THE SCHRODINGER AND DIRAC FREE PARTICLE EQUATIONS WITHOUT QUANTUM-MECHANICS

Einstein's theory of Brownian Movement has provided a well accepted mi croscopic model oi diffusion for many years. Until recently the relati onship between this model and Quantum Mechanics has been completely fo rmal. Brownian motion provides a microscopic model for diffusion, but quantum mechanics and diffusion are related by a formal analytic conti nuation, so the relationship between Brownian motion and Quantum Mecha nics has been correspondingly vague. Some recent work has changed this picture somewhat and here we show that a random walk model of Brownia n motion produces the diffusion equation or the telegraph equations as a descriptions of particle densities, while at the same time the corr elations in the space-time geometry of these same Brownian particles o bey the Schrodinger and Dirac equations respectively. This is of inter est because the equations of Quantum Mechanics appear here naturally i n a classical context without the problems of interpretation they have in the usual context. (C) 1996 Academic Press, Inc.