The quantum Darwinism approach offered by Wojciech Zurek (Physics Today, October 2014, page 44) is based on a quantum “credo” embedded in the usual mathematical postulates of quantum mechanics: A quantum state is a vector in a Hilbert space, it undergoes a unitary evolution, and composite systems are described by tensor products that allow entangled states. In what may be a hint at something else, Zurek adds a repeatability postulate stating that an immediately repeated measurement yields the same outcome. He justifies the postulate with the argument that “classical repeatability is a given: Measurements reveal classical states, so repeatability follows from their objective existence… . Repeatability is key for the very idea of a state as a predictive tool: The simplest prediction is that a state is what it is.” Then Zurek’s goal is to deduce the usual next “postulates” of quantum mechanics, the so-called collapse postulate and Born’s rule.
In our opinion, the main trouble with his (quite respectable) attempt is that it starts from a purely mathematical credo: Vectors in a Hilbert space come directly from the sky, and you must believe in them to reach enlightenment. That approach may not be the best to reach physical conclusions, and before one speaks about vectors in a Hilbert space, some physics may be required to specify what the “state” really is.
As we have discussed in our work,1,2 such a “quantum state without mathematics,” which we call a modality, has a very specific feature: It does not belong to a system, as it would in classical physics, but jointly to the system and to its context—the arrangement of experimental equipment that gives access to the system. And in a given context, such a modality is indeed certain and repeatable—that is, it is real and objective. Perhaps that is what Zurek actually means when he writes, “A state is what it is.” We offer a simple example: A photon does not “have” a polarization at 45°, but it will be transmitted with certainty (a property of the system) through a polarizer oriented at 45° (a property of the context).
Such thinking will not invalidate Zurek’s arguments, but it will turn them on their heads: The credo actually already contains the conclusion he wants to reach—that the experiments must be defined classically; without that, a quantum state has no meaning.2 Therefore, the Physics Today article does not explain, as Zurek says, “why we experience our world as classical.” Rather, it shows—remarkably—that quantum mechanics is a consistent theory.
