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The present paper shows that Edward Nelson's stochastic mechanics approachfor quantum mechanics can be derived from the two classical elasticallycolliding particles with masses M and m satisfying a collision momentumpreserving equation. The properties of the classical elastic momentum collisionexpression determine the full Edward Nelson energy collision energy for bothparticles. This classical total energy expression does not require astatistical expectation since no process was defined for the energy and itmodels the main and incident particle velocities perfectly. Quantum mechanicscan be obtained by modelling the incident particle as a non-random potentialusing stochastic processes modelling the forward, post-collision and backwardpre-collision velocities of the main particle. This presents the Schroedingerequation exactly the way that Nelson proposed in 1966 except for the diffusionconstant. In this case the average energy is conserved in time and the forward,post-collision and backward pre-collision velocities of the system are relatedusing statistical methods. If the incident particle does not have a potentialthe additional constraints for the movement of the incident particle leads toanother Schroedinger equation. Finally, under suitable conditions it will beshown that the colliding particles satisfy Minkowski metric in specialrelativity. This last example shows how gravity can be quantized using detailsof this energy expression.

Classical Elastic Two-Particle Collision Energy Conservation using Edward Nelson's Energy, Double Diffusion and Special Relativity