"Fully covariant radiation force on a polarizable particle" - Reply to the Comment by Volokitin and Persson

TL;DR

This paper clarifies and reconciles different theoretical approaches to calculating the electromagnetic radiation force on a moving polarizable particle, emphasizing the role of evanescent waves and Lorentz contraction.

Contribution

It demonstrates the agreement among various theories on the force due to evanescent waves and discusses the impact of unit choices and integral transformations on the results.

Findings

Theories agree on evanescent wave contributions to the force.

Differences in propagating photon contributions are identified.

Lorentz contraction plays a key role in force calculations.

Abstract

We argue that the theories of Volokitin and Persson [Comment arXiv:1405:2525], of Dedkov and Kyasov [J. Phys.: Condens. Matter 20 (2008) 354006], and Pieplow and Henkel [New J. Phys. 15 (2013) 023027] agree on the electromagnetic force on a small, polarizable particle that is moving parallel to a planar, macroscopic body, as far as the contribution of evanescent waves is concerned. The apparent differences are discussed in detail and explained by choices of units and integral transformations. We point out in particular the role of Lorentz contraction in the procedure used by Volokitin and Persson, where a macroscopic body is "diluted" to get the force on a small particle. Differences that appear in the contribution of propagating photons are briefly mentioned.