryon number violation in standard electroweak processes, align with experimental null results, and suggest that D-branes’ theoretical inconsistency challenges their physical realizability, offering testable predictions for gauge theories and deepening our understanding of their ontological implications.

In electromagnetics, the term magnetic field refers to two distinct but closely related vector fields: magnetic flux density B and magnetic field intensity H. These fields differ in how they account for the medium and magnetization M. In a vacuum, they are related by 𝑩 = 𝜇 0 𝑯. In a magnetized material, this relation becomes 𝑩 = 𝜇 0 (𝑯 + 𝑴). Within the framework of the World-Universe Cosmology (WUC), the Cosmic Medium (CM)-comprising protons, electrons, photons, neutrinos, and Universe-Created Particles (UCPs)-acts as a universal agent governing all physical processes and is inherently a magnetized medium. UCPs, conceptualized as DIRAC dipoles formed by Dirac's magnetic monopoles, possess a magnetic dipole moment proportional to the Bohr magneton. Any local concentration of DIRACs within any material, including CM, induces both a magnetization field M and a magnetic field intensity H. This approach to magnetic fields within WUC offers a framework for explaining a wide range of observed magnetic phenomena, including the dark magnetic field, the large-scale structure of the Milky Way's magnetic field, and other magnetic effects that are only partially correlated with objects observable in other spectral ranges.

Recibido el 14 de mayo de 2007; aceptado el 4 de septiembre de 2007 By using simple concepts of special relativity and the differential representations of the Faraday and Ampère-Maxwell laws, we deduce their Gelman-Monsivais integral representation. The relativistic transformation laws of the electromagnetic field are also obtained without using tensorial analysis or covariant concepts.

We propose a novel interpretation of electromagnetism as a manifestation of coherence torque—a rotational tension within and between coherence fields arising from phase misalignment across spatial gradients. In contrast to classical formulations which treat electric and magnetic fields as vector quantities transmitted through empty space, this framework grounds electromagnetic behavior in the internal dynamics of informational phase structures.

We introduce the concept of phase torsion, a coherence-based analog to magnetic rotation, wherein the twisting of a coherence field generates the equivalent of magnetic effects, while lateral coherence strain corresponds to electric field phenomena. The Lorentz force is reinterpreted as a local field’s response to imposed gradient torque, not as an external action at a distance but as a relational adjustment under the field’s own retention logic.

By modeling charge as localized asymmetry in phase retention, and current as directional phase drift, we derive electromagnetic interactions from first principles of coherence alignment and torque redistribution. This unifies magnetism and electricity as dual aspects of coherence deformation and rotation, offering new insight into phenomena such as inductance, polarization, and field propagation.

The theory reproduces key results of Maxwell’s equations in limiting cases, but generalizes them within a coherence framework that anticipates non-classical behavior in high-density, nonlinear, or biologically sensitive environments. It also provides a natural mechanism for field coupling, wave propagation, and phase-locked structures like solenoids, nerve signal propagation, and plasma rotation. This reinterpretation lays the groundwork for a coherence-based reformulation of all gauge interactions and electromagnetic field engineering.

This word discusses approximate solutions of linear parabolic equations with initial-boundary conditions. The primary focus is on methods that effectively find such solutions by employing a moving finite difference analog of the differential equation. This approach allows us to formulate an approximate analytical solution, significantly simplifying the computation process. By transitioning from the differential equation to an algebraic equation, we obtain a single equation, the solution of which represents an approximate analytical solution to the original problem. However, to achieve higher accuracy in this solution, we apply additional moving nodes, which enhances the results. By using multipoint moving nodes, we can form a system of algebraic equations, the solution of which provides us with an improved analytical solution. The article also presents numerical experiments that confirm the effectiveness of the proposed method and its advantages over traditional approaches.

Assume we are given an open triangle η. Recently, there has been much interest in the derivation of pseudo-n-dimensional, non-embedded rings. We show that Y ∼ l. This reduces the results of [14] to well-known properties of quasi-regular subgroups. Now this could shed important light on a conjecture of Fourier.

Let Jv ≥ ∞ be arbitrary. Every student is aware that there exists a characteristic and ordered compactly Q-associative, stochastic isometry acting freely on a pseudo-Euclidean, globally Möbius curve. We show that j ⊂ ∥ Ō∥. Here, ellipticity is clearly a concern. Recent developments in non-linear graph theory [45] have raised the question of whether there exists a super-d'Alembert quasi-orthogonal, Siegel function.

