video:
*The quantum measure (and how to measure it)* Rafael Sorkin https://www.youtube.com/watch?v=fJb47yt9hgc references: *Quantum Mechanics as Quantum Measure Theory* Rafael D. Sorkin https://arxiv.org/abs/gr-qc/9401003 The additivity of classical probabilities is only the first in a hierarchy of possible sum-rules, each of which implies its successor. The first and most restrictive sum-rule of the hierarchy yields measure-theory in the Kolmogorov sense, which physically is appropriate for the description of stochastic processes such as Brownian motion. The next weaker sum-rule defines a {\it generalized measure theory} which includes quantum mechanics as a special case. The fact that quantum probabilities can be expressed ``as the squares of quantum amplitudes'' is thus derived in a natural manner, and a series of natural generalizations of the quantum formalism is delineated. Conversely, the mathematical sense in which classical physics is a special case of quantum physics is clarified. The present paper presents these relationships in the context of a ``realistic'' interpretation of quantum mechanics. *Quantum Measure Theory and its Interpretation* Rafael D. Sorkin https://arxiv.org/abs/gr-qc/9507057 We propose a realistic, spacetime interpretation of quantum theory in which reality constitutes a *single* history obeying a "law of motion" that makes definite, but incomplete, predictions about its behavior. We associate a "quantum measure" |S| to the set S of histories, and point out that |S| fulfills a sum rule generalizing that of classical probability theory. We interpret |S| as a "propensity", making this precise by stating a criterion for |S|=0 to imply "preclusion" (meaning that the true history will not lie in S). The criterion involves triads of correlated events, and in application to electron-electron scattering, for example, it yields definite predictions about the electron trajectories themselves, independently of any measuring devices which might or might not be present. (So we can give an objective account of measurements.) Two unfinished aspects of the interpretation involve *conditonal* preclusion (which apparently requires a notion of coarse-graining for its formulation) and the need to "locate spacetime regions in advance" without the aid of a fixed background metric (which can be achieved in the context of conditional preclusion via a construction which makes sense both in continuum gravity and in the discrete setting of causal set theory). *Dynamical Wave Function Collapse Models in Quantum Measure Theory* Fay Dowker, Yousef Ghazi-Tabatabai https://arxiv.org/abs/0712.2924 The structure of Collapse Models is investigated in the framework of Quantum Measure Theory, a histories-based approach to quantum mechanics. The underlying structure of coupled classical and quantum systems is elucidated in this approach which puts both systems on a spacetime footing. The nature of the coupling is exposed: the classical histories have no dynamics of their own but are simply tied, more or less closely, to the quantum histories. other references: *Quantum measure theory* Stan Gudder https://www.degruyter.com/view/j/ms.2010.60.issue-5/s12175-010-0040-8/s12175-010-0040-8.xml *Quantum measure and integration theory* Stan Gudder https://aip.scitation.org/doi/10.1063/1.3267867 @philipthrift -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/66cd7523-f875-485f-858c-e6277878981c%40googlegroups.com.
