Bohm’s version of quantum mechanics

David Z. Albert

Gerhard Grössing, Siegfried Fussy, J Mesa Pascasio +1 more

Basil J. Hiley, R. E. Callaghan

In this paper we present for the first time a complete description of the Bohm model of the Dirac particle. This result demonstrates again that the common perception that it is not possible to construct a fully relativistic version of the Bohm approach is incorrect. We obtain the fully relativistic version by using an approach based on Clifford algebras outlined in two earlier papers by Hiley and by Hiley and Callaghan. The relativistic model is different from the one originally proposed by Bohm and Hiley and by Doran and Lasenby. We obtain exact expressions for the Bohm energy-momentum density, a relativistic quantum Hamilton-Jacobi for the conservation of energy which includes an expression for the quantum potential and a relativistic time development equation for the spin vectors of the particle. We then show that these reduce to the corresponding non-relativistic expressions for the Pauli particle which have already been derived by Bohm, Schiller and Tiomno and in more general form by Hiley and Callaghan. In contrast to the original presentations, there is no need to appeal to classical mechanics at any stage of the development of the formalism. All the results for the Dirac, Pauli and Schroedinger cases are shown to emerge respectively from the hierarchy of Clifford algebras C(13),C(30), C(01) taken over the reals as Hestenes has already argued. Thus quantum mechanics is emerging from one mathematical structure with no need to appeal to an external Hilbert space with wave functions.

Lazar Mayants

Basil J. Hiley

David R. Ferry

The Solvay physics conferences resumed in 1948, and this version was held in Brussels, Belgium. This chapter provides the strict view expressed by David Bohm fits with the description provided by A. Einstein. After the 1933 Solvay conference, the conferences were suspended, not to be begun again until after the coming global conflagration. The field exploded with earth shaking effects, but in the postwar world of quantum mechanics, work by Bohm would create a fire storm. Einstein attempted to explain more thoroughly his objections to the completeness of quantum mechanics. Bohm put together his causal theory after being unhappy with the general state of quantum mechanics as he found it during the time he was writing his book. Bohm goes on to criticize the usual interpretation of quantum theory on his fundamental approach. The usual interpretation of quantum mechanics takes little accord of the particle and the origin of the interference becomes difficult to understand.