A Comprehensive First-Principles Derivation Of The Lorentz Transformation Equations In Special Relativity

This paper presents a rigorous first-principles derivation of the Lorentz transformation equations, grounded in the fundamental postulates of special relativity. The approach systematically constructs the transformations from the invariance of the spacetime interval and causality constraints. This refined formulation highlights the necessity of Lorentz transformations in relativistic kinematics, providing a precise and technically enriched perspective on their foundational role in physics.