G. N. Ord,1 E. Harley,2 R. B. Mann,3 Andrew Lauritzen,4 Zenon Harley,5 and Qin Qin Lin5
1 Dept. of Mathematics, Ryerson University
2 Dept. of Computer Science, Ryerson University
3 Dept. of Physics, University of Waterloo
4 University of Waterloo
5 University of Toronto
In quantum mechanics, particles are commonly represented as wave-packets. However recent work related to Feynman's ‘Chessboard Model' has shown that to a certain extent the picture may be reversed. Particle waves may be formed by carefully pairing together portions of a spacetime path that are traversed in opposite directions with respect to macroscopic time. This essentially builds a field of particles and antiparticles that in the continuum limit is best described by a complex amplitude. In this picture, the equations of quantum mechanics appear as the direct result of a simple classical stochastic process without the necessity of a formal analytic continuation. We illustrate the emergence of complex amplitudes from paired paths with a series of numerical experiments. The experiments are explicit constructions of spacetime densities from single paths and they allow us to probe macroscopically reversible propagation originating from stochastic processes.