Pristinism under Pressure—Ruetsche on the Interpretation of Quantum Theories

Interpreting Quantum Theories attempts and achieves no less than three different goals. First, it provides an accessible introduction to the conceptual foundations of the algebraic approach to quantum theories—today’s most promising rigorous framework for the formulation of quantum theories that includes those applying to systems with an infinite number of degrees of freedom. Second, it presents the most important interpretive challenges posed by these latter theories, collectively referred to by Ruetsche as “QM∞”. Third, it relates the problem of interpreting QM∞ to more general topics in the philosophy of science, in particular the much discussed issue of scientific realism. The overall structure of the book is as follows: Chapter 1 sets the stage for what follows by providing some background considerations in terms of more general philosophy of science on what it means to interpret a physical theory. Chapters 2-4 introduce the conceptual basics of the algebraic formulation of quantum theories with particular emphasis on how it generalises standard Hilbert space quantum mechanics (“QM”). After a review of axiomatic approaches in Chapter 5, some apparently very natural, yet competing, interpretive strategies for theories of QM∞ are outlined in Chapter 6, discussed in some detail here further below. Chapters 7 and 8 focus on one particular challenge posed by the interpretation of QM∞, namely that in these theories, unlike in ordinary QM, the algebras of linear operators used to describe quantum systems typically do not include any finite-dimensional projections. One of the startling implications of this is that the standard preparation recipes for quantum states as familiar from ordinary QM become problematic in the context of QM∞ in that no operators projecting the premeasurement state on a putative “collapsed” or (appealing to Lüders’ Rule as a generalised version of the projection postulate) “Lüders conditionalized state”1 are at hand. On similar grounds, the issue of the bearers of probabilities seems much more complicated in QM∞ than in ordinary QM. See p. 171. Where not specified otherwise, quotations are from “Interpreting Quantum Theories”.