arXiv subjects

Michael E. Crenshaw

Publications and source records attributed to Michael E. Crenshaw.

At least 19 recordsLinked to original sources

arXiv2022

Conservation of energy and momentum for an electromagnetic field propagating into a linear medium from the vacuum

The form of the energy-momentum tensor when a quasimonochromatic field propagates into and through an antireflection-coated, sourceless, transparent, continuous, linear magneto-dielectric medium, initially at rest in the local frame, remains controversial. The Minkowski energy-momentum tensor is the main component of the electromagnetic conservation law. It has been known for over a century that the electromagnetic conservation law is unsound as evidenced by alternative energy-momentum tensors that have been proposed to ameliorate known physical deficiencies (violation of conservation of angular and linear momentum) and by the various material energy-momentum tensors and coupling forces that have been introduced to repair or complete the law. The extant resolution is to treat the continuum electromagnetic system as a subsystem and add a phenomenological material subsystem energy-momentum tensor. We show that the four-divergence of the total, electromagnetic plus material, energy-momentum tensor produces an energy continuity theorem in which the two non-zero terms depend on different powers of the refractive index $n$. Then the extant resolution of the Abraham-Minkowski controversy is self-inconsistent.

physics.optics↗

arXiv2022

Alternative formulation of the macroscopic field equations in a linear magneto-dielectric medium: Lagrangian field theory and spacetime setting

A transparent linear magneto-dielectric material in free space that is illuminated by a finite quasimonochromatic field is a thermodynamically closed system, definitively, regardless of what field and material subsystems that one defines. The energy--momentum tensor that is formally derived from the Maxwell--Minkowski field equations is inconsistent with both angular and linear momentum conservation in this closed system; this very solid fact is the foundational and continuing issue of the Abraham--Minkowski controversy. The extant resolution of the Abraham--Minkowski dilemma is to treat Maxwellian continuum electrodynamics as being a subsystem and to write the total energy--momentum tensor as the sum of a Maxwellian electromagnetic subsystem energy--momentum tensor and a phenomenological material subsystem energy--momentum tensor. We prove that fundamental principles of physics are violated by Maxwellian continuum electrodynamics and that fundamental principles of physics are violated by Maxwellian continuum electrodynamics supplemented by the material subsystem conjecture. We use field theory to derive legitimate equations for macroscopic electromagnetic fields in a transparent linear magneto-dielectric medium. The new field equations are a part of a self-consistent formulation of macroscopic electrodynamics, conservation laws, special relativity, and invariance in a continuous linear medium. In the new formulation, the temporal and spatial coordinates are renormalized by the continuous linear medium instead of the permittivity and permeability being carried as independent material parameters. Then an isotropic, homogeneous, flat, four-dimensional, continuous, linear, non-Minkowski spacetime is the proper setting for the continuum electrodynamics of a simple linear medium in which the effective speed of light is $c/n$ and each medium will be associated with a different spacetime.

physics.class-ph↗

arXiv2019

Alternative formulation of the macroscopic field equations in a linear magneto-dielectric medium: Field equations

We derive an alternative formulation of the field equations for macroscopic electromagnetic fields in a linear magneto-dielectric medium as an identity of the Maxwell--Minkowski equations, complementing a variety of other representations including the Ampère, Chu, Lorentz, and Minkowski formulations of continuum electrodynamics. In the new formulation of the macroscopic field equations, the material properties are carried as a renormalization of the temporal and spatial coordinates instead of as independent material constants. The new representation of the field equations raises some interesting physical issues with relativity and boundary conditions.

physics.class-ph↗

arXiv2019

Application of axiomatic formal theory to the Abraham--Minkowski controversy

We treat continuum electrodynamics as an axiomatic formal theory based on the macroscopic Maxwell--Minkowski equations applied to a thermodynamically closed system consisting of an antireflection-coated block of a simple linear dielectric material situated in free-space that is illuminated by a quasimonochromatic field. We prove that valid theorems of the formal theory of Maxwellian continuum electrodynamics are inconsistent with conservation laws for the inviscid incoherent flow of non-interacting particles (photons) in the continuum limit (light field) in the absence of external forces, pressures, or constraints. We also show that valid theorems of Maxwellian continuum electrodynamics are contradicted by the refractive index-independent Lorentz factor of von Laue's application of Einstein's special relativity to a dielectric medium. Obviously, the fundamental physical principles in the vacuum are not affected. However, the extant theoretical treatments of electrodynamics, special relativity, and energy--momentum conservation must be regarded as being mutually inconsistent in a simple linear dielectric in which the effective speed of light is $c/n$. Having proven that the established applications of fundamental physical principles to dielectric materials lead to mutually inconsistent theories, we derive, from first principles, a mutually consistent, alternative theoretical treatment of electrodynamics, special relativity, and energy--momentum conservation in an isotropic, homogeneous, linear dielectric-filled, flat, non-Minkowski, continuous material spacetime.

