Quantum Theory of the Classical: Quantum Jumps, Born's Rule, and Objective Classical Reality via Quantum Darwinism

Abstract: Emergence of the classical world from the quantum substrate of our Universe is a long-standing conundrum. 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 derivation of preferred sets of states that help define what exists - our everyday classical reality. They emerge as a result of 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 emergence of preferred pointer states consistent with those obtained via environment-induced superselection, or einselection. Pointer states obtained this way determine what can happen - define events - without appealing to Born's rule for probabilities. Therefore, Born's rule can be now deduced from the entanglement-assisted invariance, or envariance - a symmetry of entangled quantum states. With probabilities at hand one also gains new insights into foundations of quantum statistical physics. Moreover, one can now analyze information flows responsible for decoherence. These information flows explain how perception of objective classical reality arises from the quantum substrate: Effective amplification 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 - through quantum Darwinism.