Quantum Mechanics in a Two Dimensional Spacetime: What is a Wavefunction?

G. N. Ord

Dept. of Mathematics, Ryerson University

Conventional quantum mechanics specifies the mathematical properties of wavefunctions and relates them to physical experiments by invoking the Born postulate.  There is no  known direct connection between wavefunctions and any external physical object. However, in the case of a two dimensional spacetime there is  a completely classical context for wavefunctions where the connection with an external reality is transparent and unambiguous. By examining this case, we show how a classical stochastic process assembles a Dirac wavefunction based solely on the detailed counting  of reversible paths. A direct  comparison of how  a related  process assembles a Probability Density Function  reveals  both  how and  why  PDFs and wavefunctions differ,   including the ubiquitous implication of complex numbers for the latter. The appearance of wavefunctions in a context that is free of the complexities of quantum mechanics suggests the study of such models may shed some light on interpretive issues.

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