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
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