The algebraization of quantum mechanics and the implicate order

Zai-Zhe Zhong

In this paper, using quantum groups, noncommutative geometry, and the $q$-sequence theory, a complete algebraization scheme of quantum mechanics in view of Bohm's implicate order idea is given. It is pointed out that, in fact, there is some $q$-implicate order, and concrete expressions are given.

Istvan Montvay

William A. Ponce, Nicolas F. Raigoza

Basil J. Hiley

It is argued that in order to address the mind/matter relationship, we will have to radically change the conceptual structure normally assumed in physics. Rather than fields and/or particles-in-interaction described in the traditional Cartesian order based a local evolution in spacetime, we need to introduce a more general notion of process described by a non-commutative algebra. This will have radical implications for both for physical processes and for geometry. By showing how the Bohm interpretation of quantum mechanics can be understood within a non-commutative structure, we can give a much clearer meaning to the implicate order introduced by Bohm. It is through this implicate order that mind and matter can be seen as different aspects of the same general process.

Herman Rubin

Guido Bacciagaluppi

The paper discusses the concept of separation of quantum mechanical systems in the algebraic approach. We review known theorems, then establish a link between the C*-algebraic and the corresponding W*-algebraic concepts. A characterization of separation in terms of Bell inequalities, due to Raggio (1988), is given a C*-algebraic formulation. Finally, we comment on the implications for the understanding of the Bell inequalities.