Molecular spectroscopy makes very precise applications of quantum theory including GPS, BEC, and laser clocks. Now it can return the favor by shedding some light on modern physics mysteries by further unifying quantum theory and relativity. We first ask, “What is the simplest molecule?” Hydrogen H₂ is the simplest stable molecule. Positronium is an electron-positron (e⁺e^-)-pair. An even simpler “molecule” or “radical” is a photon-pair (γ, γ) that under certain conditions can create an (e⁺e^-)-pair. To help unravel relativistic and quantum mysteries consider CW laser beam pairs or TE-waveguides. Remarkably, their wave interference immediately gives Minkowski space-time coordinates and clearly relates eight kinds of space-time wave dilations or contractions to shifts in Doppler frequency or wavenumber. Modern physics students may find this approach significantly simplifies and clarifies relativistic physics in space-time (x,ct) and inverse time-space (ω,ck). It resolves some mysteries surrounding super-constant c=299,792,458m/s by proving “Evenson’s Axiom” named in honor of NIST metrologist Ken Evenson (1932-2002) whose spectroscopy established c to start a precision renaissance in spectroscopy and GPS metrology.

A “simplest molecule” consisting of CW- laser beam pairs helps to clarify relativity from poster board - I. In spite of a seemingly massless evanescence, an optical pair also clarifies classical and quantum mechanics of relativistic matter and antimatter. Logical extension of (x,ct) and (ω,ck) geometry gives relativistic action functions of Hamiltonian, Lagrangian, and Poincare that may be constructed in a few ruler-and-compass steps to relate relativistic parameters for group or phase velocity, momentum, energy, rapidity, stellar aberration, Doppler shifts, and DeBroglie wavelength. This exposes hyperbolic and circular trigonometry as two sides of one coin connected by Legendre contact transforms. One is Hamiltonian-like with a longitudinal rapidity parameter ρ (log of Doppler shift). The other is Lagrange-like with a transverse angle parameter σ (stellar aberration). Optical geometry gives recoil in absorption, emission, and resonant Raman-Compton acceleration and distinguishes Einstein rest mass, Galilean momentum mass, and Newtonian effective mass. (Molecular photons appear less bullet-like and more rocket-like.) In conclusion, modern space-time physics appears as a simple result of the more self-evident Evenson’s axiom: “”