Classical Physics

Φ Geometry in Physics: a Single Angle for SR, Energy—momentum, and Numerical Stability

Authors: Mikheili Mindiashvili
Comments: 3 Pages. (Note by ai.viXra.org Admin: Author name should be listed after the title; please cite and list sceintific references)

Φ geometry is a visual re-parameterization of standard relativistic relations via one angle φ on a unit (or c-scaled) circle. One diagram unifies β, γ, E, p and velocity addition. Complementarity (sin ↔ cos) removes "bad denominators" and makes edge cases numerically stable.
Category: Classical Physics

Lorentz-Covariant Hamiltonian Mechanics and its Quantization

Authors: Steven Kenneth Kauffmann
Comments: Pages.

The Lorentz-covariant upgrade of Newton's Second Law sets a particle's mass times the second derivative with respect to its Lorentz-invariant proper time of its observed space-time location equal to the four-force applied to it. Hamiltonian mechanics yields the Lorentz-covariant upgrade of Newton's Second Law when the Hamiltonian is a Lorentz-invariant function of the particle's observed space-time location and conjugate four-momentum, and the time derivatives of these two Lorentz-covariant four-vectors are taken with respect to the particle's Lorentz-invariant proper time. Very simple Lorentz-invariant Hamiltonians that yield the electromagnetic Lorentz Force Law and the gravitational geodesic equation are pointed out, as is the straightforward quantization of Lorentz-covariant Hamiltonian mechanics. The zero-mass limit of the relativistic free-particle Schrödinger equation has the simple second-order wave-equation form which is characteristic of source-free electromagnetism. The relativistic correction to the hydrogen atom without spin is a very weak, short-range complement to the Coulomb potential.
Category: Classical Physics

Solutions to Exercises in Hestenes’s Geometric Algebra Treatment of Constant-Acceleration (Parabolic) Motion

Authors: James A. Smith
Comments: 13 Pages.

As an aid to teachers and students who are learning to apply Geometric Algebra (GA) to high-school-level physics, this fi nal installment in our guide to David Hestenes’s treatment of constant-acceleration motion provides detailed solutions to the associated exercises in Hestenes’s book New Foundations for Classical Mechanics.
Category: Classical Physics

[ Exploration on The] Misconception of Work and Energy Conservation

Authors: Amrinder Singh Sohi
Comments: 22 Pages.

As we know, the work done formula that the world uses nowadays is the Force dot product of displacement (i.e. W = F.d). But there aresome contradictions which are found. The work done formula which we use nowadays is not universally applicable. There are only some special cases where this formula is applicable . In this research paper we will find wherethis formula has failed. So the actually universally applicable formula is Force multiplied by time (i.e. W = Ft).
Category: Classical Physics

The Zitter Electron Model and the Anomalous Magnetic Moment

Authors: Oliver Consa
Comments: 18 Pages.

We introduce a classical geometric model of the electron in which a primary circular Zitterbewegung motion with radius equal to the Compton radius is combined with a secondary helical component to generate a toroidal—solenoidal structure for the internal charge and current distributions. Within this geometry, weconstruct electromagnetic fields consistent with the local helical kinematics and evaluate the associated energy density, momentum flow, and current density over the toroidal volume. These quantities uniquely determine the minor radius r = R√(2α/π). The resulting magnetic moment reproduces μB and yields a correction factorg =√(1 + α/π). The analysis suggests that several intrinsic properties of the electron may admit a coherent interpretation in terms of an underlying toroidal electromagnetic geometry.
Category: Classical Physics

Analysis on Aerodynamic Characteristics of WIG : Proposal of New Green’s Function Considering Water Wave Generation Caused by Aerial Vortices

Authors: Tsutomu Hori, Manami Hori
Comments: 30 Pages. 11 Figures, 108 Equations, 10 References. Published on the Bulletin of Nagasaki Institute of Applied Science in Japan, 2026 (January), Vol.65, No.2, pp.49~78, https://nias.repo.nii.ac.jp/records/2000124

In this paper, a Green’s function considering water wave generation caused by aerial vortices is proposed. The new function is derived in the form that the influence of pressure fluctuations on the water surface is reflected by using the Fourier transform method.

By performing an asymptotic analysis for the Green’s function, it is shown that the high-speed flow field due to an aerial vortex can be represented by placing a slightly weaker vortex at the mirror image position under the water surface. As a result, asymptotic wave profiles at the high speed swells up in the neighborhood of WIG.

