  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 quantum mechanically and begin to behave
classically is still heavily debated in the physics community and subject to
theoretical and experimental research.
  This dissertation puts forward an approach to the quantum-to-classical
transition fully within quantum theory and conceptually different from already
existing models: It neither needs to refer to the uncontrollable 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
the imprecision of our measurement apparatuses. For a certain class of time
evolutions it is this mere restriction to coarse-grained measurements which is
sufficient to see the natural emergence of macroscopic realism and even the
classical Newtonian laws out of the full quantum formalism. But there also
exist "non-classical" Hamiltonians for which a classical spatiotemporal
description of the system's time evolution remains impossible even under fuzzy
measurements or decoherence. It is argued that such Hamiltonians are unlikely
to be spontaneously realized in nature because of their high complexity.
  The last part addresses the question of the origin of quantum randomness and
proposes a link with mathematical undecidability.
