Comment on “Trouble with the Lorentz Law of Force: Incompatibility with Special Relativity and Momentum Conservation”

Saldanha, Pablo L.

doi:10.1103/physrevlett.110.089403

Cited by 28 publications

(26 citation statements)

References 17 publications

(31 reference statements)

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“…4 It is by no means straightforward to obtain the Einstein-Laub force density, in particular the final hidden-momentm related term, from the microscopic Lorentz force law and it has been suggested, for this reason, that the latter is incorrect [75]. A relativistic treatment, however, reveals that the required hidden-momentum contribution arises quite naturally from the Lorentz force law [76][77][78][79][80].…”

Section: Momentum Transfer To a Half-space Magneto-dielectricmentioning

confidence: 99%

Theory of radiation pressure on magneto–dielectric materials

Barnett

Loudon

2015

New J. Phys.

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We present a classical linear response theory for a magneto-dielectric material and determine the polariton dispersion relations. The electromagnetic field fluctuation spectra are obtained and polariton sum rules for their optical parameters are presented. The electromagnetic field for systems with multiple polariton branches is quantized in three dimensions and field operators are converted to 1-dimensional forms appropriate for parallel light beams. We show that the field-operator commutation relations agree with previous calculations that ignored polariton effects. The Abraham (kinetic) and Minkowski (canonical) momentum operators are introduced and their corresponding single-photon momenta are identified. The commutation relations of these and of their angular analogues support the identification, in particular, of the Minkowski momentum with the canonical momentum of the light. We exploit the Heaviside-Larmor symmetry of Maxwell's equations to obtain, very directly, the Einsetin-Laub force density for action on a magneto-dielectric. The surface and bulk contributions to the radiation pressure are calculated for the passage of an optical pulse into a semi-infinite sample. c J rr D r Br J rr Er Hr dˆ( )ˆ( )

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Section: Momentum Transfer To a Half-space Magneto-dielectricmentioning

confidence: 99%

Theory of radiation pressure on magneto–dielectric materials

Barnett

Loudon

2015

New J. Phys.

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“…(34), we start from the relativistic formulas for the energy-density ℰ( , ) and momentum-density ( , ) of a point-particle of rest-mass o ( ) and velocity ( ) given in Eqs. (26)(27)(28). Considering that ′ ( ) = 3 • ′ / 2 , we find…”

Section: Appendix Amentioning

confidence: 96%

On the electrodynamics of moving permanent dipoles in external electromagnetic fields

Mansuripur

2014

SPIE Proceedings

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Abstract. The classical theory of electrodynamics is built upon Maxwell's equations and the concepts of electromagnetic field, force, energy and momentum, which are intimately tied together by Poynting's theorem and the Lorentz force law. Whereas Maxwell's macroscopic equations relate the electric and magnetic fields to their material sources (i.e., charge, current, polarization and magnetization), Poynting's theorem governs the flow of electromagnetic energy and its exchange between fields and material media, while the Lorentz law regulates the back-and-forth transfer of momentum between the media and the fields. The close association of momentum with energy thus demands that the Poynting theorem and the Lorentz law remain consistent with each other, while, at the same time, ensuring compliance with the conservation laws of energy, linear momentum, and angular momentum. This paper shows how a consistent application of the aforementioned laws of electrodynamics to moving permanent dipoles (both electric and magnetic) brings into play the rest-mass of the dipoles. The rest mass must vary in response to external electromagnetic fields if the overall energy of the system is to be conserved. The physical basis for the inferred variations of the rest-mass appears to be an interference between the internal fields of the dipoles and the externally applied fields. We use two different formulations of the classical theory in which energy and momentum relate differently to the fields, yet we find identical behavior for the restmass in both formulations.1. Introduction. The electrodynamics of moving media is a complex subject that has been discussed in several papers, textbooks and monographs [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18], yet continues to attract attention for its practical applications as well as its relevance to fundamental issues involving field-matter interactions. In the early days of the 20 th century, Minkowski used ideas from the newly developed theory of relativity to analyze the dynamics of arbitrarily moving bodies in the presence of electromagnetic (EM) fields. He constructed a stress-energy tensor for EM systems that incorporated the electric field E, the magnetic field H, the displacement D, and the magnetic induction B, relating the strength of these fields at each point ( , ) in space-time to the corresponding field strengths in a local rest frame of the material media at ( ′ , ′ ) [1]. Einstein and Laub initially endorsed Minkowski's analysis, and proceeded to summarize his results while presenting them in a less abstract language and in simplified form [2]. Subsequently, Einstein and Laub expressed skepticism of Minkowski's general formula for the ponderomotive force exerted on bodies in the EM field, and presented their own formulation for bodies at rest [3]. In the meantime, Abraham, also relying on notions of relativity and the Lorentz transformation of coordinates and fields between inertial frames, developed a modified version of Minkowski's stress-energy tensor for...

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“…Hidden momentum is a relativistic effect that may lead a magnetic dipole to carry linear momentum in the presence of an electric field even if it is not moving. In the situation described in Mansuripur paradox, there is a "hidden angular momentum" whose time derivative is equal to the torque in each reference frame, so there is no angular acceleration of the dipole and the physical description of the system in the different frames are equivalent [3]. One important lesson derived from Mansuripur paradox is that the validity of the Lorentz force law is thus conditioned to the existence of hidden momentum.…”

Section: Introductionmentioning

confidence: 99%

“…Such an attack to the foundations of the electromagnetic theory obviously called the attention of the scientific community [2]. However, the paradox is solved when the "hidden momentum" of the magnetic dipole is taken into account [3][4][5][6][7]. Hidden momentum is a relativistic effect that may lead a magnetic dipole to carry linear momentum in the presence of an electric field even if it is not moving.…”

Section: Introductionmentioning

confidence: 99%

Hidden momentum in a hydrogen atom and the Lorentz-force law

Filho¹,

Saldanha²

2015

Phys. Rev. A

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By using perturbation theory, we show that a hydrogen atom with magnetic moment due to the orbital angular momentum of the electron has "hidden momentum" in the presence of an external electric field. This means that the atomic electronic cloud has a nonzero linear momentum in its center-of-mass rest frame due to a relativistic effect. This is completely analogous to the hidden momentum that a classical current loop has in the presence of an external electric field. We discuss that this effect is essential for the validity of the Lorentz force law in quantum systems. We also connect our results to the long-standing Abraham-Minkowski debate about the momentum of light in material media.

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Comment on “Trouble with the Lorentz Law of Force: Incompatibility with Special Relativity and Momentum Conservation”

Abstract: A Comment on the Letter by M. Mansuripur, Phys. Rev. Lett. 108, 193901 (2012). The authors of the Letter offer a Reply.

Cited by 28 publications

References 17 publications

Theory of radiation pressure on magneto–dielectric materials

Theory of radiation pressure on magneto–dielectric materials

On the electrodynamics of moving permanent dipoles in external electromagnetic fields

Hidden momentum in a hydrogen atom and the Lorentz-force law

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