UNPREDICTABILITY OF SYMMETRY-BREAKING IN A PHASE-TRANSITION

We study the sensitive dependence on initial conditions of the final states of systems undergoing a symmetry-breaking phase transition. If the knowledge of the initial state is incomplete the macroscopic final state is unpredictable. This is demonstrated by computer simulations for two simple classical many-body systems. Next, this unpredictability is discussed within the more general framework of quantum field theories. For infinite systems a mixing property is exposed that prevents long-time predictions on the basis of local measurements. Finally, we remark on the more philosophical question whether the symmetry breaking of a highly symmetric theory after the big bang can be predicted or has to be considered as an historical accident.