The force law of classical electrodynamics: Lorentz versus einstein and laub

Research output: Chapter in Book/Report/Conference proceedingConference contribution

12 Scopus citations


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.

Original languageEnglish (US)
Title of host publicationOptical Trapping and Optical Micromanipulation X
StatePublished - Dec 11 2013
EventOptical Trapping and Optical Micromanipulation X - San Diego, CA, United States
Duration: Aug 25 2013Aug 29 2013

Publication series

NameProceedings of SPIE - The International Society for Optical Engineering
ISSN (Print)0277-786X
ISSN (Electronic)1996-756X


OtherOptical Trapping and Optical Micromanipulation X
CountryUnited States
CitySan Diego, CA


ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics
  • Computer Science Applications
  • Applied Mathematics
  • Electrical and Electronic Engineering

Cite this

Mansuripur, M. (2013). The force law of classical electrodynamics: Lorentz versus einstein and laub. In Optical Trapping and Optical Micromanipulation X [88100K] (Proceedings of SPIE - The International Society for Optical Engineering; Vol. 8810).