Unimetry: A Phase-Space Reformulation of Special Relativity

We propose a compact reformulation of special relativity in which spacetime units (time and length) are treated as phase velocities - directional derivatives of a single underlying parameter, the phase χ ∈ C. The observable Minkowski interval emerges as a conserved quantity under a change of parameter from the hidden phase coordinate χ to the observer’s proper time τ . In this unimetry formalism, familiar relativistic effects - time dilation, Lorentz factor, Doppler shift, and relativistic velocity composition - arise as elementary projections and rotations in a Euclidean phase plane. Hyperbolic features of Lorentz kinematics reappear after a reparameterization of time, yielding the standard relations without altering empirical content. We provide closed-form derivations of the longitudinal/transverse Doppler factors, identify a simple lemma equating the total phase speed to the conserved Minkowski norm, and outline connections to gauge phases, rapidity, and a cosmological time gauge.