A unified extension of special relativity for objects with mass and photons

This paper proposes an extension of the theory of special relativity, starting from the need to eliminate certain paradoxical situations arising from unclear interpretations of the equations, culminating in the integration of photons as a reference point for measurements of other types of particles. To resolve these physically unfounded and merely assumed situations, the paper introduces an interaction factor.This factor modifies the Lorentz transformation equations, leading to a new formula for the Lorentz factor.