A Democritean phenomenology for quantum scattering theory

The basic operational devices in a particle theory are detectors which show that a particle is here, now rather than there, then. Successful operation of these devices requires a limiting velocity. Given auxiliary devices which can change particle velocities in both magnitude and direction, the Lorentz-invariant mass can be defined. The wave-particle duality operationally required to explain the scattering of particles from a diffraction grating then predicts fluctuations in particle number (the Wick-Yukawa mechanism), if we postulate a smallest mass. We show that this suffices to establish the conventional quantum mechanical scattering formalism without postulating either interactions or analyticity. By introducing the phase change due to external electromagnetic fields, we can describe the auxiliary devices assumed above to an accuracy ofe2/hc, thus completing the operational definition to that accuracy.