physics.optics↗

arXiv2019

Representation Independent Boundary Conditions for a Piecewise-Homogeneous Linear Magneto-dielectric Medium

At a boundary between two transparent, linear, isotropic, homogeneous materials, derivations of the electromagnetic boundary conditions and the Fresnel relations typically proceed from the Minkowski {E,B,D,H} representation of the macroscopic Maxwell equations. However, equations of motion for macroscopic fields in a transparent linear medium can be written using Ampere {E,B}, Chu {E,H}, Lorentz, Minkowski, Peierls, Einstein-Laub, and other formulations of continuum electrodynamics. We present a representation-independent derivation of electromagnetic boundary conditions and Fresnel relations for the propagation of monochromatic radiation through a piecewise-homogeneous, transparent, linear, magneto-dielectric medium. The electromagnetic boundary conditions and the Fresnel relations are derived from energy conservation coupled with the application of Stokes's theorem to the wave equation. Our representation-independent formalism guarantees the general applicability of the Fresnel relations. Specifically, the new derivation is necessary so that a valid derivation of the Fresnel equations exists for alternative, non-Minkowski formulations of the macroscopic Maxwell field equations.

physics.class-ph↗

arXiv2019

Reconciliation of the Rosen and Laue theories of special relativity in a linear dielectric medium

The theory of dielectric special relativity was derived by Laue from a fundamental physical basis in Einstein's special relativity and the relativistic velocity sum rule. The Laue theory is experimentally verified by the Fizeau water tube experiment. In contrast, the Rosen version of dielectric special relativity was derived heuristically and has no experimental validation. Consequently, the Rosen theory and its consequences are mostly ignored in the scientific literature and there is little to no discussion about the incompatibility of the two theories of relativity in a dielectric. In this article, the Laue theory is developed from boundary conditions using inertial reference frames moving at constant velocity along the interface between a simple linear dielectric medium and the vacuum. Then, the Rosen theory is derived in the context of inertial frames of reference moving at constant velocity in the interior of an arbitrarily large linear isotropic homogeneous dielectric medium. These derivations show that the Laue and Rosen theories of dielectric special relativity are both correct but have different regimes of applicability. The Rosen theory applies to physics in the interior of a simple linear dielectric and the Laue theory is used to relate these physics to a Laboratory Frame of Reference in the vacuum where measurements can be performed.

physics.class-ph↗

arXiv2017

The total energy--momentum tensor for electromagnetic fields in a dielectric

There are various formulations of energy--momentum tensors for an electromagnetic field in a linear dielectric. The total energy--momentum tensor, comprised of electromagnetic and material components, must be unique. We discuss the construction of the total energy--momentum tensor and the associated conservation laws.

physics.optics↗

arXiv2016

The Role of Conservation Principles in the Abraham--Minkowski Controversy

The Abraham--Minkowski controversy refers to a long-standing inability to adequately address certain issues involving the conservation of the momentum of an electromagnetic field in a linear dielectric medium. We apply the usual assumption of a material subsystem that couples to the electromagnetic subsystem such that the total energy and total momentum are conserved. We then construct the total energy--momentum tensor from the total energy density and the total momentum density. Applying conservation principles to the total energy--momentum tensor, we construct the tensor energy--momentum continuity equation. We show that one of the components of the tensor energy--momentum continuity equation, the energy continuity equation, is manifestly false. We conclude that the Abraham--Minkowski controversy is unresolvable because the extant principles of conservation are inconsistent in a simple linear dielectric medium.

physics.optics↗

arXiv2015

Photon Momentum in Linear Dielectric Media

According to the scientific literature, the momentum of a photon in a simple linear dielectric is either $\hbarω/(nc)$ or $n\hbarω/c$ with a unit vector ${\bf \hat e}_k$ in the direction of propagation. These momentums are typically used to argue the century-old Abraham--Minkowski controversy in which the momentum density of the electromagnetic field in a dielectric is either the Abraham momentum density, ${\bf g}_A={\bf E}\times{\bf H}/c$, or the Minkowski momentum density, ${\bf g}_M={\bf D}\times{\bf B}/c$. The elementary optical excitations, photons, are typically known as polaritions in the particular case of light traveling in a dielectric medium. Applying the relativistic energy formula, we find that the total momentum that is attributable to a polariton in a dielectric is $\hbarω{\bf \hat e}_k/c$ corresponding to a total momentum density ${\bf g}_T=n{\bf E}\times{\bf B}/c$.

