Conservation laws and evolution of pure states into mixed states

T. Banks, Leonard Susskind, Michael E. Peskin

Josep Amengual i Batle, Angel Ricardo Plastino, M. Casas +1 more

V. V. Dodonov, Salomon Sylvain Mizrahi

María Esther Burgos

James L Park, William Band

Ordinary quantal conservation laws are associated with null operators for time rate of change and are valid for causal evolution of the system through either pure or mixed states. There is, however, a larger class of quantal constants of the motion, some of which are conserved only for pure state evolution. After an analysis of the theoretical origins of these exotic conserved quantities, several illustrations are presented with empirical interpretations based on the quorum theory methods used in Paper I.

William George Unruh, Robert M. Wald

It has been argued that any evolution law taking pure states to mixed states in quantum field theory necessarily gives rise to violations of either causality or energy-momentum conservation in such a way as to have unacceptable consequences for ordinary laboratory physics. We show here that this is not the case by giving a simple class of examples of Markovian evolution laws where rapid evolution from pure states to mixed states occurs for a wide class of states with appropriate properties at the ``Planck scale,'' suitable locality and causality properties hold for all states, and the deviations from ordinary dynamics (and, in particular, violations of energy-momentum conservation) are unobservably small for all states which one could expect to produce in a laboratory. In addition, we argue (via consideration of other, non-Markovian models) that conservation of energy and momentum for all states is not fundamentally incompatible with causality in dynamical models in which pure states evolve to mixed states.