Quantum dynamics from the Brownian recoil principle

We formulate a theory of the Brownian motion for particle ensembles, whose diffusive evolution is entirely generated by the surrounding random environment. By demanding the validity of the momentum conservation law on all conceivable scales adopted for the investigation of individual particle scattering (collisions) on the medium constituents, we are forced to incorporate the environmental recoil effects in the formalism. The Brownian recoil principle elevates the individually negligible phenomena to the momentum conservation law on the ensemble average. The resultant dynamics of the statistical ensemble is governed by the Schrödinger equation, once the diffusion constant D is identified with ħ/2m.