Analysis of the Abraham-Minkowski Controversy by Means of Two Simple Examples

Using a very simple example, H. M. Lai [1] argued in favor of Abraham's proposal for defining electromagnetic field momentum density. Later, using another simple device, Johnson et al. [2] argued in favor of Minkowski's proposal. This indicates that the Abraham-Minkowski controversy remains open. Both models consider nonmagnetic media ( = 1). In this work we analyze both models pointing out some weak points and extend the analysis to magnetic media ( 1). We show that in this case Minkowski's proposal is better than Abraham's. Our analysis throws some light on this very old controversy.     

Division of the energy and of the momentum of electromagnetic waves in linear media into electromagnetic and material parts

We defend a natural division of the energy density, energy flux and momentum density of electromagnetic waves in linear media in electromagnetic and material parts. In this division, the electromagnetic part of these quantities have the same form as in vacuum when written in terms of the macroscopic electric and magnetic fields, the material momentum is calculated directly from the Lorentz force that acts on the charges of the medium, the material energy is the sum of the kinetic and potential energies of the charges of the medium and the material energy flux results from the interaction of the electric field with the magnetized medium. We present reasonable models for linear dispersive non-absorptive dielectric and magnetic media that agree with this division. We also argue that the electromagnetic momentum of our division can be associated with the electromagnetic relativistic momentum, inspired on the recent work of Barnett [Phys. Rev. Lett. 104 (2010) 070401] that showed that the Abraham momentum is associated with the kinetic momentum and the Minkowski momentum is associated with the canonical momentum.     

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.     

Long Series in Mechanics: Janzen–Rayleigh Expansion for a Circle

We reconsider the transonic controversy – whether a given airfoil can exhibit a continuous range of shock-free supersonic flow. We employ the circle as our airfoil, and examine the Janzen–Rayleigh expansion in even powers of the free-stream Mach number, which we previously carried to 29 terms. In addition to expressing doubt about our previous conclusions, we introduce a promising modification of the graphical ratio test of Domb and Sykes.Sommario.In questo lavoro si prende nuovamente in considerazione la controversia transonica, e cioè la questione se un dato profilo alare possa presentare una sequenza continua di configurazioni di flusso localmente supersonico senza onde d'urto. Quale profilo alare consideriamo il cerchio ed esaminiamo lo sviluppo in serie di Janzen–Rayleigh secondo le potenze pari del numero di Mach asintotico, serie di cui avevamo in precedenza considerato 29 termini. Oltre ad esprimere dubbi riguardo alle nostre precedenti conclusioni, introduciamo una promettente modifica del test del rapporto noto come grafico di Domb e Sykes.     

Decomposition of the total 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 total energy and the macroscopic total momentum are entirely electromagnetic in nature for a simple linear dielectric in the absence of significant reflections.     

The role of solvent models in stabilizing nonclassical ions

A molecular dynamics simulation is performed for a system of classical and nonclassical 2-norbornyl cations surrounded by a model solvent. Comparison of the energies of stabilization of the two ions due to the model solvent medium indicates that the difference in stabilization energies of the two ions is less than 1 kcal/mol.     

Once Upon a Time in Physics When Both Mathematics and Experiment Were Helpless: A Strange Life of Voltaic Contact Potential

This paper aims to answer the question of why the debate over the voltaic contact effect was so prolonged without a consensus during the nineteenth century. I propose that both experiment and mathematics were helpless to decide who was right. To demonstrate this, I will focus on the voltaic debates between James Clerk Maxwell and the Maxwellians, on the one hand, and William Thomson and the Thomsonians, on the other, and examine ten points: (1) the fundamental assumption, (2) the seat of the voltaic potential difference, (3) the role of the contact, (4) the magnitude of the potentials of two contacted metals, (5) the definition of potential, (6) the electrostatic measurement, (7) the thermoelectric measurement, (8) the physical interpretation of the same mathematical formula, (9) experiments in different media, and (10) experiments in the vacuum – all of which were in dispute between the Thomsonian and Maxwellian parties. I show that the two parties differed in theory, in the interpretation of measured data, in the physical interpretation of mathematical relationship, and in what they believed would constitute a crucial experiment. I assert that the Maxwellian and Thomsonian voltaic theories were incommensurable, but that this incommensurability was not exactly symmetrical because it mainly resided on the side of William Thomson.     

Relativistic analysis of the dielectric Einstein box: Abraham, Minkowski and total energy-momentum tensors

We analyse the “Einstein box” thought experiment and the definition of the momentum of light inside matter. We stress the importance of the total energy-momentum tensor of the closed system (electromagnetic field plus material medium) and derive in detail the relativistic expressions for the Abraham and Minkowski momenta, together with the corresponding balance equations for an isotropic and homogeneous medium. We identify some assumptions hidden in the Einstein box argument, which make it weaker than it is usually recognized. In particular, we show that the Abraham momentum is not uniquely selected as the momentum of light in this case.