The Individuality of a Quantum Event
Yutaka Tanaka
Summary
The distinction between two modes of analysis of an actual occasion, i.e. genetic and coordinate, is fundamental in Whitehead's "epochal" theory of time. Genetic analysis divides the "concrescence" (the process of becoming concrete), and coordinate analysis divides the concrete (thing). The concrete is in its "satisfaction", but the concrescence is the passage from real potentiality to actuality. Both can be objects for analysis but under the different perspectives. Whitehead states:
physical time makes its appearance in the coordinate analysis of the satisfaction. The actual entity is the enjoyment of a certain quantum of physical time. But the genetic process is not the temporal succession: such a view is exactly what is denied by the epochal theory of time. Each phase in the genetic process presupposes the entire quantum, and so does each feeling in each phase. The subjective unity dominating the process forbids the division of that extensive quantum which originates with the primary phase of the subjective aim. The problem dominating the concrescence is the actualization of the quantum in solido.The above passages seem to have annoyed many commentators ofProcess and Reality. The genetic analysis of an actual occasion (Part III) divides the concrescence into primary, intermediate, and final phases, which, according to Whitehead, are not "in" the physical (i.e. coordinate) time. One phase of genetic divisions must be prior to another: but what sort of priority is this? William Christian discusses and rejects four possible ways of interpretation, i.e. (i) priority in physical time,(ii) the logical priority of a premise to a conclusion, (iii) a whole-part relation, and (iv) a dialectical process of the Hegelian development of an idea. Then he says, though genetic priority may have some analogies with other sorts of priority, we must accept it as something of its own kind, but he does not analyse further the sui generis character of genetic divisions." Charles Hartshorne also questions the validity of "genetic" analysis, and proposes to accept only the succession of phases in the physical time.
What I will show in this paper is the importance of the distinction between "genetic" and "coordinate" analysis and its relevance to the interpretation of quantum physics, especially the relation of Heisenberg's indeterminacy principle to temporality, Bohr-Einstein debates, and the recent experimental refutation of the Bell Inequality.
If we take into consideration the impact of quantum physics on the emergence of Whitehead's metaphysics, as Lewis Ford shows in detail in his book, we naturally expect that the "epochal" theory of time has something to do with the quantum "jump", or the discontinuous transition from potentiality to actuality. But we need some cautions. The references of quantum physics in Science and the Modern World (1925) is mainly to the primary stage of quantum theory in the early 1920's, and there is no textual evidence concerning whether Whitehead knows the final stage of quantum physics established by Bohr, Heisenberg, Schrördinger and other contemporary physicists. The composition of Process and Reality began at the Gifford Lectures in 1927, and the same year was memorable to the history of quantum physics: Bohr stated his principle of "complementariry" and stressed the "individuality" of quantum event in his Como Lectures, and Heisenberg published his paper of Indeterminacy Principle in Zeitschrift für Physik. Only two years later,Process and Reality was published (1929): although Whitehead did not mention Bohr's principle of "complementarity", nor Heisenberg's indeterminacy principle, there are indeed a striking correspondence between Whitehead's metaphysical analysis of an actual occasion on the one hand and Bohr's and Heisenberg's physical analysis of quantum events on the other hand.
The purpose of this paper is not to confirm or disconfirm the historical influence of Bohr's or Heisenberg's ideas on Whitehead's metaphysics. That is an interesting study in itself, but will remain only a conjecture. Rather, I will consider the problem of temporality in the interpretation of Heisenberg's indeterminacy principle, and then discuss Bohr's concept of "individuality" of quantum events under the Whiteheadian perspective. I will show that Whitehead's distinction between "genetic" and "coordinate" analysis of an actual occasion proves to be relevant to the interpretation of the delayed-choice experiment in quantum physics: this experiment is about the indeterminate past, which will catch the attention of process thinkers who take the determinate past for granted and think that only the future is indeterminate.
Lastly, I will present a new approach of quantum logic to analyse Bohr's concept of "individuality" of a quantum event. This approach uses the concept of "divisibility" of an event by another event, and defines the concept of "commensurability" of events. Then I will characterize the classical world by saying that all events are commensurable with each other whereas the quantum world is characterized by saying that some events are incommensurable with each other. This analysis may be interesting to Whiteheadian scholars because it will teach us that the concept of individuality of an quantum event denies atomism in so far as atomism presupposes the divisibility of an complex event into atomic component events. Many scholars think of Whitehead's epochal theory of time as temporal atomism, and arbitrarily conjecture the existence of a temporal atom with a very minute scale of duration. Once we accept the quantum logical analysis and apply it to the epochal theory of time, we will understand the key concept is the individuality of an actual occasion and not atomism of any kind.
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