Exposing ‘‘hidden momentum’’

Comay, E.

doi:10.1119/1.18452

Cited by 24 publications

(17 citation statements)

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“…Note also that the last term of Eq. (19), associated with the force experienced by M, simply eliminates the contribution of the hidden momentum o × .…”

Section: Electromagnetic Force and Momentummentioning

confidence: 99%

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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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“…Note also that the last term of Eq. (19), associated with the force experienced by M, simply eliminates the contribution of the hidden momentum o × .…”

Section: Electromagnetic Force and Momentummentioning

confidence: 99%

“…Returning to Eq. (19), the symmetry between P and M may be restored if we rewrite the final expression as…”

Section: Electromagnetic Force and Momentummentioning

confidence: 99%

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

Mansuripur

2014

Frontiers in Optics 2014

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“…This work points out the significance of the energy-momentum tensor of physical fields. For example, the Shockley-James hidden momentum enigma [1] has been settled by means of this tensor, which provides explicit expressions that show the required momentum balance [3].…”

Section: Discussionmentioning

confidence: 99%

“…Their analysis relies on general conservation properties of the energy-momentum tensor. Later, Comay analyzed the energy-momentum tensor of the Shockley and James system [3]. This analysis proves that an explicit mechanical linear momentum exists in the system.…”

Section: Introductionmentioning

confidence: 86%

On the Significance of the Fields’ Energy-Momentum Tensor

Comay¹

2019

PSIJ

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This work discusses the significance of the energy-momentum tensor of physical fields of an elementary particle. The Noether theorem shows how this tensor can be derived from the Lagrangian density of a given field. This work proves that the energy-momentum tensor can also be used for a consistency test of a field theory. The results show that the Dirac Lagrangian density of a spin-1/2 massive particle yields consistent results. On the other hand, problems exist with the present structure of quantum electrodynamics, and with quantum fields of massive particles that are described by a second order differential equation. All problematic results are confirmed by an independent analysis.

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“…The torque and angular momentum densities in the Lorentz formulation may be determined by cross-multiplying the position vector r into Eq. (14). We will have…”

Section: Electromagnetic Torque and Angular Momentummentioning

confidence: 99%

Force, torque, linear momentum, and angular momentum in classical electrodynamics

Mansuripur

2017

Appl. Phys. A

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Abstract. The classical theory of electrodynamics is built upon Maxwell's equations and the concepts of electromagnetic (EM) field, force, energy, and momentum, which are intimately tied together by Poynting's theorem and by the Lorentz force law. Whereas Maxwell's equations relate the fields to their material sources, Poynting's theorem governs the flow of EM energy and its exchange between fields and material media, while the Lorentz law regulates the back-andforth transfer of momentum between the media and the fields. An alternative force law, first proposed by Einstein and Laub, exists that is consistent with Maxwell's 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 magnetized medium, the Einstein-Laub (E-L) formulation of EM force and torque does not invoke hidden entities under such circumstances. Moreover, total force/torque exerted by EM fields on any given object turns out to be independent of whether the density of force/torque is evaluated using the law of Lorentz or that of Einstein and Laub. Hidden entities aside, the two formulations differ only in their predicted force and torque distributions inside matter. Such differences in distribution are occasionally measurable, and could serve as a guide in deciding which formulation, if either, corresponds to physical reality.

show abstract

Exposing ‘‘hidden momentum’’

Cited by 24 publications

References 0 publications

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

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

On the Significance of the Fields’ Energy-Momentum Tensor

Force, torque, linear momentum, and angular momentum in classical electrodynamics

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