We explore a new (simpler) formulation of the electromagnetic 4-force. The result is shown to be expressible using the 4D vector product of ref. [8] (ref. [8] is attached for reference). The electromagnetic 4-force is shown to be expressible as the 4D cross product of the 4-velocity with a 4-vector function Y which combines the E and H field. Maxwell's equations are also expressible in terms of Y.

Este artículo propone una hipótesis interdisciplinaria que integra conceptos de cosmología, teoría cuántica, neurociencia especulativa y teosofía. Se plantea que la conciencia universal (el UNO) podría actuar como agente generador de estados cuánticos fundamentales (quarks) mediante una simbiosis con estructuras conscientes complejas, como los microtúbulos neuronales presentes en la Tierra. Esta generación cuántica no solo contribuiría a la materia observable, sino también a la propia expansión del universo.

Hukum Gauss merupakan salah satu pilar utama dalam elektromagnetisme dan mekanika klasik yang memberikan wawasan mendalam mengenai bagaimana fluks medan listrik atau gravitasi tersebar dalam ruang. Hukum ini dinyatakan dalam bentuk integral yang menggambarkan hubungan antara jumlah total muatan atau massa dalam suatu volume tertutup dengan medan yang dihasilkan di sekelilingnya. Melalui formulasi matematisnya, hukum ini menunjukkan keterkaitan antara sumber muatan atau massa dengan fluks yang melingkupinya, menegaskan prinsip keterhubungan fundamental dalam fisika.

Hukum Gauss merupakan salah satu pilar utama dalam elektromagnetisme dan mekanika klasik yang memberikan wawasan mendalam mengenai bagaimana fluks medan listrik atau gravitasi tersebar dalam ruang. Hukum ini dinyatakan dalam bentuk integral yang menggambarkan hubungan antara jumlah total muatan atau massa dalam suatu volume tertutup dengan medan yang dihasilkan di sekelilingnya. Melalui formulasi matematisnya, hukum ini menunjukkan keterkaitan antara sumber muatan atau massa dengan fluks yang melingkupinya, menegaskan prinsip keterhubungan fundamental dalam fisika.

Hukum Gauss merupakan salah satu pilar utama dalam elektromagnetisme dan mekanika klasik yang memberikan wawasan mendalam mengenai bagaimana fluks medan listrik atau gravitasi tersebar dalam ruang. Hukum ini dinyatakan dalam bentuk integral yang menggambarkan hubungan antara jumlah total muatan atau massa dalam suatu volume tertutup dengan medan yang dihasilkan di sekelilingnya. Melalui formulasi matematisnya, hukum ini menunjukkan keterkaitan antara sumber muatan atau massa dengan fluks yang melingkupinya, menegaskan prinsip keterhubungan fundamental dalam fisika.

Hukum Gauss merupakan salah satu pilar utama dalam elektromagnetisme dan mekanika klasik yang memberikan wawasan mendalam mengenai bagaimana fluks medan listrik atau gravitasi tersebar dalam ruang. Hukum ini dinyatakan dalam bentuk integral yang menggambarkan hubungan antara jumlah total muatan atau massa dalam suatu volume tertutup dengan medan yang dihasilkan di sekelilingnya. Melalui formulasi matematisnya, hukum ini menunjukkan keterkaitan antara sumber muatan atau massa dengan fluks yang melingkupinya, menegaskan prinsip keterhubungan fundamental dalam fisika.

Hukum Gauss merupakan salah satu pilar utama dalam elektromagnetisme dan mekanika klasik yang memberikan wawasan mendalam mengenai bagaimana fluks medan listrik atau gravitasi tersebar dalam ruang. Hukum ini dinyatakan dalam bentuk integral yang menggambarkan hubungan antara jumlah total muatan atau massa dalam suatu volume tertutup dengan medan yang dihasilkan di sekelilingnya. Melalui formulasi matematisnya, hukum ini menunjukkan keterkaitan antara sumber muatan atau massa dengan fluks yang melingkupinya, menegaskan prinsip keterhubungan fundamental dalam fisika.

