Zero-point electromagnetic stress tensor for studying Casimir forces on colloidal particles in media

Abstract

We address the question of the correct electromagnetic stress tensor in media and its consequences for the Casimir force. The latter being due to the zero-point momentum of the electromagnetic field, competing approaches based on the Abraham or Maxwell stress tensor lead to different predictions. We consider the test scenario of two colloidal spherical particles submerged in a dielectric medium and use three criteria to distinguish the two approaches: we show that the Abraham stress tensor, and not the Maxwell stress tensor, leads to a Casimir force that is form-equivalent to Casimir-Polder and van der Waals forces, obeys duality as a fundamental symmetry and is consistent with microscopic many-body calculations. On this basis, we derive general formulas for the dispersion forces on one and between two colloidal particles in arbitrary liquid-media environments in terms of their dipole polarisabilities, allowing for more elaborate theoretical descriptions and bridging the gap between microscopic and macroscopic accounts.