Consistent histories

"Some months before Feynman's death in 1988, Gell-Mann described to a class at Caltech the status of our work on decoherent histories at that time. Feynman was in attendance, and at the end of the class, he stood up, and some of the students expected an exciting argument. But his comment was, "I agree with everything you said.""

"In the consistent-histories approach, the classical limit can be studies by using appropriate subspaces of the quantum Hilbert space as a "coarse graining," analogous to dividing up phase space into nonoverlapping cells in classical statistical mechanics. This coarse graining can then be used to construct quantum histories. It is necessary to show that the resulting family of histories is consistent, so that the probabilities assigned by quantum dynamics make good quantum mechanical sense. Finally, one needs to show that the resulting quantum dynamics is well approximated by appropriate classical equations."

"There is nothing absurd or inconsistent about the decoherent histories approach in particular, or about the general idea that the state vector serves only as a predictor of probabilities, not as a complete description of a physical system. Nevertheless, it would be disappointing if we had to give up the “realist” goal of finding complete descriptions of physical systems, and of using this description to derive the Born rule, rather than just assuming it. We can live with the idea that the state of a physical system is described by a vector in Hilbert space rather than by numerical values of the positions and momenta of all the particles in the system, but it is hard to live with no description of physical states at all, only an algorithm for calculating probabilities."