The modal interpretation of algebraic quantum field theory

Abstract

In a recent Letter, Dieks [1] has proposed a way to implement the modal interpretation of quantum theory in algebraic quantum field theory. We show that his proposal fails to yield a well-defined prescription for which observables in a local spacetime region possess definite values. On the other hand, we demonstrate that there is a well-defined and unique way of extending the modal interpretation to the local algebras of quantum field theory. This extension, however, faces a potentially serious difficulty in connection with ergodic states of a field.

Non-Relativistic Quantum Mechanics

“…For an initial foray into modal interpretations of quantum field theory, see Clifton (2000). For a discussion of this foray especially as it relates to the issue of Lorentz-invariance, see Earman and Ruetsche (2006), which also includes references to the earlier work on Lorentz-invariance in modal interpretations.…”

Philosophical Aspects of Quantum Field Theory: I

“…Given the propensity of many interpretations of ordinary QM to code the condition a quantum system is ‘really’ in with a pure state (consider, for example, the value states of modal interpretations), this complicates the extension of strategies for interpreting ordinary QM to QM ∞ . Clifton (2000) offers, on behalf of modal interpretations, a way through the complication; Earman and Ruetsche (2005) criticize the result for saying too little about too many systems of interest.…”

On the Problem of Hidden Variables in Algebraic Quantum Field Theory

“…Clifton (2000) determined the maximal beable algebra for each faithful normal state in a von Neumann algebra under the condition that the beable algebra is determined solely in terms of the faithful normal state and the algebraic structure of the von Neumann algebra (Clifton, 2000, Proposition 1). The following theorem is a generalaized Clifton's theorem.…”

“…Bell (2004) argued that it is not physically proper to impose that condition on hidden variables although it is proper to impose it on quantum mechanical states (pp. [4][5][6]. Then Bell (2004) defined a hidden variable which was not bound by the condition on incompatible observational propositions, and showed that no such hidden variable in nonrelativistic quantum mechanics exists (pp.…”