  The macroscopic behavior of many physical systems can be approximately
described by classical quantities. However, quantum theory demands the
existence of omnipresent quantum fluctuations on top of this classical
background -- which, albeit small, should have some impact onto its dynamics.
The correct treatment of this quantum back-reaction is one of the main problems
in quantum gravity and related to fundamental questions such as the initial
(big bang) singularity or the cosmological constant. By means of the
qualitative analogy between gravity and fluid dynamics, we try to shed some
light onto these problems and show some of the difficulties associated with the
calculation of the quantum back-reaction starting from the classical
(macroscopic) equation of motion.
