Resolution of the Abraham-Minkowski debate: Implications for the electromagnetic wave theory of light in matter

Abstract

A century has now passed since the origins of the Abraham-Minkowski controversy pertaining to the correct form of optical momentum in media. Experiment and theory have been applied at both the classical and quantum levels in attempt to resolve the debate. The result of these efforts is the identification of Abraham’s kinetic momentum as being responsible for the overall center of mass translations of a medium and Minkowski’s canonical or wave momentum as being responsible for translations within or with respect to a medium. In spite of the recent theoretical developments, much confusion still exists regarding the appropriate theory required to predict experimental outcomes and to develop new applications. In this paper, the resolution of the longstanding Abraham-Minkowski controversy is reviewed. The resolution is presented using classical electromagnetic theory and logical interpretation of experiments disseminated over the previous century. Emphasis is placed on applied physics applications: modeling optical manipulation of cells and particles. Although the basic interpretation of optical momentum has been resolved, there is still some uncertainly regarding the complete form of the momentum continuity equation describing electromagnetics. Thus, while a complete picture of electrodynamics has still yet to be fully interpreted, this correspondence should help clarify the state-of-the-art view.

Photon momentum transfer in inhomogeneous dielectric mixtures and induced tractor beams

“…25, the exchange of momentum between light and matter, and therefore, the forces exerted on objects, is still dependent on the particularities of the situation. 24,27,29 Experimental results suggest that when an interface is present, the Minkowski formula should be used to correctly obtain the related optical force 14 (see Section 2 in Supplementary Information for details).…”

“…After a century of debate, it is not yet known which stress tensor (ST), force law and photon momentum scheme in matter are most appropriate to use in this scenario (e.g., Table I in Ref. 24). It appears that because the identification of an adequate 'particle momentum' is quite ambiguous and challenging, 31 the recent resolution of the Abraham-Minkowski dilemma 25 still cannot adequately address the question of the appropriate ST and force law to be employed in complex (mixed) backgrounds.…”

“…These questions motivate us to investigate the fundamental physics governing the momentum transfer from light to a particle within an inhomogeneous (mixed) background medium, which invokes the Abraham-Minkowski controversy. [23][24][25][26][27][28][29][30] In general, both Minkowskian 24,28,29 and non-Minkowskian 10,30 formulations have been proposed for the measurement of the optical momentum transfer from a homogeneous background to an embedded particle. After a century of debate, it is not yet known which stress tensor (ST), force law and photon momentum scheme in matter are most appropriate to use in this scenario (e.g., Table I in Ref.…”

“…25, the exchange of momentum between light and matter, and therefore, the forces exerted on objects, is still dependent on the particularities of the situation. 24,27,29 Experimental results suggest that when an interface is present, the Minkowski formula should be used to correctly obtain the related optical force 14 (see Section 2 in Supplementary Information for details).As illustrated in Figure 1a, the changes in the momentum of the light rays from air to water through the scatterer itself can be calculated by summing up the momentum change associated with each refraction. As a close approximation, only two refractions, corresponding to DP ray 5DP ray,1 1DP ray,2 (see Section 1 in Supplementary Information for details), are considered: DP ray,1 5P 0 (T 1 A 1t 1R 1 A 1r 2A 1i ) and DP ray,2 5P 0 (T 1 T 2 A 2t 1T 1 R 2 A 2r 2T 1 A 1t ).…”

Axiomatic Geometrical Optics, Abraham-Minkowski Controversy, and Photon Properties Derived Classically

“…The traditional arguments can be found in reviews like Refs. [56][57][58][59][60][61][62] and references therein, too numerous to be listed in this paper. Let us mention only briefly that two alternative forms of the PDM momentum are adopted most commonly,…”