Quantum Reality Filters

TL;DR

This paper explores how quantum measures and integrals can be used as reality filters to identify the unique actual reality in quantum systems, emphasizing the mathematical properties and uniqueness of quadratic realities.

Contribution

It introduces three quantum integral-based reality filters and analyzes their existence, relations, and the uniqueness of quadratic realities within an anhomomorphic logic framework.

Findings

Quadratic reality generated by a quantum measure is unique.

Quantum measures can actualize specific realities via quantum integrals.

The paper establishes conditions for the existence and uniqueness of reality filters.

Abstract

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.