Electromagnetic momentum density in matter solved

Optical Force Measurement. Credit: eecs.northwestern.edu

"(PhysOrg.com) -- Researchers from the NIST Center for Nanoscale Science and Technology and the University of British Columbia have shown that the interaction between a light pulse and a light-absorbing object, including the momentum transfer and resulting movement of the object, can be calculated for any positive index of refraction using a few, well-established physical principles combined with a new model for mass transfer from light to matter."

Electromagnetic radiation, like light, carries momentum and can transfer its momentum to matter via radiation pressure. In the past century, there has been a controversy over the correct form of the electromagnetic momentum density in matter.

There was two forms:

•  In the “Minkowski formulation,” the momentum density is proportional to the index of refraction;
• in direct contrast, the “Abraham formulation” finds it to be inversely proportional. 

And the two equations for the momentum in a dielectric with refractive index n are:

• The Minkowski version:

• The Abraham version:

where h is the Planck constant, ν is the frequency of the light and c is the speed of light in vacuum.

In 2011, an optical experiment was performed to study this problem based on first principles. It tested the velocity-addition formula of light in a reversed Fizeau experiment. The result was that the light speed c= 299,792,458m/s in vacuum of Lorentz transformation should be replaced by c/n to describe electrodynamic phenomena in a dielectric medium^[1] Consequently, the momentum of a photon in vacuum is p=E/c and the value should be p=E/(c/n)=nE/c in media, although it is not measured directly.^[2] It is asserted, that this confirms Minkowski's formulation.

[1] Wang Zhong-Yue, Wang Pin-Yu, Xu Yan-Rong (2011). "Crucial experiment to resolve Abraham-Minkowski Controversy". Optik 122 (22): 1994–1996. doi:10.1016/j.ijleo.2010.12.018

[2] Wang, Zhong-Yue. Graphene, neutrino mass and oscillation. arXiv:/0909.1856

The recently published in Applied Physics support the Abraham formulation: Revisiting the Balazs thought experiment in the presence of loss: electromagnetic-pulse-induced displacement of a positive-index slab having arbitrary complex permittivity and permeability, K. J. Chau and H. J. Lezec, Applied Physics A 105, 267-281 (2011).

"The researchers propose a set of postulates for light-matter interaction that encompass: a) the Maxwell equations, which govern classical electromagnetic behavior; b) a generalized Lorentz force law, which describes the force felt by matter in the presence of an electromagnetic field; c) a model for electromagnetic mass density transfer to an absorbing medium; and d) the Abraham formulation of momentum density. Using both closed-form calculations and numerical simulations of the interaction between an electromagnetic pulse and a test slab, the researchers demonstrated that their postulates yield results that are consistent with conservation of energy, mass, momentum, and center-of-mass velocity at all times." ( PhysOrg)

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