Concepts of inertial, gravitational and elementary particle masses

TL;DR

This paper analyzes the concept of mass within the frameworks of relativity and quantum physics, emphasizing its invariance, the conditions under which mass-energy relations hold, and its role in gravitation and inertia.

Contribution

It clarifies the conditions and limitations of the mass-energy relation and explores the discrete nature of mass in bound quantum systems.

Findings

Mass is invariant under Lorentz transformations.

The relation m=E/c^2 is not universally valid, especially for radiation and fields.

Mass in quantum systems changes discretely in atoms and nuclei.

Abstract

In this article the concept of mass is analyzed based on the special and general relativity theories and particle (quantum) physics. The mass of a particle (m=E(0)/c^2) is determined by the minimum (rest) energy to create that particle which is invariant under Lorentz transformations. The mass of a bound particle in the any field is described by m<E80)/c^2 and for free particles in the non-relativistic case the relation m=E/c^2 is valid. This relation is not correct in general, and it is wrong to apply it to the radiation and fields. In atoms or nuclei (i.e. if the energies are quantized) the mass of the particles changes discretely. In non-relativistic cases, mass can be considered as a measure of gravitation and inertia.