The emergence of the classical world from the quantum substrate of our Universe is a long-standing conundrum. In this paper, I describe three insights into the transition from quantum to classical that are based on the recognition of the role of the environment. I begin with the derivation of preferred sets of states that help to define what exists—our everyday classical reality. They emerge as a result of the breaking of the unitary symmetry of the Hilbert space which happens when the unitarity of quantum evolutions encounters nonlinearities inherent in the process of amplification—of replicating information. This derivation is accomplished without the usual tools of decoherence, and accounts for the appearance of quantum jumps and the emergence of preferredpointer statesconsistent with those obtained via environment-induced superselection, oreinselection. The pointer states obtained in this way determine what can happen—define events—without appealing to Born’s Rule for probabilities. Therefore,pk=|ψk|2can now be deduced from the entanglement-assisted invariance, orenvariance—a symmetry of entangled quantum states. With probabilities at hand, one also gains new insights into the foundations of quantum statistical physics. Moreover, one can now analyse the information flows responsible for decoherence. These information flows explain how the perception of objective classical reality arises from the quantum substrate: the effective amplification that they represent accounts for the objective existence of the einselected states of macroscopic quantum systems through the redundancy of pointer state records in their environment—throughquantum Darwinism.This article is part of a discussion meeting issue ‘Foundations of quantum mechanics and their impact on contemporary society’.
Williamson theorem in classical, quantum, and statistical physics
