QUANTUM HISTORIES

There are good motivations for considering some type of quantum histor ies formalism. Several possible formalisms are known, defined by diffe rent definitions of event and by different selection criteria for sets of histories. These formalisms have a natural interpretation, accordi ng to which nature somehow chooses one set of histories from among tho se allowed, and then randomly chooses to realise one history from that set; other interpretations are possible, but their scientific implica tions are essentially the same. The selection criteria proposed to dat e are reasonably natural and certainly raise new questions. For exampl e, the validity of ordering inferences which we normally take for gran ted - such as that a particle in one region is necessarily in a larger region containing it - depends on whether or not our history respects the criterion of ordered consistency, or merely consistency. However, the known selection criteria, including consistency and medium decohe rence, are very weak. It is not possible to derive the predictions of classical mechanics or Copenhagen quantum mechanics from the theories they define, even given observational data in an extended time interva l Attempts to refine the consistent histories approach so as to solve this problem by finding a definition of quasiclassicality have so far not succeeded. On the other hand, it is shown that dynamical collapse models, of the type originally proposed by Ghirardi-Rimini-Weber, can be re-interpreted as set selection criteria within a quantum histories framework in which context they appear as candidate solutions to the set selection problem. This suggests a new route to relativistic gener alisation of these models, since covariant definitions of a quantum ev ent are known.