physics.optics↗

arXiv2015

Continuum electrodynamics and the Abraham--Minkowski momentum controversy

Continuum electrodynamics is an axiomatic formal theory based on the macroscopic Maxwell equations and the constitutive relations. We apply the formal theory to a thermodynamically closed system consisting of an antireflection coated block of dielectric situated in free-space and illuminated by a quasimonochromatic field. We show that valid theorems of the formal theory are proven false by relativity and by conservation laws. Then the axioms of the formal theory are proven false at a fundamental level of mathematical logic. We derive a new formal theory of continuum electrodynamics for macroscopic electric and magnetic fields in a four-dimensional flat non-Minkowski material spacetime in which the speed of light is c/n.

physics.optics↗

arXiv2015

Continuum Electrodynamics of a Piecewise-Homogeneous Linear Medium

The energy--momentum tensor and the tensor continuity equation serve as the conservation laws of energy, linear momentum, and angular momentum for a continuous flow. Previously, we derived equations of motion for macroscopic electromagnetic fields in a homogeneous linear dielectric medium that is draped with a gradient-index antireflection coating (J. Math Phys. 55, 042901 (2014) ). These results are consistent with the electromagnetic tensor continuity equation in the limit that reflections and the accompanying surface forces are negligible thereby satisfying the condition of an unimpeded flow in a thermodynamically closed system. Here, we take the next step and derive equations of motion for the macroscopic fields in the limiting case of a piecewise-homogeneous simple linear dielectric medium. The presence of radiation surface forces on the interface between two different homogeneous linear materials means that the energy--momentum formalism must be modified to treat separate homogeneous media in which the fields are connected by boundary conditions at the interfaces. We demonstrate the explicit separation of the total momentum into a field component and a material motion component, we derive the radiation pressure that transfers momentum from the field to the material, we derive the electromagnetic continuity equations for a piecewise homogeneous dielectric, and we provide a lucid reinterpretation of the Jones and Richards experiment.

physics.class-ph↗

arXiv2015

Energy-Momentum Tensor for the Electromagnetic Field in a Dielectric

The total momentum of a thermodynamically closed system is unique, as is the total energy. Nevertheless, there is continuing confusion concerning the correct form of the momentum and the energy-momentum tensor for an electromagnetic field interacting with a linear dielectric medium. Here we investigate the energy and momentum in a closed system composed of a propagating electromagnetic field and a negligibly reflecting dielectric. The Gordon momentum is easily identified as the total momentum by the fact that it is, by virtue of being invariant in time, conserved. We construct continuity equations for the energy and the Gordon momentum and use the continuity equations to construct an array that has the properties of a traceless, diagonally symmetric energy-momentum tensor. Then the century-old Abraham-Minkowski momentum controversy can be viewed as a consequence of attempting to construct an energy-momentum tensor from continuity equations that contain densities that correspond to nonconserved quantities.

physics.optics↗

arXiv2015

Electromagnetic Energy, Momentum, and Angular Momentum in an Inhomogeneous Linear Dielectric

In a previous work, Optics Communications 284 (2011) 2460--2465, we considered a dielectric medium with an anti-reflection coating and a spatially uniform index of refraction illuminated at normal incidence by a quasimonochromatic field. Using the continuity equations for the electromagnetic energy density and the Gordon momentum density, we constructed a traceless, symmetric energy--momentum tensor for the closed system. In this work, we relax the condition of a uniform index of refraction and consider a dielectric medium with a spatially varying index of refraction that is independent of time, which essentially represents a mechanically rigid dielectric medium due to external constraints. Using continuity equations for energy density and for Gordon momentum density, we construct a symmetric energy--momentum matrix, whose four-divergence is equal to a generalized Helmholtz force density four-vector. Assuming that the energy-momentum matrix has tensor transformation properties under a symmetry group of space-time coordinate transformations, we derive the global conservation laws for the total energy, momentum, and angular momentum.

physics.optics↗

arXiv2015

Electromagnetic momentum and the energy-momentum tensor in a linear medium with magnetic and dielectric properties

