version 19 Quantum Dynamics without the Wave Function

When suitably generalized and interpreted, the path-integral offers an al-ternative to the more familiar quantal formalism based on state-vectors, selfadjoint operators, and external observers. Mathematically one general-izes the path-integral-as-propagator to a quantal measure µ on the space Ω of all “conceivable worlds”, and this generalized measure expresses the dy-namics or law of motion of the theory, much as Wiener measure expresses the dynamics of Brownian motion. Within such “histories-based ” schemes new, and more “realistic ” possibilities open up for resolving the philosophi-cal problems of the state-vector formalism. In particular, one can dispense with the need for external agents by locating the predictive content of µ in its sets of measure zero: such sets are to be “precluded”. But unrestricted application of this rule engenders contradictions. One possible response would remove the contradictions by circumscribing the application of the preclusion concept. Another response, more in the tradition of “quantum logic”, would accommodate the contradictions by dualizing Ω to a space of “co-events ” and effectively identifying reality with an element of this dual space. Reading the literature on “quantum foundations”, you could easily get the impression that the problems begin and end with non-relativistic quantum mechanics. Perhaps most authors have limited themselves to this special case because they thought that no essentiall