Process, Clifford Algebras and "Weak Values"

Birkbeck College
University of London

A recent exploration of Bohm's notion of "structure process", assumed to be the deeper structure from which quantum mechanics arises, shows how the Clifford algebra naturally arises in this context. These algebras describe both the orthogonal properties of spacetime and the symplectic structure of the kinematics providing a way to develop a noncommutative background geometry. The existence of a hierarchy of orthogonal Clifford algebras provides a natural setting for the hierarchy of the Schrödinger, Pauli and Dirac particles with Penrose's twistors defining the top level. Information normally contained in the wave function is encoded in the ideal structure of the algebra itself. Bob Callaghan and I recently showed how these algebras could completely reproduce the standard theory but in a form that gave direct relevance to the Bohm momentum, the Bohm energy and the quantum potential. Recently Leavens and Wiseman have shown that these quantities appear as weak values that can be measured experimentally in weak measurements. I will show how these values can be calculated using the Clifford algebra so that we can extend the weak values to include the Pauli and ultimately the Dirac particles. I will also indicate how the Moyal algebra (symplectic Clifford) gives rise to what Gilbert and Murray call Dirac derivatives.