A Phenomenological Two-Channel Model for the Lorentz Factor

Abstract

We present a phenomenological model that reproduces the Lorentz factor γ = 1/ p 1 − v 2/c2 using simple operational definitions and a two-channel budget principle. The model is based on the reduced Compton wavelength of the electron as a natural length scale (the “step”) and the corresponding light travel time as the fundamental time unit (the “tick”). A postulated conservation law k 2 + R2 = 1 expresses the fixed total capacity per tick shared between a progress channel and an internal cycling channel. Using reversal symmetry and a first-order expansion, we obtain linear rates for the two channels, and the requirement that both channels must complete for a tick to occur leads to the geometric mean as the effective rate. The Lorentz factor then follows directly. The model is not intended as a replacement for special relativity, but as a complementary phenomenological picture that highlights the counting origin of time dilation. Limitations and possible extensions are discussed.

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