A Note On Galilean Invariants In Semi-Relativistic (original) (raw)

Unifying the Galilei and the Special Relativity II: the Galilei Electrodynamics

viXra, 2015

Using the concept of absolute time introduced in a previous work \cite{carvalho} we define two coordinate systems for spacetime, the Galilean and the Lorentzian systems. The relation between those systems allows us to develop a tensor calculus that transfer the Maxwell electrodynamics to the Galilean system. Then, by using a suitable Galilean limit, we show how this transformed Maxwell theory in the Galilei system results in the Galilei electrodynamics formulated by Levy Leblond and Le Bellac.

From Galilean covariance to Maxwell equations: A thermodynamic insight to electromagnetism

international symposium on electromagnetic theory, 2013

Galilean electromagnetism is derived from a thermodynamic approach. Attention is paid on various regimes allowed by the quasistatic limit. It is emphasized that classical definition of electro-quasi-stationary and magneto-quasi-static regimes does not cover all the low-frequency case studies. As suggested by the thermodynamic approach of electromagnetism, it is proposed to: 1) discuss the validity of the regimes at the device scale and 2) derive the set of equations underlying the regimes from the variations of the magnetic and electrostatic powers instead of the magnitudes of the magnetic flux density and the electric field.

Galilean Covariance versus Gauge Invariance

Eprint Arxiv 0912 2360, 2009

We demonstrate for the first time and unexpectedly that the Principle of Relativity dictates the choice of the "gauge conditions" in the canonical example of a Gauge Theory namely Classical Electromagnetism. All the known "gauge conditions" of the literature are interpreted physically as electromagnetic continuity equations hence the "gauge fields". The existence of a Galilean Electromagnetism with TWO dual limits ("electric" and "magnetic") is the crux of the problem [1]. A phase-space with the domains of validity of the various "gauge conditions" is provided and is shown to depend on three characteristic times : the magnetic diffusion time, the charge relaxation time and the transit time of electromagnetic waves in a continuous medium [2].

Relativistic Invariance of Electromagnetic Fields and Maxwell's Equations in Theory of Electrodynamics

Relativistic Invariance of Electromagnetic Fields and Maxwell’s Equations in Theory of Electrodynamics, 2023

We reexamined the four-dimensional spacetime formulation of invariance of electromagnetic fields between two inertial frames under Lorentz transformation, which predicts a pure electric (magnetic) field in one inertial frame is composed the Cartesian components of a pure both electric and magnetic fields in another inertial frame. This contradicts the Lorentz invariance condition which requires that the vector quantities in one inertial frame must have the same form in another inertial frame. In this work, we introduce a three-dimensional quasi-time vector to modify the classical four-dimensional spacetime (3+1) to a new six-dimensional spacetime (3+3) and derive spacetime metric equation and relativistic velocity. We use the classical vector transformation theory to derive expressions for Cartesian components of relativistic velocity and net electromagnetic force vectors. Considering two massive inertial frames form a closed system, we integrated the transformed relativistic velocity with the law of conservation of energy to prove that contrary to the common belief, the electromagnetic field that appears as a purely electric (magnetic) field in one massive inertial frame, it also appears as a pure electric (magnetic) field in another massive inertial frame under Lorentz transformation. As an application of the proposed six-dimensional spacetime theory, we prove Lorentz invariance of Maxwell's equations with and without charge and current source. We also prove the scalar electromagnetic wave equations with and without charge and current source and the conservation laws of the continuity equations of current and densities of electromagnetic energy and linear and angular momentums between two massive inertial frames under Lorentz transformation.

On Galilean invariance and nonlinearity in electrodynamics and quantum mechanics

Physics Letters A, 2001

Recent experimental results on slow light heighten interest in nonlinear Maxwell theories. We obtain Galilei covariant equations for electromagnetism by allowing special nonlinearities in the constitutive equations only, keeping Maxwell's equations unchanged. Combining these with linear or nonlinear Schrödinger equations, e.g. as proposed by Doebner and Goldin, yields a Galilean quantum electrodynamics.

Non-relativistic model of the laws of gravity and electromagnetism, invariant under the change of inertial and non-inertial coordinate systems

2015

Under the classical non-relativistic consideration of the space-time we propose the model of the laws of gravity and Electrodynamics, invariant under the galilean transformations and moreover, under every change of non-inertial cartesian coordinate system. Being in the frames of non-relativistic model of the space-time, we adopt some general ideas of the General Theory of Relativity, like the assumption of invariance of the most general physical laws in every inertial and non-inertial coordinate system and equivalence of factious forces in non-inertial coordinate systems and the force of gravity. Moreover, in the frames of our model, we obtain that the laws of Non-relativistic Quantum Mechanics also invariant under the change of inertial or non-inertial cartesian coordinate system.

On some applications of Galilean electrodynamics of moving bodies

American Journal of Physics, 2007

We discuss the seminal article in which Le Bellac and Lévy-Leblond have identified two Galilean limits of electromagnetism [1], and its modern implications. Recent works have shed a new light on the choice of gauge conditions in classical electromagnetism. We discuss various applications and experiments, such as in quantum mechanics, superconductivity, electrodynamics of continuous media, etc. Much of the current technology, where waves are not taken into account, is actually based on Galilean electromagnetism.

Galilean relativistic fluid mechanics

Continuum Mechanics and Thermodynamics, 2017

Single component nonrelativistic dissipative fluids are treated independently of reference frames and flow-frames. First the basic fields and their balances, then the related thermodynamic relations and the entropy production are calculated and the linear constitutive relations are given. The usual basic fields of mass, momentum, energy and their current densities, the heat flux, pressure tensor and diffusion flux are the time-and spacelike components of the third order mass-momentum-energy density-flux four-tensor. The corresponding Galilean transformation rules of the physical quantities are derived. It is proved, that the non-equilibrium thermodynamic frame theory, including the thermostatic Gibbs relation and extensivity condition and also the entropy production is independent of the reference frame and also the flow-frame of the fluid. The continuity-Fourier-Navier-Stokes equations are obtained almost in the traditional form if the flow of the fluid is fixed to the temperature. This choice of the flow-frame is the thermo-flow. A simple consequence of the theory is that the relation between the total, kinetic and internal energies is a Galilean transformation rule.

From Galilean Covariance to Maxwell Equations: Back to the Quasi-Static Regimes

IEEE Transactions on Magnetics, 2014

Galilean electromagnetism is derived from a thermodynamic approach. Attention is paid on various regimes allowed by the quasi-static limit. It is emphasized that classical definition of electro-quasistationary and magneto-quasistatic regimes does not cover all the low-frequency case studies. As suggested by the thermodynamic approach of electromagnetism, it is proposed (i) to discuss the validity of the regimes at the device scale; and (ii) to derive the set of equations underlying the regimes from the variations of the magnetic and electrostatic powers instead of the magnitudes of the magnetic flux density and the electric field.