  Classical and quantum phase transitions involve observables which are
non-analytic as functions of a controlled thermodynamical variable. As occurs
with the self-consistent Fermi Golden Rule, one condition to obtain the
discontinuous behavior is the proper evaluation of a classical or quantum
thermodynamic limit. We show that in presence of an environment, the
oscillatory dynamics of a quantum two-level system, in analogy with a classical
damped oscillator, can undergo a quantum dynamical phase transition to a
non-oscillatory phase. This is obtained from a self-consistent solution of the
Generalized Landauer Buettiker Equations, a simplified integral form of the
Keldysh formalism. I argue that working at each side of the transition implies
standing under different paradigms in the Kuhn's sense of the word. In
consequence, paradigms incommensurability obtains a sound mathematical
justification as a consequence of the non-analyticity of the observables. A
strong case is made upon the need to deepen the public's intuition and
understanding on the abrupt transition from static to dynamical friction
regimes.
  Keywords: Self Consistent Fermi Golden Rule, Paradigm Shift, Quantum
Dynamical Phase Transition, Decoherence, Energy-time Wigner Function,
Dissipative Two-level system, Keldysh Formalisma, Generalized
Landauer-Buettiker Equations, Loschmidt Echo, Mesoscopic Echo, Spin Dynamics,
Solid State NMR, Dynamical Quantum Zeno Effect, Liquid Crystal NMR.
