Quantum reality filters
Stan Gudder · Journal of Physics A Mathematical and Theoretical · 2010
An anhomomorphic logic $\ascript ^*$ is the set of all possible realities for a quantum system. Our main goal is to find the "actual reality" $ϕ_a\in\ascript ^*$ for the system. Reality filters are employed to eliminate unwanted potential realities until only $ϕ_a$ remains. In this paper, we consider three reality filters that are constructed by means of quantum integrals. A quantum measure $μ$ can generate or actualize a $ϕ\in\ascript ^*$ if $μ(A)$ is a quantum integral with respect to $ϕ$ for a density function $f$ over events $A$. In this sense, $μ$ is an "average" of the truth values of $ϕ$ 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.