Non-Commutative Quantum Geometry: A Reappraisal of the Bohm Approach to Quantum Theory

Abbas Farmany, Roshanak Lotfikar, Shahryar Abbasi +2 more

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.

Uwe Krey

The four items mentioned in the title are put into context in an informal way.

Partha Nandi, Sayan Kumar Pal, Aritra N Bose +1 more

Robert H. Parmenter, Andrew L. DiRienzo

The causal interpretation of quantum mechanics, as originally stated by deBroglie and Bohm, had several attractive features. Among these is the possibility that it could address some of the most fundamental questions on quantum phenomena. However, subsequent theoretical conjectures, which have now been included in the orthodox view of the deBroglie Bohm theory, are unphysical and have done much to undermine the original theory's appeal. We, therefore, return to the original theory as our starting point and address one of its perplexing areas: the quantum potential. By avoiding the unphysical conjectures we are led to an understanding of the quantum potential which is distinctly different from that of the orthodox deBroglie Bohm view.

Veeravalli S. Varadarajan