A New Kinematical Derivation of the Lorentz Transformation and the Particle Description of Light

TL;DR

This paper presents a new derivation of the Lorentz Transformation based on three simple postulates and demonstrates that light must be composed of massless particles, aligning with classical electrodynamics.

Contribution

It introduces a kinematical derivation of the Lorentz Transformation using minimal postulates and links the transformation to the particle nature of light.

Findings

Lorentz Transformation derived from three simple postulates

Light must be composed of massless particles (photons)

Kinematics consistent with classical electrodynamics

Abstract

The Lorentz Transformation is derived from only three simple postulates: (i) a weak kinematical form of the Special Relativity Principle that requires the equivalence of reciprocal space-time measurements by two different inertial observers; (ii) Uniqueness, that is the condition that the Lorentz Transformation should be a single valued function of its arguments; (iii) Spatial Isotropy. It is also shown that to derive the Lorentz Transformation for space-time points lying along a common axis, parallel to the relative velocity direction, of two inertial frames, postulates (i) and (ii) are sufficient. The kinematics of the Lorentz Transformation is then developed to demonstrate that, for consistency with Classical Electrodynamics, light must consist of massless (or almost massless) particles: photons.