In a continuum setting, the energy-momentum tensor embodies the relations between conservation of energy, conservation of linear momentum, and conservation of angular momentum. The well-defined total energy and the well-defined total momentum in a thermodynamically closed system with complete equations of motion are used to construct the total energy-momentum tensor for a stationary simple linear material with both magnetic and dielectric properties illuminated by a quasimonochromatic pulse of light through a gradient-index antireflection coating. The perplexing issues surrounding the Abraham and Minkowski momentums are bypassed by working entirely with conservation principles, the total energy, and the total momentum. We derive electromagnetic continuity equations and equations of motion for the macroscopic fields based on the material four-divergence of the traceless, symmetric total energy-momentum tensor. We identify contradictions between the macroscopic Maxwell equations and the continuum form of the conservation principles. We resolve the contradictions, which are the actual fundamental issues underlying the Abraham-Minkowski controversy, by constructing a unified version of continuum electrodynamics that is based on establishing consistency between the three-dimensional Maxwell equations for macroscopic fields, the electromagnetic continuity equations, the four-divergence of the total energy-momentum tensor, and a four-dimensional tensor formulation of electrodynamics for macroscopic fields in a simple linear medium.

physics.optics↗

arXiv2014

The Theory of Electrodynamics in a Linear Dielectric

We adopt the continuum limit of a linear, isotropic, homogeneous, transparent, dispersion-negligible dielectric of refractive index $n$ and examine the consequences of the effective speed of light in a stationary dielectric, $c/n$, for D'Alembert's principle and the Lagrange equations. The principles of dynamics in the dielectric-filled space are then applied to the electromagnetic Lagrangian and we derive equations of motion for the macroscopic fields. A direct derivation of the total energy--momentum tensor from the field strength tensor for the electromagnetic field in a dielectric is used to demonstrate the utility of the new theory by resolving the century-old Abraham--Minkowski electromagnetic momentum controversy in a way that preserves the principles of conservation of energy, conservation of linear momentum, and conservation of angular momentum.

physics.class-ph↗

arXiv2013

Decomposition of the Total Electromagnetic Momentum in a Linear Dielectric into Field and Matter Components

The long-standing resolution of the Abraham--Minkowski electromagnetic momentum controversy is predicated on a decomposition of the total momentum of a closed continuum electrodynamic system into separate field and matter components. Using a microscopic model of a simple linear dielectric, we derive Lagrangian equations of motion for the electric dipoles and show that the dielectric can be treated as a collection of stationary simple harmonic oscillators that are driven by the electric field and produce a polarization field in response. The macroscopic energy and momentum are defined in terms of the electric, magnetic, and polarization fields that travel through the dielectric together as a pulse of electromagnetic radiation. We conclude that both the macroscopic energy and the macroscopic momentum are entirely electromagnetic in nature for a simple linear dielectric in the absence of significant reflections.

physics.optics↗

arXiv2012

Electromagnetic momentum in a dielectric and the energy--momentum tensor

The Abraham--Minkowski momentum controversy is the outwardly visible symptom of an inconsistency in the use of the energy-momentum tensor in the case of a plane quasimonochromatic field in a simple linear dielectric. We show that the Gordon form of the electromagnetic momentum is conserved in a thermodynamically closed system. We regard conservation of the components of the four-momentum in a thermodynamically closed system as a fundamental property of the energy--momentum tensor. Then the first row and column of the energy--momentum tensor is populated by the electromagnetic energy density and the Gordon momentum density. We derive new electromagnetic continuity equations for the electromagnetic energy and momentum that are based on the Gordon momentum density. These continuity equations can be represented in the energy-momentum tensor using a material four-divergence operator in which temporal differentiation is performed with respect to ct/n.

physics.class-ph↗

arXiv2009

Electrodynamics in a Filled Minkowski Spacetime with Application to Classical Continuum Electrodynamics

Minkowski spacetime is a convenient setting for the study of the relativistic dynamics of particles and fields in the vacuum. In order to study events that occur in a dielectric or other linear medium, we adopt the familiar continuum assumption of a linear, isotropic, homogeneous, transparent medium of refractive index n filling all space and seek the principle of relativity that applies in the filled spacetime. Applying the Einstein postulates with c/n as the speed of light, we show how the effective signal velocity results in a scaling of the proper time by the refractive index and examine the consequences for D'Alembert's principle, the Lagrange equations, and the canonical momentum field. The principles of dynamics in the filled spacetime are then applied to the electromagnetic Lagrangian and we derive equations of motion that are invariant with respect to a material Lorentz transformation. The new representation of the dynamics of macroscopic fields is shown to be consistent with the equal-time commutation relation for quantized macroscopic fields, quantum--classical correspondence, the principle of superposition, and electromagnetic boundary conditions.

physics.class-ph↗