Related papers: Forces from Connes' geometry
We will display the fundamental structure of classical electrodynamics. Starting from the axioms of (1) electric charge conservation, (2) the existence of a Lorentz force density, and (3) magnetic flux conservation, we will derive Maxwell's…
We apply a simple decomposition to the energy of a moving particle. Based on this decomposition, we identify the potential and kinetic energies, then use them to give general definitions of momentum and the various kinds of forces exerted…
Traditionally, Electromagnetism is taught following the chronological development of the matter. The final product of this path is a presentation of Electromagnetism realized by adding one layer over another with the risk of transferring…
The axiomatic structure of the electromagnetic theory is outlined. We will base classical electrodynamics on (1) electric charge conservation, (2) the Lorentz force, (3) magnetic flux conservation, and (4) on the Maxwell-Lorentz spacetime…
We give a detailed description of electrodynamics as an emergent theory from condensed-matter-like structures, not only {\it per se} but also as a warm-up for the study of the much more complex case of gravity. We will concentrate on two…
Connes' non-commutative geometry (NCG) is a generalization of Riemannian geometry that is particularly apt for expressing the standard model of particle physics coupled to Einstein gravity. In a previous paper, we suggested a reformulation…
Some key notions of line geometry are recalled, along with their application to mechanics. It is then shown that most of the basic structures that one introduces in the pre-metric formulation of electromagnetism can be interpreted directly…
We give a critical overview of various attempts to describe gravity as an emergent phenomenon, starting from examples of condensed matter physics, to arrive to more sophisticated pregeometric models. The common line of thought is to view…
We derive the Lorentz self force for an arbitrarily moving charged particle via averaging the retarded fields. The derivation is simple and at the same time pedagogically accessible. We obtain the radiation reaction for a charged particle…
Starting from the generalised London equations, which include a gravitomagnetic term, the gravitational and the electromagnetic properties of superconductors are derived. A phenomenological synthesis of those properties is proposed.
We present a 3-dimensional model for massive gravity with masses induced by topological (Chern-Simons) and Proca-like mass terms. Causality and unitarity are discussed at tree-level. Power-counting renormalizability is also contemplated.
Using the weak field approximation, we can express the theory of general relativity in a Maxwell-type structure comparable to electromagnetism. We find that every electromagnetic field is coupled to a gravitoelectric and gravitomagnetic…
Connes' notion of non-commutative geometry (NCG) generalizes Riemannian geometry and yields a striking reinterepretation of the standard model of particle physics, coupled to Einstein gravity. We suggest a simple reformulation with two key…
This study proposes that all the known fundamental forces including gravity may be described by local gauge theories. Gravitational, electroweak, and strong interactions on length scales from 10^{-33} cm to 10^{28} cm are systematically…
This review presents an overview of various kinds of models -- physical, abstract, mathematical, visual -- that can be used to present the concepts and applications of Einstein's general theory of relativity at the level of undergraduate…
Electromagnetic force and torque are typically derived from a stress tensor in conjunction with Maxwell's equations of classical electrodynamics. In some instances, the Principle of Least Action (built around a Lagrangian) can be used to…
If potential energy is the timelike component of a four-vector, then there must be a corresponding spacelike part which would logically be called the potential momentum. The potential four-momentum consisting of the potential momentum and…
The fallacies associated with the gauge concept in electromagnetism are illustrated. A clearer and more valid formulation of the basics of classical electromagnetism is provided by recognizing existing physical constraints as well as the…
The purpose of this course is to provide an introduction to Electromagnetic Theory. The foundations of electrodynamics starting from the nature of electrical force up to the level of Maxwell equations solutions are presented. It starts with…
In the first part of the present work, we focus on the theory of gravitoelectromagnetism (GEM), and we derive the full set of equations and constraints that the GEM scalar and vector potentials ought to satisfy. We discuss important aspects…