Physics – Mathematical Physics
Scientific paper
2010-02-22
J.Phys.A43:485301,2010
Physics
Mathematical Physics
25 pages
Scientific paper
10.1088/1751-8113/43/48/485301
An anhomomorphic logic $\ascript ^*$ is the set of all possible realities for a quantum system. Our main goal is to find the "actual reality" $\phi_a\in\ascript ^*$ for the system. Reality filters are employed to eliminate unwanted potential realities until only $\phi_a$ remains. In this paper, we consider three reality filters that are constructed by means of quantum integrals. A quantum measure $\mu$ can generate or actualize a $\phi\in\ascript ^*$ if $\mu (A)$ is a quantum integral with respect to $\phi$ for a density function $f$ over events $A$. In this sense, $\mu$ is an "average" of the truth values of $\phi$ with weights given by $f$. We mainly discuss relations between these filters and their existence and uniqueness properties. For example, we show that a quadratic reality generated by a quantum measure is unique. In this case we obtain the unique actual quadratic reality.
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