This study focuses on an in-depth exploration of the characteristics of light propagation velocity in a moving medium. The traditional argumentation based on the relativistic velocity addition principle for the Fizeau experiment constitutes an approximate proof with certain limitations (where the medium's moving velocity v << c). To overcome this dilemma, we have constructed a physical model distinct from the traditional relativistic velocity addition principle, taking into full consideration the wave-particle duality of light, particularly its particle-like nature. This model vividly illustrates the dynamic process of photon movement within the medium and the interactions between photons and medium molecules. Through this model, we can visually observe how photons exchange energy with the medium under the influence of an electric field and conduct an in-depth analysis of how changes in the relative velocities between photons and the electric field, as well as between photons and the medium, collectively affect the propagation velocity of light in the medium. It clearly presents the mechanical landscape of interactions among the electric field, photons, and the medium. To verify this physical model, we simulated the motion of a small ball within the medium using a computer, accurately calculating the ball's velocity and comparing it with the theoretical predictions based on the Fizeau experiment. The simulation results align perfectly with the theoretical predictions, strongly supporting the validity of our proposed model. This study innovatively provides a proof that does not require approximation, representing a significant breakthrough compared to the traditional approximate argumentation (where the medium's moving velocity v << c) based on the relativistic velocity addition principle for the Fizeau experiment. This research deepens our understanding of the propagation velocity of light in a moving medium. The clear mechanical landscape facilitates the analysis and calculation of energy exchange between light and the medium, particularly offering new research perspectives and methods for application fields that require precise control of light energy.

Hukum Gauss merupakan salah satu prinsip fundamental dalam elektromagnetisme dan gravitasi yang menyatakan bahwa fluks medan listrik atau gravitasi melalui suatu permukaan tertutup sebanding dengan jumlah muatan atau massa di dalamnya. Lebih dari sekadar hukum fisika, Hukum Gauss mencerminkan keteraturan, simetri, dan keterhubungan mendasar dalam alam semesta. Artikel ini mengeksplorasi Hukum Gauss dari perspektif ilmiah dan filsafat, serta menggali konteks historis di balik rumusannya oleh Carl Friedrich Gauss. Melalui lensa epistemologi, hukum ini dipahami tidak hanya sebagai hasil eksperimen, melainkan juga sebagai pengetahuan sintetis a priori sebagaimana dikemukakan oleh Kant, yang menekankan struktur kognitif manusia dalam memahami realitas. Dalam pandangan Platonik, hukum ini merupakan jendela terhadap dunia ide yang lebih tinggi. Pembahasan ini juga mengaitkan hukum Gauss dengan konsep simetri dalam fisika modern, teori informasi, dan entropi, serta relevansinya dalam kosmologi dan teori medan kuantum. Artikel ini menegaskan bahwa penemuan Gauss tidak hanya lahir dari kejeniusannya, tetapi juga dari jejaring pengetahuan dan pengaruh personal dalam kehidupannya. Dengan demikian, Hukum Gauss bukan hanya kerangka ilmiah dalam fisika, tetapi juga refleksi mendalam tentang bagaimana manusia mengonstruksi pengetahuan dan memahami tatanan semesta.

Kata kunci: Hukum Gauss, fluks, simetri, epistemologi, Carl Friedrich Gauss, filsafat sains

The author found that magnetic fields can be measured using the ampere force on a small current element, or using a small loop current coil. Using a small loop coil current measurement actually measures the average magnetic field on the loop. Under quasi-static or magnetic quasi-static conditions, the average magnetic field measured on the loop and the magnetic field measured using a linear current element are the same. Two definitions are equivalent. There are also two methods for measuring magnetic fields for changing currents or alternating electromagnetic fields using a small coil and a linear current element. The magnetic field obtained from the measurement of alternating magnetic field by a small coil on the loop under quasi-static or magnetic quasi-static conditions is the same as that obtained from the measurement of linear current element. We usually say that a magnetic field is the curl of a vector potential. More precisely, the average magnetic field defined on the loop is the curl of the vector potential. Regardless of whether the average magnetic field is under quasi-static conditions or under magnetic quasi-static conditions, it remains the same as the magnetic field measured by the linear current element. Therefore, we can say that a magnetic field is the curl of a vector potential. But this no longer holds true in the case of radiated electromagnetic fields. For radiated electromagnetic fields, it refers to the retarded electromagnetic field. The average electromagnetic field measured on the loop and the magnetic field measured by the linear current element are different. Therefore, for electromagnetic waves, it is incorrect for the curl of the magnetic vector potential to be the magnetic field. The curl of the magnetic vector potential corresponds to the average magnetic field on the loop. This article describes the author's discovery. The author's discovery stems from the mutual energy theorem proposed by the author in 1987. People argue that this theorem is not an energy theorem, but a reciprocity theorem. In 2017, the author successfully proved that this theorem is indeed the energy theorem and developed it into the law of conservation of energy. The author further proposed the theorem of mutual energy flow. The author believes that mutual energy flow transfer the electromagnetic energy and it is the photon. The author believes that self energy flow does not transfer energy and should radiate reactive power. That is to say, electromagnetic waves should be reactive power. This indicates that the electric and magnetic fields of electromagnetic waves should maintain a 90 degree phase difference, rather than being in phase. We know that according to Maxwell's electromagnetic theory, the electric and magnetic fields of electromagnetic waves are in phase. This indicates that the energy conservation law and the mutual energy flow theorem proposed by the author conflict with Maxwell's electromagnetic theory. Thus, a loophole in Maxwell's electromagnetic theory was discovered. This vulnerability is a confusion between the average magnetic field measured on a circular coil and the magnetic field measured with a straight wire. The average magnetic field on a loop is completely different from the magnetic field on a straight wire. The original definition of a magnetic field was defined by a linear current element or straight wire. This has led to a problem with the definition of the magnetic field for radiating electromagnetic waves in Maxwell's electromagnetic theory. This issue requires us to revise some of Maxwell's radiation electromagnetic field theory.

