Heller, Michael. “Generalizations: From Quantum Mechanics to God."

According to Michael Heller, the evolution of concepts is a driving force in science. New concepts inherit much from their predecessors and yet are open to future generalizations. When they produce paradoxes and inconsistencies, a crisis arises which can be called a conceptual revolution or, more properly, an evolution within a conceptual framework. One example of a conceptual evolution is the origin of rational discourse about the world begun in sixth-century BCE Greece. Another is current research in quantum mechanics. A sign of such conceptual evolution is an increasing generalization in which the old concepts are restricted to a smaller domain of validity than they originally enjoyed. Both science and theology can be seen as attempts to catch reality in a net of concepts and theories, attempts which always fail. Still we should not remain silent, at least about God, since it is better to say something even if it is always tentative. All language demands interpretation, as quantum physics clearly shows. The breakdown of language in physics points to the need to generalize; perhaps theology could learn something by analogy from this fact. Thus the goal of this essay is to look at contemporary quantum theory and to derive from it a lesson for theology.

Heller’s starting point is the fact that the main distinguishing feature of quantum mechanics is its noncommutativity; he seeks to show the degree of generalization already present in quantum theory by using the recently discovered noncommutative geometry. It not only clearly shows the generalizing mechanisms underlying the present theory, but it also points towards further possible generalizations. Heller explores the possibility that at its fundamental level, physics is modeled by noncommutative geometry. Quite independently of whether this hypothesis will prove true, he claims that we can learn a lesson from it. Heller analyzes a few concepts, such as causality, probability and chance, which are of great importance for philosophy and theology when they are transferred from their usual context to the environment of the “noncommutative world.” The main characteristic of this world is its a-temporality and a-spatiality. It turns out, for instance, that in this a-temporal world authentic dynamics (albeit in a generalized sense) is possible.

Heller does not claim that concepts elaborated in noncommutative geometry can be used directly in theology. Instead he tries to draw consequences for theological discourse from the fact that even in physics some concepts undergo such drastic evolution that they distance themselves from our everyday linguistic intuition. He begins with an algebraic formulation of quantum mechanics based on general C^*-algebra; this formulation allows one to recover the more limited formulation in terms of Hilbert spaces. C^*-algebras that are relevant to quantum mechanics are noncommutative algebras, and it is this noncommutativity which is responsible, according to Heller, for all the peculiarities of quantum theory. Algebraic formulation also leads to the possibility of geometrizing quantum mechanics. The so-called “noncommutative spaces” are totally global in character; no local concept can be given any meaning. This in turn could lead to the unification of quantum mechanics and general relativity. The idea is that fundamental physics is based on a noncommutative geometry that is nonlocal; only at a higher level does the distinction between spatio-temporal geometry and physical dynamical processes arise. Even at this fundamental level, there can be an authentic, though generalized, dynamics. But here the distinction between singular and nonsingular is lost, undermining such ideas as the beginning of the universe and the concept of the individual. Instead, and unlike previous approaches in physics and philosophy, singularities are a part of our macroscopic perspective, but their distinctive character is meaningless at the fundamental level. Equally, nonlocal phenomena, such as those which the EPR experiment points to, are explained within the noncommutative approach.

In his closing sections, Heller shows how important theological concepts, such as causality, are reshaped by the noncommutative framework and its properties of timelessness and nonlocality. Causality becomes a “dynamical nexus” rather than a temporal ordering of cause and effect, a combination of a-temporal and nonlocal behavior that is fertile ground for thinking theologically about God as Creator.

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