  In this paper a one to one correspondence is established between space-time
metrics of general relativity and the wave equations of quantum mechanics. This
is done by first taking the square root of the metric associated with a space
and from there, passing directly to a corresponding expression in the dual
space. It is shown that in the case of a massless particle, Maxwell's equation
for a photon follows while in the case of a particle with mass, Dirac's
equation results as a first approximation. Moreover, this one to one
correspondence suggests a natural explanation of wave-particle duality. As a
consequence, the distinction between quantum mechanics and classical
relativistic mechanics is more clearly understood and the key role of initial
conditions is emphasized. PACS NUMBERS: 03.65, 04.60