The research shows that the theory of quasi-static electromagnetic field and the theory of radiated electromagnetic field satisfying Maxwell's equation are two different systems. In these two systems, the definition formula of electric field and magnetic field is identical. The author found that the physical meaning of the definition of the electric field is the same. But the meaning of the definition of magnetic field is different. The author puts forward two new axioms of electromagnetic field theory, (1) N current elements should satisfy the law of conservation of energy. (2) The energy of electromagnetic radiation should not overflow the universe. The theory of quasi-static electromagnetic field can well satisfy these two laws. However, the theory of radiated electromagnetic field satisfying Maxwell's equation does not satisfy these two electromagnetic field laws. These two electromagnetic field laws are self-evident. It is also related. As long as one is true, the other is also true. The conflict between the theory of satisfying Maxwell's equation and these two laws shows that Maxwell's electromagnetic theory has problems. The author first thought that maybe the electromagnetic wave is a wave of reactive power, that is, the electric field and magnetic field of the electromagnetic wave maintain a 90-degree phase difference. The average value of energy transmitted by this wave is 0. However, Maxwell's equation does not support this kind of wave, so the author adds time reversal wave to Maxwell's electromagnetic theory. The time reversal wave causes the reverse collapse of the electromagnetic wave. In this way, electromagnetic waves will not overflow the universe. The propagation of electromagnetic wave energy can be completed by mutual energy flow. The author believes that the mutual energy flow is photon. Recently, the author studied the energy flow transfer from the primary coil to the secondary coil of the transformer. Studying the energy flow transfer from the transmitting antenna to the receiving antenna, it is found that the electromagnetic wave should be reactive power, otherwise it is difficult to establish the physical model of the receiving electromagnetic wave. Therefore, the author began to replace the concept of reverse collapse of electromagnetic wave with reactive power electromagnetic wave. Recently, the author studied the measurement of magnetic field and found that the quasi-static magnetic field can be measured by ring current or straight wire. The values obtained by the two methods are identical. However, for the magnetic field of electromagnetic wave, the measurement with ring antenna and straight-wire antenna has different phases. If the correct method for measuring magnetic field should be straight-wire antenna rather than circular current antenna, then the definition of magnetic field of electromagnetic wave must be revised. The author revised the definition of magnetic field of electromagnetic wave. After the revision, the two laws of electromagnetic field proposed by the author were satisfied. The author believes that the definition of magnetic field of electromagnetic wave in Maxwell's electromagnetic theory is wrong. However, the definition of electric field in Maxwell's electromagnetic wave theory is still valid. This ensures that Maxwell's electromagnetic theory is still correct for most engineering problems. Because the reception of electromagnetic waves mainly involves the induced electromotive force, which is only related to the electric field and has nothing to do with the definition of magnetic field. The problems caused by this defect of Maxwell's theory are mainly problems related to wave-particle duality. The correction of this defect leads us to correctly explain the collapse of waves, the shape of photons, quantum entanglement and other phenomena. If the electromagnetic wave is a reactive power wave, in fact, the wave of other particles, such as the wave of electrons satisfies Schrodinger equation and Dirac equation, may also be reactive power. In short, due to the modification of the definition of magnetic field of electromagnetic wave, the definition of many physical quantities will be affected.

A short view on the electromagnetic mass source's problem is sketched in association with the complex space's framework. Within this framework two of the electrodynamic' Maxwell equations were completed by some new imaginary terms. Finally, it has been shown how a single electron moving in the complex 'paraspace' interacts with itself rendering, in such a way, an additional resistance to its motion.

