Constraining Validity of the Minkowski Energy-Momentum Tensor

TL;DR

This paper evaluates the validity of the Minkowski energy-momentum tensor in dielectric media, providing conditions for its safe use and comparing its predictions with experimental results and the Abraham tensor.

Contribution

It derives specific conditions under which the simplified Minkowski tensor can be reliably used, clarifying its limitations and compatibility with experimental data.

Findings

The Minkowski tensor's simplified form is valid under certain conditions.

The proposed conditions ensure conservation of angular momentum.

Predictions using the Minkowski tensor agree with experimental results when conditions are met.

Abstract

There exist two popular energy-momentum tensors for an electromagnetic wave in a dielectric medium. The Abraham expression is robust to experimental verification but more mathematically demanding, while the Minkowski expression is the foundation of a number of simplifications commonly found within the literature, including the relative refractive index transformation often used in modelling optical tweezers. These simplifications are based on neglecting the Minkowski tensor's material counterpart, a process known to be incompatible with conservation of angular momentum, and in conflict with experimental results, yet they are very successful in a wide range of circumstances. This paper combines existing constraints on their usage with recent theoretical analysis to obtain a list of conditions which much be satisfied to safely use the simplified Minkowski approach. Applying these conditions to an experiment proposed by Padgett et al., we find their prediction in agreement with that obtained using the total energy-momentum tensor.