2006/10/24 by Rafael D. Sorkin · 5 citations
Arts and Humanities · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Philosophy and History of Science #Quantum Mechanics and Applications #gr-qc #hep-th #math.LO #quant-ph
paper · pdf · doi:10.1088/1751-8113/40/12/s20
published as J.Phys.A40:3207-3222,2007 · plainTeX, 24 pages, no figures. To appear in a special volume of {\it Journal of Physics A: Mathematical and General} entitled ``The Quantum Universe'' and dedicated to Giancarlo Ghirardi on the occasion of his 70th birthday. Most current version is available at http://www.physics.syr.edu/~sorkin/some.papers/ (or wherever my home-page may be)
arxiv created 2006/10/24 · openalex publication_date 2007/03/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
When suitably generalized and interpreted, the path-integral offers an alternative to the more familiar quantal formalism based on state-vectors, selfadjoint operators, and external observers. Mathematically one generalizes the path-integral-as-propagator to a quantal measure µ on the space Ω of all “conceivable worlds”, and this generalized measure expresses the dynamics 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 philosophical 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