We propose a novel canonical formulation of general relativity that promotes the local freedom in clock synchronization to a gauge symmetry, thereby establishing a consistent, physically meaningful definition of time. Unlike conventional coordinate time reparameterizations, which only relabel time without affecting physical clocks, the proposed gauge transformation alters the mapping from coordinate time to proper time, thereby affecting physical clock synchronization. To enforce local invariance, we introduce a compensating gauge field that renders the ADM lapse and shift gauge invariant. This yields a gauge-invariant time evolution vector and an intrinsic time variable in quantum gravity that deparameterizes the Hamiltonian constraint and restores unitary evolution. In addition, we show that our formulation resolves the cosmological constant problem, modifies Maxwell's equations, and produces concrete, testable predictions.

This article by French mathematical researcher Guy Duhaut (1948-2024) explores the use of quaternionic and Clifford algebra structures in the formulation of spherical spinors and their applications in quantum mechanics. The author reformulates classical vector calculus and Maxwell’s equations using the quaternionic field "H", distinguishing between polar and axial vectors. This approach simplifies the angular decomposition of the Laplacian and leads to a natural emergence of spherical spinors as eigenfunctions of angular momentum operators.

Key contributions include:

- **Quaternionic Reformulation**: Vector calculus is expressed using quaternions, allowing a more unified treatment of rotations and spinorial actions.
- **Spherical Spinors**: These are introduced as quaternion-valued eigenfunctions of the angular momentum operator L. They generalize Pauli spinors and are used to expand functions on the sphere.
- **Dirac Equation**: The Dirac operator is constructed in a Clifford algebra framework. Plane wave solutions and their helicities are analyzed, and the equation is solved in the presence of a Coulomb potential using spherical spinor expansions.
- **Fine Structure and Zeeman Effect**: The fine structure of hydrogen-like atoms is derived without introducing imaginary units to make radial functions real. The Zeeman effect is studied in both weak and strong magnetic fields, recovering known results like the Paschen–Back and Lorentz triplets.
- **Transition Integrals**: The article provides detailed computations of radial and spherical integrals for electromagnetic transitions, including selection rules and approximations up to second order in perturbation theory.

The work is mathematically rigorous and bridges abstract algebraic structures with concrete physical applications, particularly in atomic and quantum field theory.

Einstein's theory of relativity was based on the horizontal interference experiments of Michelson and Morley in 1887, which showed no shift in the interference fringes. The null result of these experiments allowed Einstein to postulate the speed of light as a constant in an absolute empty vacuum that has no physical structure. We present new experiments with the Leonov linear rotor vertical interferometer which consistently showed a shift of interference fringes in the amount of 74 fringes per one rotation of the rotor in the vertical plane of the Earth's gravitational field. The effect of gravity on the change in the electromagnetic field of laser radiation was discovered and registered. For the first time, a direct method of converting the gravitational field into an electrical signal using the light interference method was used to record the time-varying intensity of the Earth's gravitational field and its oscillations. These new experiments by Leonov on the interference of light in the Earth's gravitational field undermine the foundations of Einstein's theory of relativity, which has failed its main experimental test. 23 pages, 20 figures.

Malgré l’avènement de nouveaux matériaux, Les aciers fer-carbone restent d’une importance capitale pour le monde industriel. Les matériaux sont le foyer de multitudes de défauts lors de leurs élaborations ainsi que lors de leurs exploitations sous l’action de la fatigue, de la corrosion et des accidents. Le contrôle non destructif est utilisé pour déceler dans une pièce sans la détériorer et en respectant son intégrité toute particularité de sa structure pouvant avoir une influence sur son comportement en service. L&#39;inspection visuelle est la plus simple de toutes les techniques du contrôle non destructif. Des défauts extérieurs peuvent être indiqués par des méthodes pénétrantes ou magnétiques. Les défauts internes sont mis en évidence par les ultrasons ou la radiographie. L’objet de ce travail est d’étudier la méthode de contrôle par courants de Foucault afin d’évaluer ses performances dans l’industrie

Este artículo de investigación deriva una generalización no lineal de las ecuaciones de Maxwell a partir de un enfoque variacional, cuando la acción mide la variabilidad del tensor métrico. El espacio propio es un espacio de Weyl, donde la derivada covariante del tensor métrico no necesita desaparecer. La ley de fuerza de Lorentz se deriva de las mismas métricas que una ecuación geodésica. Se muestra que la densidad de carga obedece a una ecuación de onda covariante, lo que indica que la densidad de carga es un campo que se propaga a la velocidad de la luz. Este punto de vista promueve la imagen ondulatoria del electrón. Los resultados indican que la ecuación de Dirac también es una ecuación geométrica. Como la fuerza electrodinámica, es decir, la fuerza de Lorentz, se puede relacionar directamente con la estructura métrica del espacio-tiempo, conduce directamente a la explicación del fenómeno de Zitterbewegung y también de las ondas mecánicas cuánticas.

