Generalized Relativistic Transformation and Its Outcomes on Fundamental Metrological Quantities

Based on the recently proposed Generalized Relativistic Transformation (GRT) [1,2], which describes both; the relativistic reference frame information from the observer's point of view, and the projection of the observer's proper quantities onto the relativistic reference frame. A systematic approach was developed to describe relativistic quantities. This allows us to define which quantities are truly relativistic invariants and which require relativistic corrections, as well as to find their dependencies. In this work, we applied GRT framework to arrive at a comprehensive construction of a Relativistic System of Quantities and Units. Surprising results were obtained, such as the invariance of the speed of light directly from the proposed equations, and the relativistic dependence of some fundamental constants, for instance, Planck's constant, elementary charge and spin. Finally, we establish the conservation of energy in the relativistic scenario with photon energy correction.