  Unfortunately, the analogy is problematic. Statistical mechanics does not say that the above situation never occurs but only that the probability of its occurrence is extremely low. The question then reduces to that of ‘why is this probability so low?’ The answer to that is typically given in terms of the very low number of states corresponding to the tea boiling compared to the vast number of states for which it remains cold. Why, then, this disparity in the number of accessible states? Or, equivalently, why do we find ourselves in situations in which entropy increases? One answer takes us back to the initial conditions of the Big Bang. A similar line can then be taken in the case of quantum statistics. Why do we never observe non-symmetric states? Because that is the way the universe is and we should not expect quantum mechanics alone to have to explain why certain initial conditions obtain and not others. Here we recall that the symmetry of the Hamiltonian ensures that if a particle is in a state of a particular symmetry (corresponding to Bose-Einstein statistics, say, or Fermi-Dirac) to begin with, it will remain in states of that symmetry. Hence, if non-symmetric states do not feature in the initial conditions which held at the beginning of the universe, they will remain forever inaccessible to the particles. The issue then turns on different views of the significance of the above ‘surplus structure’ (see Belousek 2000.)