Various representations of the quantity Newton called inertial mass

TL;DR

This paper explores different representations of inertial mass within fundamental dynamical equations, offering new insights into its nature by analyzing mass-like parameters for waves and particles.

Contribution

It introduces a unified discussion of inertial mass representations in wave and particle equations, providing a novel perspective on the origin and meaning of inertial mass.

Findings

Mass-like parameters are identified in wave and particle equations.

The physical meaning of these parameters offers new insights into inertial mass.

The study connects fundamental dynamical equations with the concept of inertial mass.

Abstract

Newton introduced the concept of mass in his {\it Principia} and gave an intuitive explanation for what it meant. Centuries have passed and physicists as well as philosophers still argue over its meaning. Three types of mass are generally identified: inertial mass, active gravitational mass and passive gravitational mass. In addition to the question of what role mass plays in dynamical equations and why, the origin of the particular amount of matter associated with an elementary particle as a consequence of fundamental fields has long been a topic of research and discussion. In this paper, various representations of inertial mass are discussed within the framework of fundamental (either Galilean or Poincar\'e invariant) dynamical equations of waves and point particles. It is shown that the derived equations have mass-like and mass parameters for waves and point particles, respectively, and that the physical meaning of these parameters sheds a new light on the fundamental problem of the nature of inertial mass.