Interpreting Quantum Theories

Abstract

Laura Ruetsche, Interpreting Quantum Theories. Oxford: Oxford University Press. Pp. xvii, 377. Most philosophical work on quantum physics has concerned simple systems. And for good reason. Even one or two particle systems can exhibit the striking features we have come to associate with quantum physics—features such as entanglement, interference, and non-locality. But as far as physics goes, such systems barely scrape the surface. In particular, they have only a finite number of degrees of freedom, which means their states are characterized by a finite number of independent parameters. The systems studied in fields such as high energy particle physics and many-body physics, meanwhile, have uncountably many degrees of freedom. They are far more complicated than the usual philosophical fare. This is untroubling as long as the conceptual heart of quantum physics can be effectively condensed down. But what if philosophers’ toy systems are fundamentally different from realistic ones? That would be a problem. And indeed, as Laura Ruetsche convincingly argues in Interpreting Quantum Theories, systems with uncountable degrees of freedom—what Ruetsche collectively calls QM ∞ —are fundamentally different from the systems that have become the stock and trade of philosophy of physics, in ways that change the interpretational project. Ruetsche’s book does two things exceedingly well. The first is to provides a (comparatively) accessible and philosophically-oriented introduction to the algebraic approach to quantum physics, which is essential for understanding QM ∞ . This is a valuable contribution. The algebraic approach is the setting for much recent philosophical work. And yet learning it is notoriously difficult, as even pedagogical texts are aimed at research-level mathematicians. Ruetsche’s book is technically demanding, but it works to bring non-mathematicians along. It is, without a doubt, the best place to enter this literature. Second, the book sets the agenda for future work on QM ∞ , by effectively and judiciously drawing important foundational questions out of a sprawling and difficult physics literature. In this regard, it is a close cousin to John Earman’s excellent Bangs, Crunches, Whimpers, and Shrieks, which has had a significant influence on subsequent philosophy of spacetime physics. 1 Philosophers of physics will be addressing the questions Ruetsche has raised, in many cases for the first time, for years to come. Interpreting Quantum Theories centers on what might be called the problem of inequivalent representations. The quantum theories that philosophers are accustomed to are set in a mathematical structure known as a (separable) Hilbert space, which is an at-most countably infinite dimensional complex vector space. Rays in a Hilbert space represent possible states of a physical system, and self- adjoint operators on that Hilbert space correspond to properties of the system. 1 John Earman, Bangs, Crunches, Whimpers, and Shrieks (Oxford: Oxford University Press, 1995).