Quantum mechanics has ruled the sub-atomic realm for over a century, asserting that the laws governing sub-atomic particles differ from those prevailing at the macro level. The implementation of wave-particle duality, the Schrodinger wave equation and its associated wavefunction have eclipsed all other schools of thought with regard to the sub-atomic realm. Now Augmented Newtonian Dynamics (AND), challenges this outlook and implements Newtonian Dynamics at the sub-atomic level by stating that photons are not created externally to the electron as excitations of the electromagnetic field but rather are produced internally within the electron as a means of mediating its energy. This new paradigm of photon production enables the production and emission of photons at rates that comply with the latest findings through the observation of optical atomic clocks indicating that electrons emit photons in the hundreds of trillions per second. This has enabled the explanation of every branch of physics, not through the inaccurate, and esoteric implementation of wave-functions but through the easily understood and calculable classical physics paradigms. In this paper the conduction of electricity and the formation of radio-waves is discussed.

Se presenta el modelo Kronos, una propuesta que organiza las cuatro interacciones fundamentales basadas en partículas preónicas​
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La dinámica de las entidades LuCron se describe mediante una Lagrangiana con términos no locales y operadores de derivadas fraccionarias, lo que da lugar a emergentes efectos gravitacionales y perfiles de densidad compatibles con observaciones de curvas de rotación galáctica y anisotropías del CMB. El flujo de RG conduce a un punto fijo estable λ*≈10⁻

Además, el modelo hace predicciones falsas: exceso de potencia en multipolos altos del CMB (ℓ>2000), resonancias fraccionarias en el LHC (mK∼2–5 TeV), y un pico secundario en el espectro de ondas gravitacionales primordiales (f∼10⁻² Hz) accesible a LISA y al Einstein Telescope. Así, LuCron ofrece un marco coherente que integra teoría de cuerdas, gravedad cuántica de bucles y datos observacionales, abriendo nuevas vías para la unificación y la física más allá del Modelo Estándar.

Las propuestas aquí presentadas, distribuidas a lo largo de cuatro capítulos temáticos (Energía Hidrocinética y Resonancia Rankine, Modelado Cuántico-MHD y Reactores Compactos de Cuasifusión, Ecuaciones de Campo de Einstein y Modelado FEM en 15 Dimensiones y Control Adaptativo e Inteligencia Artificial en Sistemas Físicos),  no pretenden ser respuestas definitivas, sino instrumentos conceptuales abiertos a la revisión, crítica y puesta a prueba. Invocamos la participación activa de instituciones académicas, organizaciones públicas y privadas, y actores especializados en campos interrelacionados con la Física Fundamental, la energía aplicada, la dinámica de fluidos, los sistemas cuánticos y el control adaptativo.

Este legado se ofrece como un conjunto articulado de hipótesis modeladas rigurosamente, cuya validación dependerá de entornos de ensayo experimental bien estructurados. El llamado está hecho: abrir fronteras de conocimiento implica articular teoría, cálculo y prototipado físico con visión científica y ética profesional.

Arterial stiffness is an important biomarker for many cardiovascular diseases. Shear wave elastography is a recent technique aimed at estimating local arterial stiffness using guided wave inversion (GWI), i.e. matching the computed and measured wave dispersion. This paper develops and validates a new GWI approach by synthesizing various recent observations and algorithms: (a) refinements to signal processing to obtain more accurate experimental dispersion curves; (b) an efficient forward model to compute theoretical dispersion curves for immersed, incompressible cylindrical waveguides; (c) an optimization framework based on the recent observation that the measured dispersion curve is multimodal, i.e. it matches for not one but two different wave modes in two different frequency ranges. The resulting inversion approach is validated using extensive experimental data from rubber tube phantoms, not only for modulus estimation but also to simultaneously estimate modulus and wall thickness. The observations indicate that the modulus estimates are best performed with the information on wall thickness. The approach, which takes less than half a minute to run, is shown to be accurate, with the modulus estimated with less than 4% error for 70% of the experiments.