Transactions of the Charles S. Peirce Society: A Quarterly Journal in American Philosophy

714 Book Reviews Quantum Mechanics and the Philosophy of Alfred North Whitehead Michael Epperson New York: Fordham University Press, 2004 xiv + 261 pp. There are strong motivations for a book, or several books, examining the relations between the two topics mentioned in the tide of this book. Quantum mechanics (QM), more than any other branch of physics, has impinged on philosophical matters. As to Whitehead's Philosophy of Organism, it is a prime candidate for being the most ambitious and scientifically well-informed system of metaphysics developed in the twentieth century, and hence a plausible locus for accommodating the philosophical implications of QM and possibly for suggesting modifications of them. Epperson enthusiastically develops one of the possible theses concerning the relation of QM to Whitehead's philosophy: that they mesh admirably. After surveying the various interpretations of the formalism of QM and outiining his preference for the family of "decoherence" interpretations, he asserts, "Careful analysis reveals that this family of interpretations of quantum mechanics can be characterized as a detailed and fundamental exemplification of Whitehead's philosophy of organism as it pertains to the physical sciences" (p.226). I shall assess this strong claim by examining his philosophical treatment of the quantum mechanical measurement problem. To get quickly to the heart of the matter I assume that the reader is familiar with the standard formalism of QM, as presented in excellent textbooks. I warn that Epperson does not provide an adequate summary of this formalism. For example, although he explains the mathematical concept of a vector |r>, which according to QM represents the complete state of a physical object, he also uses the notation without an explanation, even though it is essential to his concept of the density matrix on p. 78; nor does he explain the rules for calculating the probabilities of experimental outcomes when the density matrix is specified. The measurement problem arises when the initial state of an object S of interest is represented by a vector|v> = ai|r!> + a2|r2>, where |r¡> represents the maximally specified state of the object characterized by the value r¡ of an appropriately comprehensive physical property R, with the protocol that each |r¡ > has inner product unity with itself, and in which each coefficient a¡ is non-zero and their absolute squares sum to unity. It is a physical postulate of QM that if R is ideally measured the outcome will be one Transactions of the Charles S. Peirce Society Summer, 2005, Vol. XLI, No. 3 Book Reviews 715 of the values of R appearing in the expression for |v>, the probability of obtaining the outcome r¡ being |a¡|2. It must be stressed that |v> cannot be interpreted as representing a state of affairs in which, antecedent to the measurement, the property R definitely has either the value T1 or the value r2, but which one is unspecified. To prove this important statement it suffices to consider an ensemble of systems all prepared in state |v> and on each member of the ensemble measure a quantity Q which has a definite value q in the state|v> — a quantity that can be proved to exist and be well defined when the formalism of QM is assumed. QM then implies that the result of measurements of Q on the members of this ensemble will always be q, whereas the rejected state of affairs implies that some of the results would be q and some would have some other value. Heisenberg interpreted this peculiar situation by saying that although |v> represents an objective physical state and not just a psychological entity like a subjective belief, its objective content is a network of potentialities rather than actualities — an important conceptual interpretation which Epperson endorses (pp. 75-6). One might conjecture that a sufficient, though perhaps not a necessary, condition for a property R to have an actual value is the performance of a measurement of R. In an idealized treatment of measurement, an appropriately constructed physical system A is put into proper interaction with S in such a way that initially A is in a "ready" state |w0>, but the composite system S+A temporally evolves in accordance with standard quantum dynamics...