  In this paper we show how Dirac, in 1947, anticipated the Bohm approach using
an argument based on what is now called the Heisenberg picture. From a detailed
examination of these ideas, we show that the role played by the Dirac standard
ket is equivalent to the introduction and use of the idempotent in the
orthogonal and symplectic Clifford algebras. This formalism is then used to
show that the so-called `Bohm trajectories' are the average of an ensemble of
individual stochastic Feynman paths. Since the Bohm approach can be simply
reduced to classical mechanics, the algebraic formalism presented here provides
a natural way to relate quantum mechanics to classical mechanics without the
need for decoherence. We show that this approach suggests an underlying fractal
space-time of the type discussed by Nottale.
