Naive Realism about Operators

A source of much difficulty and confusion in the interpretation of quantum mechanics is a “naive realism about operators.” By this we refer to various ways of taking too seriously the notion of operator-as-observable, and in particular to the all too casual talk about “measuring operators” that occurs when the subject is quantum mechanics. Without a specification of what should be meant by “measuring” a quantum observable, such an expression can have no clear meaning. A definite specification is provided by Bohmian mechanics, a theory that emerges from Schr̈odinger’s equation for a system of particles when we merely insist that “particles” means particles. Bohmian mechanics clarifies the status and the role of operators as observables in quantum mechanics by providing the operational details absent from standard quantum mechanics. It thereby allows us to readily dismiss all the radical claims traditionally enveloping the transition from the classical to the quantum realm—for example, that we must abandon classical logic or classical probability. The moral is rather simple: Beware naive realism, especially about operators!