Quantum, classical & coarse-grained measurements

Abstract

The descriptions of the quantum realm and the macroscopic classical world differ significantly not only in their mathematical formulations but also in their foundational concepts and philosophical consequences. When and how physical systems stop to behave quantumly and begin to behave classically is still heavily debated in the physics community and subject to theoretical and experimental research. Conceptually different from already existing models, we have developed a novel theoretical approach to understand this transition from the quantum to a macrorealistic world. It neither needs to refer to the environment of a system (decoherence) nor to change the quantum laws itself (collapse models) but puts the stress on the limits of observability of quantum phenomena due to our measurement apparatuses. First, we demonstrated that for unrestricted measurement accuracy a system’s time evolution cannot be described classically, not even if it is arbitrarily large and macroscopic. Under realistic conditions in every-day life, however, we are only able to perform coarse-grained measurements and do not resolve individual quantum levels of the macroscopic system. As we could show, it is this mere restriction to fuzzy measurements which is sufficient to see the natural emergence of macroscopic realism and even the classical Newtonian laws out of the full quantum laws: the system’s time evolution governed by the Schrödinger equation and the state projection induced by measurements. This resolves the apparent impossibility of how classical realism and deterministic laws can emerge out of fundamentally random quantum events. We find the sufficient condition for these classical evolutions for isolated systems under coarse-grained measurements. Then we demonstrate that nevertheless there exist ”non-classical” Hamiltonians which are in conflict with macroscopic realism. Thus, though at every instant of time the quantum state appears as a classical mixture, its time evolution cannot be understood classically. We argue why such Hamiltonians are unlikely to be realized in nature.