Pilot-Wave Theory overview from Quanta Magazine

ALGEBRAS, QUANTUM THEORY AND PRE-SPACE by F. A. M. FRESCURA and B. J. HILEY
Department of Physics, Birkbeck College, London WC1E 7HX UK
(Received In February, 22, 1984) [Published in Revista Brasileira de Fisica, Volume Especial, Julho 1984, Os 70 anos de Mario Schonberg, pp. 49-86.]

The relationship between the algebraic formulation of quantum mechanics, algebraic geometry and pre-space, a notion that arises in Bohm's implicate order, is discussed with particular reference to Schönberg's contributions in this area. The Heisenberg algebra is examined and it is shown that Dirac's standard ket can be considered as a primitive idempotent, which needs to be introduced into the Heisenberg algebra in order to complete its structure. We discuss the relationship between this idempotent and the vacuum state of the boson algebra. A fermion algebra based on the method of Cartan is presented. These a1gebras enab1e us to generalise the ordinary notions of functions and of Grassmann functions together with their differentials without reference to a continuous space-time manifold. The implications of the algebraic structure to the study of pre-space are discussed.

Bohmian Non-commutative Dynamics: History and New Developments. by B. J. Hiley.
TPRU, Birkbeck, University of London, Malet Street, London WC1E 7HX∗

The reality of Bohm’s intellectual journey is very different from what is often claimed by the proponents of Bohmian Mechanics" and others as we will explain in this paper. He did not believe a mechanical explanation of quantum phenomena was possible. Central to his thinking, and incidentally to Bohr’s also, was the notion of ‘unbroken wholeness’, a notion that is crucial for understanding quantum properties like quantum nonlocality. His proposals were based on a primitive notion of ‘process’ or ‘activity’, producing a more ‘organic’ approach to quantum phenomena. He published many papers outlining these new ideas, some plausible, some less so, but was not able to develop a coherent mathematical structure to support the work. Over the last ten years much of that missing mathematics has been put in place. This paper will report this new work, concentrating on providing a coherent overview of the whole programme