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

Vanzella, Daniel A. T.

doi:10.1103/physrevlett.110.089401

Cited by 36 publications

(70 citation statements)

References 9 publications

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“…As was the case with the EM force discussed in Sec.5, the total EM torque exerted on an isolated object always turns out to be the same in the Lorentz and Einstein-Laub formulations; any differences between the two approaches can be reconciled by subtracting the contributions of the hidden angular momentum density, × ( o × ), from the Lorentz torque [26][27][28].…”

Section: Electromagnetic Torque and Angular Momentummentioning

confidence: 84%

The Force Law of Classical Electrodynamics: Lorentz versus Einstein and Laub

Mansuripur

2014

Frontiers in Optics 2014

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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 backand-forth transfer of momentum between the media and the fields. As it turns out, an alternative force law, first proposed in 1908 by Einstein and Laub, exists that is consistent with Maxwell's macroscopic equations and complies with the conservation laws as well as with the requirements of special relativity. While the Lorentz law requires the introduction of hidden energy and hidden momentum in situations where an electric field acts on a magnetic material, the Einstein-Laub formulation of electromagnetic force and torque does not invoke hidden entities under such circumstances. Moreover, the total force and the total torque exerted by electromagnetic fields on any given object turn out to be independent of whether force and torque densities are evaluated using the Lorentz law or in accordance with the Einstein-Laub formulas. Hidden entities aside, the two formulations differ only in their predicted force and torque distributions throughout material media. Such differences in distribution are occasionally measurable, and could serve as a guide in deciding which formulation, if either, corresponds to physical reality.

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Section: Electromagnetic Torque and Angular Momentummentioning

confidence: 84%

The Force Law of Classical Electrodynamics: Lorentz versus Einstein and Laub

Mansuripur

2014

Frontiers in Optics 2014

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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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“…Concluding remarks. It has been argued by some that the Lorentz force should be treated as a 4-vector if momentum conservation and the principles of special relativity are to be upheld [11][12][13][14]. While this is possible (and helpful) in some instances, it is impracticable in many other situations where alternative inertial frames cannot be identified.…”

Section: Magnetized Ring Carrying a Radially-directed Electric Currentmentioning

confidence: 99%

The Lorentz Force Law and its Connections to Hidden Momentum, the Einstein–Laub Force, and the Aharonov–Casher Effect

Mansuripur¹

2014

IEEE Trans. Magn.

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The Lorentz force of classical electrodynamics, when applied to magnetic materials, gives rise to hidden energy and hidden momentum. Removing the contributions of hidden entities from the Poynting vector, from the electromagnetic momentum density, and from the Lorentz force and torque densities simplifies the equations of the classical theory. In particular, the reduced expression of the electromagnetic force-density becomes very similar (but not identical) to the Einstein-Laub expression for the force exerted by electric and magnetic fields on a distribution of charge, current, polarization and magnetization. Examples reveal the similarities and differences among various equations that describe the force and torque exerted by electromagnetic fields on material media. An important example of the simplifications afforded by the Einstein-Laub formula is provided by a magnetic dipole moving in a static electric field and exhibiting the Aharonov-Casher effect.

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

Cited by 36 publications

References 9 publications

The Force Law of Classical Electrodynamics: Lorentz versus Einstein and Laub

The Force Law of Classical Electrodynamics: Lorentz versus Einstein and Laub

Theory of radiation pressure on magneto–dielectric materials

The Lorentz Force Law and its Connections to Hidden Momentum, the Einstein–Laub Force, and the Aharonov–Casher Effect

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