On the relativistic Heisenberg uncertainty with respect to the mass-action equivalence

Abstract

Abstract Relativistic Heisenberg Uncertainty relation (RHU), i.e. Δ p Δ x ≥ ℏ /2 1 - v 2 c 2 - 1 has been built as the different version of the relation which corresponds to the Generalized Uncertainty Principle (GUP), i.e. Δ p Δ x ≥ ℏ /2 1 + β Δ p 2 + ⋯ . This version of uncertainty relation is the function of average (group) velocity such a way that it causes the magnification of the phase space’s minimum limit in the relativistic domain. At the certain average velocity, this phenomenon will change our point of view from the conservation of energy to that of action spontaneously and gives the impact to the mass. Based on the action conservation, we need the concept of mass-action equivalence instead of the mass-energy equivalence to explain the missing or getting mass of the particle.