The Isotropy Factor in Lorentz Contraction: A Mathematical Derivation from the Invariance of Light Speed Measurement

This paper examines the standard interpretation of the Lorentz–FitzGerald length contraction, which posits contraction occurs solely in the direction of relative motion. By rigorously applying the operational definition of length—determined by the time-of-flight of a light pulse within a frame—a logical tension with the postulates of relativity is revealed. To resolve this, we propose that the Lorentz transformations inherently describe a contraction effect along the direction of the measuring light pulse. We derive a universal scale factor, Λ, for the light-cone equation under transformation and demonstrate its equivalence to the relativistic Doppler factor: Λ = (1 – v/c)/(1 + v/c). This derivation shows that length contraction is an isotropic (geometric-optical) phenomenon relative to the measurement act. This interpretation simultaneously upholds both the principle of relativity and the constancy of the speed of light in all directions within any inertial frame, offering a more unified conceptual framework for Special Relativity.