Anisotropy of Mass and Generalization of Hamilton’s OpticoMechanical Analogy

Abstract

This article attempts to introduce the concept of mass as a tensor quantity, in contrast to the conventional view of mass as a scalar. It is shown that, in general, mass exhibits the property of anisotropy. The reduced optico-mechanical analogy of Hamilton, which can be applied to all scales of describing the motion of material bodies, is extended to the case of mass anisotropy. Examples from cosmology and condensed matter physics (quasiparticles) are considered, and a justification for such a generalization is provided.