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AIP conference proceedings

Non-commutative geometry, the Bohm interpretation and the mind-matter relationship

Basil J. Hiley

Published Jan 1, 2001• 45 citations
Publisher

Abstract

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.

DOI
10.1063/1.1388680

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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.
In this paper we discuss the notion of a ‘particle’ and its ‘trajectory’ in the Bohm approach to quantum theory in the context of a non-commutative dynamics which has classical mechanics as a commutative sub-algebra. We study the von Neumann-Moyal algebra and show that the key equations used in the Bohm approach are already contained within this structure. They appear as projections from the non-commutative phase space into space-time. This structure leads us to a more radical view of quantum processes involving individual particles.
In this paper I give a new information-theoretic analysis of the formalisms and interpretations of quantum mechanics (QM) in general, and of two mainstream interpretations of quantum mechanics in particular: The Copenhagen interpretation and David Bohm’s interpretation of quantum mechanics. Adopting Juan G. Roederer’s reading of the notion of pragmatic information, I argue that pragmatic information is not applicable to the Copenhagen interpretation since the interpretation is primarily concerned with epistemology rather than ontology. However it perfectly fits Bohm’s ontological interpretation of quantum mechanics in the realms of biotic and artificial systems. Viewing Bohm’s interpretation of QM in the context of pragmatic information imposes serious limitations to the qualitative aspect of such an interpretation, making his extension of the notion active information to every level of reality illegitimate. Such limitations lead to the idea that, contrary to Bohm’s claim, mind is not a more subtle aspect of reality via the quantum potential as active information, but the quantum potential as it affects particles in the double-slit experiment represents the non-algorithmic aspect of the mind as a genuine information processing system. This will provide an information-based ground, firstly, for refreshing our views on quantum interpretations and secondly, for a novel qualitative theory of the relationship of mind and matter in which mind-like properties are exclusive attributes of living systems. To this end, I will also take an information-theoretic approach to the notion of intentionality as interpreted by John Searle.
This chapter focuses on the work of David Bohm carried out together and then pursued and amplified by his collaborator Basil Hiley. Like the case studies in the other chapters, quantum physics played a key role in this approach too, especially the notion of non-local order. Bohm distinguishes between “implicate order” and “explicate order,” with the former constituting the psychophysically neutral realm similar to Pauli and Jung’s Unus Mundus from which both the mental and the physical emerge as explications. In this view, meaning is involved at the deep, implicate level through the notion of “active information”. When the implicate order (an undivided whole) is explicated into a multiplicity, this does naturally imply correlations that constitute the mind-matter connection. We also explore Hiley’s algebraic accounts linking back to Eddington’s ideas, as well as some of Bohm’s views of the relation between perception, language, and reality.
The persistent interpretation problem for quantum mechanics may indicate an unwillingness to consider unpalatable assumptions that could open the way toward progress. With this in mind, I focus on the work of David Bohm, whose earlier work has been more influential than that of his later. As I’ll discuss, I believe two assumptions play a strong role in explaining the disparity: 1) that theories in physics must be grounded in mathematical structure and 2) that consciousness must supervene on material processes. I’ll argue that the first assumption appears to lead us toward Everett’s many worlds interpretation, which suggests a red flag. I’ll also argue that the second assumption is suspect due to the persistent explanatory gap for consciousness. Later, I explore ways that Bohm’s later work holds some promise in providing a better fit with our world, both phenomenologically and empirically. Also, I’ll address the possible problem of realism.
Abstract The paper proposes that quantum theory implies a radically new notion of matter which has not been properly understood before David Bohm’s groundbreaking work. Bohm proposed that the fundamental particles of physics (such as electrons) are not merely pushed around mechanically by classical forces but are also able to respond to information. Information is thus assumed to be an objective commodity which can exist independently of the human mind and which actively guides or instructs physical processes. This notion of active information also applies in computational, biological and psychological phenomena, thus helping us to understand how the mental and the physical sides of reality are related. It may even help us to understand the nature of conscious experience. The latter part of the paper considers the deeper mathematical and physical background of quantum theory and suggests that we need to revise our basic assumptions about quantum objects, such as the role of the wave function.
Quantum nonseparability is central to most philosophical puzzles related to quantum mechanics. Yet, it is not an exclusive property of quantum mechanics, as it is also found in theoretical generalizations thereof. Investigating the implications of quantum nonseparability in a broader context could shed a new light on the conceptual problems in quantum physics. This work focuses on an operational theory called the process matrix formalism that generalizes quantum mechanics by relaxing the assumption of a well-defined causal structure. That broader theoretical context allows for the existence of quantum processes that are causally nonseparable, i.e. for which there is no definite global causal order among its interacting elements. Therefore, this notion of causal nonseparability somehow extends the notion of entanglement to the geometry of spacetime.