Furthermore, the lift force and wave-making resistance acting on the WIG are analyzed based on the momentum theorem, and thereby smart calculation formulae are presented for the two forces. Based on the developed theory, specific numerical calculations of aerodynamic forces and water wave profiles are performed for NACA airfoils as an example of thick wings. Thereby a certain amount of knowledge was obtained about the water surface effects of WIG.
Category: Classical Physics

Motion of a Particle on a Catenary Curve: A Lagrangian Mechanics Approach with Elliptic Integral Solutions

Authors: Luv Gupta
Comments: 6 Pages. (Note by viXra Admin: Please cite and list scientific references)

This paper aims to find the motion of a particle that is restricted to move along a catenary curve. The method used to find the dynamics of the particle , we use Lagrangian mechanics along with elliptical integrals to find solve the obtained equation of motion for time. We transform the kinetic and potential energies one generalized coordinate, which results in a short Lagrangian formulation.After applying the Euler—Lagrange equation and using lagrange multiplier which shortens it down and helps us to find the constraint force needed helps us to reach to a differential equation i.e., the equation of motion is derived, analyzing the interaction between inertial and gravitational forces. A similar process is carried upon for the particle going on a catenary under influence of gravity and gravity too. The Euler Lagrange Equation is modified for non conservative forces and a equation of motion is derived. Using Lagrangian Mechanics yield a simple and elegant method
Category: Classical Physics

Three Physics Identities; Navigating the Decimal Universe Using the NIST Codata

Authors: Mark A. Thomas
Comments: 4 Pages.

Three possible identities are presented. The identities use physics values from the NIST 2022 CODATA. The Newton constant G is realigned withinCodata against values having more precision, accuracy and lower uncertainties. That the identities match to 7-8 significant figures are a curiosity and is either a coincidence or remains to be explained. It is also made interesting in that two relations incorporate similar physics values.
Category: Classical Physics

Gravity Emerges from the Continuous Absorption of Virtual Energy Particles, Which Are Required to Maintain the Electron’s Fixed State Within an Atom

Authors: Sanjay Shah, Yashvi Shah
Comments: 12 Pages.

Gravity has traditionally been described by two prevailing paradigms: (1) Newton's law of universal gravitation as an attractive force (Newton, 1687), and (2) Einstein's general theory of relativity, which interprets gravity as the curvature of spacetime (Einstein, 1915). Although these frameworks adeptly account for numerous macroscopic observations, they fall short in explaining gravitational phenomena at quantum scales. To date, no empirical evidence for quantum gravity has been observed, and the postulated graviton—integral to extensions of the Standard Model of particle physics—remains undetected (Weinberg, 1967). This discrepancy positions gravity as one of the most profound enigmas in contemporary physics.This study introduces a novel model wherein gravity arises from the perpetual absorption of Virtual Energy Particles (VEPs) by atoms, essential for sustaining the stable orbital configuration of electrons. The incessant uptake of these particles induces a directional flux toward the atomic nucleus, manifesting as a gravitational field. Within this paradigm, gravity transcends mere attraction or geometric distortion, emerging instead as a fundamental mechanism for energy redistribution that underpins atomic integrity and cosmic equilibrium.The concept of virtual particles is substantiated by quantum vacuum fluctuations (Heisenberg, 1927), Feynman diagrams in quantum electrodynamics (Feynman, 1949), and empirical phenomena such as the Casimir effect (Casimir, 1948). Diverging from classical mechanics and general relativity, this model conceptualizes gravity as a flux of virtual particles, reconciling quantum microscopic dynamics with macroscopic cosmic behavior. Accordingly, this theory posits that VEPs serve as the primary mediators of gravitational fields and atomic stability, providing a prospective avenue for unifying gravity across disparate scales.
Category: Classical Physics

Let There Be Light in Quantum Theory: A φ-Geometric Model of Relativistic and Cosmological Limits

Authors: Mikheili Mindiashvili
Comments: 15 Pages.

This paper introduces a new geometric model of spacetime, constructed from a right triangle inscribed in a circle. In this construction, the hypotenuse coincides with the diameter of the circle. From this configuration, a universal parameter naturally emerges — the angle φ, which links gravitational effects, relativistic transformations, and quantum transitions. This geometry provides a new way to interpret physical phenomena, ranging from classical cosmology to quantum mechanics. It avoids deep singularities and transforms them into "light" singularities. These milder forms open the way for further physical analysis.
Category: Classical Physics

The Non-Relativistic Bi-Level Electron Model

Authors: Martin Kraus
Comments: 7 Pages. This revision adds clarifying footnotes about the mass distributions represented by the model and the constraint on the speed of the center of charge.

This work presents the bi-level electron model, a quantitative model of a point-like spinning electron, which was inspired by similar classical models of spinning electrons that interpret the Zitterbewegung of Dirac electrons as a spin motion of point-like electrons. The new model is consistent with de Broglie's internal clock hypothesis and other features of a modified Born-Infeld model of electrons, as well as with Larmor precession of the electron spin in a uniform magnetic field. The equations of motion are discussed in non-relativistic approximation, while the relativistic case is left for future work.
Category: Classical Physics